In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…

The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in…

Despite the importance of teacher fractional knowledge, there are several areas of teacher understanding that are not well understood. The purpose of this study was to characterise profiles of pre-service teachers' (PSTs) mathematical competence on the topic of fraction multiplication by examining PSTs' understanding of multiplication of fractions…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

The author suggests that slope be introduced as a topic independent of graphs, and that it be presented in a way that makes some sense of using a fraction to represent it. Many examples are included. (MNS)

This collection of booklets deals with minumum standards in mathematics for beginning eleventh grade students. There is a statement of the standards with related skills, a test to assess competency with accompanying answer sheet and answer key, and eight booklets presenting problems covered by six of the standards. The booklets cover: percentages;…

Considering a fraction as directions for graphing a line through the origin of the x-y plane is suggested. Strengths and weaknesses of the idea are also discussed. (MNS)

This book suggests creative, classroom-tested mathematics activities to teach number recognition and counting, number formation, sorting and classification, measuring (including time and date), shapes, graphing, estimating, ordinal positions, money, patterning, tallying, and fractions. Activities are presented in the forms of games, crafts, songs,…

This teacher's guide and student guide are designed to accompany a general mathematics textbook that contains supplemental readings, activities, and methods adapted for secondary students who have disabilities and other students with diverse learning needs. The materials are designed to help these students succeed in regular education content…

Students are given the opportunity to deal with many kinds of data as they make graphs and interpret the results of polls. Worksheets are provided on filling in a graph grid and making bar and circle graphs as well as interpreting each. (MNS)

This video offers an exciting four-part adventure about two teenage sleuths who discover the presence of an alien below New York City. As they try to make contact with the alien, they are confronted with a series of mathematical challenges that test their knowledge of the content strands recommended by the National Council of Teachers of…

This print guide to the "XY Encounter" video offers an exciting four-part adventure about two teenage sleuths who discover the presence of an alien below New York City, and expands upon themes presented in the video. As the students try to make contact with the alien, they are confronted with a series of mathematical challenges that test their…

Describes an activity in which students examine bicycle chain-rings, cogs, and gear ratios as a means of exploring algebraic relationships, data collection, scatter plots, and lines of best fit. (KHR)