This study reflects on the importance of problem solving and the need to be aware of different methods and strategies to respond to the challenges posed by current mathematics education. The experience was carried out on the island of Tenerife and aimed to assess the training of primary education teachers in problem solving strategies. For this…

Recent reform efforts state the importance of providing students with opportunities to persevere with challenging mathematics to make meaning. We posit translanguaging practice as a vital option by which Latinx bilingual students can sustain collective perseverance during problem solving. In this paper, we employ a constant-comparative overlay…

Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

Teaching mathematics to students at the elementary level needs logical thinking, the students have to be encouraged to study hard to improve solving skills. The objective of this study is to improve the learner's problem solving skill in mathematics 2. This research aims to find out how the implementation of the visualize, represent and solve…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

Perseverance is vital for the process of learning mathematics with understanding. To do so, students must wrestle with obstacles and amend their problem-solving plan when necessary. I collected qualitative data to investigate the nature of perseverance for 11 ninth-grade algebra students working on a challenging task for which they affirmed…

The mathematical domain of fraction division continues to be an area of great difficulty for many teachers and preservice teachers (Lo and Luo, Journal for Mathematics Teacher Education 15:481-500, 2012; Newton, American Educational Research Journal 45:1080-1110, 2008; Rizvi and Lawson, International Education Journal 8(2):377-392, 2007; Young and…

The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

The empirical law of large numbers is an important content in secondary school mathematics. Tasks used to analyze students' understanding of this law are often based on the hospital problem, but vary in various features, leading to mixed and conflicting empirical results. To identify task features that support students when approaching this type…

We recognise that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term…

A core aim of contemporary science, technology, engineering, and mathematics (STEM) education is the development of robust problem-solving skills. This can be achieved by fostering both discipline knowledge expertise and general cognitive abilities associated with problem solving. One of the most important cognitive abilities in STEM education is…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

How students' rigid perceptions of mathematics persist over years has been a conundrum. Students not only think that only one solution exists for a mathematical task (Schoenfeld 1985) but also rigidly fuse mathematical concepts with specific tasks. Students deserve to learn a variety of mathematical strategies to flexibly deploy at will. Teaching…