Podcasts about Mathematics

This conversation explores the intersection of mathematics and human experience, focusing on historical figures, philosophical debates, and the ethical implications of scientific progress. Jason Socrates Bardi discusses his book 'The Great Math War', which delves into the personal stories of mathematicians, the challenges of teaching math, and the relevance of these themes in today's world, particularly in the context of AI and misinformation.Takeaways The personal experiences of mathematicians shape their work. Philosophical clashes in mathematics reflect broader societal issues. Hilbert's optimism about problem-solving parallels today's AI discussions. Historical context is crucial in understanding mathematical developments. Ethics in science must be prioritized to avoid past mistakes. There are limits to human knowledge that we must acknowledge. Mathematics is a fundamental human skill, not just for the gifted. The future of mathematics will be influenced by AI and technology. Understanding historical fallacies can inform current practices. Kovalevsky's story is an inspiring example of overcoming barriers.Chapters 00:00 The Personal Journey Behind The Great Math War 03:08 The Philosophical Clash in Mathematics 05:13 The Great Math War: Key Players and Their Missions 07:38 The Foundations of Mathematics: Paradoxes and Theories 08:55 The Role of Historical Context in Mathematics 10:00 The Human Side of Mathematics: Stories of Resilience 12:36 Ethics in Science and the Modern Age 14:56 The Future of Mathematics and Technology 25:32 The Spectrum of Idealism and Realism 26:13 Understanding Ignoramus et Ignoramnibus 29:04 Neuroscience and the Evolution of Mathematics 33:12 The Future of AI and Consciousness 35:31 Fallacies and Paradoxes in Mathematics 38:31 The Legacy of Sofia Kovalesky 43:10 The Great Math War: A Reflection on Logic and HumanityFollow Jason on LinkedIn, Twitter, and find his new book here.Subscribe to Breaking Math wherever you get your podcasts.Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTokFollow Autumn on Twitter, BlueSky, and InstagramBecome a guest hereemail: breakingmathpodcast@gmail.com

We start the episode discussing the outcome of the 2025 World Series and the MLB season as a whole and even find a way to relate it to our usual topics. We also share our latest video game experiences and have a fairly indepth discussion about anime phenomenon Chainsaw Man!

Dr. Julia Stoyanovich is Institute Associate Professor of Computer Science and Engineering, Associate Professor of Data Science, Director of the Center for Responsible AI, and member of the Visualization and Data Analytics Research Center at New York University. She is a recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE) and a Senior member of the Association of Computing Machinery (ACM). Julia's goal is to make “Responsible AI” synonymous with “AI”. She works towards this goal by engaging in academic research, education and technology policy, and by speaking about the benefits and harms of AI to practitioners and members of the public. Julia's research interests include AI ethics and legal compliance, and data management and AI systems. Julia is engaged in technology policy and regulation in the US and internationally, having served on the New York City Automated Decision Systems Task Force, by mayoral appointment, among other roles. She received her M.S. and Ph.D. degrees in Computer Science from Columbia University, and a B.S. in Computer Science and in Mathematics & Statistics from the University of Massachusetts at Amherst.Links:https://engineering.nyu.edu/faculty/julia-stoyanovich https://airesponsibly.net/nyaiexchange_2025/ Hosted on Acast. See acast.com/privacy for more information.

S. Suherman talks about the research "Role of mathematics academic performance and attitude towards mathematics: the mediating role of english learning achievement". Read the article in the journal "Psychological Science and Education" 2025 # 5.

— What if reality isn't material at all—but a shared dream, woven by infinite, eternal minds? In James book, The Dream of Matter, he explores the radical idea that our brains are not just organs of survival, but reflections of the soul's deeper activity. If that's true, then the existence of the soul is not only real, but measurable—visible in the patterns of thought, the rhythms of brainwaves, and the coherence or incoherence of our lives. This is more than spiritual speculation. By decoding the mathematics behind mind and matter, the book offers a structured, rational approach to consciousness—showing how personal growth, mental health, and even the future of civilization depends on the same principle: the evolution of mind toward coherence. Mental health, in this light, is not a private luxury but social infrastructure. When minds fracture, families, institutions, and nations fracture with them. Drawing on neuroscience, ontological mathematics, and systems theory, The Dream of Matter reveals how the soul can be approached as rigorously as any science—and why recovering it is essential for both individual well-being and collective survival. From the intimate journey of self-actualization to the emergence of a new social logic, this is a vision of coherence as both healing practice and civilizational compass. Valeria interviews James Croall — He is the author of "The Dream Of Matter: Neuroscience And Decoding The Mathematics Of The Soul." James is a former Silicon Valley cybersecurity leader turned neurotherapy practitioner and the author of the upcoming book The Dream of Matter: Neuroscience and Decoding the Mathematics of the Soul. After years of grappling with attention issues, burnout, and daytime fatigue, James discovered neurotherapy—an experience that profoundly reshaped his brain, his performance, and ultimately, his path. He now specializes in quantitative EEG (QEEG brain mapping), neurostimulation, and applied neurofeedback training. James holds certification as a QEEG technician and is trained in neurofeedback approaches that help clients build healthier brain patterns over time. Drawing from both systems engineering and cutting-edge neuroscience, he helps people manage and overcome symptoms related to focus, stress, mood, and trauma—without relying on medication or traditional talk therapy. His mission is to raise awareness of these science-backed tools, which remain surprisingly unknown to the general public despite their potential to change lives. The Dream of Matter grew out of a convergence between James's technical background, his transformation through neurotherapy, and a lifelong spiritual search for meaning and coherence. The book explores the deep structure of consciousness—arguing that the soul is real, governed by the same elegant mathematics that underlies the physical world, and may even be measurable. To learn more about James Croall and his work, please visit: https://thedreamofmatter.com/ and https://peakmind.health/

What is Chapel? This week, Technology Now explores the programming language, Chapel. We ask what it is, how it was designed, and we explore why people would use it instead of some of the more established languages.This is Technology Now, a weekly show from Hewlett Packard Enterprise. Every week, hosts Michael Bird and Aubrey Lovell look at a story that's been making headlines, take a look at the technology behind it, and explain why it matters to organizations.About Brad Chamberlain:https://www.linkedin.com/in/brad-chamberlain-3ab358105 Sourceshttps://www.britannica.com/biography/Ada-Lovelacehttps://www.adalovelaceinstitute.org/about/https://cdn.britannica.com/31/172531-050-E009D42C/portion-Charles-Babbage-Analytical-Engine-death-mill-1871.jpghttps://commons.wikimedia.org/wiki/File:PunchedCardsAnalyticalEngine.jpghttps://www.mpg.de/female-pioneers-of-science/Ada-Lovelace

Stephen Grootes speaks to Rajesh Pasungili, CEO of Resolute Education, about how the organisation uses coding and robotics to bridge the gap between school and university learning. Founded by two engineering students, Resolute combines Rajesh’s passion for teaching with his co-founder Gareth’s experience overcoming severe dyslexia to enhance academic performance across subjects like Science, Mathematics, English, and Economics. By engaging students through play, Resolute helps them overcome the fear of failure, bring their ideas to life, and develop the technological skills needed for a future where most emerging careers will rely heavily on technology. The Money Show is a podcast hosted by well-known journalist and radio presenter, Stephen Grootes. He explores the latest economic trends, business developments, investment opportunities, and personal finance strategies. Each episode features engaging conversations with top newsmakers, industry experts, financial advisors, entrepreneurs, and politicians, offering you thought-provoking insights to navigate the ever-changing financial landscape.    Thank you for listening to a podcast from The Money Show Listen live Primedia+ weekdays from 18:00 and 20:00 (SA Time) to The Money Show with Stephen Grootes broadcast on 702 https://buff.ly/gk3y0Kj and CapeTalk https://buff.ly/NnFM3Nk For more from the show, go to https://buff.ly/7QpH0jY or find all the catch-up podcasts here https://buff.ly/PlhvUVe Subscribe to The Money Show Daily Newsletter and the Weekly Business Wrap here https://buff.ly/v5mfetc The Money Show is brought to you by Absa     Follow us on social media   702 on Facebook: https://www.facebook.com/TalkRadio702 702 on TikTok: https://www.tiktok.com/@talkradio702 702 on Instagram: https://www.instagram.com/talkradio702/ 702 on X: https://x.com/CapeTalk 702 on YouTube: https://www.youtube.com/@radio702   CapeTalk on Facebook: https://www.facebook.com/CapeTalk CapeTalk on TikTok: https://www.tiktok.com/@capetalk CapeTalk on Instagram: https://www.instagram.com/ CapeTalk on X: https://x.com/Radio702 CapeTalk on YouTube: https://www.youtube.com/@CapeTalk567 See omnystudio.com/listener for privacy information.

In this episode of The Grading Podcast, Sharona Krinsky and Robert Bosley sit down with Dr. Wendy Smith, Director of the Center for Science, Mathematics, and Computer Education at the University of Nebraska–Lincoln. Wendy shares how her journey into alternative grading began long before the term even existed—rooted in her own struggles as a math student who learned deeply, but not always “on time.”From those early experiences in the 1990s to her current work preparing future math teachers, Wendy reflects on how grading policies shape motivation and equity, and how she helps pre-service teachers design classrooms that measure learning, not behavior. Her “no penalty for late work” approach—anchored in neuroscience and compassion—helps future educators focus on what students know, not when they know it.LinksPlease note - any books linked here are likely Amazon Associates links. Clicking on them and purchasing through them helps support the show. Thanks for your support!Center for Science, Mathematics, and Computer Education – University of Nebraska–LincolnTransformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active LearningThe Mathematics Teacher Education Partnership: The Power of a Networked Improvement Community to Transform Secondary Mathematics Teacher PreparationResourcesThe Center for Grading Reform - seeking to advance education in the United States by supporting effective grading reform at all levels through conferences, educational workshops, professional development, research and scholarship, influencing public policy, and community building.The Grading Conference - an annual, online conference exploring Alternative Grading in Higher Education & K-12.Some great resources to educate yourself about Alternative Grading:The Grading for Growth BlogThe Grading ConferenceThe Intentional Academia BlogRecommended Books on Alternative Grading:Grading for Growth, by Robert Talbert and David ClarkSpecifications Grading, by Linda Nilsen

Join The Deep Dive(Life-changing teachings for spiritual mastery, guided sound journeys, and access to live community gatherings to share your most authentic self) https://iamemilioortiz.com/the-deep-d...Nikola Tesla's forgotten insights are resurfacing in ways that challenge everything we thought we knew about reality. In this powerful conversation, Oxford physicist Dr. David Clements reveals how Tesla's vision of plasma, living energy, and cosmic intelligence connects with urgent messages from higher civilizations such as the Arcturians. We explore why the collapse of old reality is already underway, what Tesla may have understood about the future of humanity, and how star beings are guiding us into a new paradigm of consciousness and technology.From the end of “dead physics” to the rise of living energetics, Dr. Clements explains how our emanation bends reality, why simulation theory keeps us trapped, and what it means for humanity's evolution as we approach a collective shift. This episode bridges science and spirituality with practical revelations on heart intelligence, cosmic plasma, and Tesla's role as a forerunner of the New Earth. Dr. David Clements is a theoretical physicist and consciousness researcher who bridges advanced science with spirituality and higher intelligence. Dr Clements studied at University of Oxford and Advanced Study in Mathematics and Theoretical Physics at University of Cambridge. Guided by beings like the Arcturians and Pleiadians, he moved beyond structural science to explore "living energetics"—the fluid, heart-centered reality that underlies our physical world. ___________________PODCAST CHAPTERS00:00 - Dr David Clements Intro3:13 – What Excites Dr. Clements About Humanity's Future5:39 – How Our Emanations Bend Reality7:30 – Clearing Old Energetics & Awakening the Heart11:22 – Rediscovering Wonder & the Infinite Cosmos13:15 – From Physics & Academia to Higher Realms of Energy15:33 – First Encounters with Living Energetics & Invention17:28 – Why Mathematics Fails to Describe Living Energy19:29 – Lessons from the Arcturians on Heart-Centered Perception21:18 – Remote Perception & Seeing Reality Through the Heart22:43 – What Nikola Tesla Was Really Onto24:55 – Tesla vs. Einstein: Energy in Matter or Space?28:01 – Living Energetic Devices & Emotional Clearing30:23 – Living Energetics vs. Artificial Intelligence34:01 – Plasma Technology & Multi-Dimensional Ships38:59 – Living with One Foot in 3D and One Foot in the Quantum41:53 – Luminescent Bodies & The Future of Human Evolution45:29 – Disease, Healing & The Role of Source Light in the Body49:03 – The Fortress Around the Human Heart54:54 – Releasing Old Energies & Becoming Response-Able58:04 – Morning Practices & Holding Source Energy All Day1:01:20 – How Advanced Races Use the Mind in Harmony with the Heart1:04:02 – Moving Beyond Duality & Returning to Source1:08:51 – How to Discern the Energy of Beings1:11:11 – What Determines the Speed of Consciousness Expansion1:15:23 – Is Reality a Simulation? 1:24:09 – A Transmission from the Arcturians1:36:21 – Future Discoveries & Time Capsule Message___________________Guest: Dr David Clements, Physicist✦ Website | https://infinitesourcecreations.com/✦ Patreon |   / infinitesourcecreations  ✦ Energy Harmonizing Devices | https://isee-infynergy.com/Host: Emilio Ortiz✦ IG |   / iamemilioortiz  ✦ Subscribe to Channel |    / emilioortiz  ___________________© 2025 Emilio Ortiz. All rights reserved. Content from Just Tap In Podcast is protected under copyright law.Legal Disclaimer: The views, thoughts, and opinions expressed by guests on Just Tap In are solely those of the guest and do not necessarily reflect the views or opinions of Emilio Ortiz or the Just Tap In Podcast. All content is for informational purposes only and should not be considered professional advice.

