Teacher research--often called "action research"--is an intentional and systematic inquiry into one's own classroom practice with the goal of improved student learning (Cochran-Smith and Lytle 1993). In this article, the authors present a teacher research project undertaken to improve student understanding of the gas laws in a high…

The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

In this experimental study, use of Computer Assisted Instruction (CAI) followed by use of an Intelligent Tutoring System (CAI+ITS) was compared to the use of CAI (CAI only) in tutoring students on the topic of Algebraic Expression. Two groups of students participated in the study. One group of 32 students studied algebraic expression in a CAI…

"Focus on Basics" is a publication of the US Division of World Education, Inc. It presents best practices, current research on adult learning and literacy, and how research is used by adult basic education teachers, counselors, program administrators, and policymakers. "Focus on Basics" is dedicated to connecting research with…

Pedagogical maps provide a graphic depiction of the way in which teachers exploit the presence of Computer Algebra Systems (CAS) in their classrooms. They can show differences, and can also show growth, as well as personal preferences and reactions to particular teaching assignments. They might also be used for teachers to reflect on their own…

This article describes a student-oriented classroom activity for exploring polynomials. In this activity teacher candidates apply technology to explore mathematics that they will teach but that they have not studied since high school. (Contains 10 figures.)

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…

In this 15-week study the effects of motivational email messages on learner self-efficacy and achievement in an asynchronous math course were investigated. A repeated measures design was used. One hundred, ninety-six participants were randomly assigned to control and experimental groups. Specially designed email messages were sent weekly to both…

This paper reports on a project to improve Beginning Algebra students' understanding of basic algebraic concepts through fully integrated use of the TI-83 graphing calculator. The methodology incorporated an intervention case study including approximately 700 Beginning Algebra students at an open-door community college of 8,500 students in the…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…

Students explore the Pythagorean theorem and an extension using jelly beans to measure areas. Deductive thinking and algebraic notation help establish connections. (Contains 8 figures.)

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

This proceedings volume of InCoTEPD 2018 covers many ideas for handling a wide variety of challenging issues in the field of education. The outstanding ideas dealing with these issues result in innovation of the system. There are many innovation strategies resulting from recent research that are discussed in this book. These strategies will become…

To investigate whether games may serve as useful formative assessment environments, this study examined, experimentally, the effects of two aspects of formative assessment on math achievement, game play, and help-seeking behaviors: (a) making assessment criteria explicit through the explanation of scoring rules and (b) incentivizing the use of…