Contribution: We present a framework for teachers to investigate the relationships between attributes of students' solutions in the process of problem solving or computational thinking. We provide visualization and evaluation techniques to find hidden patterns in the students' solutions which allow teachers to predict the specific behavior of…

Pattern recognition is an important skill in computational thinking. In this study, an equation puzzle game was developed by combining pattern recognition with algebraic reasoning, and scaffolding was designed to support learners' learning. Sixty participants were enrolled in this study, divided into a control group and an experimental group to…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

There is a crucial debate concerning the nature of chess chunks: One current possibility states that chunks are built by encoding particular combinations of pieces-on-squares (POSs), and that chunks are formed mostly by "close" pieces (in a "Euclidean" sense). A complementary hypothesis is that chunks are encoded by abstract,…

Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…

The card game SET has attracted the attention of math and game enthusiasts alike. In this article, I present a first semester Abstract Algebra project that guides the students through an algebraic formulation of the game. There are many interesting mathematical questions that one can ask about the game, and I illustrate how the project can be used…

Describes two activities involving sorting, counting, and determining relationships that use sameness and difference, spatial skills, pattern identification, number bonds, and generalization. (DDR)

This is a not-so-serious discussion of accidental patterns involving chance patterns between mathematics and natural laws and accidental patterns involving the numbers "pi" and "e." (Author/SA)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Presented are simple activities that can be completed by students at home with the help of a parent. Activities include the topics of sorting, patterning, counting and numbers, geometry, adding, subtracting, and measuring. Each activity describes a series of sequenced tasks related to one of the topics. (KR)