When the Government unveiled it's maths action plan in August last year, we spoke to Distinguished Maths Professor Gaven Martin. Widely regarded as New Zealand's leading mathematician, Gaven gave the new plan better odds of working than curriculum under the previous Government. Now, more than 40 maths educators and researchers have written an open letter calling on the Ministry of Education and Erica Stanford to pause the latest curriculum rollout immediately. They are questioning why the maths curriculum has been re-written for the third time in three years, saying they were “deeply concerned” by both the changes themselves and the process used for its development. LISTEN ABOVESee omnystudio.com/listener for privacy information.

Do you consider yourself lucky? Or do you consider yourself have earned it by working hard? Or, is it both? Our guest today is Dr. Michael Orkin, is a statistics expert and he shares with us some surprising insights.TODAY'S WIN-WIN:In order to increase your chances, you need to put yourself in positions where opportunities can occur and create more chance.LINKS FROM THE EPISODE:Schedule your free franchise consultation with Big Sky Franchise Team: https://bigskyfranchiseteam.com/. You can visit our guest's website at: https://drmikeorkin.com/Attend our Franchise Sales Training Workshop:  https://bigskyfranchiseteam.com/franchisesalestraining/Connect with our guest on social:https://www.linkedin.com/in/dr-mike-orkin-5600584/recent-activity/all/ABOUT OUR GUEST:DR. MICHAEL ORKIN is a distinguished professor, consultant, researcher, and author with a wealth of experience that offers unique insights into the concepts of chance and luck. He holds a BA in Mathematics and a PhD in Statistics from the University of California, Berkeley. Throughout his career, Dr. Orkin has made significant contributions to the field of statistics, particularly in the gaming industry, where he frequently serves as a consultant. His extensive research has been published in numerous academic papers, and he has delivered invited talks on these topics, including a notable presentation at Google Tech Talks. Dr. Orkin is a Professor Emeritus of Statistics at California State University, East Bay, and he currently serves on the mathematics faculty at Berkeley City College. His expertise and experience make him a leading authority on the statistical principles underlying games, chance, and the role of luck in various aspects of life.    ABOUT BIG SKY FRANCHISE TEAM:This episode is powered by Big Sky Franchise Team. If you are ready to talk about franchising your business you can schedule your free, no-obligation, franchise consultation online at: https://bigskyfranchiseteam.com/.The information provided in this podcast is for informational and educational purposes only and should not be considered financial, legal, or professional advice. Always consult with a qualified professional before making any business decisions. The views and opinions expressed by guests are their own and do not necessarily reflect those of the host, Big Sky Franchise Team, or our affiliates. Additionally, this podcast may feature sponsors or advertisers, but any mention of products or services does not constitute an endorsement. Please do your own research before making any purchasing or business decisions.

Episode: 1465 In which random statistical clusters look significant.  Today, we flip six heads in a row.

In this conversation, Drs. Gaurav Suri and Jay Mcclelland delves into the intricate relationship between artificial intelligence and human cognition, exploring similarities and differences, the evolution of AI from rule-based systems to learning models, and the concept of emergence in both fields. The discussion also touches on the efficiency of human learning compared to AI, the role of consciousness, and the ethical implications of AI technology.Takeaways AI and human intelligence share similarities in neural network frameworks. Artificial systems lack the goal-directed nature inherent in humans. Humans learn more efficiently than current AI systems. Neural networks can adapt to language nuances better than rule-based systems. Emergence explains how collective intelligence arises from individual components. Memory in neural networks is represented through connections, not individual units. Mathematics is both invented and discovered, shaped by human needs. Understanding consciousness is crucial for AI development. Human misuse of AI poses significant risks. Recognizing ourselves as processes can foster empathy and morality.Chapters 00:00 Introduction and Backgrounds 01:00 AI vs Human Mind: Similarities and Differences 03:32 The Shift from Rule-Based AI to Learning Systems 09:07 Emergence in Cognition: Ant Colonies and Intelligence 15:25 Distributed Representations and Memory Storage 23:53 The Nature of Memory and Its Malleability 25:40 Emergence of Mathematical Concepts 29:50 The Invention vs. Discovery Debate in Mathematics 32:19 Learning Mechanisms: Brain vs. AI 36:48 Consciousness: Function and Implications 41:13 AI Risks: Human Misuse vs. AI Autonomy 43:45 Living with Emergence: Understanding Ourselves and Others 48:22 Exploring the Emergent MindFollow Gaurav Suri on LinkedIn. Follow Jay McClelland on Twitter and find their new book here.Subscribe to Breaking Math wherever you get your podcasts.Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTokFollow Autumn on Twitter, BlueSky, and InstagramBecome a guest hereemail: breakingmathpodcast@gmail.com

About Walid Amarir:Walid Amarir is the Co-founder and CEO of WaLead.ai, a LinkedIn automation tool built to solve the scalability problems he experienced firsthand running a LinkedIn marketing agency. At just 23, Walid has an unconventional background—he was a professional eSports player earning his parents' salaries by age 18, then studied Physics and Mathematics in the UK before realizing he preferred building businesses to academia. After identifying critical gaps in existing LinkedIn automation tools while scaling his agency, Walid made the jump from service provider to SaaS founder, building a lean, efficient platform that maintains authenticity while automating outreach at scale.About WaLead.ai:WaLead.ai is a LinkedIn automation and prospecting platform designed for B2B companies that need to scale their outbound sales without sacrificing personalization. Built by someone who lived the pain points of existing tools, WaLead solves the core problem that legacy platforms face: they're built for individual users, not for teams managing multiple accounts and campaigns. The platform integrates seamlessly with existing sales workflows, helping companies automate LinkedIn outreach while maintaining the human touch that drives real conversations and conversions.Show Notes:00:00 Introduction to Walid and His Journey02:48 Transition from Agency to Building WaLead.ai05:48 Strategies for LinkedIn Success09:04 Building a Scalable LinkedIn Tool11:59 Managing Integrations14:41 Geographical Advantages and Market Strategy18:01 Metrics and Follow-Up Strategies20:53 Building an Effective LinkedIn Profile23:44 Engagement and Community Building on LinkedIn26:37 Final Thoughts and Future Directions

Aubrey Masango is joined by Themba Dladla, Teacher and HOD of Mathematics and Science at Riverlea High School and he speaks to us his love for teaching, reasons behind ensuring that his students do well in Maths and Science and his hopes for the future generations of SA as far as education is concerned. Tags: 702, Aubrey Masango show, Aubrey Masango, Bra Aubrey, Themba Dladla, Mathematics, Science, Riverlea High School The Aubrey Masango Show is presented by late night radio broadcaster Aubrey Masango. Aubrey hosts in-depth interviews on controversial political issues and chats to experts offering life advice and guidance in areas of psychology, personal finance and more. All Aubrey’s interviews are podcasted for you to catch-up and listen. Thank you for listening to this podcast from The Aubrey Masango Show. Listen live on weekdays between 20:00 and 24:00 (SA Time) to The Aubrey Masango Show broadcast on 702 https://buff.ly/gk3y0Kj and on CapeTalk between 20:00 and 21:00 (SA Time) https://buff.ly/NnFM3Nk Find out more about the show here https://buff.ly/lzyKCv0 and get all the catch-up podcasts https://buff.ly/rT6znsn Subscribe to the 702 and CapeTalk Daily and Weekly Newsletters https://buff.ly/v5mfet Follow us on social media: 702 on Facebook: https://www.facebook.com/TalkRadio702 702 on TikTok: https://www.tiktok.com/@talkradio702 702 on Instagram: https://www.instagram.com/talkradio702/ 702 on X: https://x.com/Radio702 702 on YouTube: https://www.youtube.com/@radio702 CapeTalk on Facebook: https://www.facebook.com/CapeTalk CapeTalk on TikTok: https://www.tiktok.com/@capetalk CapeTalk on Instagram: https://www.instagram.com/ CapeTalk on X: https://x.com/CapeTalk CapeTalk on YouTube: https://www.youtube.com/@CapeTalk567 See omnystudio.com/listener for privacy information.

How is mathematical knowledge recorded and preserved across generations? Contrary to the idea that mathematics itself is somehow ‘permanent', in this talk we will explore heritage-making in mathematics, that is the people, institutions, and material objects that can give mathematical ideas longevity. We will explore the heritage-making found in two very different types of French nineteenth-century libraries: those of famous mathematicians and those of secondary schools. We will especially focus on how the recording – and forgetting – of mathematical ideas is influenced by their publishing, political, and intellectual contexts.This lecture was recorded by Professor Caroline Ehrhardt on 8th October 2025 at Barnard's Inn Hall, London.Caroline Ehrhardt is Professor of History of Science and Deputy Director of IDHE.S at Université Paris 8 professor in history of science at the Université Paris 8 (France). Her research concerns the history of mathematics in France and Europe (1789–1914). She has published on Evariste Galois, on Galois theory and on mathematics education.Caroline is currently coordinating a collective project funded by the French Agence Nationale de la Recherche, entitled ‘Heritage and patrimonialisation of mathematics, 18th-20th centuries'. She also focuses on the practice of mathematics within French life insurance companies, on interactions between the mathematical and actuarial communities, and the production of mortality tables.The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/watch-now/heritage-mathsGresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/Website:  https://gresham.ac.ukTwitter:  https://twitter.com/greshamcollegeFacebook: https://facebook.com/greshamcollegeInstagram: https://instagram.com/greshamcollegeSupport the show

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What is Chat HPE? This week, Technology Now dives into the world of workplace assistants and examines what must be considered when designing them. We explore why businesses want them, how they are created, and ask how good Chat HPE could be when designing a podcast... Jose M Mejias, a Distinguished Technologist working in the Data Office tells us more.This is Technology Now, a weekly show from Hewlett Packard Enterprise. Every week, hosts Michael Bird and Aubrey Lovell look at a story that's been making headlines, take a look at the technology behind it, and explain why it matters to organizations.About Jose: https://pr.linkedin.com/in/jose-mejias-1233b323Sources:Joseph Weizenbaum. 1966. ELIZA—a computer program for the study of natural language communication between man and machine. Commun. ACM 9, 1 (Jan. 1966), 36–45. https://doi.org/10.1145/365153.365168https://www.ibm.com/think/insights/eliza-effect-avoiding-emotional-attachment-to-aihttps://www.theguardian.com/technology/2023/jul/25/joseph-weizenbaum-inventor-eliza-chatbot-turned-against-artificial-intelligence-ai

