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The objective of this site is to show examples of thinking in math, whether it is original solutions from students of problems, or ways to include an inquiry based approach in mathematics education. The idea for the project came from Chris Hunter as a comment on a blog post. I, David Wees, think it is such a terrific idea that I am working on implementing it. I welcome ideas and input from anyone who is interested and would like to help support student thinking in mathematics. Please send an email with your example of original mathematical thinking by a student, or an example of a project students can do to support inquiry in mathematics

Abstract: "This research seeks to look into the design process that promotes the development of an educational computer game that supports teaching and learning processes. The research specifically looks at the design of an educational computer game for teaching and learning of the topic of functions. The topic is essential in the teaching and learning of Mathematics courses such as Discrete Mathematics, Real Analysis and Calculus among others at Jomo Kenyatta University of Agriculture and Technology (JKUAT) Kenya. The computer game was developed using the Basic Unified process (BUP) which is a streamlined version of the rational unified process (RUP). This is an object oriented methodology mostly used for small projects with few end users. Due to the few numbers of end users we used interview method of data collection to gather requirements for the computer game. A paper prototype was used to validate the requirements. Use cases were used for both analysis and design of the game while Class diagrams and activity diagrams were purely used for the design of the game. Owens' six top level design anatomy aided in the design of the computer game. The overall computer game design was based on Crawfords' computer game design sequence model. The well designed and developed game met all its user requirements and was able to facilitate the teaching and learning of functions to Bachelor of Science in Mathematics and Computer Science students who were taking Discrete mathematics in their first year of study at JKUATs' Taita/Taveta campus. Development of heuristics for measuring interest, fun and motivation are recommendations given to aid in the evaluation of user satisfaction of educational computer games."

abstract: "In this paper I address the use of digital tools (GeoGebra) in open ended design activities, with primary school children. I present results from the research and development project "Creative Digital Mathematics", which aims to use the pupil's development of mathematical board games as a vehicle for teaching skills with GeoGebra, as well as an entrepreneurial attitude towards mathematics. Using the instrumental approach I discuss how open ended transdisciplinary design activities can support instrumental genesis, by considering the extent to which the pupils address mathematical knowledge in their work with GeoGebra and how they relate their work with GeoGebra and mathematics to fellow pupils and real life situations. The results show that pupils' consider development of board games as meaningful mathematical activity, and that they develop skills with GeoGebra, furthermore the pupils considers potential use of their board game by classmates in their design activities."

Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children.

Abstract: "Together, brain science and learning design inform Adaptive Interaction Design (AID), a technique for curriculum planning and development. Mathematics is a particular case in which AID can help. The Way of the Game is vital to learning design. There are many definitions of "game." Here, we mean game to be the means by which spontaneous play becomes responsible learning. That innovative games figure as the centerpiece of many 21st century curricula is no accident. Games are a critical element in modern theories of learning design especially when related to insights from neuroscience and online learning/teaching methods. But beyond simple gamification, can games provide the disruptive transformation to mathematics education that is required to effect substantive and sustainable improvement? Can we game the educational system to ensure students' success in mathematics? To find out, we will look at the AID process and two sample products for the development of mathematical thinking and practice based on the Way of the Game."

"This book is designed to provide mathematics undergraduates with some historical background to the material that is now taught universally to students in their final years at school and the first years at college or university: the core subjects of calculus, analysis, and abstract algebra, along with others such as mechanics, probability, and number theory. All of these evolved into their present form in a relatively limited area of western Europe from the mid sixteenth century onwards, and it is there that we find the major writings that relate in a recognizable way to contemporary mathematics."

"I often sit on a Thursday evening about 2000hrs and watch the ukedchat hashtag. This week it was about physical education. Although this is not one of my strong subjects in teaching (or even in real life) I was interested in the first question which asked how physical education could be related to literacy and/or mathematics. Just like a GSCE multiple choice essay question I chose to answer how it could be related to mathematics. You can see the full tweet chat conversation here - but I thought I would expand my response in this week's waffle."

From the abstract: "We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry." (Full text requires subscription.

