Historical Hex Congressional Districts
An interactive cartogram spanning all 119 U.S. Congresses, with each congressional district represented as a five-hex tile.
ResearchData Visualization
General
A compact index of projects, applets, talks, and writing.
A complete, automatically generated catalog of public Site Items, grouped by format so the whole collection remains easy to browse.
Applications
Interactive projects and tools
Playable prototypes, practical tools, and data-rich public projects.
KidLinks
A lightweight relationship map for keeping track of a child's friends and the parents or guardians connected to them.
Product Design
N's Logic Puzzler
A mobile-friendly logic-grid puzzle collection with X/O deduction marks, coins, unlocks, and quick beginner puzzles.
Games & Play
Oakland A's Roster Eras
An interactive history of Oakland Athletics roster eras from 1968 through 2024, tracing player continuity, season results, and defining cores.
ResearchData Visualization
V's Play Studio
A touch-first play studio with original characters for making temporary stickers, mixing foods, and building board games.
Product DesignGames & Play
WriteSpacer
A browser tool that turns dense worksheet images into printable pages with room for students to show mathematical work.
Product DesignMathEd
Algebuds V1 Prototype
The deployed Algebra 1 prototype in which students tutor a constrained chatbot through their mathematical reasoning.
Interactive MathMathEdAlgebra
Split Coins
A digital manipulative for exploring partitioning and arithmetic structure through coin-like pieces.
Interactive MathArithmeticFractions
Velocity Game
A playable exploration of motion, graphing, and intuition, built as a small interactive math experience.
Interactive MathGames & Play
Case Studies
Product and learning-design work
Substantive accounts of problems, design decisions, prototypes, and evidence.
Algebuds: Student Tutors Chatbot
An Algebra 1 prototype that flips tutoring roles: students explain their thinking to a constrained chatbot and learn by watching it apply their ideas.
Product DesignResearchMathEdAlgebra
Designing KidLinks: Connecting with the Parents of Your Kids' Friends
A case study of the relationship map designed to help families keep track of the parents behind children's friendships.
Product Design
Khan Academy Early Product Development
Collaborative research and prototyping on open-ended activities, creative math worlds, and dynamic representations for online learning.
Product DesignResearchMathEd
Teacher Flow Interactive Slides
A product argument for keeping interactive math tools inside the flow of classroom instruction instead of forcing teachers to juggle windows and links.
Product DesignMathEd
Math Applets
Interactive math sketches
Native applets and preserved constructions for exploring mathematical relationships.
Collatz Glyphs
Animate one Collatz glyph, then compare literal-scale glyph fields on a hundred chart and an Ulam spiral.
Interactive MathNumber Theory
Swing Hyp Down 2024 mod 5s
A GeoGebra animation exploring swing hyp down 2024 mod 5s.
Interactive MathGeometry
Two coins rotate
A GeoGebra animation exploring two coins rotate.
Interactive MathStatistics & Probability
Aperiodic Monotile
Explore the geometry of the 2023 hat monotile, a single shape that tiles the plane only aperiodically.
Interactive MathGeometry
Pattern block areas
A GeoGebra drag and notice exploring pattern block areas.
Interactive MathGeometry
Teardrop reconstruction
A GeoGebra construction exploring teardrop reconstruction.
Interactive MathGeometry
Variance kareem carr doodling
A GeoGebra drag and notice exploring variance kareem carr doodling.
Interactive MathStatistics & Probability
California solar system scale model
A GeoGebra modeling exploring california solar system scale model.
Interactive MathMathematical Modeling
Factor all the quads segments
A GeoGebra drag and notice exploring factor all the quads segments.
Interactive MathAlgebra
Sixes Up simulation
A GeoGebra simulation exploring sixes up simulation.
Interactive MathStatistics & Probability
Tiling from a cutout 20gon
A GeoGebra generative art exploring tiling from a cutout 20gon.
Interactive MathGeometry
President popular vote
A GeoGebra modeling exploring president popular vote.