Pam Harris, Exploring the Power & Purpose of Number Strings ROUNDING UP: SEASON 4 | EPISODE 4 I've struggled when I have a new strategy I want my students to consider and despite my best efforts, it just doesn't surface organically. While I didn't want to just tell my students what to do, I wasn't sure how to move forward. Then I discovered number strings.  Today, we're talking with Pam Harris about the ways number strings enable teachers to introduce new strategies while maintaining opportunities for students to discover important relationships.  BIOGRAPHY Pam Harris, founder and CEO of Math is Figure-out-able™, is a mom, a former high school math teacher, a university lecturer, an author, and a mathematics teacher educator. Pam believes real math is thinking mathematically, not just mimicking what a teacher does. Pam helps leaders and teachers to make the shift that supports students to learn real math. RESOURCES Young Mathematicians at Work by Catherine Fosnot and Maarten Dolk  Procedural fluency in mathematics: Reasoning and decision-making, not rote application of procedures position by the National Council of Teachers of Mathematics Bridges number string example from Grade 5, Unit 3, Module 1, Session 1 (BES login required) Developing Mathematical Reasoning: Avoiding the Trap of Algorithms by Pamela Weber Harris and Cameron Harris Math is Figure-out-able!™ Problem Strings TRANSCRIPT Mike Wallus: Welcome to the podcast, Pam. I'm really excited to talk with you today. Pam Harris: Thanks, Mike. I'm super glad to be on. Thanks for having me. Mike: Absolutely.  So before we jump in, I want to offer a quick note to listeners. The routine we're going to talk about today goes by several different names in the field. Some folks, including Pam, refer to this routine as “problem strings,” and other folks, including some folks at The Math Learning Center, refer to them as “number strings.” For the sake of consistency, we'll use the term “strings” during our conversation today.  And Pam, with that said, I'm wondering if for listeners, without prior knowledge, could you briefly describe strings? How are they designed? How are they intended to work? Pam: Yeah, if I could tell you just a little of my history. When I was a secondary math teacher and I dove into research, I got really curious: How can we do the mental actions that I was seeing my son and other people use that weren't the remote memorizing and mimicking I'd gotten used to?  I ran into the work of Cathy Fosnot and Maarten Dolk, and [their book] Young Mathematicians at Work, and they had pulled from the Netherlands strings. They called them “strings.” And they were a series of problems that were in a certain order. The order mattered, the relationship between the problems mattered, and maybe the most important part that I saw was I saw students thinking about the problems and using what they learned and saw and heard from their classmates in one problem, starting to let that impact their work on the next problem. And then they would see that thinking made visible and the conversation between it and then it would impact how they thought about the next problem. And as I saw those students literally learn before my eyes, I was like, “This is unbelievable!” And honestly, at the very beginning, I didn't really even parse out what was different between maybe one of Fosnot's rich tasks versus her strings versus just a conversation with students. I was just so enthralled with the learning because what I was seeing were the kind of mental actions that I was intrigued with. I was seeing them not only happen live but grow live, develop, like they were getting stronger and more sophisticated because of the series of the order the problems were in, because of that sequence of problems. That was unbelievable. And I was so excited about that that I began to dive in and get more clear on: What is a string of problems?  The reason I call them “problem strings” is I'm K–12. So I will have data strings and geometry strings and—pick one—trig strings, like strings with functions in algebra. But for the purposes of this podcast, there's strings of problems with numbers in them. Mike: So I have a question, but I think I just want to make an observation first. The way you described that moment where students are taking advantage of the things that they made sense of in one problem and then the next part of the string offers them the opportunity to use that and to see a set of relationships. I vividly remember the first time I watched someone facilitate a string and feeling that same way, of this routine really offers kids an opportunity to take what they've made sense of and immediately apply it. And I think that is something that I cannot say about all the routines that I've seen, but it was really so clear. I just really resonate with that experience of, what will this do for children? Pam: Yeah, and if I can offer an additional word in there, it influences their work. We're taking the major relationships, the major mathematical strategies, and we're high-dosing kids with them. So we give them a problem, maybe a problem or two, that has a major relationship involved. And then, like you said, we give them the next one, and now they can notice the pattern, what they learned in the first one or the first couple, and they can let it influence. They have the opportunity for it to nudge them to go, “Hmm. Well, I saw what just happened there. I wonder if it could be useful here. I'm going to tinker with that. I'm going to play with that relationship a little bit.” And then we do it again. So in a way, we're taking the relationships that I think, for whatever reason, some of us can wander through life and we could run into the mathematical patterns that are all around us in the low dose that they are all around us, but many of us don't pick up on that low dose and connect them and make relationships and then let it influence when we do another problem.  We need a higher dose. I needed a higher dose of those major patterns. I think most kids do. Problem strings or number strings are so brilliant because of that sequence and the way that the problems are purposely one after the other. Give students the opportunity to, like you said, apply what they've been learning instantly [snaps]. And then not just then, but on the next problem and then sometimes in a particular structure we might then say, “Mm, based on what you've been seeing, what could you do on this last problem?” And we might make that last problem even a little bit further away from the pattern, a little bit more sophisticated, a little more difficult, a little less lockstep, a little bit more where they have to think outside the box but still could apply that important relationship. Mike: So I have two thoughts, Pam, as I listen to you talk.  One is that for both of us, there's a really clear payoff for children that we've seen in the way that strings are designed and the way that teachers can use them to influence students' thinking and also help kids build a recognition or high-dose a set of relationships that are really important.  The interesting thing is, I taught kindergarten through second grade for most of my teaching career, and you've run the gamut. You've done this in middle school and high school. So I think one of the things that might be helpful is to share a few examples of what a string could look like at a couple different grade levels. Are you OK to share a few? Pam: You bet. Can I tack on one quick thing before I do? Mike: Absolutely. Pam: You mentioned that the payoff is huge for children. I'm going to also suggest that one of the things that makes strings really unique and powerful in teaching is the payoff for adults. Because let's just be clear, most of us—now, not all, but most of us, I think—had a similar experience to me that we were in classrooms where the teacher said, “Do this thing.” That's the definition of math is for you to rote memorize these disconnected facts and mimic these procedures. And for whatever reason, many of us just believed that and we did it. Some people didn't. Some of us played with relationships and everything. Regardless, we all kind of had the same learning experience where we may have taken at different places, but we still saw the teacher say, “Do these things. Rote memorize. Mimic.”  And so as we now say to ourselves, “Whoa, I've just seen how cool this can be for students, and we want to affect our practice.” We want to take what we do, do something—we now believe this could be really helpful, like you said, for children, but doing that's not trivial. But strings make it easier. Strings are, I think, a fantastic differentiated kind of task for teachers because a teacher who's very new to thinking and using relationships and teaching math a different way than they were taught can dive in and do a problem string. Learn right along with your students. A veteran teacher, an expert teacher who's really working on their teacher moves and really owns the landscape of learning and all the things still uses problem strings because they're so powerful. Like, anybody across the gamut can use strings—I just said problem strings, sorry—number strengths—[laughs] strings, all of us no matter where we are in our teaching journey can get a lot out of strings. Mike: So with all that said, let's jump in. Let's talk about some examples across the elementary span. Pam: Nice. So I'm going to take a young learner, not our youngest, but a young learner. I might ask a question like, “What is 8 plus 10?” And then if they're super young learners, I expect some students might know that 10 plus a single digit is a teen, but I might expect many of the students to actually say “8, 9, 10, 11, 12,” or “10, 11,” and they might count by ones given—maybe from the larger, maybe from the whatever. But anyway, we're going to kind of do that. I'm going to get that answer from them. I'm going to write on the board, “8 plus 10 is 18,” and then I would have done some number line work before this, but then I'm going to represent on the board: 8 plus 10, jump of 10, that's 18. And then the next problem's going to be something like 8 plus 9. And I'm going to say, “Go ahead and solve it any way you want, but I wonder—maybe you could use the first problem, maybe not.” I'm just going to lightly suggest that you consider what's on the board. Let them do whatever they do. I'm going to expect some students to still be counting. Some students are going to be like, “Oh, well I can think about 9 plus 8 counting by ones.” I think by 8—”maybe I can think about 8 plus 8. Maybe I can think about 9 plus 9.” Some students are going to be using relationships, some are counting. Kids are over the map.  When I get an answer, they're all saying, like, 17. Then I'm going to say, “Did anybody use the first problem to help? You didn't have to, but did anybody?” Then I'm going to grab that kid. And if no one did, I'm going to say, “Could you?” and pause.  Now, if no one sparks at that moment, then I'm not going to make a big deal of it. I'll just go, “Hmm, OK, alright,” and I'll do the next problem. And the next problem might be something like, “What's 5 plus 10?” Again, same thing, we're going to get 15. I'm going to draw it on the board.  Oh, I should have mentioned: When we got to the 8 plus 9, right underneath that 8, jump, 10 land on 18, I'm going to draw an 8 jump 9, shorter jump. I'm going to have these lined up, land on the 17. Then I might just step back and go, “Hmm. Like 17, that's almost where the 18 was.” Now if kids have noticed, if somebody used that first problem, then I'm going to say, “Well, tell us about that.” “Well, miss, we added 10 and that was 18, but now we're adding 1 less, so it's got to be 1 less.” And we go, “Well, is 17 one less than 18? Huh, sure enough.” Then I give the next set of problems. That might be 5 plus 10 and then 5 plus 9, and then I might do 7 plus 10. Maybe I'll do 9 next. 9 plus 10 and then 9 plus 9. Then I might end that string. The next problem, the last problem might be, “What is 7 plus 9?” Now notice I didn't give the helper. So in this case I might go, “Hey, I've kind of gave you plus 10. A lot of you use that to do plus 9. I gave you plus 10. Some of you use that to do plus 9, I gave you plus 10. Some of you used that plus 9. For this one, I'm not giving you a helper. I wonder if you could come up with your own helper.”  Now brilliantly, what we've done is say to students, “You've been using what I have up here, or not, but could you actually think, ‘What is the pattern that's happening?' and create your own helper?” Now that's meta. Right? Now we're thinking about our thinking. I'm encouraging that pattern recognition in a different way. I'm asking kids, “What would you create?” We're going to share that helper. I'm not even having them solve the problem. They're just creating that helper and then we can move from there.  So that's an example of a young string that actually can grow up. So now I can be in a second grade class and I could ask a similar [question]: “Could you use something that's adding a bit too much to back up?” But I could do that with bigger numbers. So I could start with that 8 plus 10, 8 plus 9, but then the next pair might be 34 plus 10, 34 plus 9. But then the next pair might be 48 plus 20 and 48 plus 19. And the last problem of that string might be something like 26 plus 18. Mike: So in those cases, there's this mental scaffolding that you're creating. And I just want to mark this. I have a good friend who used to tell me that part of teaching mathematics is you can lead the horse to water, you can show them the water, they can look at it, but darn it, do not push their head in the water. And I think what he meant by that is “You can't force it,” right?  But you're not doing that with a string. You're creating a set of opportunities for kids to notice. You're doing all kinds of implicit things to make structure available for kids to attend to—and yet you're still allowing them the ability to use the strategies that they have. We might really want them to notice that, and that's beautiful about a string, but you're not forcing. And I think it's worth saying that because I could imagine that's a place where folks might have questions, like, “If the kids don't do the thing that I'm hoping that they would do, what should I do?” Pam: Yeah, that's a great question. Let me give you another example. And in that example I'll talk about that.  So especially as the kids get older, I'm going to use the same kind of relationship. It's maybe easier for people to hang on to if I stay with the same sort of relationship. So I might say, “Hey everybody. 7 times 8. That's a fact I'm noticing most of us just don't have [snaps] at our fingertips. Let's just work on that. What do you know?” I might get a couple of strategies for kids to think about 7 times 8. We all agree it's 56.  Then I might say, “What's 70 times 8?” And then let kids think about that. Now, this would be the first time I do that, but if we've dealt with scaling times 10 at all, if I have 10 times the number of whatever the things is, then often kids will say, “Well, I've got 10 times 7 is 70, so then 10 times 56 is 560.” And then the next problem might be, “I wonder if you could think about 69 times 8. If we've got 70 eights, can I use that to help me think about 69 eights?” And I'm saying that in a very specific way to help ping on prior knowledge. So then I might do something similar. Well, let's pick another often missed facts, I don't know, 6 times 9. And then we could share some strategies on how kids are thinking about that. We all agree it's 54. And then I might say, “Well, could you think about 6 times 90?” I'm going to talk about scaling up again. So that would be 540. Now I'm going really fast. But then I might say, “Could we use that to help us think about 6 times 89?” I don't know if you noticed, but I sort of swapped. I'm not thinking about 90 sixes to 89 sixes. Now I'm thinking about 6 nineties to help me think about 6 eighty-nines. So that's a little bit of a—we have to decide how we're going to deal with that. I'll kind of mess around with that. And then I might have what we call that clunker problem at the end. “Notice that I've had a helper: 7 times 8, 70 times 8. A lot of you use that to help you think about 69 times 8. Then I had a helper: 6 times 9, 6 times 90. A lot of you use that to help you think about 6 times 89. What if I don't give you those helpers? What if I had something like”—now I'm making this up off the cuff here, like—“9 times 69. 9 times 69. Could you use relationships we just did?”  Now notice, Mike, I might've had kids solving all those problems using an algorithm. They might've been punching their calculator, but now I'm asking the question, “Could you come up with these helper problems?” Notice how I'm now inviting you into a different space. It's not about getting an answer. I'm inviting you into, “What are the patterns that we've been establishing here?” And so what would be those two problems that would be like the patterns we've just been using? That's almost like saying when you're out in the world and you hit a problem, could you say to yourself, “Hmm, I don't know that one, but what do I know? What do I know that could help me get there?” And that's math-ing. Mike: So, you could have had a kid say, “Well, I'm not sure about how—I don't know the answer to that, but I could do 9 times 60, right?” Or “I could do 10 times”—I'm thinking—“10 times 69.” Correct? Pam: Yes, yes. In fact, when I gave that clunker problem, 9 times 69, I said to myself, “Oh, I shouldn't have said 9 because now you could go either direction.” You could either “over” either way. To find 9 I can do 10, or to find 69 I can do 70. And then I thought, “Ah, we'll go with it because you can go either way.” So I might want to focus it, but I might not. And this is a moment where a novice could just throw it out there and then almost be surprised. “Whoa, they could go either direction.” And an expert could plan, and be like, “Is this the moment where I want lots of different ways to go? Or do I want to focus, narrow it a little bit more, be a little bit more explicit?” It's not that I'm telling kids, but I'm having an explicit goal. So I'm maybe narrowing the field a little bit. And maybe the problem could have been 7 times 69, then I wouldn't have gotten that other “over,” not the 10 to get 9. Does that make sense? Mike: It absolutely does. What you really have me thinking about is NCTM's [National Council of Teachers of Mathematics'] definition of “fluency,” which is “accuracy, efficiency, and flexibility.” And the flexibility that I hear coming out of the kinds of things that kids might do with a string, it's exciting to imagine that that's one of the outcomes you could get from engaging with strings. Pam: Absolutely. Because if you're stuck teaching memorizing algorithms, there's no flexibility, like none, like zilch. But if you're doing strings like this, kids have a brilliant flexibility. And one of the conversations I'd want to have here, Mike, is if a kid came up with 10 times 69 to help with 9 times 69, and a different kid came up with 9 times 70 to help with 9 times 69, I would want to just have a brief conversation: “Which one of those do you like better, class, and why?” Not that one is better than the other, but just to have the comparison conversation. So the kids go, “Huh, I have access to both of those. Well, I wonder when I'm walking down the street, I have to answer that one: Which one do I want my brain to gravitate towards next time?” And that's mathematical behavior. That's mathematical disposition to do one of the strands of proficiency. We want that productive disposition where kids are thinking to themselves, “I own relationships. I just got to pick a good one here to—what's the best one I could find here?” And try that one, then try that one. “Ah, I'll go with this one today.” Mike: I love that.  As we were talking, I wanted to ask you about the design of the string, and you started to use some language like “helper problems” and “the clunker.” And I think that's really the nod to the kinds of features that you would want to design into a string. Could you talk about either a teacher who's designing their own string—what are some of the features?—or a teacher who's looking at a string that they might find in a book that you've written or that they might find in, say, the Bridges curriculum? What are some of the different problems along the way that really kind of inform the structure? Pam: So you might find it interesting that over time, we've identified that there's at least five major structures to strings, and the one that I just did with you is kind of the easiest one to facilitate. It's the easiest one to understand where it's going, and it's the helper-clunker structure. So the helper-clunker structure is all about, “I'm going to give you a helper problem that we expect all kids can kind of hang on.” They have some facility with, enough that everybody has access to. Then we give you a clunker that you could use that helper to inform how you could solve that clunker problem. In the first string I did with you, I did a helper, clunker, helper, clunker, helper, clunker, clunker. And the second one we did, I did helper, helper, clunker, helper, helper, clunker, clunker. So you can mix and match kind of helpers and clunkers in that, but there are other major structures of strings. If you're new to strings, I would dive in and do a lot of helper-clunker strings first. But I would also suggest—I didn't create my own strings for a long time. I did prewritten [ones by] Cathy Fosnot from the Netherlands, from the Freudenthal Institute. I was doing their strings to get a feel for the mathematical relationships for the structure of a string. I would watch videos of teachers doing it so I could get an idea of, “Oh, that move right there made all the difference. I see how you just invited kids in, not demand what they do.” The idea of when to have paper and pencil and when not, and just lots of different things can come up that if you're having to write the string as well, create the string, that could feel insurmountable.  So I would invite anybody out listening that's like, “Whoa, this seems kind of complicated,” feel free to facilitate someone else's prewritten strings. Now I like mine. I think mine are pretty good. I think Bridges has some pretty good ones. But I think you'd really gain a lot from facilitating prewritten strings.  