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School of the Mathematical Future

School of the Mathematical Future is organized by Natural Math family learning network, Math 2.0 interest group, and P2PU (Peer to Peer University). We are building an open learning environment for mathematics educators working in diverse communities and networks. Our classes are open and free.

Course list

P2PU has moved to a new home - please go to to see our current courses. If you want to see what courses were previously run on this site, here's a selection of completed courses:
Course Name Organiser Course Status
Moebius noodles: Rich math for familiesMath is more than counting! What can your preschooler do with symmetry, fractals, patterns and more in 5-10 minutes of fun games?Show more details
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Young children are naturally drawn to harmony, balance and order. They are naturally drawn to math, the math that goes beyond counting and simple arithmetic. Math is beautiful and fun and it all starts early on with a few simple games.

This is what this course is about - quick, simple and fun games that parents can play with kids to explore math.

Every weekday for the next 4 weeks you will see

  • a new math activity to try with your child that takes virtually no time to prepare
  • a math concept behind it
  • how to adapt it for children of different ages, from infants to elementary school students
  • variations to keep it interesting for children with various learning styles - and for parents!

Once a week you will have an opportunity to join us and other parents in live webinars to learn more about teaching math to your child naturally, and to share your stories.

You can also share your ideas, photos, and stories by e-mailing the group, uploading picture to Flickr, or joining the Moebius Noodles Facebook group.

Vi Hart Polyhedra Balloons
Photo: Vi Hart with balloon polyhedra

Maria Droujkova
Maria Droujkova's picture
Create+Share Math InteractivesRapid Development and Sharing of Interactives (GeoGebra, Screencasts, more details
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"Create and Share Math Interactives" is a course aimed at anyone who ever had a question about math and wants to explore and answer the question in a visual and then AV format. For example: What is the largest triangle that I can get inside a circle? See: We will learn and use the free and excellent math software GeoGebra, we will learn and make screencasts using the freeware Jing and we will post our coursework on a free Wikispaces website and our resulting interactives on the Models for Math site

Linda Fahlberg-St...
Linda Fahlberg-Stojanovska's picture
Mathematics for Game DesignersThe idea is to take the basic concepts of "games" and explore them using mathematics.Show more details
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(There is an etherpad version of this text at -- feel free to edit there if you want to make quick changes/suggestions.)

The intial outline (subject to change) is as follows. This is  developing in a conversation with Stefan Kreitmayer and Daniel Chiquito. The idea is to take the basic concepts of "games" and explore them using mathematics.  In this course we will focus on two mathematical ideas: discrete differential equations (difference equations, differential equations on graphs, whatever you want to call it), and strategy/proofs.
The course is emphasizes the needs and interests of game designers, but programmers or math fans are welcome to enroll.  We will expect to meet for voice conversations twice a week.  Budget at least a couple of hours for homework as well.
Exercises are optional (but encouraged) and are structured in such a way that they can be done with or with out programming.  Feel free to invent your own exercises or projects and share them with the group!  We will particularly aim to support development in Python with examples and tools being added during the course.

We will aim to document what we learn on PlanetMath, Wikipedia and/or a next-generation "clone" of PlanetMath.  Details will be discussed during the course.  If you need to contact the course organizer about anything, you can post in the discussion area here or email directly,

Week 1: Space (including graphs and other combinatorial models of space)
Here  I was thinking that we would come up with a graph visualization  framework - hence the importance of graphics libraries.  But more  importantly to make sure that everyone is on the same page with what a  mathematical graph is G = (V,E) where V is vertices and E is edges, and so  on.
Possible design/programming exercise:  Choose a platform or medium in which to do simulations or to create art work that sketches your ideas, and use this medium to explore the idea of "space".  
Week 2: Time (focusing on movement)
In  this phase I wanted to look at simple differential equations on  graphs.  What I mean by this is, suppose we have a certain quantity of  "stuff" at a vertex v and we want to know where the stuff goes.  We can  write a function (or whatever, a differential or difference equation)  that will say where the stuff goes at time t.
Melting snowman example:
X            X
X   -->     XX   -->    XXX  --> X  X  X -->
Possible design/programming exercise: Create an environment that has some interesting "physics" to it, e.g. snowmen melting, leafs blowing, cities growing, perhaps the space itself expanding or changing shape...
Week 3: strategy and proof, part 1: Introduction to game theory
Some online resources for self-study (feel free to add more here or add reviews):
The task this week is to analyze, to the extent possible, the game of your choice, using ideas from game theory.
Possible programming exercises: Make the environment interactive, and/or add bots (NPCs) that interact with the game world.
Week 4: strategy and proof, part 2: Iterative Games and learning as you go.
People often learn the strategy to use for winning a game by playing it a lot.  How does this work?  (Get readings for this.)