Interactive MathMathematical Modeling
Triangle inequality vector addition
A GeoGebra construction exploring triangle inequality vector addition.
Interactive MathGeometry
Bees Bombs Circles
A GeoGebra drag and notice exploring bees bombs circles.
Interactive MathGeometry
Closest rational to pi and e
A GeoGebra drag and notice exploring closest rational to pi and e.
Interactive MathNumber Theory
Cones from a Circle
Cut and fold a circle into cone models and compare how radius, arc length, and height move together.
Interactive MathGeometryMathematical Modeling
Cshearer41 hexagon problem
A GeoGebra drag and notice exploring cshearer41 hexagon problem.
Interactive MathGeometry
Curvature Steering
A GeoGebra drag and notice exploring curvature steering.
Interactive MathCalculus
Intertia smooth animation
A GeoGebra animation exploring intertia smooth animation.
Interactive MathGeometry
Lines through irrational root pair polynomial extrema integer coefficients
A GeoGebra drag and notice exploring lines through irrational root pair polynomial extrema integer coefficients.
Interactive MathNumber Theory
Lots of congruent angles
A GeoGebra proof exploring lots of congruent angles.
Interactive MathGeometry
Parabolic reflector v2
A GeoGebra drag and notice exploring parabolic reflector v2.
Interactive MathGeometry
Persistence recursion past 100 v2
A GeoGebra drag and notice exploring persistence recursion past 100 v2.
Interactive MathNumber Theory
Spinning Dots3D v3 squares
A GeoGebra animation exploring spinning dots3d v3 squares.
Interactive MathGeometry
Spinning Dots3D v5 redo
A GeoGebra animation exploring spinning dots3d v5 redo.
Interactive MathGeometry
Triangle ineq proof question
A GeoGebra proof exploring triangle ineq proof question.
Interactive MathGeometry
Bart station elevations
A GeoGebra modeling exploring bart station elevations.
Interactive MathMathematical Modeling
Complex Double Num Line
A GeoGebra drag and notice exploring complex double num line.
Interactive Math
Factorable Quadratics
Drag the coefficient point and watch how a monic quadratic's graph, factorability, and integer roots line up.
Interactive MathAlgebra
Heartbeats
A GeoGebra drag and notice exploring heartbeats.
Interactive MathStatistics & Probability
Lines in a Circle
Animate lines rotating through a circle and watch the paths and envelopes they create.
Interactive MathGeometry
Multiply imaginary points - powers of i power version
A GeoGebra drag and notice exploring multiply imaginary points - powers of i power version.
Interactive Math
Swing Hyp Down
Use a swinging right-triangle animation to connect a changing hypotenuse with geometric motion.
Interactive MathGeometry
Swing Hyp Down all at once
A GeoGebra animation exploring swing hyp down all at once.
Interactive MathGeometry
7ths and 13ths 2017
A GeoGebra drag and notice exploring 7ths and 13ths 2017.
Interactive MathNumber Theory
Circle Inversion
Drag points through an inversive geometry construction and see lines, circles, and distances transform.
Interactive MathGeometry
Cobweb Chaos
Use a cobweb diagram to watch repeated function iteration settle, cycle, or become chaotic.
Interactive MathGeometryAlgebra
Complete Graph Turning
A GeoGebra generative art exploring complete graph turning.
Interactive MathGeometry
Complex Sequence
Follow an iterated complex sequence as its orbit draws structure, repetition, and divergence in the plane.
Interactive Math
Diagonals Cut - Exterior Edition
A GeoGebra drag and notice exploring diagonals cut - exterior edition.
Interactive MathGeometry
Incenter Spirograph
Animate a triangle and trace its incenter into a family of geometric, spirograph-like curves.
Interactive MathGeometry
L and w ratio recttriarea
A GeoGebra drag and notice exploring l and w ratio recttriarea.
Interactive MathGeometry
Machine Learning Gradient Descent
A three-dimensional sketch of an optimization path descending across a mathematical surface.