Can I make one quick differentiation that I'm running into more and more? So I have had some sharp people say to me, “Hey, sometimes you have extra problems in your string. Why do you have extra problems in your string?” And I'll say—well, at first I said, “What do you mean?” Because I didn't know what they were talking about. Are you telling me my string's bad? Why are you dogging my string? But what they meant was, they thought a string was the process a kid—or the steps, the relationships a kid used to solve the last problem. Does that make sense? Mike: It does. Pam: And they were like, “You did a lot of work to just get that one answer down there.” And I'm like, “No, no, no, no, no, no. A problem string or a number string, a string is an instructional routine. It is a lesson structure. It's a way of teaching. It's not a record of the relationships a kid used to solve a problem.” In fact, a teacher just asked—we run a challenge three times a year. It's free. I get on and just teach. One of the questions that was asked was, “How do we help our kids write their own strings?” And I was like, “Oh, no, kids don't write strings. Kids solve problems using relationships.” And so I think what the teachers were saying was, “Oh, I could use that relationship to help me get this one. Oh, and then I can use that to solve the problem.” As if, then, the lesson's structure, the instructional routine of a string was then what we want kids to do is use what they know to logic their way through using mathematical relationships and connections to get answers and to solve problems. That record is not a string, that record is a record of their work. Does that make sense, how there's a little difference there? Mike: It totally does, but I think that's a good distinction. And frankly, that's a misunderstanding that I had when I first started working with strings as well. It took me a while to realize that the point of a string is to unveil a set of relationships and then allow kids to take them up and use them. And really it's about making these relationships or these problem solving strategies sticky, right? You want them to stick. We could go back to what you said. We're trying to high-dose a set of relationships that are going to help kids with strategies, not only in this particular string, but across the mathematical work they're doing in their school life. Pam: Yes, very well said. So for example, we did an addition “over” relationship in the addition string that I talked through, and then we did a multiplication “over” set of relationships and multiplication. We can do the same thing with subtraction. We could have a subtraction string where the helper problem is to subtract a bit too much. So something like 42 minus 20, and then the next problem could be 42 minus 19. And we're using that: I'm going to subtract a bit too much and then how do you adjust? And hoo, after you've been thinking about addition “over,” subtraction “over” is quite tricky. You're like, “Wait, why are we adding what we're subtracting?” And it's not about teaching kids a series of steps. It's really helping them reason. “Well, if I give you—if you owe me 19 bucks and I give you a $20 bill, what are we going to do?” “Oh, you've got to give me 1 back.” Now that's a little harder today because kids don't mess around with money. So we might have to do something that feels like they can—or help them feel money. That's my personal preference. Let's do it with money and help them feel money.  So one of the things I think is unique to my work is as I dove in and started facilitating other people's strings and really building my mathematical relationships and connections, I began to realize that many teachers I worked with, myself included, thought, “Whoa, there's just this uncountable, innumerable wide universe of all the relationships that are out there, and there's so many strategies, and anything goes, and they're all of equal value.” And I began to realize, “No, no, no, there's only a small set of major relationships that lead to a small set of major strategies.” And if we can get those down, kids can solve any problem that's reasonable to solve without a calculator, but in the process, building their brains to reason mathematically. And that's really our goal, is to build kids' brains to reason mathematically. And in the process we're getting answers. Answers aren't our goal. We'll get answers, sure. But our goal is to get them to build that small set of relationships because that small set of strategies now sets them free to logic their way through problems. And bam, we've got kids math-ing using the mental actions of math-ing. Mike: Absolutely. You made me think about the fact that there's a set of relationships that I can apply when I'm working with numbers Under 20. There's a set of relationships, that same set of relationships, I can apply and make use of when I'm working with multidigit numbers, when I'm working with decimals, when I'm working with fractions. It's really the relationships that we want to expose and then generalize and recognize this notion of going over or getting strategically to a friendly number and then going after that or getting to a friendly number and then going back from that. That's a really powerful strategy, regardless of whether you're talking about 8 and 3 or whether you're talking about adding unit fractions together. Strings allow us to help kids see how that idea translates across different types of numbers. Pam: And it's not trivial when you change a type of number or the number gets bigger. It's not trivial for kids to take this “over” strategy and to be thinking about something like 2,467 plus 1,995—and I know I just threw a bunch of numbers out, on purpose. It's not trivial for them to go, “What do I know about those numbers? Can I use some of these relationships I've been thinking about?” Well, 2,467, that's not really close to a friendly number. Well, 1,995 is. Bam. Let's just add 2,000. Oh, sweet. And then you just got to back up 5. It's not trivial for them to consider, “What do I know about these two numbers, and are they close to something that I could use?” That's the necessary work of building place value and magnitude and reasonableness. We've not known how to do that, so in some curriculum we create our whole extra unit that's all about place value reasonableness. Now we have kids that are learning to rote memorize, how to estimate by round. I mean there's all this crazy stuff that we add on when instead we could actually use strings to help kids build that stuff naturally kind of ingrained as we are learning something else.  Can I just say one other thing that we did in my new book? Developing Mathematical Reasoning: Avoiding the Trap of Algorithms. So I actually wrote it with my son, who is maybe the biggest impetus to me diving into the research and figuring out all of this math-ing and what it means. He said, as we were writing, he said, “I think we could make the point that algorithms don't help you learn a new algorithm.” If you learn the addition algorithm and you get good at it and you can do all the addition and columns and all the whatever, and then when you learn the subtraction algorithm, it's a whole new thing. All of a sudden it's a new world, and you're doing different—it looks the same at the beginning. You line those numbers still up and you're still working on that same first column, but boy, you're doing all sorts—now you're crossing stuff out. You're not just little ones, and what? Algorithms don't necessarily help you learn the next algorithm. It's a whole new experience. Strategies are synergistic. If you learn a strategy, that helps you learn the next set of relationships, which then refines to become a new strategy. I think that's really helpful to know, that we can—strategies build on each other. There's synergy involved. Algorithms, you got to learn a new one every time. Mike: And it turns out that memorizing the dictionary of mathematics is fairly challenging. Pam: Indeed [laughs], indeed. I tried hard to memorize that. Yeah. Mike: You said something to me when we were preparing for this podcast that I really have not been able to get out of my mind, and I'm going to try to approximate what you said. You said that during the string, as the teacher and the students are engaging with it, you want students' mental energy primarily to go into reasoning. And I wonder if you could just explicitly say, for you at least, what does that mean and what might that look like on a practical level? Pam: So I wonder if you're referring to when teachers will say, “Do we have students write? Do we not have them write?” And I will suggest: “It depends. It's not if they write; it's what they write that's important.”  What do I mean by that? What I mean is if we give kids paper and pencil, there is a chance that they're going to be like, “Oh, thou shalt get an answer. I'm going to write these down and mimic something that I learned last year.” And put their mental energy either into mimicking steps or writing stuff down. They might even try to copy what you've been representing strategies on the board. And their mental effort either goes into mimicking, or it might go into copying.  What I want to do is free students up [so] that their mental energy is, how are you reasoning? What relationships are you using? What's occurring to you? What's front and center and sort of occurring? Because we're high-dosing you with patterns, we're expecting those to start happening, and I'm going to be saying things, giving that helper problem. “Oh, that's occurring to you? It's almost like it's your idea—even though I just gave you the helper problem!” It's letting those ideas bubble up and percolate naturally and then we can use those to our advantage. So that's what I mean when [I say] I want mental energy into “Hmm, what do I know, and how can I use what I know to logic my way through this problem?” And that's math-ing. Those are the mental actions of mathematicians, and that's where I want kids' mental energy. Mike: So I want to pull this string a little bit further. Pun 100% intended there. Apologies to listeners.  What I find myself thinking about is there've got to be some do's and don'ts for how to facilitate a string that support the kind of reasoning and experience that you've been talking about. I wonder if you could talk about what you've learned about what you want to do as a facilitator when you're working with a string and maybe what you don't want to do. Pam: Yeah, absolutely. So a good thing to keep in mind is you want to keep a string snappy. You don't want a lot of dead space. You don't want to put—one of the things that we see novice, well, even sometimes not-novice, teachers do, that's not very helpful, is they will put the same weight on all the problems.  So I'll just use the example 8 plus 10, 8 plus 9, they'll—well, let me do a higher one. 7 times 8, 70 times 8. They'll say, “OK, you guys, 7 times 8. Let's really work on that. That's super hard.” And kids are like, “It's 56.” Maybe they have to do a little bit of reasoning to get it, because it is an often missed fact, but I don't want to land on it, especially—what was the one we did before? 34 plus 10. I don't want to be like, “OK, guys, phew.” If the last problem on my string is 26 plus 18, I don't want to spend a ton of time. “All right, everybody really put all your mental energy in 36 plus 10” or whatever I said. Or, let's do the 7 times 8 one again. So, “OK, everybody, 7 times 8, how are you guys thinking about that?” Often we're missing it. I might put some time into sharing some strategies that kids use to come up with 7 times 8 because we know it's often missed. But then when I do 70 times 8, if I'm doing this string, kids should have some facility with times 10. I'm not going to be like, “OK. Alright, you guys, let's see what your strategies are. Right? Everybody ready? You better write something down on your paper. Take your time, tell your neighbor how….” Like, it's times 10. So you don't want to put the same weight—as in emphasis and time, wait time—either one on the problems that are kind of the gimmes, we're pretty sure everybody's got this one. Let's move on and apply it now in the next one. So there's one thing. Keep it snappy. If no one has a sense of what the patterns are, it's probably not the right problem string. Just bail on it, bail on it. You're like, “Let me rethink that. Let me kind of see what's going on.” If, on the other hand, everybody's just like, “Well, duh, it's this” and “duh, it's that,” then it's also probably not the right string. You probably want to up the ante somehow.  So one of the things that we did in our problem string books is we would give you a lesson and give you what we call the main string, and we would write up that and some sample dialogs and what the board could look like when you're done and lots of help. But then we would give you two echo strings. Here are two strings that get at the same relationships with about the same kind of numbers, but they're different and it will give you two extra experiences to kind of hang there if you're like, “Mm, I think my kids need some more with exactly this.” But we also then gave you two next-step strings that sort of up the ante. These are just little steps that are just a little bit more to crunch on before you go to the next lesson that's a bit of a step up, that's now going to help everybody increase. Maybe the numbers got a little bit harder. Maybe we're shifting strategy. Maybe we're going to use a different model. I might do the first set of strings on an area model if I'm doing multiplication. I might do the next set of strings in a ratio table. And I want kids to get used to both of those.  When we switch up from the 8 string to the next string, kind of think about only switching one thing. Don't up the numbers, change the model, and change the strategy at the same time. Keep two of those constant. Stay with the same model, maybe up the numbers, stay with the same strategy. Maybe if you're going to change strategies, you might back up the numbers a little bit, stick with the model for a minute before you switch the model before you go up the numbers. So those are three things to consider. Kind of—only change up one of them at a time or kids are going to be like, “Wait, what?” Kids will get higher dosed with the pattern you want them to see better if you only switch one thing at a time. Mike: Part of what you had me thinking was it's helpful, whether you're constructing your own string or whether you're looking at a string that's in a textbook or a set of materials, it's still helpful to think about, “What are the variables at play here?” I really appreciated the notion that they're not all created equal. There are times where you want to pause and linger a little bit that you don't need to spend that exact same amount of time on every clunker and every helper. There's a critical problem that you really want to invest some time in at one point in the string. And I appreciated the way you described, you're playing with the size of the number or the complexity of the number, the shift in the model, and then being able to look at those kinds of things and say, “What all is changing?” Because like you said, we're trying to kind of walk this line of creating a space of discovery where we haven't suddenly turned the volume up to 11 and made it really go from like, “Oh, we discovered this thing, now we're at full complexity,” and yet we don't want to have it turned down to, “It's not even discovery because it's so obvious that I knew it immediately. There's not really anything even to talk about.” Pam: Nice. Yeah, and I would say we want to be right on the edge of kids' own proximal development, right on the edge. Right on the edge where they have to grapple with what's happening. And I love the word “grapple.” I've been in martial arts for quite a while, and grappling makes you stronger. I think sometimes people hear the word “struggle” and they're like, “Why would you ever want kids to struggle?” I don't know that I've met anybody that ever hears the word “grapple” as a negative thing. When you “grapple,” you get stronger. You learn. So I want kids right on that edge where they are grappling and succeeding. They're getting stronger. They're not just like, “Let me just have you guess what's in my head.” You're off in the field and, “Sure hope you figure out math, guys, today.” It's not that kind of discovery that people think it is. It really is: “Let me put you in a place where you can use what you know to notice maybe a new pattern and use it maybe in a new way. And poof! Now you own those relationships, and let's build on that.” And it continues to go from there.  When you just said—the equal weight thing, let me just, if I can—there's another, so I mentioned that there's at least five structures of problem strings. Let me just mention one other one that we like, to give you an example of how the weight could change in a string. So if I have an equivalent structure, an equivalent structure looks like: I give a problem, and an example of that might be 15 times 18. Now I'm not going to give a helper; I'm just going to give 15 times 18. If I'm going to do this string, we would have developed a few strategies before now. Kids would have some partial products going on. I would probably hope they would have an “over,” I would've done partial products over and probably, what I call “5 is half a 10.”  So for 15 times 18, they could use any one of those. They could break those up. They could think about twenty 15s to get rid of the extra two to have 18, 15. So in that case, I'm going to go find a partial product, an “over” and a “5 is half a 10,” and I'm going to model those. And I'm going to go, “Alright, everybody clear? Everybody clear on this answer?” Then the next problem I give—so notice that we just spent some time on that, unlike those helper clunker strings where the first problem was like a gimme, nobody needed to spend time on that. That was going to help us with the next one. In this case, this one's a bit of a clunker. We're starting with one that kids are having to dive in, chew on. Then I give the next problem: 30 times 9. So I had 15 times 18 now 30 times 9. Now kids get a chance to go, “Oh, that's not too bad. That's just 3 times 9 times 10. So that's 270. Wait, that was the answer to the first problem. That was probably just coincidence. Or was it?” And now especially if I have represented that 15 times 18, one of those strategies with an area model with an open array, now when I draw the 30 by 9, I will purposely say, “OK, we have the 15 by 18 up here. That's what that looked like. Mm, I'll just use that to kind of make sure the 30 by 9 looks like it should. How could I use the 15 by 18? Oh, I could double the 15? OK, well here's the 15. I'm going to double that. Alright, there's the 30. Well, how about the 9? Oh, I could half? You think I should half? OK. Well I guess half of 18. That's 9.”  So I've just helped them. I've brought out, because I'm inviting them to help me draw it on the board. They're thinking about, “Oh, I just half that side, double that side. Did we lose any area? Oh, maybe that's why the products are the same. The areas of those two rectangles are the same. Ha!” And then I give the next problem. Now I give another kind of clunker problem and then I give its equivalent. And again, we just sort of notice: “Did it happen again?” And then I might give another one and then I might end the string with something like 3.5 times—I'm thinking off the cuff here, 16. So 3.5 times 16. Kids might say, “Well, I could double 3.5 to get 7 and I could half the 16 to get 8, and now I'm landing on 7 times 8.” And that's another way to think about 3.5 times 16. Anyway, so, equivalent structure is also a brilliant structure that we use primarily when we're trying to teach kids what I call the most sophisticated of all of the strategies. So like in addition, give and take, I think, is the most sophisticated addition. In subtraction, constant difference. In multiplication, there's a few of them. There's doubling and having, I call it flexible factoring to develop those strategies. We often use the equivalent structure, like what's happening here? So there's just a little bit more about structure. Mike: There's a bit of a persona that I've noticed that you take on when you're facilitating a string. I'm wondering if you can talk about that or if you could maybe explain a little bit because I've heard it a couple different times, and it makes me want to lean in as a person who's listening to you. And I suspect that's part of its intent when it comes to facilitating a string. Can you talk about this? Pam: So I wonder if what you're referring to, sometimes people will say, “You're just pretending you don't know what we're talking about.” And I will say, “No, no, I'm actually intensely interested in what you're thinking. I know the answer, but I'm intensely interested in what you're thinking.” So I'm trying to say things like, “I wonder.” “I wonder if there's something up here you could use to help. I don't know. Maybe not. Mm. What kind of clunker could—or helper could you write for this clunker?”  So I don't know if that's what you're referring to, but I'm trying to exude curiosity and belief that what you are thinking about is worth hearing about. And I'm intensely interested in how you're thinking about the problem and there's something worth talking about here. Is that kind of what you're referring to? Mike: Absolutely.  OK. We're at the point in the podcast that always happens, which is: I would love to continue talking with you, and I suspect there are people who are listening who would love for us to keep talking. We're at the end of our time. What resources would you recommend people think about if they really want to take a deeper dive into understanding strings, how they're constructed, what it looks like to facilitate them. Perhaps they're a coach and they're thinking about, “How might I apply this set of ideas to educators who are working with kindergartners and first graders, and yet I also coach teachers who are working in middle school and high school.” What kind of resources or guidance would you offer to folks? Pam: So the easiest way to dive in immediately would be my brand-new book from Corwin. It's called Developing Mathematical Reasoning: Avoiding the Trap of Algorithms. There's a section in there all about strings. We also do a walk-through where you get to feel a problem string in a K–2 class and a 3–5 [class]. And well, what we really did was counting strategies, additive reasoning, multiplicative reasoning, proportional reasoning, and functional reasoning. So there's a chapter in there where you go through a functional reasoning problem string. So you get to feel: What is it like to have a string with real kids? What's on the board? What are kids saying? And then we link to videos of those. So from the book, you can go and see those, live, with real kids, expert teachers, like facilitating good strings. If anybody's middle school, middle school coaches: I've got building powerful numeracy and lessons and activities for building powerful numeracy. Half of the books are all problem strings, so lots of good resources.  If you'd like to see them live, you could go to mathisfigureoutable.com/ps, and we have videos there that you can watch of problem strings happening.  If I could mention just one more, when we did the K–12, Developing Mathematical Reasoning, Avoiding the Trap of Algorithms, that we will now have grade band companion books coming out in the fall of '25. The K–2 book will come out in the spring of '26. The [grades] 3–5 book will come out in the fall of '26. The 6–8 book will come out and then six months after that, the 9–12 companion book will come out. And those are what to do to build reasoning, lots of problem strings and other tasks, rich tasks and other instructional routines to really dive in and help your students reason like math-y people reason because we are all math-y people. Mike: I think that's a great place to stop. Pam, thank you so much for joining us. It's been a pleasure talking with you. Pam: Mike, it was a pleasure to be on. Thanks so much. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org

