Reading mathematics problems can frustrate students to the point of shutting down. Although Pólya's four-step plan is a well-known problem-solving framework, the author's students benefited from a more concrete and detailed approach: chunking the reading. In this article, the author describes an approach to problem solving used with eighth-grade…

The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17-18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems…

The looking-back stage is rarely observed in students' problem solving in spite of its recognized importance. The importance of this stage is attributed to practices of engagement with queries on verification of the obtained solution(s), comparative consideration of alternative solutions, and formulation of implications for future problem solving.…

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with…

Proportional reasoning and knowledge of fractions are critical skills for completing algebra successfully, yet many students with mathematics learning disabilities (MLD) enter algebra classes without adequate prior knowledge of these skills. This study used a single-subject/case research, combined multiple-baseline and alternating-treatment design…

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (n = 76) were randomly assigned to word-problem intervention (n = 56)…

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

Background: Developing self-directed learning (SDL) skills in engineering students is critical to support life-long learning. This research was conducted at Iron Range Engineering (IRE), an innovative, problem-based learning (PBL) engineering program, which has suffused the concept of metacognition throughout its curriculum. Purpose/Hypotheses:…

This case study presents a problem-based learning (PBL) model that guides general education history students to practice and acquire more advanced problem-solving skills -- those found in postformal thinking systems -- and to apply these thinking skills to develop and share solution alternatives both to periodized historical issues and to current…

Solving arithmetic word problems has been a challenge for primary students due to difficulties in understanding the problem structure and relating the quantities in the problem to each other. This paper reports on an action research study to enhance students' subtraction word problem-solving skills. The authors observed that their students had…

This explanatory sequential mixed methods study, which consisted of QUAN [right arrow] to qual investigated the impact of mathematics word problems among African American students in the seventh grade. This study applied a culturally relevant education (CRE) lens to examine how students solve mathematics word problems. Ladson-Billings (1997) and…

Universal Design (UD) involves the creation of accessible, flexible products that are functional for a wide population of users. Our problem-based learning exercise challenges student teams to create products and services guided by the principles of UD. After teams generate their new product concept, a spokesperson from each team pitches it in…

In the years 2005 to 2019, the number of American women receiving a degree in engineering was below 20 percent. Furthermore, even after receiving a degree in engineering, 40% of those girls do not enter the profession. While the above graduation data is essential for understanding the problem at the end of the educational journey, it doesn't point…

Background: A defining characteristic of expertise is the use of intuition to navigate tasks. The construct of intuition and its importance is well-studied in other disciplines, but little is known about how it translates to engineering. Existing literature on intuition does not clearly define the construct and its relationship to problem solving,…

Collaborative problem solving (CPS) enables student groups to complete learning tasks, construct knowledge, and solve problems. Previous research has argued the importance of examining the complexity of CPS, including its multimodality, dynamics, and synergy from the complex adaptive systems perspective. However, there is limited empirical…