At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus…

Education professionals, regardless of their specialist area, are broadly aware of the importance of numeracy. Internationally, definitions of numeracy (known elsewhere as mathematical literacy or quantitative reasoning), describe "an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts... reasoning…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Middle grades are a critical time for capturing the interest and imagination and developing the potential of mathematically promising students. This is a time for students to make sense of mathematics, build a solid foundation and enthusiasm, and set the course for the highest levels of mathematics in the future. This is a time to explore their…

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

Describes the use of a spreadsheet in running a hands-on prey/predator simulation that enables students to see the effect of selection pressure on one allele in a gene pool. Discusses setting up and running the simulation, class discussion issues, exploring assumptions, and extensions. (JRH)

This book provides a collection of 191 mathematical problems aimed at the advanced high school student level and above. Problems cover general mathematical areas including plane geometry, three-dimensional geometry, number theory, algebra, combinatorics and graph theory, and a number of miscellaneous questions that combine mathematical…

Presents remarks adapted from the Presidential address from the 1999 annual meeting of the National Council of Teachers of Mathematics (NCTM). Argues that the mathematics classroom teacher must create an environment that supports students' interests and mathematics growth at many different levels and ways in which to achieve this. Considers…

Presents the President's address from the 1999 annual meeting of the National Council of Teachers of Mathematics (NCTM). Asserts that the mathematics classroom teacher must create an environment that supports students and mathematics growth at many different levels, and suggests ways in which to achieve this. Considers the changing societal…

Presents remarks adapted from the presidential address of the 1999 annual meeting of the National Council of Teachers of Mathematics (NCTM). Argues that the mathematics classroom teacher must create an environment that supports students' interests and mathematical growth at many different levels, and suggests ways to accomplish this. Considers…

This manuscript contains 13 curriculum units designed to enhance differentiated instruction for learners with special needs from grades 1-12, including gifted students. It integrates Benjamin S. Bloom's levels of cognitive understanding with Howard Gardner's eight domains of intelligence to provide a framework for individualized instruction. Each…

This book is a guide to educating and nurturing children with mathematical talent. Chapter 1 presents and refutes 12 myths about mathematically talented students, especially the idea that it is best not to deviate from regular programming. The second chapter is a guide for parents in their efforts to advocate for their child in the regular school…

Preschool children (n=115) in Poland were tested in five areas: counting, equipotency of sets, dividing, adding, and comparing. Results showed that these children already had informal knowledge of many of the concepts and skills included in the mathematics curriculum in the early grades. (PDD)