2026 TOK Essay Title 3: Is the power of knowledge determined by the way in which the knowledge is conveyed? Discuss with reference to mathematics and one other area of knowledge. Can knowledge stand on its own, or does its impact entirely depend on the packaging? That is the provocative challenge of the 2026 TOK Essay Title 3: "Is the power of knowledge determined by the way in which the knowledge is conveyed?" This question is particularly complex when applied to Mathematics, where facts are absolute yet their transformative power often lies hidden behind specialized notation and formal proofs. To navigate this question, I've brought back one of our sharpest and most valued podcast guests to help us dissect how the delivery system shapes the destiny of knowledge. Guest: Mr. Kevin Hoye (TOK & IB English Literature Teacher) Music: Our school orchestra performance of Shostakovich, May 2025

SummaryIn this episode, Shannon Valenzuela and Dr. Merrill Roberts explore the beauty of the quadrivium for the middle school classroom.  They discuss the integration of nature studies, mathematics, and science in middle school education, highlighting the importance of play, joy, and sensory learning. The discussion also delves into the relationship between mathematics and beauty, the role of the imagination in learning, and the interconnectedness of disciplines across the curriculum. The conversation concludes with reflections on the importance of arts and music in education and the profound impact of experiencing the night sky on students' understanding of the universe.Topics Covered:The quadrivium and middle school math and scienceBeauty and wonder in math and science educationPlay and joy as pedagogical toolsLearning through the senses and working toward abstraction The quadrivium across the curriculumArts and music are integral to a classical educationThe power of dark skiesToday's Guests:Dr. Merrill Roberts received his Bachelor's in Liberal Arts from Thomas Aquinas College in 2003. He earned his Ph.D. in Physics from The Catholic University of America in 2018, where he has also served as a Lecturer in Physics, teaching multiple courses, including a course in Solar Physics designed for students planning to teach in primary and secondary schools. He worked for over a decade as a researcher at NASA Goddard Space Flight Center in Greenbelt, MD, where he studied solar coronal transients and performed forward modeling for the Parker Solar Probe mission. Dr. Roberts is a Senior Faculty Consultant for the Institute for Catholic Liberal Education (ICLE), giving workshops and developing curriculum centered around the Quadrivial Arts since 2013, and is also an Associate Fellow at the Boethius Institute, helping with the creative retrieval of the Quadrivium. He combines his passions for nature and education as the Nature Studies teacher at St. Jerome Academy in Hyattsville, MD, where he has instructed 5th through 8th graders since 2010. He is also, along with his wife Elizabeth, the Co-director of Music at St. Jerome Parish, where he strives to emphasize the beauty and truth inherent in the Mass.Timestamps:00:00 Introduction03:27 From NASA to the Classroom06:41 St. Jerome Academy's Model of Education10:44 Experiential Learning and the Senses17:09 Playing with What We Don't Fully Understand24:50 The Relationship Between Questions and Answers39:16 The Quadrivium and the Imagination44:28 The Importance of Music50:19 Experiencing the Night Sky: A Learning Journey55:25 ConclusionUniversity of Dallas Links:Classical Education Master's Program at the University of Dallas: udallas.edu/classical-edSt. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/Resources Mentioned in Today's Episode:More on the Quadrivium Retrieval: https://quadriviumretrieval.org/Support the showIf you enjoyed the show, please leave a rating and review — it helps others find us!

