Quantitative Reasoning for Professionals is a two-semester general education sequence that teaches basic and intermediate algebra through the lens of quantitative reasoning. In this course sequence, we emphasize communication and inference-making while teaching practical algebra skills for students in programs such as business, nursing, and social…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

No matter what path students pursue in postsecondary education and in life, they need to be able to problem-solve and think critically. The study of mathematics teaches skills and habits of mind that are an essential part of the formula for students to succeed in further studies and in their careers. Requiring all students, regardless of the…

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

This study aims to investigate the similarities and differences between prospective mathematics teachers' creative thinking skills in paper-pencil test and on a GeoGebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried…

Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school…

Historically, math education at the high school and introductory college levels has focused on computational skills. With the advancement of computational technologies, problemsolving and other higher-order thinking skills should become the focal point. This article discusses ways in which the University of Minnesota has integrated problem-solving…

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students' higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a…

Solving mathematical (math) word problems (MWP) automatically is a challenging research problem in natural language processing, machine learning, and education (learning) technology domains, which has gained momentum in the recent years. Applications of solving varieties of MWPs can increase the efficacy of teaching-learning systems, such as…

This work seeks to understand the emergent nature of mathematical activity mediated by learners' engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of…

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of…

This empirical paper reports on the development of a professional development initiative, namely the word sum-wheel, which teachers developed collaboratively. The study's objective was to determine how teachers' mathematics word problem-solving instruction could be enhanced through the development of the word-sum wheel using participatory action…

This cohort-sequential study explored the working memory (WM) structures that underlie growth in mathematical word problem solving (WPS) performance in elementary school emergent bilingual children whose first language (L1) is Spanish. To this end, children (N = 429) in Grades 1, 2, and 3 in southwest U.S. school districts at Wave 1 were…