How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the…

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

Integrating mathematics with family and consumer sciences (FCS) has enabled youth to pass the Minnesota 8th Grade Math Basic Skills test. The test focuses on the eight content areas: (1) problem solving with whole numbers and fractions; (2) problem solving with percentage/ratio; (3) number sense; (4) estimation; 5) measurement; (6) tables and…

This study investigates middle school mathematics students' views and interpretations of graphical representations as they use graphs to answer algebraic questions--specifically, questions that require them to extrapolate information from graphs. From data gathered in videotaped interviews, students' verbal responses were analyzed as well as any…

This guide describes 47 number and numeration learning activities that can be used with elementary school students. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in developing further…

This study compared the results of group tests of computational skills and tests of knowledge and skills in mathematics between three groups of first and fifth grade students from the United States, Japan, and Taiwan. The battery of tests were constructed after reviewing the mathematics textbooks used in each location and discussing the major…

The numeracy handbook is a practical guide for teachers of numeracy and literacy to learners of English as a Second Language. Focus is on teaching numeracy and integrating numeracy and literacy. It considers issues in defining and teaching numeracy, examines numeracy in the workplace, designing a course and a unit of work, and analyzes numeracy…