Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students' visual attention to the teacher's gestural cues during collaborative problem solving remains a largely unexplored field in mathematics…

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,…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

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…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

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…

The present study attempted to replicate the previous results of Hu et al. (Learning and Instruction 35:85-93 2015) and further examined the boundary condition of tracing gesture whether its cognitive effect is merely comparable with other attention-guiding means, i.e., textual attention cueing, in two different learning tasks in nature. In two…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

Engineering design was integrated into K-12 science education in the "Next Generation Science Standards" (NGSS Lead States, 2013), but teaching design remains a challenge for educators. Design problems are ill-defined, ill-structured, and complex problem-solving tasks. Their solutions require creativity and recursive, metacognitive…

The effect of metacognitive scaffolding for learning by teaching was investigated and compared against learning by being tutored. Three versions of an online learning environment for learning algebra equations were created: (1) APLUS that allows students to interactively teach a synthetic peer with a goal to have the synthetic peer pass the quiz…

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…

This study investigated how question prompts and feedback influenced knowledge acquisition and cognitive load when learning Newtonian mechanics within a web-based multimedia module. Participants were one hundred eighteen 9th grade students who were randomly assigned to one of four experimental conditions, forming a 2 x 2 factorial design with the…

Solving mathematics story problems requires text comprehension skills. However, previous studies have found few connections between traditional measures of text readability and performance on story problems. We hypothesized that recently developed measures of readability and topic incidence measured by text-mining tools may illuminate associations…

Children with HFA/AS are outperformed by their neuro-typical peers on mathematical problem solving skills even though they have average-to-above-average intelligence (Dickerson Mayes & Calhoun, 2003b); have average-to-above-average computation skills (Chiang & Lin, 2007); and, are educated in the general education setting (Twenty Eighth…