Your students are halfway through a unit, and you need to know whether they actually understand what you’ve taught. Should you grade them now, or should you use the information to adjust tomorrow’s lesson? This episode explains the crucial distinction between formative and summative assessment through a realistic classroom example. You’ll learn how to recognize each type even when the Praxis avoids explicitly naming it.

A student becomes anxious every time the teacher announces a quiz, while another starts turning in homework because doing so earns extra computer time. Both behaviors involve learning, but they illustrate two very different types of conditioning. In this episode, we distinguish classical from operant conditioning and apply both concepts to realistic classroom situations. You’ll also learn the reinforcement-versus-punishment distinction that commonly causes confusion on teacher exams.

Monolithic iOS codebases have a way of growing quietly out of control — slow builds, tangled dependencies, and features bleeding into places they were never meant to go. This episode of DEV.co tackles the problem head-on, drawing on this guide to Swift Package Manager and modular iOS architecture to lay out a clear, practical path from chaos to clarity. Whether you're starting a new project or migrating years of legacy code, the principles here are grounded in how real teams actually ship

OpenAIが数学とAIの独立諮問委員会を新設しました。背景には未解決問題を解く力をAIの物差しにすることへの数学者の懸念があります。同じ問いはAnthropicのリーマン予想関連の検証体制や、Google DeepMindのAI for Math Initiative、IMO 2026の監査評価にも共通していました。AIの数学的成果を誰がどう検証するか、その仕組みが問われる時代に入っています。〇Advisory Group on Mathematics and Artificial Intelligence（OpenAI、2026年）https://openai.com/index/advisory-group-on-mathematics-and-ai/〇Claude's progress on the Riemann hypothesis（Anthropic、2026年8月）https://www.anthropic.com/research/riemann-zeta〇Google DeepMind and Google.org announce AI for Math

Number of the Day - "16" This podcast is produced by Klassic Studios. Check out our other podcasts there! Sources Number sequence definitions come from the On-Line Encyclopedia of Integer Sequences (OEIS). Historical material is adapted from Wikipedia, used under the Creative Commons Attribution-ShareAlike licence. Minor planet details come from the NASA/JPL Small-Body Database. Learn more about your ad choices. Visit megaphone.fm/adchoices

We explore the development of Qwen-Drive 1.0, a pioneering vision-language model designed to merge autonomous driving capabilities with conversational intelligence. To solve the problem of "catastrophic forgetting," where an AI loses general knowledge while learning specialized tasks, engineers utilized a frozen base model enhanced by two external modules. These additions include a Bird's-Eye-View (BEV) perception head for real-time 3D mapping and a planning expert for calculating safe maneuv...

Why do some pupils seem to thrive in maths while others struggle to access the same lesson?Jon and Becky discuss the latest PISA findings and the widening gap between higher and lower attainers, before exploring what that looks like in real primary classrooms. They talk about teaching for mastery, adaptive teaching, pre-teaching, the pressures of a packed timetable and why taking time to simply observe pupils can be so valuable.With place value being taught in classrooms everywhere at this point in

Budgeting for a new website in 2026 means navigating a landscape that AI has genuinely disrupted — but not in the way most people assume. This episode of DEV.co examines the real breakdown of website design costs in 2026, separating the hype from the concrete shifts that affect what you should actually plan to spend. Spoiler: the total budget doesn't disappear. It redistributes.Here's what the episode covers: Baseline costs haven't collapsed. A professional informational site still

Academia on the Line is a podcast where two mathematicians talk with academics about mathematics, STEM, and higher education. Episode Summary: Two weeks ago, on Labor Day, NYU mathematician Tristan Buckmaster posted three preprints and a statement detailing some troubling interactions with OpenAI and a need to rush to get his results out with collaborator Levent Alpöge (who works for Anthropic). The next day, OpenAI announced a solution to the Navier-Stokes Millennium prize problem. The...

arXiv math.NTの新着論文19本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-21/On permutation-invariant construction of glued latticesExtreme value laws for intrinsic Diophantine approximation on spheresEigenvectors of $p$-Curvature for Geometric Difference EquationsGalois deformation rings and modularity in the residually reducible caseOn The Cyclicity of Algebraic LatticesThe large sieve for square moduli under Hooley's hypothesis $R^*$Annular Frobenius Classification of

arXiv math.RAの新着論文8本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-ra/episodes/2026-09-21/Just-Infinite Loops and Loop AlgebrasA classification of group gradings on incidence algebras over commutative ringsLocal and Quasi Derivations of the Mirror Heisenberg-Virasoro AlgebraNoncommutative resolutions of noncommutative isolated singularitiesSuper adaptable graphs and the realization problemStructure and Representations of Restricted Lie color triple systemsRestricted (Relative)

arXiv math.ACの新着論文2本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-ac/episodes/2026-09-21/A one-dimensional coherent domain with non-Pr\"ufer integral closureClassification of Tor algebras for rings from general points by Waring Rank

arXiv math.RTの新着論文11本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-rt/episodes/2026-09-21/Double flag varieties of Levi type with a finite number of orbitsMinuscule Relations in Quantum $K$-Theory of Flag VarietiesA Gelfand model for the Okada algebraCategorical Lie-Rinehart modules and Shen-Larsson functorsSome freezing limits for Bessel functions and Bessel processes with drift of type $B_N$Eigenvectors of $p$-Curvature for Geometric Difference EquationsStructure and Representations

arXiv math.AGの新着論文17本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-ag/episodes/2026-09-21/Abelian Relations are Liouvillian$K$-regularity for finite quotient singularitiesA geometric approach to the density of rank-metric codesTangent bundles of Quot schemes of vector bundles on curvesDouble shuffle relations via the Hodge defectBound of automorphisms of fibred surfaces in positive characteristicOn Fano varieties of index one that are linear sections of Grassmannians of linesBounds on

Number of the Day - "15"This podcast is produced by Klassic Studios. Check out our other podcasts there! Sources Number sequence definitions come from the On-Line Encyclopedia of Integer Sequences (OEIS). Historical material is adapted from Wikipedia, used under the Creative Commons Attribution-ShareAlike licence. Minor planet details come from the NASA/JPL Small-Body Database. Learn more about your ad choices. Visit megaphone.fm/adchoices

Neste episódio do Estatística com H, vamos desvendar a Resolução 886/66 do IBGE de forma super simples, prática e sem termos difíceis. Vais perceber o motivo real por trás da criação deste critério de arredondamento e como uma regra simples — a Regra do Algarismo Par— impede que os dados fiquem distorcidos ou "viciados" para cima.Vem entender como o número 5 trabalha nos bastidores para manter o equilíbrio perfeito na ciência, na economia e nos grandes censos que moldam o nosso mundo!

Recent data from the James Webb Space Telescope has revealed a massive stellar cavity at the center of the galaxy Abell 402-BCG, spanning roughly 3,200 light-years across. While astronomers previously believed this void was merely a cloud of cosmic dust, infrared observations confirmed the area is actually a dead zone missing two billion stars. This phenomenon is caused by an ultramassive binary black hole system with a combined mass 60 billion times that of our sun. Through a process called ...

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Number of the Day - "14" This podcast is produced by Klassic Studios. Check out our other podcasts there! Sources Number sequence definitions come from the On-Line Encyclopedia of Integer Sequences (OEIS). Historical material is adapted from Wikipedia, used under the Creative Commons Attribution-ShareAlike licence. Minor planet details come from the NASA/JPL Small-Body Database. Learn more about your ad choices. Visit megaphone.fm/adchoices