"SRI International, Worcester Polytechnic Institute (WPI), and the University of Maine have received a $3.5 million award from the Institute of Education Sciences at the U.S. Department of Education to evaluate the effectiveness of an online tutoring system for mathematics homework. The research team will study seventh-grade mathematics students and teachers in more than 50 schools throughout Maine using WPI's ASSISTments system. ASSISTments aims to transform homework by giving students instant feedback and tutoring adapted to their individual needs. It also provides teachers with customized reports each morning on their students' nightly progress. Teachers in the study will receive training in how to use these reports to adapt their lesson plans to better suit students' needs."

This practice guide provides five recommendations for improving students' mathematical problem solving in grades 4 through 8. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students.

Review of Conway's Mathematical Connections, written for undergraduate mathematics courses, with the aim that instructors help students find connections across branches of math. Two similar books for undergraduates, recently published, are mentioned as well.

"Several of our classes involve students using mathematical expressions, but there was no way for us to automatically check this work. The stated solution to a problem may be x+y, but if a student answers y+x, our system needs to understand that this is also correct." "sympy, an open source Python library for symbolic mathematics," is proposed as a solution.

"This is a resource page for anyone who is interested in research in mathematics education." (Facebook)

Game Classroom is an educational games website catering to the K-6 market. Game Classroom offers mathematics games and language arts games. Games can be found by selecting a grade level and then a subject area. Both the mathematics and language arts categ

"overview of the landscape of K-12 STEM education by considering different school models, highlighting research on effective STEM education practices, and identifying some conditions that promote and limit school- and student-level success in STEM. It can serve as a guide for those involved in K-12 education at all levels: policy makers; decision makers at the school and district levels; local, state, and federal government agencies; curriculum developers; educators; and parent and education advocacy groups." Findings, according to a Science magazine news story indicate that STEM teaching matters more than specialized STEM schools. Report does indicate steps to improve STEM education, involving investments in resources and teacher training, see :http://bit.ly/kRPyH3

by dr. sarah-marie belcastro, "You might wonder why one would want to knit mathematical objects. One reason is that the finished objects make good teaching aids; a knitted object is flexible and can be physically manipulated, unlike beautiful and mathematically perfect computer graphics. And the process itself offers insights: In creating an object anew, not following someone else's pattern, there is deep understanding to be gained. To craft a physical instantiation of an abstraction, one must understand the abstraction's structure well enough to decide which properties to highlight. Such decisions are a crucial part of the design process, but for the specifics to make sense, we must first consider knitting geometrically."

From the abstract: "ew innovations by math- ematicians themselves are starting to harness the power of social computation to create new modes of mathematical production. We study the effectiveness of one such system, and make proposals for enhancement, drawing on AI and computer based mathematics. We analyse the content of a sample of questions and responses in the community ques- tion answering system for research mathematicians, math- overflow . We find that mathoverflow is very effective, with 90% of our sample of questions answered completely or in part. A typical response is an informal dialogue, allowing error and speculation, rather than rigorous mathematical argument: 37% of our sample discussions acknowledged er- ror. Responses typically present information known to the respondent, and readily checked by other users: thus the effectiveness of mathoverflow comes from information shar- ing. We conclude that extending and the power and reach of mathoverflow through a combination of people and machines raises new challenges for artificial intelligence and compu ta- tional mathematics, in particular how to handle error, anal - ogy and informal reasoning."

Published November 2012. "The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. "

From the abstract: "Studies on creative mathematics conducted in the past decades revealed that the importance of creation of learning and teaching environment favourable to the identification and nurturing creativity in mathematics. Based on psychological, methodological and didactical models created by Krutetskii (2006), Shchedrovtiskii (2008), Brousseau (2007) and Sierpinska (2004), we have developed our challenging situation approach. During 5 years of field study in the elementary grade VII classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical creativity in very young children, keeping and increasing their interest towards more advanced mathematics curriculum. This article is an humble attempt to present our model and illustrate how it works in the mixedability classroom. We will also discuss different roles that teachers and students might play in this kind of environment and how each side could benefit from it."

In defense of mathematics and mathematical literacy

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