Music is math that you can dance to. The fact that certain notes sound good when played together, or in succession, is related to the mathematical properties of the frequencies to which they correspond, an idea that goes back as far as Pythagoras himself. These days we have a much more intricate understanding of these relationships and how to manipulate them. I talk to composer and music theorist Dmitri Tymoczko about how different musical scales are constructed and the math underlying what sounds good.Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/10/20/332-dmitri-tymoczko-on-the-mathematics-behind-music/Support Mindscape on Patreon.Dmitri Tymoczko received a Ph.D. in music composition from the University of California, Berkeley. He is currently a professor of music at Princeton University as well as a composer and performer. He has been the recipient of Rhodes and Guggenheim fellowships. As a composer, his works have been performed by multiple groups, and recorded on several albums.Personal web sitePrinceton web pageMad Musical ScienceSpiral diagrams: rock music, classical musicGoogle Scholar publicationsAmazon author pageWikipediaWilliam Sethares's Tuning Timbre Spectrum ScaleSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Today I'm joined by Stuart Wemyss, a highly respected financial advisor and author who recently distilled everything he's learned about property creation through wealth into what he calls the 4 Golden Rules of property investing. If you've been paying attention to the property market lately, you'll know there's no shortage of advice out there – some good, some… not so good. But in today's episode of the Michael Yardney podcast, we cut through all the noise so you can base your decisions on decades of real evidence, proven strategies, and a few timeless principles? These aren't gimmicks or quick fixes. They're powerful principles grounded in data – and they've stood the test of time. Whether you're just starting out or looking to fine-tune your property portfolio, you're going to get plenty of practical insights from this conversation.   Takeaways  ·         Focus on capital growth before income in property investment. ·         Understanding property cycles can fast track investment success. ·         Investment-grade properties are crucial for long-term growth. ·         The math behind property investment is essential for success. ·         Future buyer capacity influences property demand and value. ·         Evidence-based investing helps cut through mixed messages. ·         Location and land value are key to capital growth. ·         Timing the market is less important than time in the market. ·         Investors should be cautious of unrealistic return expectations. ·         A multifaceted approach to financial planning enhances investment outcomes.   Chapters    00:00 The Rise of AI and Its Implications 01:36 Introduction to Rules-Based Investing 04:15 The Four Golden Rules of Property Investing 07:03 Understanding Investment Grade Properties 12:01 Navigating Property Cycles 17:17 The Mathematics of Property Investment 23:00 Future Buyer Capacity and Demand   Links and Resources:   Answer this week's trivia question here- www.PropertyTrivia.com.au ·         Win a hard copy of Michael Yardney's Guide to Investing ·         Everyone wins a copy of a fully updated property report – What's ahead for property for 2026 and beyond.   Get a bundle of eBooks and Reports at www.PodcastBonus.com.au     Michael Yardney – Subscribe to my Property Update newsletter here    Get the team at Metropole to help build your personal Strategic Property Plan Click here and have a chat with us   Stuart Wemyss – Prosolution Private Clients   Also, please subscribe to my other podcast Demographics Decoded with Simon Kuestenmacher – just look for  Demographics Decoded wherever you are listening to this podcast and subscribe so each week we can unveil the trends shaping your future.

Friendships & Relationships Explained with Mathematics | Philosophy

In this episode of the Plutopia News Network Podcast, hosts Jon Lebkowsky, Scoop Sweeney, and Wendy Grossman talk with mathematician and juggler Colin Wright, who holds a PhD in pure…

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue's Theory of Integration. He lives in St. Paul, Minnesota. Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/new-books-network

I am excited to share with you my conversation with Melody Morton, a movement specialist specialized in Pilates, who found a path from loss to purpose. How? Like many of you, Melody discovered "The Fingerprint of God" in the world around her. In our chat, she shares her deeply personal story of navigating divorce and the near-collapse of her business during the pandemic. In that season of ruin, she reached for a faith she hadn't grown up with—and in return, she found her anchor. My hope is that you can find it too. Beyond her own powerful testimony, Melody explains how science, physics, and mathematics all point to a divine design. Everything from the spirals of a sunflower to the helical coils of our own DNA, to the golden ratio found in galaxies and the human body reflects this design. Through this powerful conversation, you will learn how to use your body as a temple, integrating scripture, neuroscience, and movement to heal from trauma and align your life with God's intentional design. You will leave with a renewed sense of purpose, understanding that faith and science are not enemies, but two languages God uses to speak to us. And if you go check the links below you can discover how Melody is using all this to help you. She offers a 4-week Pilates and somatic recalibration workbook to help you rewire trauma loops, regulate your nervous system, and reconnect to your core self. Originally created for women recovering from narcissistic abuse, this program works for anyone ready to identify emotional patterns and shift them through daily Pilates, movement, sound, color, fascia release, and journaling. This isn't mindset work — it's somatic rewiring through the body. Topics covered: Christian entrepreneurship, resilience, faith and science, God's divine design, healing from trauma, finding purpose, Fibonacci sequence, Golden Ratio, Melody Morton, somatic healing, scripture and science, biblical principles, spiritual growth, finding God, pilates, recovery from trauma, somatic work. Want to dive deeper? "Do you not know that your bodies are temples of the Holy Spirit, who is in you, whom you have received from God? You are not your own; you were bought at a price. Therefore honor God with your bodies." — 1 Corinthians 6:19–20 God's unique signature is visible everywhere through the Fibonacci sequence and the Golden Ratio (phi, φ). These mathematical patterns aren't just abstract ideas; they are the fundamental building blocks of nature. From the perfect spirals of a pinecone and the elegant arrangement of sunflower seeds to the coiled shape of a galaxy and the intricate structure of the human ear, this same divine proportion appears with remarkable consistency. This undeniable order and precision, found across all of creation, serves as a powerful testament that the universe was not a product of chaos, but was instead designed with purpose and intentional beauty. This same divine proportion is woven into the very fabric of our bodies, appearing in the helical coils of our collagen, the spirals of our fascia, our cardiac fibers, and the intricate micro-architecture of our bones. Through the helical coils of the Pilates reformer springs, our bodies' natural spirals are retrained and realigned, allowing us to be shaped like "clay in God's hands" according to a lawful, divine pattern.4. Water, Fascia & Memory The body's intricate design reveals its responsive nature, particularly through its water. As Viktor Schauberger observed that water naturally moves in life-giving spirals, Thomas Myers' work shows that our fascia—a water-rich network throughout the body—transmits force and even stores emotion. This living blueprint can be rewritten through breath and movement, a concept echoed by Dr. Masaru Emoto's research that demonstrated how water's structure can be influenced by our very intentions. Together, these ideas paint a picture of a body intentionally designed to be a living, responsive canvas. Scientist & Mathematician Quotes Galileo (attributed): "Mathematics is the language in which God has written the universe." Johannes Kepler: "Geometry is one and eternal… it reflects the thoughts of God." Nikola Tesla: "If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration." Did you enjoy this episode and would like to share some love?

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue's Theory of Integration. He lives in St. Paul, Minnesota. Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoices

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue's Theory of Integration. He lives in St. Paul, Minnesota. Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/science

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue's Theory of Integration. He lives in St. Paul, Minnesota. Mark Molloy is the reviews editor at MAKE: A Literary Magazine.

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue's Theory of Integration. He lives in St. Paul, Minnesota. Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoices

Send us a textWelcome to Safe Dividend Investing's Podcast 245- (18 October 2025) This week is a departure from my usual podcast content. It responds to a Fidelity investment advisor with whom one of my readers discussed my approach to investing.  The Fidelity advisor stated that Ian Duncan MacDonald's investment ideas were the craziest ideas she had ever heard of.   What makes this email particularly Interesting to me is that the reader has a PhD in Applied Statistics and Mathematics. This would indicate a familiarity with scoring systems and the ability to judge the validity of my investment approach.The reader raised the interesting question of why would a simple easy way of assessing the safe investment value of a stock not be taught in school. Most investors have a very limited understanding of the wealth of investment information that is free and immediately available on the internet from such websites as Yahoo Finance. All they need to be shown is what information is important and how to interpret it. I write my investment books for those who do not invest in individual stocks for fear that they will lose their life savings. My books show  investors  an easy, safe way to select financially strong, safe companies who pay high dividends .  I have been successfully investing this way for twenty years .My portfolio of strong dividend stocks provides not only provide a reliable, growing source of income but over time has greatly increase the value of my portfolio.Unlike mutual funds - where investors have no control over their investment and  only a vague idea as to what stocks are in the fund - a self-directed investor can fully understand  and appreciate the value of the portfolio they create.In this podcast (with a written transcript attached) you can get an understanding of why the stock scoring software supplied with my books is so effective.For more information on self-directed investing go to my website www,.informus.ca or  listen to the previous 245 weekly podcasts. The first 160 podcasts are devoted to answering questions from investors just like you. The remainder give you an opportunity to practice choosing stocks and introduce new relevant topics.Ian Duncan MacDonald Author and Commercial Risk Consultant,President of Informus Inc 2 Vista Humber Drive Toronto, Ontario Canada, M9P 3R7 Toronto Telephone - 416-245-4994 New York Telephone - 929-800-2397 imacd@informus.ca

Episode: 1459 A tongue-tied attempt to say what teaching is.  Today, teaching and ambiguity.

