Researchers have repeatedly found schematic diagrams, both as part of Modified Schema Based Instruction and outside of this problem-solving approach, effective for teaching students with disabilities, including intellectual and developmental disabilities (IDD), to solve math word problems. The current study was a systematic replication of Bouck,…

The hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base-ten concepts. Kindergarten and first-grade students were assigned to three instructional conditions in which they worked with a…

Prior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students' mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom…

Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

Mathematical problem solving takes on many different forms and has long been established in school curricula with the terms, problems and problem solving taking on varied meanings. This article proposes a way of engaging students in mathematical open inquiry using a video clip as stimulus. It discusses findings from a recent study conducted in a…

Research has uncovered a semantic cue effect for short inconsistent word problems; the presence of functionally related objects makes them easier for pupils than the presence of categorically related ones. This study builds on this result by investigating other types of problems. Variants of problems differing in a semantic cue were solved by…

Teaching mathematics through problem solving is central to contemporary approaches to mathematics instruction, whilst augmenting problem-solving tasks through enabling and extending prompts ensures that a diverse community of learners are provided with opportunities to be optimally challenged, supporting an inclusive classroom environment.…

We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class…

Students' judgments about "what counts" as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as…

Students often experience difficulty with attaching meaning to mathematics symbols. Many students react to symbols, such as the equal sign, as a command to "do something" or "write an answer" without reflecting upon the proper relational meaning of the equal sign. One method for assessing equal-sign understanding is through…

In this article Debbie Verzosa and Joanne Mulligan suggest a new approach to addressing the difficulties that NESB students encounter when solving word problems.

The present research investigated whether an illustration and/or a warning could help students to (a) build a situational model of the problem situation and (b) solve problematic word problems (P-items) that require realistic thinking more realistically. In 2 similar studies conducted in Turkey and Belgium, the authors presented 10- to 11-year-old…

What is childhood like today? Is it a world fraught with endless joy, fun, and games, or are children experiencing a much different reality? A child's social interactions can be a source of great enjoyment and are essential to early development. Conversely, young children routinely experience tension, ambiguity, and conflict as they navigate the…