Modeling activities enriched with 3D printers are effective in providing teachers with the skills they should have and in using the technology in mathematics education. In this regard, in the present study, ten-week modeling activities were carried out with 3D printers that are widely used in different fields along with educational environments…

Studying worked examples has been found to be effective for learning problem solving, especially among students. However, students need to actively process example content to benefit from it and content must be structured in a manner that facilities knowledge construction. This study investigated the use of worked examples for teaching and…

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

The cognition processes of students with autism spectrum disorder (ASD) in solving mathematical problems is still rarely studied in depth, although the prevalence of the students is increasing. The purpose of this research was to describe the cognition processes of students with ASD in solving mathematical problems. The subjects in this research…

Typical physics textbook problems often include supportive diagrams that visualize the physical situation although the potential benefits of providing such diagrams is not yet fully established. We used eye tracking to explore the role of supportive diagrams in problem solving. Including a supportive diagram with the text of the problem improved…

Schematic chunks denote patterns, schemes, or sophisticated rules and knowledge stored in the long-term memory in the form of chunks. We investigated whether schematic chunking is effective in improving the performance of students with math difficulties (MD) and students at risk of math failure, and how the complexity level of geometry problems…

The author was an engineer for 20 years in both development and applications followed by 15 years as adult educator primarily at a Midwestern urban university with under-represented students. Beginning fall 2008 and for the next 7 years, he developed interventions for "underprepared" STEMM (STEM and pre-Medical) students. This freshmen…

The researchers conducted a qualitative case study to describe the experiences of two seventh grade students with mild intellectual disability as they engaged in mathematics word problems involving proportions. The researchers analyzed student performance in large group settings and with individualized instruction to gain perspective on the…

We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as…

This article introduces a center-based direct instruction lesson using picture-based situation cards paired with a problem-solving poster that teachers can implement within the classroom to proactively teach the skill of problem-solving to children between the ages of 3 and 5 years old.

In this exploratory case study, the researchers conducted a qualitative analysis of six teaching sessions to describe the use of gestures and diagrams by a teacher and her students with learning disabilities when engaging in secondary level algebra (e.g., Algebra I & II content). The teacher and her students used gestures, such as pointing and…

Mathematics is a subject that challenges many Brunei secondary school students. The Bar Method of instruction uses visual or pictorial representations to make mathematics easier to understand. The survey participants consisted of 127 randomly selected teachers (24 males and 103 females). Male teachers had significantly higher negative attitudes…

The purpose of this study was to analyze organic chemistry students' annotations of reaction coordinate diagrams to better understand how they sought connections between reactions and reaction coordinate diagrams. Thirty-six students enrolled in Organic Chemistry II participated in semistructured, think-aloud interviews that asked students to…

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the…