The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

This teacher guide helps build a solid foundation in algebra for students in grades 3-5 in which students gain essential understanding of properties of numbers, variables, functions, equations, and formulas. Throughout the problem solving activities, students use computational skills and gain a deeper understanding of the number system. Students…

This collection of activities is designed to show how graphics display calculators can be used to foster algebraic thinking in middle school students. The collection consists of five activities addressing such topics as functions, estimation and scatterplots, and patterns. Blackline masters for the activities are included. (MM)

Identifies and addresses fundamental ideas that build the foundations of algebraic thinking and reasoning. Focuses on developing appropriate instructional approaches to these concepts. Explains what is meant by "composite unit" and how this concept framed the development of an instructional sequence to help students make sense of and find meaning…

Introduces an algebra lesson plan on two people saving money over the course of a week and the problems they encounter for early elementary school students. (YDS)

Participants at the Summer Institute Pattern Exploration: Integration Math and Science in the Middle Grades used and developed a method treat arithmetic, algebra and geometry as one entity. The use of iterative geometric constructions is seen to reinforce the concepts of exponents, ratios and algebraic expressions for the nth stage of the…

Presents an activity that explores the completion of squares from the geometric point of view. (ASK)

Proves that there really are people who use algebra in their jobs and that there are issues in society that require an understanding of mathematical concepts and processes which can be taught in an Algebra I class. Provides real-life situations and activities that use algebra. (ASK)

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

One problem that students have with mathematics is that they often view the topic as a series of unrelated ideas. Sometimes they are aware that they have to know one concept to move to the next, but what is done in geometry is not necessarily related to anything in algebra. This failure to recognize mathematical connections limits students'…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

This report summarizes findings on strategies chosen by students (n=38) when solving algebra problems related to various functions with the freedom to use a TI-83 graphing calculator, influences on student problem-solving strategy choices, student ability to approach algebra problems with use of multiple representations, and student beliefs on how…

Shows how sequenced learning activities can help students build conceptual bridges from arithmetic to algebra. Focuses on understanding equivalent algebraic expressions, an area in which U.S. students scored poorly on the Third International Mathematics and Science Study (TIMSS). (YDS)

Provides activities that support students as they develop their intuitive notions of graphs. Activities help students describe the relationships expressed in the graphs and make generalizations about inferences on the basis of the visual image. (ASK)

Takes the concept of using a geometrical or visual approach to teach algebraic concepts and extends it to connect with the section on binomial expansion by using three dimensional objects. (ASK)