This article describes a preservice teacher training in line with meeting the Common Core State Standards for Mathematics (CCSSM) using geometric reasoning, spatial sense, measurement, representation, communication, and problem solving. The author infers that when preservice teachers lack pedagogical content knowledge they cannot successfully…

In this paper we investigate how competition among tutees in the context of learning by teaching affects tutors' engagement as well as tutor learning. We conducted this investigation by incorporating a competitive Game Show feature into an online learning environment where students learn to solve algebraic equations by teaching a synthetic…

Learning situations that concentrate on conceptual understanding are particularly challenging for learners with limited proficiency in the language of instruction. This article presents an intervention on fractions for Grade 7 in which linguistic challenges and conceptual mathematical challenges were treated in an integrated way. The quantitative…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

A test of the effectiveness of patterning instruction was conducted with 140 first-graders. First, 383 first-graders from 20 classes were screened on a patterning test. The eight in each class who scored worst were given individual 15-minute lessons on patterning or reading or mathematics or social studies three times weekly for a period of 6 1/2…

The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem…

Over the last four years of the senior capstone seminar at Western Carolina University, we have redesigned the course substantially to comply with our institutional Quality Enhancement Plan for engaged student learning and to follow the guidelines proposed by the Mathematical Association of America's Committee on Undergraduate Programs in…

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

This article presents an instructional model (inclusively responsive instruction) that takes advantage of student diversity in order to differentiate student learning while maintaining high expectations. In the history of U.S. education, diversity and academic rigor were often considered at odds, and educators tried to emphasize one at the expense…

Background: Robot-math is a term used to describe mathematics instruction centered on engineering, particularly robotics. This type of instruction seeks first to make the mathematics skills useful for robotics-centered challenges, and then to help students extend (transfer) those skills. A robot-math intervention was designed to target the…

The purpose of this mixed methods study was to determine the impact of synchronous online tutoring services on struggling middle school students' mathematics achievement. The online tutoring was provided as a response to intervention (RTI) Tier 3 support (intensive, individualized intervention) in schools implementing a school-wide mathematics…

Objective: Children from low-income families are often not well-prepared for kindergarten entry, especially in mathematical skills. Caregivers may lack the knowledge and confidence to teach early mathematical skills. The purpose of this study was to develop a parent-child activities-based mathematics learning programme and test its acceptability…

The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five…