Possible design/programming exercises: Design or build bots with some ability to learn and change their behaviour.  Neural Networks is one way to approach this.
Week 5: strategy and proof, part 3: Proof strategies
Possible design/programming exercise: Enhance your game by creating some objectives or scenarios and letting the bots or players interact in these scenarios (e.g. create the ability to "win").
Week 6: Cybernetics and ecology (building and interacting with systems)
Final project: Design/build a world simulator or a new game.
Some recent news that may entice people to take the class:
Joe Corneli
Joe Corneli's picture
CPD through Twitter for Maths TeachersHow can I use Twitter to help my development as an educator in mathematics?Show more details
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So, I've heard about Twitter and other kinds of social media, but is it really useful for helping me on a day-to-day basis with my teaching?

The aim of this course is to show you the power of using Twitter as one of the tools in your professional development as a teacher involved in mathematics.  The sign-up task is designed to make sure that you can communicate with other members of the group and, from then on, you proceed at your own pace through the four stages of the course.

Most of the communication will happen through Twitter itself, but you will also be expected to contribute to the group's learning goals and take part, when possible, in some of the synchronous meetings.

The main aim of this course is to help you feel more confident about using Twitter as another point of access for your continuing professional development as a teacher, and you can complete the stages in six to twelve weeks as best suits your needs.

Some questions we will look at could include:

How immediate is the response I can get?
What if I need to discuss things which are sensitive?  Can I protect my views?
How can I best share information or find it using Twitter?
Do scheduled chats help me or should I use hashtags? [Help, I don't know what this is!]
How can I adapt Twitter for my own needs as a teacher (of mathematics)?

Colin Graham
Colin Graham's picture
Introduction to Math ArtIntroduce a computer language design to create mathematical patterns. Ideal for parents with elementary school kids.Show more details
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This is a hands on course where participants will create mathematical art and share it.
We will use a computer language I co-designed with my colleague David Rosenthal.
The language can be downloaded from:

Parts of the course will cover chapters in the book that is available in a PDF format
Using the link: 

Depending on the student skills and interest it may touch other topics like Math and Music,  Creating Games and dynamic Mathematical Art.

Dani Novak
Dani Novak's picture
Psychology of Math LearningCan psychological theories such as personality style help explain why some students take naturally to math while others struggle?Show more details
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  More than almost any other discipline, mathematics can cause real angst for those students who just "don't get it" (have you ever heard of "history anxiety" or "art anxiety"?). But why do some students find math to be a fun, natural, and creative discipline, while others struggle and just can't seem to figure it out, no matter how hard they work on it? To answer this question, educators tend to focus on the "nurture" factors, such as the parents' abilities and feelings about math, whether the student lives in a math-rich environment, the quality of the math teachers, or the type of curriculum followed. But in this class, we'll be exploring the "nature" side of the question. We will look at psychological theories, such as personality style, learning style, and gender differences, to see if they can illuminate why some of us think math is joy, while for others it seems more like a nightmare.
Carol Cross
Carol Cross's picture
Multiplication Models SeminarWhat interactive models of multiplication are most useful, meaningful, beautiful or fun?Show more details
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The goal of this course is to aggregate a curated, reviewed collection of interactive multiplication models. Some of the communities and projects involved in this include Natural Math, Etoys, Illuminations, The Mathman, and SubQuan.


Maria Droujkova
Maria Droujkova's picture
Mathematics Curriculum DevelopmentA course on curriculum development ideas of the last decade and the near future, through participation in educator communities.Show more details
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Welcome to the adventures in mathematics curriculum development! This course is offered for credit at Arcadia University graduate school, as well as for open participation from larger mathematics education community.

Course events and activities will be coordinated through ED534Arcadia wiki.