Interactive MathCalculusMathematical Modeling
Min distance to edges
A GeoGebra construction exploring min distance to edges.
Interactive MathGeometry
Rectangle Center To Circle Center
A GeoGebra drag and notice exploring rectangle center to circle center.
Interactive MathGeometry
Repeated perpendiculars of right triangles
A GeoGebra construction exploring repeated perpendiculars of right triangles.
Interactive MathGeometry
Similar triangles of the unit circle
A GeoGebra construction exploring similar triangles of the unit circle.
Interactive MathAlgebra
Tax Brackets
See marginal tax brackets as a piecewise model rather than a single rate applied to all income.
Interactive MathAlgebraMathematical Modeling
Triangular coin probability
A GeoGebra simulation exploring triangular coin probability.
Interactive MathStatistics & Probability
03 Rect Overflow freeplay
A GeoGebra drag and notice exploring 03 rect overflow freeplay.
Interactive MathGeometry
Completing the Square
Drag through a visual model of completing the square and watch the algebraic structure take shape.
Interactive MathAlgebra
Quadratic ancestors
A GeoGebra drag and notice exploring quadratic ancestors.
Interactive MathAlgebra
Simpsons diversity
A GeoGebra drag and notice exploring simpsons diversity.
Interactive MathStatistics & Probability
Various forecasts
A GeoGebra simulation exploring various forecasts.
Interactive MathStatistics & Probability
Why the Unit Circle?
A GeoGebra drag and notice exploring why the unit circle?.
Interactive MathAlgebra
Alternate Interior Angles -- When are they congruent?
A GeoGebra proof exploring alternate interior angles -- when are they congruent?.
Interactive MathGeometry
Kate nowak paper folding
A GeoGebra drag and notice exploring kate nowak paper folding.
Interactive MathGeometry
When does Angle Side Side work?
A GeoGebra drag and notice exploring when does angle side side work?.
Interactive MathGeometry
Distances to Vertices
Move a point around a triangle and study how its distances to the vertices change together.
Interactive MathGeometry
Distances to Vertices
A GeoGebra construction exploring distances to vertices.
Interactive MathGeometry
Unit Circle Trig Segments Reference
A GeoGebra drag and notice exploring unit circle trig segments reference.
Interactive MathAlgebra
Generating Sine and Cosine from the Circle
Use circular motion as a live generator for sine and cosine waves.
Interactive MathAlgebra
Unit Circle Trigonometry
Connect a rotating point on the unit circle to trigonometric values and their geometry.
Interactive MathAlgebra
Area vs. Perimeter
Investigate which area and perimeter combinations are possible for rectangles, adapted from a Malcolm Swan prompt.
Interactive MathGeometryMathematical Modeling
Triangulation Mics
A GeoGebra drag and notice exploring triangulation mics.
Interactive MathGeometry
Time Angles
Drag the time slider and use clock hands as a changing angle diagram for noticing and conjecturing.
Interactive MathGeometry
Angle bisect a trapezoid
A GeoGebra construction exploring angle bisect a trapezoid.
Interactive MathGeometry
Distances to Vertices
Explore how distances from a movable point to triangle vertices change and what patterns emerge.
Interactive MathGeometry
Epsilon and Delta Limits
Manipulate epsilon and delta intervals so the formal limit definition has a dynamic picture.
Interactive MathCalculus
Euclid's Pythagorean Proof
Step through a visual proof of the Pythagorean theorem and the geometric moves behind the result.
Interactive MathGeometry
Painting with Linear Factors
Use factors as visible controls for shaping a graph, adapted from Riley Lark's activity idea.
Interactive MathAlgebra
Sine unit circle oct2013
A GeoGebra drag and notice exploring sine unit circle oct2013.
Interactive MathAlgebra
Square Not Square
Compare what stays square, what only looks square, and what changes under dragging.
Interactive MathGeometry
Triangle Inequality Drag
Drag segment lengths and watch possible triangles appear, disappear, or collapse at the boundary.
