In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This paper discusses several applications of combinational mathematics to social situations and problems in the social sciences. (SD)

The author suggests having students work on the related inequalities to given equations comparing and graphing the three solutions on the same number line. Using individual activity cards, the student picks replacements and computes, continuing this process until they can determine the complete solution. (LS)

This article displays the graphs of number patterns obtained by writing each number in the pattern as an ordered pair, plotting the ordered pairs, and joining consecutive points by straight lines. (DT)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

This article describes a series of activities and worksheets to provide students with experience in graphing number pairs. Students at different lev els can use the activities to relate basic arithmetical operations to graphs. (Worksheets are included.) (SD)

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include addition and multiplication in terms of absolute value, graphs of absolute value in the Cartesian…

This is part one of a two-part SMSG elementary school text for third-grade students. The development of mathematical ideas in the text is grounded in appropriate experiences with things from the physical world and the immediate environment. Chapter topics include: (1) sets of points; (2) addition and subtraction; (3) describing points and numbers;…

A Math Rummy card game, a stock market enrichment activity, and a puzzle in logical reasoning, all used with seventh and eighth graders, are described; directions for constructing a clock with suggestions for its use at the first grade level are given. (DT)

The lesson details an approach to teaching positive and negative numbers which uses number pairs and generates inverses that initially avoid any mention or use of negative signs. The material moves pupils from development of key concepts to the use of more standardized notation for number operations. (MP)

This computer software program helps to make classroom worksheets, take home assignments, and school mathematics tests easy to design and manufacture. The accompanying printed teaching guide provides technical information for setting up and using the program, along with sample worksheets and instructions on how to create them using the software.…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include absolute value, addition and multiplication in terms of absolute value, graphs of absolute…