According to the National Council of Teachers of Mathematics (NCTM) (1989, 2000), students at all levels should be exposed to geometry and measurement topics. Standards documents have identified the importance of primary school students selecting appropriate units for measurements in one- and two-dimensional space (NCTM 1989, 2000). This paper…

The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

Children are exploring elements of literacy and numeracy. Such explorations begin in the earliest days of life and are a natural outgrowth of children's curiosity and interest in how the world works. Based on experiences, children build a reservoir of knowledge about language, reading, and mathematics that they take with them to kindergarten,…

Does speed provide a "model for" rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the "model for" rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14-15 year old students at…

Vavoso and Apanay discuss revitalizing the Workshop Cycle for the purpose of creating the intellectual environment necessary in teaching for mathematical understanding, which lies at the intersection of the National Council of Teachers of Mathematics' Process and Content Standards. (Contains 2 tables, 3 figures, and a bibliography.)

Children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about everyone's lives as individuals and as community members. This article addresses one approach to introducing children of all achievement levels to introductory…

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

The new program of study for KS3 and the proposed changes in Y11 assessment for 2012 are now demanding teachers to focus again on the processes of learning. Teachers are being told they must "allow students to select the mathematics to use", "allow students to explore connected problems" and encourage them to work with real…

Although many students who enter kindergarten are cognitively ready to meet the demands of the kindergarten mathematics curriculum, some students arrive without the early abstract reasoning abilities necessary to benefit from the instruction provided. Those who do not possess key cognitive abilities, including understandings of conservation,…

This book discusses algebra in a non-threatening, fun way. It explains concepts, vocabulary, and strategies of algebra in understandable terms. Chapter titles include: "Numbers with Interesting Properties"; "Important Concepts"; "Fraction Refresher"; "Terms, Factors, and Polynomials"; "Rearranging Expressions"; "Handy Tricks and Magic Words";…

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

This book contains "math mind benders," puzzles that are worked like crossword puzzles except that each square is filled with a digit rather than a letter. Clues to the puzzles are interrelated with each other and a given story. Clear thinking and deductive reasoning must be used to find potential answers and eliminate those that fail to meet all…

Suggesting that children's literature has a powerful role to play in restoring story to the teaching and learning of mathematics, this book shows how stories are natural invitations for learners to explore the mathematics of their own lives and the lives of others. Each chapter of the book explores books on a given topic and gives some examples of…

This paper will examine the use of software environments and dynamic visualization in mathematics education. This examination will be based on theoretical papers and research reports from substantial literature on visualization. How the term "visualization" is used in mathematics education field is also discussed. The thesis of this…