This fast-paced, highly interactive online course introduces participants to curriculum development ideas of the last decade, concepts from the near future, and tried-and-true classics. All course tasks happen live in vibrant, growing online educator communities. Research topics of the course contribute to current events and ongoing hot disputes in mathematics education. Throughout the course, participants will only use free and open educational resources, software and communication platforms, contributing to their teaching and learning toolkit. Course themes include:

  • Learning fundamental ideas of algebra, geometry, calculus, and statistics
  • Meaning and significance of mathematics
  • Problem-posing, problem-solving and modeling
  • Math 2.0: computational software and social media
  • Humanistic mathematics
  • Psychology of mathematics education for curriculum development


Maria Droujkova
Maria Droujkova's picture
Math-rich baby and toddler environmentA course for sharing know-how about creating mathematically rich environments for young children.Show more details
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Live meeting recordings

To join meetings (during announced times) follow this link:

  • January 31 Topics:
    • Is it OK to count on fingers?
    • More advanced finger counting systems.
    • "Pet names" for math objects, roleplay.
    • Music and mathematics
  • February 7th Topics:
    • The kid just plays with objects! Where is math?
    • Subitizing (instant quantity recognition)
    • Montessori, Waldorf, Reggio Emilia - comparing early education systems
  • February 19 Topics:
    • Course design
    • Fractal computer game

MindMap of participant questions (link)

In this course, participants will share their know-how about creating math-rich environments for babies and young children. Two groups of parents will participate in this course. Parents in the first group want to share their own love of math, science and technology with the next generation of little geeklets. The second group are parents anxious or less successful in math who want their kids to avoid such a fate. Developers of early childhood programs and materials, and educators who work with families will also join as peers.

We will meet online once a week and will use an email group and other platforms for asynchronous communication. During each of the six weeks, we will create activities focused on a particular fundamental math topic, such as functions or patterns. Those of us who currently have children will run the activities, and share their experiences of putting "fun" in "fundamental." We will also aggregate tools and ideas that apply across topics and activities, such as child's eye-level displays of math collections.

Maria Droujkova
Maria Droujkova's picture
Getting Started with ScilabWish to learn Scilab and Scilab programming? Visit Scilab is Free software for matrix and linear algebraShow more details
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NOTE: This course has shifted to the new P2PU site that can be accessed at You can login with the same account you use on the old site. In case you face any difficulty with registration, send me an email at satish DOT annigeri AT gmail DOT com

This course is for beginners with no previous experience with Scilab or other software similar to it (names not listed because it is part of the assignment for registering!).

Scilab is a free software for numerical computations and has its own interpreted programming language that can extend its existing capabilities. This course is intended for a beginner new to matrix software tools. Scilab has a large feature set, but this course covers only the basics.

The following points make Scilab an attractive choice for anyone requiring software for matrix algebra computations:

  • An interactive numerical tool with ability to plot 2D and 3D graphs and visualize data
  • Similar to Matlab(R) but free and open source with a license compatible with GNU GPL
  • Comes with a large library of built-in functions for matrix algebra
  • Comes with a large number of toolboxes developed by the community for a variety of applications including signal and image processing, control systems, genetic algorithms, neural networks etc.
  • Has a vibrant community
  • Has a built-in interpreted programming language to extend its existing capabilities
  • Has a C/C++ API
  • Under constant development

The primary motivation behind learning and using Scilab is that one can focus on the problem being solved instead of getting involved in programming and debugging C/C++/Fortran code for matrix algebra operations.

The course will cover the following topics:

  • Scilab environment, help system and workspace
  • Scilab data types, operators, statements
  • Defining and using matrices, sub-matrix operations and ranges
  • Plotting 2D graphs
  • Scilab programming language
  • Writing Scilab scripts
  • Writing Scilab functions
  • Some simple applications
Satish Annigeri
Satish Annigeri's picture
Short CalculusWe will work together, using various free learning tools, to create a repository of solved problems in Calculus 1.Show more details
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(There is an etherpad version of this content at, feel free to edit there if you want to make quick changes/suggestions.)

The plan for this course is to work together, using various free learning tools, to create a repository of solved problems in Calculus 1.

The plan for the course is based on the outline at -- see this link for some more details, but note that we will certainly not be restricting ourselves to this resource!

The high-level outline for the course is:

  • Week 1: sequences & series
  • Week 2: limits and continuity
  • Week 3: differentiation
  • Week 4: integration
  • Week 5: techniques of integration
  • Week 6: taylor polynomials and power series

We will meet for live conversations one or two times per week (frequency and exact schedule to be decided by course participants).


Joe Corneli
Joe Corneli's picture