In the realm of mathematics education, geometry problems assume a pivotal role by fostering abstract thinking, establishing a connection between theory and practice, and offering a tangible portrayal of reality. This study focuses on comprehending problem-solving methodologies by observing the eye movements of 45 primary and multi-year grammar…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

This systematic literature review investigates the effectiveness of the think aloud pair problem-solving (TAPPS) and storyboarding strategies in enhancing students' abilities to solve algebra word problems. Notably, algebra word problems pose a significant challenge to students due to their inherent complexity, requiring strong cognitive,…

Multiple representations are widely recognized for their significant role in concept learning. This study aimed to investigate the multiple representation translation skills of high school students at different grade levels about the concept of one-dimensional motion. 239 9th, 10th, and 11th-grade students participated in the study using a…

In the era of 21st century learning, many secondary students with learning disabilities continue to struggle with mathematics problem solving. Emerging evidence suggests self-regulated strategy development can be combined with existing evidence-based and promising practices during mathematics instruction. These practices include explicit…

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…

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…

The Common Core State Standards in Mathematics outline both the content and practices students must engage in at each grade level to become mathematically proficient. Mathematical processes include problem solving, reasoning and proof, communication, and procedural fluency, which includes flexible thinking. The purpose of this study was to…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

Educators aim to equip students with learning strategies they can apply when approaching new problems on their own. Teaching design-thinking strategies may support this goal. A first test would show that the strategies are good for learning and that students spontaneously transfer them beyond classroom instruction. To examine this, we introduce…

This article describes how to teach fraction and percentage word problems using a model-drawing strategy. This cognitive strategy places emphasis on explicitly teaching students how to draw a schematic diagram to represent the qualitative relations described in the problem, and how to formulate the solution based on the schematic diagram. The…

A visual representation, such as a diagram, can be a powerful strategy for solving mathematical word problems. However, using a representation to solve mathematical word problems is not as simple as it seems! Many students with learning disabilities struggle to use a diagram effectively and efficiently. This article provides a framework for…

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

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…