Interactive MathGeometry
Talks
Presentations
Conference pages with slides, handouts, applets, and related ideas.
Exploring High School Math with GeoGebra and Desmos
A fast-moving collection of high school mathematics explorations built for an explorable-explanations gathering in San Francisco.
MathEdInteractive MathAlgebra
Principles to Action with Technology
A session on using technology to make students' mathematical thinking visible, moving beyond answer-only systems toward aggregate views of open work.
MathEdInteractive MathGeometry
GeoGebra: From Construction to Abstraction
A presentation about using dynamic construction as a path toward more abstract mathematical relationships.
MathEdInteractive MathGeometry
If a picture is worth 1000 words, what is GeoGebra worth?
A collection of dynamic mathematics demonstrations built around the claim that interaction can communicate more than a static diagram.
MathEdInteractive MathGeometry
Writing & Research
Articles and research publications
Selected public writing and formal research, preserved with accurate dates, authorship, and source context.
Generalizing Expert Misconception Diagnoses through Common Wrong Answer Embedding
Mapped expert diagnoses onto neural embeddings of millions of Khan Academy answers to predict misconceptions on previously unseen questions.
ResearchMathEd
Distributed Representation of Misconceptions
Used neural embeddings and large-scale Khan Academy response data to surface shared mathematical misconceptions across varied problem instances.
ResearchMathEd
Students and Teachers Using a Digital Curriculum and Pedagogy in Secondary Mathematics
Compared how Desmos and Khan Academy shaped student discourse, mathematical exploration, and teachers' roles in a secondary classroom.
ResearchMathEd
Evaluative Listening and Khan Academy
Archive note: this post is preserved as evidence of Scott's product, technology, and math education thinking. The original text is preserved with modern media fallbacks.
MathEd
CMC North Asilomar Wrapup Part 2! Technology: Conceptual Understanding and Intellectual Need
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
ResearchInteractive Math
Quickie Lesson Description: Zombies and Capped Exponential Growth
Archive note: this older WordPress post is preserved with its original wording. Media has been recovered where available and otherwise marked for a later pass.
MathEd
2015 CMC North Asilomar Wrapup - Part 1
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathResearch
Comments from other sites: Four animated gifs of the same awesome problem (dy/dan)
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry
Academic Paper Breakdown: Lampert "Teaching while students work independently"
Archive note: this older WordPress post is preserved with its original wording. Media has been recovered where available and otherwise marked for a later pass.
ResearchMathEd
Dandy Candies and OEIS
Archive note: this older WordPress post is preserved with its original wording. Media has been recovered where available and otherwise marked for a later pass.
MathEd
If Triangle Proofs are the aspirin, what is the headache?
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Geometry
#ContinuumMath - join the movement!
Archived writing from Scott Farrar's math education practice.
Interactive MathGeometry
Student Inquiry into the Neighborhood of the Special Case
Archived writing from Scott Farrar's math education practice.
Interactive MathGeometry
The effects of User Interface design on testing
Archive note: this post is preserved as evidence of Scott's product, technology, and math education thinking. The original text is preserved with modern media fallbacks.
MathEd
The Lines are Not Always Parallel! A geogebra approach to Alternate Interior Angles
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry
Geogebra Doodads
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry
WCYDWT: Displaced Water
Archive note: this older WordPress post is preserved with its original wording. Media has been recovered where available and otherwise marked for a later pass.
Algebra
WCYDWT: Escalator
Archive note: this older WordPress post is preserved with its original wording. Media has been recovered where available and otherwise marked for a later pass.
Algebra
Nice motivator, Holt.
Archive note: this brief post is an early snapshot of Scott's writing about textbook motivators and the limits of surface-level real-world framing. The original text is preserved.
Geometry
Triangles by side
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry
Circumcenters and Epicenters
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry
Introductory Geogebra Lesson
Archive note: this post is part of the early interactive mathematics and GeoGebra thread in Scott's writing. The original text is preserved; recovered media is linked or displayed where possible.
Interactive MathGeometry