When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

"I CAN Learn"[R] is a computer software system that provides math instruction through a series of interactive lessons. These lessons are delivered with a one-to-one student-to-computer ratio. Students determine the pace of each lesson and must demonstrate mastery of the lesson before progressing to the next one. Teachers provide…

Looking beyond the right or wrong answer is imperative to the development of effective educational environments conducive to Pre-AP work in math. This presentation explores a system of evaluation in math that provides a personalized, student-reflective model correlated to consortia-based assessment. Using examples of students' work that includes…

Students experience a variety of challenges as they move from one level in school to the next. In this session, we consider and discuss two central questions related to students' progressions through their mathematical experience, particularly at transitions roughly characterized as elementary to middle school, middle school to high school, and…

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

In this research we present the use of some technologies in problem solving activities (at different secondary school grades), aimed at finding a model for a geometric configuration, and representing this model in various ways: through a construction, through a Cartesian graph, etc. The task is part of a teaching experiment, in which students used…

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and…

Multiple-choice items are commonly viewed as a summative check for skill attainment, but they can be used to assess other dimensions of student learning. The purpose of this article is to offer an expanded view of the use of multiple-choice items in the middle level mathematics classroom. It presents three alternative uses of multiple-choice items…

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

Mr. Carter is about to start a two-day lesson on subtraction of integers with his sixth-grade prealgebra students. He plans to use contextualized problems that will allow his students to develop an interpretation of subtraction that involves the idea of "difference." This article outlines one way to teach students develop number line…

Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the…

A teacher can be the most important resource in a school. When the teacher's attitude derives from asset-based thinking, positive impact can occur for both teacher and student. Asset-based thinking is defined as "a way of viewing reality." Those who embrace this model approach things from a positive as opposed to a negative perspective.…

Imagine high school students glued to computer screens--not playing video games but applying their mathematical knowledge of functions to the design of three-dimensional sculptures. Imagine these students engaging in rich discourse as they transform functions of their choosing to design unique creations. Now, imagine these students using…

The aim of this study is to determine the effects of computer-assisted teaching (CAT) on remedying misconceptions students often have regarding some probability concepts in mathematics. Toward this aim, computer-assisted teaching materials were developed and used in the process of teaching. Within the true-experimental research method, a pre- and…

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…