Austin revealed a pretty disturbing photo, we try to figure out some DB math, and we determine the age gap for Unc.

******Support the channel******Patreon: https://www.patreon.com/thedissenterPayPal: paypal.me/thedissenterPayPal Subscription 1 Dollar: https://tinyurl.com/yb3acuuyPayPal Subscription 3 Dollars: https://tinyurl.com/ybn6bg9lPayPal Subscription 5 Dollars: https://tinyurl.com/ycmr9gpzPayPal Subscription 10 Dollars: https://tinyurl.com/y9r3fc9mPayPal Subscription 20 Dollars: https://tinyurl.com/y95uvkao ******Follow me on******Website: https://www.thedissenter.net/The Dissenter Goodreads list: https://shorturl.at/7BMoBFacebook: https://www.facebook.com/thedissenteryt/Twitter: https://x.com/TheDissenterYT This show is sponsored by Enlites, Learning & Development done differently. Check the website here: http://enlites.com/ Dr. Rafael Núñez is a Professor of Cognitive Science at the University of California, San Diego. Dr. Núñez investigates cognition from the perspective of the embodied mind. He is particularly interested in high-level cognitive phenomena such as conceptual systems, abstraction, and inference mechanisms, as they manifest themselves naturally through largely unconscious bodily/mental activity (e.g., gesture production co-produced with a variety of conceptual mappings). He is the author of Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. In this episode, we talk about embodied cognition, time and space, and mathematics. We first discuss embodied cognition. We talk about how we process time and space cognitively. We then get into what numbers are, and how numerical cognition develops. Finally, we discuss where mathematics comes from.--A HUGE THANK YOU TO MY PATRONS/SUPPORTERS: PER HELGE LARSEN, JERRY MULLER, BERNARDO SEIXAS, ADAM KESSEL, MATTHEW WHITINGBIRD, ARNAUD WOLFF, TIM HOLLOSY, HENRIK AHLENIUS, ROBERT WINDHAGER, RUI INACIO, ZOOP, MARCO NEVES, COLIN HOLBROOK, PHIL KAVANAGH, SAMUEL ANDREEFF, FRANCIS FORDE, TIAGO NUNES, FERGAL CUSSEN, HAL HERZOG, NUNO MACHADO, JONATHAN LEIBRANT, JOÃO LINHARES, STANTON T, SAMUEL CORREA, ERIK HAINES, MARK SMITH, JOÃO EIRA, TOM HUMMEL, SARDUS FRANCE, DAVID SLOAN WILSON, YACILA DEZA-ARAUJO, ROMAIN ROCH, DIEGO LONDOÑO CORREA, YANICK PUNTER, CHARLOTTE BLEASE, NICOLE BARBARO, ADAM HUNT, PAWEL OSTASZEWSKI, NELLEKE BAK, GUY MADISON, GARY G HELLMANN, SAIMA AFZAL, ADRIAN JAEGGI, PAULO TOLENTINO, JOÃO BARBOSA, JULIAN PRICE, HEDIN BRØNNER, DOUGLAS FRY, FRANCA BORTOLOTTI, GABRIEL PONS CORTÈS, URSULA LITZCKE, SCOTT, ZACHARY FISH, TIM DUFFY, SUNNY SMITH, JON WISMAN, WILLIAM BUCKNER, PAUL-GEORGE ARNAUD, LUKE GLOWACKI, GEORGIOS THEOPHANOUS, CHRIS WILLIAMSON, PETER WOLOSZYN, DAVID WILLIAMS, DIOGO COSTA, ALEX CHAU, AMAURI MARTÍNEZ, CORALIE CHEVALLIER, BANGALORE ATHEISTS, LARRY D. LEE JR., OLD HERRINGBONE, MICHAEL BAILEY, DAN SPERBER, ROBERT GRESSIS, JEFF MCMAHAN, JAKE ZUEHL, BARNABAS RADICS, MARK CAMPBELL, TOMAS DAUBNER, LUKE NISSEN, KIMBERLY JOHNSON, JESSICA NOWICKI, LINDA BRANDIN, VALENTIN STEINMANN, ALEXANDER HUBBARD, BR, JONAS HERTNER, URSULA GOODENOUGH, DAVID PINSOF, SEAN NELSON, MIKE LAVIGNE, JOS KNECHT, LUCY, MANVIR SINGH, PETRA WEIMANN, CAROLA FEEST, MAURO JÚNIOR, 航 豊川, TONY BARRETT, NIKOLAI VISHNEVSKY, STEVEN GANGESTAD, TED FARRIS, HUGO B., JAMES, JORDAN MANSFIELD, AND CHARLOTTE ALLEN!A SPECIAL THANKS TO MY PRODUCERS, YZAR WEHBE, JIM FRANK, ŁUKASZ STAFINIAK, TOM VANEGDOM, BERNARD HUGUENEY, CURTIS DIXON, BENEDIKT MUELLER, THOMAS TRUMBLE, KATHRINE AND PATRICK TOBIN, JONCARLO MONTENEGRO, NICK GOLDEN, CHRISTINE GLASS, IGOR NIKIFOROVSKI, AND PER KRAULIS!AND TO MY EXECUTIVE PRODUCERS, MATTHEW LAVENDER, SERGIU CODREANU, ROSEY, AND GREGORY HASTINGS!

It's easy to take maps for granted. After all, most of us have a pretty good map in our pockets at all times, ready to show us how to get anywhere on the globe. But to make a map useful, you have to decide what to keep in and what to leave out—and, most importantly, which mathematical equations to use. Beyond navigating from point A to point B, math and maps come together for a wide variety of things, like working out the most efficient route to deliver packages, calculating the depth of the ocean floor, and more. Host Ira Flatow is joined by Paulina Rowińska, mathematician and author of Mapmatics: A Mathematician's Guide to Navigating the World, to go on a journey through the math at the heart of all kinds of maps. Guest: Dr. Paulina Rowińska is a mathematician, writer, science journalist and author of Mapmatics: A Mathematician's Guide to Navigating the World.Transcripts for each episode are available within 1-3 days at sciencefriday.com. Subscribe to this podcast. Plus, to stay updated on all things science, sign up for Science Friday's newsletters.

Tim Rinehart is the Principal Double Bassist of the Oregon Symphony. A graduate of Rice University's Shepherd School of Music, Tim studied with Paul Ellison while also earning a Bachelor of Science in Mathematics. He is the winner of the 2025 International Society of Bassists Orchestral Division Competition and has performed with numerous prestigious orchestras including the Boston Symphony, London Symphony, and Houston Symphony. Tim shares his journey through multiple auditions in a single season, revealing the breakthrough preparation strategies that led to winning his current. He discusses mental performance techniques, systematic practice methods, committee expectations, his education with Paul Ellison at Rice University, and his new role with the Oregon Symphony. Connect with Tim: Website Instagram YouTube Oregon Symphony profile Connect with DBHQ: Join Our Newsletter Double Bass Resources Double Bass Sheet Music Double Bass Merch Gear used to record this podcast: Zoom H6 studio 8-Track 32-Bit Float Handy Recorder Rode Podmic Sony Alpha 7 IV Full-frame Mirrorless Interchangeable Lens Camera Sony FE 16-35mm F2.8 GM Lens Sony FE 24-70mm F2.8 GM Lens   When you buy a product using a link on this page, we may receive a commission at no additional cost to you. Thank you for supporting DBHQ.   Thank you to our sponsors! Upton Bass - From Grammy Award winners and Philharmonic players like Max Zeugner of the New York Philharmonic, each Upton Bass is crafted with precision in Connecticut, USA, and built to last for generations.  Discover your perfect bass with Upton Bass today! Carnegie Mellon University Double Bass Studio is a valued part of an innovative fine arts community in a top research university. Students receive weekly private lessons and solo classes with Micah Howard, and Peter Guild teaches weekly Orchestral Literature and Repertoire. They encourage students to seek lessons and guidance from local bassists. Members of the Symphony, the Opera, and the Ballet provide annual classes and individual attention. Visit Micah's website to sign up for a free online trial lesson here. Theme music by Eric Hochberg

How do we know if our AI… is really AI? This week, Technology now goes under the hood of AI products when Baradji Diallo, an AI Innovation Architect in Technology Strategy and Evaluation working in the office of the CTO joins us to tell us more about how he and his team investigate whether AI products are really what they claim to be.This is Technology Now, a weekly show from Hewlett Packard Enterprise. Every week, hosts Michael Bird and Aubrey Lovell look at a story that's been making headlines, take a look at the technology behind it, and explain why it matters to organizations.About Baradji Diallo: https://www.linkedin.com/in/baradji-diallo/Sources:https://www.statista.com/outlook/tmo/artificial-intelligence/worldwidehttps://www.historyofdatascience.com/ai-winter-the-highs-and-lows-of-artificial-intelligence/https://www.techtarget.com/searchenterpriseai/definition/AI-winterFunding a Revolution: Government Support for Computing Research. National Academy Press. Archived from the original on 12 January 2008. Retrieved 08 September 2025https://web.archive.org/web/20080112001018/http://www.nap.edu/readingroom/books/far/ch9.htmlhttps://www.birow.com/az-elso-ai-telhttps://www.holloway.com/g/making-things-think/sections/the-second-ai-winter-19871993https://www.forbes.com/sites/johnwerner/2024/04/09/three-lessons-learned-from-the-second-ai-winter/

Today we meet with the phenomenal Sam Wheeler is a physics instructor at the North Carolina School of Science and Mathematics, where he teaches AP Physics C, General Physics, and Elements of Satellite Design—a course in which students design, test, and fly CubeSats on a campus zipline. His career has included remarkable opportunities such as co-hosting a live math and science TV show, flying student experiments on Zero-G flights, connecting students with astronauts aboard the ISS, and conducting astrobiology research in Death Valley. A Fulbright Scholar to Japan, former NCSTA President, and recipient of the Presidential Award for Excellence in Math & Science Teaching, Sam has also served as an Albert Einstein Distinguished Educator Fellow at the U.S. Department of Energy. He holds undergraduate degrees in physics and science education and a PhD in Science (Physics) Education from NC State University.

This show, we preview the Eastern Conference and give our win predictions. We will do an in-depth Pacers Preview next week. Go Pacers!Links1. Vegas O/U2. Patreon

A native Rhode Islander, Amy is a mild-mannered health data analyst by day, shamelessly bold improviser by night Her educational background includes a bachelor's degree in Mathematics, a Master of Library and Information Science, and a multitude of classes and workshops with Groundlings School, Impro Theatre, Freestyle Love Supreme Academy, and numerous other instructors from London to Los Angeles. Currently, she can be found coaching and performing at Kismet Improv in Pawtucket, playing on stage in the fast-paced high energy games of The Bit Players in Newport, and taking tarot-inspired improv to various festival stages with Whatever Fate Decides.You can follow her work and performance dates here: kismetimprov.com and bitplayers.netShe also has a couple of special shows coming up in NYC at The PIT LAB -- October 19, 6pm NYC Sketchfest'25 "Tell Me More" and November 8, 8pm "Shotgun Improv."Enjoy this one!This episode, like all episodes of If This Is True, brings forth what drives creatives to do what they do. For more of this content and interaction, you can also go to my substack, coolmite25.substack.com. Hosted on Acast. See acast.com/privacy for more information.

