The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

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…

This study takes a closer look at Form Four students' initial mathematical modelling process when solving mathematical problems using GeoGebra. The modelling process was observed from cognitive perspective to learn the difficulties students faced during the process and the result would give ideas for intervention. Qualitative approach by using…

While school performance suggests students with learning disabilities require intervention to demonstrate mathematics proficiency, little is known about how they approach problem solving in secondary geometry. Think aloud protocols highlight the higher order thinking skills underlying complex academic tasks. We conducted an exploratory descriptive…

Despite progress toward gender equity, troubling disparities in mathematical problem-solving performance and related outcomes persist. To investigate why, we build on recurrent findings in previous studies to introduce a new construct, "bold problem solving," which involves approaching mathematics problems in inventive ways. We introduce…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is "embodied" -- inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

One of the primary skills required by mathematics teachers is the ability to provide effective explanations to their students. Using Kay's (2014) theory-based framework for creating instructional videos, this study explored the quality and growth of explanations embedded in mathematical instructional videos created by 37 pre-service teachers…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide…