The purpose of this mixed methods study was to investigate the implementation of a researcher-created numberless word problem instructional unit designed to introduce second-grade students to word problems in the semantic category of "compare with the word more, smaller unknown." The 10-day instructional unit incorporated three elements:…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

This mixed methods study is aimed to examine the feasibility of integrating mathematical problem solving with architectural design via a 3D epistemic simulation game to promote active mathematics learning for middle-school students. The experimental-control pretest/posttest group design was adopted to examine whether the experience of interacting…

This research examined the effects of two instructional treatments on training performance in solid volume measurement and potential effects on solving capacity and displaced volume problems by two related studies. Fifty-three fifth-graders from a public elementary school in Taipei, Taiwan, participated. In the Phase 1 study, the children (n = 27)…

In this mixed-methods study, we examined if students benefitted from a game design course offered during an enrichment hour in terms of gains in their system analysis and design skills. Students at a rural middle school in Southeast US (n = 19) attended a 1-hour game design course offered weekly during an academic enrichment class period, for the…

Previous experiments have shown a deleterious effect of visual representations on college students' ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree…

Tabular presentations of student data often hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Kanim on "escalator diagrams," which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and postinstruction…

Despite the importance placed on how children come to solve single-digit addition problems, many children count on to solve these problems when they are expected to use accurate retrieval-based strategies. In this study, we assessed if a subitising intervention improved the rate at which problem-solving practice promoted retrieval, using a…

Novice learners are typically unfamiliar with abstract engineering symbols. They are also often unaccustomed to instructional materials consisting of a combination of text, diagrams, and equations. This raises the question of whether instruction on elementary electrical circuit analysis for novice learners should employ contextualized…

In this study we investigated how two different approaches to drawing free body diagrams influence the development of students' understanding of Newton's laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups…

This study examined the effectiveness of two methods of increasing student learning from posterior probability lessons: diagrams and questioning while reading. Undergraduate students (N = 245) read a lesson in one of three diagram conditions and one of three questioning-while-reading conditions (embedded questions, elaboration interrogations, and…

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

In many domains, problem solving involves the application of general domain principles to specific problem representations. In 3 classroom studies with an intelligent tutoring system, we examined the impact of (learner-generated) interactions and (tutor-provided) visual cues designed to facilitate rule-diagram mapping (where students connect…

This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…

This study investigated the role of strategy instruction on solution accuracy in children with and without serious math difficulties (MD) in problem solving. Children's posttest solution accuracy was compared on standardized and experimental measures as a function of strategy conditions. Strategy conditions included curriculum materials that…