Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

Using data from a problem-posing project, this study analyzed the characteristics of middle school students' responses to problem-posing prompts that did not match our assumptions and expectations to better understand student thinking. The study found that the characteristics of middle school students' unexpected responses were distributed across…

Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

Background/purpose. The strategic goal of science, technology, engineering, and mathematics (STEM) literacy is to develop scientifically and technologically equipped global citizens who are innovators and problem-solvers in a rapidly changing world. The study contributes to this goal by drawing pedagogical implications from examining college…

In this paper, we initially investigate the capabilities of GPT-3 5 and GPT-4 in solving college-level calculus problems, an essential segment of mathematics that remains under-explored so far. Although improving upon earlier versions, GPT-4 attains approximately 65% accuracy for standard problems and decreases to 20% for competition-like…

Background/purpose. Self-efficacy plays a crucial role in enhancing performance in complex tasks such as mathematical modeling, yet its impact remains underexplored. This study examines whether there are influences on students' self-efficacy in modeling. Materials/methods. The research method employs a quantitative design, utilizing regression…

Existing research has revealed key factors influencing mathematical flexibility, defined as the capacity to understand, generate, and apply a variety of strategies in solving mathematical problems. However, there is currently a lack of an integrated theoretical framework to systematically consolidate various sources of individual differences in…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

Mathematical self-efficacy refers to an individual's belief in their ability to successfully perform tasks and solve problems in mathematics. This Snapshot examines gender differences in mathematical self-efficacy and the levels of confidence that students feel in doing a range of formal and applied mathematics tasks. It also examines the extent…

This study explores the effectiveness of different problem-posing approaches in improving learning outcomes and problem-posing abilities among prospective mathematics teachers. This study employed a pre- and post-tests control group experimental design. The experimental group engaged in online and direct problem-posing, the comparison group used…

The importance of mathematical problem solving (MPS) has been widely recognized. While there has been significant progress in developing and studying interventions to support teaching and learning MPS for students with disabilities, the research on how to accurately and effectively assess the impact of those interventions has lagged, leaving a gap…

The aim of this systematic review and meta-analysis was to identify and evaluate the effects of individual characteristics associated with mathematical word problem-solving skills among elementary school-aged children and to unpack the quality of studies investigating these associations. The systematic review was reported according to the…

This qualitative review aims to describe the current status of problem-based learning (PBL) implementation in mathematics and identify research gaps in the area of investigation. Literature was searched using the ERIC and Google Scholar search engines. The inclusion/exclusion criteria included: articles published in reputable journals in English…

In this study, we explored elementary school teachers' experiences working on open-ended mathematics tasks during a 10-day professional development (PD) workshop. Teachers engaged with the tasks daily in a session call Morning Math (MM). Thirty-two elementary teachers from three school districts in the USA participated in a 2-year professional…

Computational thinking is an essential ability for students in the 21st century. Therefore, this study described students' mathematical computational thinking process in terms of self-efficacy of eighth graders, consisting of 32 students. The applied instruments were self-efficacy questionnaires, computational thinking ability tests, and interview…