Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

Many randomized controlled experiments in the classroom have found that mathematics learning is improved dramatically when practice problems of one kind are distributed across multiple assignments (spaced) and mixed with other kinds of problems (interleaved). In two studies, we investigated students' knowledge of spacing and interleaving. In Study…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

Reasoning and constructing mathematical explanations for an audience have become increasingly important activities in elementary classrooms with the implementation of reform-oriented curriculum and standards. Mobile learning tools and applications, such as screencasts, allow students to generate multimedia presentations of their solution…

This case study documents the struggles and successes encountered by a pre-calculus teacher while using Classroom Connectivity Technology (CCT) daily in her community college mathematics course. CCT refers to a wireless communication system that connects a teacher's computer with an individual student's handheld calculator and has been associated…

THE FACTORS RELATED TO UNDERACHIEVEMENT AND LOW ACHIEVEMENT IN MATHEMATICS LEARNING WERE STUDIED. USING AN INDIVIDUAL CLINICAL APPROACH, THE STUDY WAS CONDUCTED WITH TWO SAMPLE GROUPS, 12 UNDERACHIEVERS AND 11 LOW ACHIEVERS, IN GRADES 4-6. SCORES WERE OBTAINED ON CONCRETE, SEMICONCRETE, AND ABSTRACT REASONING LEVELS FOR THE MATHEMATICS EDUCATION…

Energy is a problem affecting all individuals. To help today's students understand the problem and become realistic decision-makers, materials have been developed by the Sunny Side Up (in Mathematics) program to introduce energy concepts into the mathematics curriculum. Objectives of the program are to: (1) provide highly effective practice in…