Mathematical problem-posing and modeling are essential skills in developing students' analytical thinking and problem-solving abilities. This study aims to examine correlation between 9th-grade students' problem-posing and mathematical modeling skills within the learning domain of numbers and algebra. Additionally, it evaluates students'…

Background/purpose: Although mathematical representation ability is a significant ability and an interesting topic to study, quite a few researchers have studied this ability, and even fewer have examined it through the implementation of epistemic learning patterns based on problem-solving. In fact, this learning pattern is epistemic and makes…

In this study, we examined students' mathematical understanding and retention in a problem-based learning (PBL) classroom. The participants were 48 Grade 10 students, and the data were collected in December of 2016. After the end of the PBL lessons, the Mathematical Understanding of Function Test (MUFT) and the Retention Test (RT) were…

Launching a problem is critical in a problem-based lesson. We investigated teachers' perspectives on the use of a problem that was analogous to the one provided during a launch. Our goal was to identify teachers' underlying assumptions regarding what should constitute a launch as elements of the "practical rationality of mathematics…

It is a modern trend today when formulating the curriculum of a geometric course at the technical universities to start from a real-life problem originated in technical praxis and subsequently to define which geometric theories and which skills are necessary for its solving. Nowadays, interactive and dynamic geometry software plays a more and more…

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

This mixed methods study examines whether engaging in a problem-solving project to create Math-eos (digital videos) increases pre-service teachers' understanding of the relationship between visual, auditory, and verbal representation and critical thinking in mathematics. Additionally, the study looks at what aspects of a digital problem solving…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

The 2012 U.S. presidential election is the perfect opportunity to present a timely civics lesson on how a U.S. president is elected. More important, it offers opportunities for students to reason mathematically about election issues--for example, about how much time and resources the candidates should invest in particular states. The results of…

This study investigated the students' learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was…

Professional teachers can guarantee the progress and the promotion of society because fostering the development of next generation is up to them and depends on their professional knowledge which has two kinds of sources: content knowledge and teaching skill. The aim of the present research was studying the effect of integrating problem-based…

Written collaboratively by two former teaching partners, this paper details the journey taken by a team of teachers from a large southern Ontario school board as they completed an action research project during the 2008-2009 school year, in conjunction with ETFO and their Teachers Learning Together: A Math Journey initiative. This paper will…

This paper introduces an applied problem-solving task, set in the context of cryptography and embedded in a network of computer-based tools. This designed learning environment engaged students in a series of collaborative problem-solving activities intended to introduce the topic of functions through a set of linked representations. In a…

This study developed a computer-assisted mathematical problem-solving system in the form of a network instruction website to help low-achieving second- and third-graders in mathematics with word-based addition and subtraction questions in Taiwan. According to Polya's problem-solving model, the system is designed to guide these low-achievers…