Cognitive scientist and author Donald Hoffman returns to share discoveries reshaping how we understand perception, consciousness, and reality itself. Drawing from evolutionary game theory and quantum physics, he reveals why we don't see the world as it truly is—and what that means for science, spirituality, and awareness. Hoffman bridges rigorous mathematics with timeless wisdom, showing how awakening to truth means seeing through the interface of perception to what lies beyond.15% off Bon Charge order (Code KNOWTHYSELF):https://boncharge.com/knowthyselfUp to 43% off MUDWTR order + free frother:https://mudwtr.com/knowthyselfTo get your free shilajit today:https://fractalforest.co/knowthyselfAndrés Book Recs: https://www.knowthyselfpodcast.com/book-list___________00:00 Intro03:45 The Probability of Seeing the Truth10:20 Fitness vs. Truth in Evolutionary Theory17:30 The Limits of Our Perception24:15 How Language Shapes Reality31:10 States of Consciousness and Altered Perception38:50 The Virtual Headset of Space and Time42:04 Ad: Bon Charge46:35 Physics Agrees: Spacetime Is Doomed54:25 The Mystery of the Observer1:02:10 No Theory of Everything1:10:40 Consciousness vs. Physicalism1:19:15 Neural Correlates and the Illusion of Causation1:27:45 The Case for Consciousness as Fundamental1:29:38 Ads: MUDWTR, Fractal Forest1:36:20 From Science to Spirituality1:45:10 Introducing Markov Chains1:53:30 The Birth of Trace Logic2:04:20 Time Dilation and the Mathematics of Perception2:18:10 Beyond the Headset: Infinite Consciousness2:36:30 Science, Mystery, and Humility2:54:40 Conclusion___________Episode Resources: https://x.com/donalddhoffmanhttps://www.amazon.com/The-Case-Against-Reality/dp/0141983418/https://www.instagram.com/andreduqum/https://www.instagram.com/knowthyself/https://www.youtube.com/@knowthyselfpodcasthttps://www.knowthyselfpodcast.com

This episode of Room to Grow, Curtis and Joanie speak with Pam Harris. Pam is well known and loved for her website, podcast, books, and conference sessions all based on her core belief that “Math is FigureOutAble.” Today's discussion centers on Pam's newest publication, Developing Mathematical Reasoning: Avoiding the Traps of Algorithms.Pam starts with three distortions about math that are common among teachers, students, and the population, and can impact how educators engage students with math in their classrooms. Next the conversation shifts to what is meant by algorithms, and how they differ from strategies and formulas. Then the discussion focuses on the potential traps to learning that can result from teaching algorithms in mathematics. All of these ideas are based on the development of mathematical reasoning, from counting strategies to additive thinking, to multiplicative reasoning and proportional reasoning, then the functional reasoning that comprises much of the math students learn in high school.There are so many good ideas in this episode that will challenge you and get you thinking!Additional referenced content includes:·       Pam Harris' website, Math is FigureOutAble.·       Pam's book, Developing Mathematical Reasoning: Avoiding the Traps of Algorithms.·       Pam's podcast, Math is Figure-Out-Able!·       Find Pam on all your favorite social media platforms.Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy. 

Fractal Mathematics and Jungian Archetypes with Harry Shirley Dr. Harry Shirley is a chemist with a deep interest in Jungian psychology. His paper The Buddhabrot and the Unus Mundus: A Qualitative Exploration of Fractal Patterns and Archetypal Symbols was recently published in the International Journal of Jungian Studies. He is based in the United Kingdom. … Continue reading "Fractal Mathematics and Jungian Archetypes with Harry Shirley"

Ava N. Simmons, also known as Ava The S.T.E.M. Princess®, is a 12-year-old S.T.E.M. Ambassador, Entrepreneur, Toy Designer, Author, and the creator of educational toy brand Team Genius Squad. Diagnosed with dyslexia and dysgraphia in 2021, Ava used S.T.E.M. (Science, Technology, Engineering and Mathematics) and S.T.E.A.M. (Science, Technology, Engineering, Art, and Mathematics) and entrepreneurial activities to help overcome her academic challenges and build her confidence.  To share her learning journey and encourage others, Ava creates engaging S.T.E.M.-based educational videos, authors S.T.E.M. books, conducts peer-to-peer S.T.E.M. activities in the community, and develops S.T.E.M. toys for children ages 5-13, including children who are neurodivergent or in underserved areas. She has conducted thousands of peer-to-peer S.T.E.M. experiments with children in the community, over 700,000 households have viewed her educational videos, she has authored 3 books, and developed 15 branded S.T.E.M. Educational Toys.  Additionally, she is the Host of the PBS Kids Channel Show from PBS North Carolina called Mini Fab Science Lab, and her STEM-STEAM kits are featured in the Scholastic Catalog. During this episode, you will hear Ava talk about: ●    Her experience in school as a student with dyslexia and dysgraphia ●    How she got interested in S.T.E.M. at a young age ●    How Team Genius Squad helps make S.T.E.M./S.T.E.A.M. more accessible to kids everywhere ●    Where she gets ideas for her experiment kits ●    The origin of her PBS Kids Channel show, Mini Fab Science Lab Learn more about Ava: Team Genius Squad store Mini Fab Science Lab (PBS Kids show) Team Genius Squad on Facebook, Instagram, LinkedIn, TikTok and YouTube Team Genius Squad in the Scholastic Dollars 2025-2026 Catalog on page 33: (M) STEM Genius Lemon Light Experiment Kit with Interactive Experience Item No: 794043 Kits and Virtual Session with Ava Item No: 793745 4-Pack of Kits Only Watch the video of this interview on YouTube. Read the episode transcript. Follow the Beyond 6 Seconds podcast in your favorite podcast player. Subscribe to the FREE Beyond 6 Seconds newsletter for early access to new episodes. Support or sponsor this podcast at BuyMeACoffee.com/Beyond6Seconds! *Disclaimer: The views, guidance, opinions, and thoughts expressed in Beyond 6 Seconds episodes are solely mine and/or those of my guests, and do not necessarily represent those of my employer or other organizations. These episodes are for informational purposes only and do not substitute for professional medical advice. Consult a medical professional or healthcare provider if you are seeking medical advice, diagnoses, or treatment.*

Right-wing Christian journalist Mary Brooke tries quoting Satansplain for her wild conspiracy theories about Satanism, furries, and Charlie Kirk. Meanwhile, equally annoying left-wing people are throwing fits over a politically incorrect video of Anton LaVey. Satansplain addresses both, along with answering listener mail about the previous two episodes of Satansplain, a reiteration on Satanism and politics, reflections on the landmark Satanism podcast Satanism Today, and also something the herd calls a tool of the Devil himself: mathematics. Support Satansplain: https://satansplain.locals.com/support 00:00 - Intro 01:20 - On episodes 99 and 100 08:21 - Yes, Magister Bill is political. The Church of Satan is not, and for good reasons. 13:58 - Satanecdote: Mary Brooke's bizarre "furries + Satanism" obsession 31:24 - People Who Knew Anton LaVey 33:41 - Speak of the Devil "racist" clip 42:57 - William Seabrook book 43:57 - Questions about math 50:58 - Tips for Skill Improvement 54:49 - Answering More Math Questions 58:32 - Satanism Today (Magister David Harris' podcast)

Russ Rowlett Today's interview was first heard in episode 19 back in 2019. The conversation is with Russ Rowlett, webmaster of The Lighthouse Directory, one of the most useful lighthouse-related sites on the internet. When Russ was growing up in Richmond, Virginia, his only exposure to lighthouses was climbing the Old Cape Henry Lighthouse when his family vacationed at Virginia Beach. Russ earned a doctorate degree in math at the University of Virginia in the 1960s, and he taught math at Princeton and then the University of Tennessee at Knoxville. In 1987 he became Director of the Center for Mathematics and Science Education at the University of North Carolina at Chapel Hill. He's also known for his research on the metric system and units of measurement. Russ started his website, The Lighthouse Directory, in 1999, and it kept growing until, by 2009, it covered the whole world. The address of the site is ibiblio.org/lighthouse/   At this moment there are listings for more than 24,600 of the world's lighthouses. If there are more lighthouses out there, Russ will find them.

Read Aly's post on AI vs human tutors Visit Upchieve's School Partnership page Math scores study About The Guest Aly Murray is the Founder and Executive Director of UPchieve. She's also a proud Latina, math nerd, and community college grad. After earning an associate's degree, Aly transferred to the University of Pennsylvania where she graduated summa cum laude with a degree in Mathematics. Following Penn, Aly worked on the trading floor at J.P. Morgan for two years before leaving to commit to UPchieve full-time. Her personal experience as a low-income student drives her to fight for educational equity and work towards a world in which all students have an equal opportunity to achieve upward mobility. To date, UPchieve has provided free tutoring to more than 60,000 students nationwide and matched nearly 200,000 tutoring requests— and for her work on UPchieve, Aly has been featured on the Forbes 30 Under 30 list in Education (2021) and honored as a Roddenberry Fellow (2021).

Dr. Ivette Fuentes is a quantum physicist at the University of Southampton, where she studies the strange edge between quantum mechanics and relativity. We try to get on the same page about what it means to bend time, warp gravity, and what gives objects mass. We explore the philosophy of physics, the mystical cult of quantum woo, and how real science confronts the unsettling truth that reality might not exist the way we think it does. PATREON https://www.patreon.com/c/demystifysciPARADIGM DRIFThttps://demystifysci.com/paradigm-drift-showHOMEBREW MUSIC - Check out our new album!Hard Copies (Vinyl): FREE SHIPPING https://demystifysci-shop.fourthwall.com/products/vinyl-lp-secretary-of-nature-everything-is-so-good-hereStreaming:https://secretaryofnature.bandcamp.com/album/everything-is-so-good-here00:00 Go! 00:06:11 Teleportation Tech and Consciousness 00:12:45 Consciousness & Life 00:17:01 The Alleged Conflict Between Physics and Spirituality 00:21:01 Evolving Perspectives on Consciousness 00:25:06 Consciousness and AI 00:28:20 Emergence and Cognitive Simulation 00:33:09 Distinguishing Consciousness from Thought 00:39:53 Consciousness During Sleep and Anesthesia 00:46:06 Life and Consciousness Interconnection 00:46:16 Understanding Bodily Systems and Consciousness 00:50:14 The Concept of Self and Otherness 00:52:05 Bridging Physics and Spirituality 00:56:48 Incremental Advancements in Physics 01:02:08 Understanding Quantum Mechanics 01:08:59 Understanding the Mathematics and Physics Connection 01:12:00 Newton's Theoretical Foundations and Limitations 01:16:00 The Nature of Time in Physics 01:20:00 Relativity and Observations of Time 01:24:00 Quantum Clocks and the Ongoing Time Debate 01:31:27 The Concept of "Now" in Physics 01:34:00 Unifying Quantum Mechanics and General Relativity 01:37:44 Superposition and the Role of Gravity 01:47:52 Discoveries in Quantum Experiments 01:52:05 The Nature of Time and Quantum Mechanics 01:55:27 Exploring Quantum Reality 02:00:56 Mystical Elements of Quantum Physics 02:06:52 The Nature of Reality and Perception 02:12:55 The Evolution of Physical Understanding 02:17:56 Cautionary Tales of Mathematics 02:18:31 The Challenge of Revolutionary Ideas in Physics 02:24:00 The Role of Collaboration in Scientific Progress 02:28:00 The Importance of Experimental Validation 02:36:00 The Proposal of Detection Methods for Gravitational Waves 02:39:00 Anticipation of Future Research Contributions 02:41:00 Exploration of Energy-Conserving Models in Quantum Physics 02:43:00 Upcoming Insights on Mass and Quantum Reality 02:45:00 Enthusiastic Collaboration and Future Discussions#quantumphysics , #consciousness , #cosmology, #quantummechanics , #metaphysics, #intellectual, #curiosity, #theory, #thinking, #philosophypodcast , #sciencepodcast podcast, #longformpodcastMERCH: Rock some DemystifySci gear : https://demystifysci-shop.fourthwall.com/AMAZON: Do your shopping through this link: https://amzn.to/3YyoT98DONATE: https://bit.ly/3wkPqaDSUBSTACK: https://substack.com/@UCqV4_7i9h1_V7hY48eZZSLw@demystifysci RSS: https://anchor.fm/s/2be66934/podcast/rssMAILING LIST: https://bit.ly/3v3kz2S SOCIAL: - Discord: https://discord.gg/MJzKT8CQub- Facebook: https://www.facebook.com/groups/DemystifySci- Instagram: https://www.instagram.com/DemystifySci/- Twitter: https://twitter.com/DemystifySciMUSIC: -Shilo Delay: https://g.co/kgs/oty671