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…

Intelligent tutoring systems (ITSs) aim to deliver personalized learning support to each learner, aligning with the educational aspiration of many countries, including China. ITSs' personalized support is mainly achieved by providing individual prompts to learners when they encounter difficulties in problem-solving. The guiding principles and…

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…

Geometry education is an important aspect of STEM education and career development, but it is often overlooked in K-12 education in the United States. Although there is some research on teaching geometry to students with learning difficulties at the elementary level, there is a lack of research on teaching advanced geometry skills at high school…

Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

This manuscript proposes the use of the "I notice, I wonder" routine in college mathematics classrooms to address issues of diversity, equity, and inclusion. Examples are given of prompts that incorporate meaningful conversations about real-world issues affecting our students or about issues of inclusion, access, and representation in…

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…

Fifteen pre-service mathematics teachers studying in a teachers college participated in a unique program entitled "From high-tech to teaching" as part of a specialization program for teaching advanced secondary school mathematics. During the course, they solved various mathematical problems and then were asked to pose additional problems…

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.…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…