This study was carried out to examine proportional reasoning problem solving processes of seventh grade students. This study was conducted with the explanatory sequential mixed method design. In this respect, firstly, quantitative data from 56 students were collected and analyzed. Then, qualitative data of the study was collected from six students…

Backward transfer is when learning about a new topic influences an individual's prior ways of reasoning about a topic they previously learned about. This study looked at how quadratic functions instruction differentially influenced students' prior ways of reasoning about linear functions. Specifically, we compared students at three levels of…

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility…

How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the…

The aim of this research was to study and investigate first year university calculus students' misconceptions about how to use the definition of limit to find the first derivative of functions and then remediate these misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female and male) were selected based on…

Mathematics scores on the 2019 National Assessment of Education Progress increased by only two points for both fourth and eighth grade students since 2007, indicating that students continue to struggle in mathematics (National Center for Educational Statistics, 2007; U.S. Department of Education, 2019). The development of both conceptual and…

Students with a learning disability (LD) are experts in their lived experiences within the classroom. Yet, little is known about the ways in which students with LD perceive their instruction in mathematics and whether this instruction meets their learning needs. Similarly, the mathematical thinking and content knowledge of students with LD is…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Geometric proof-writing is a widely known cause of stress for secondary school students and teachers alike. As the textbook is the primary curricular tool utilized by novice teachers, a two-part qualitative study was conducted to determine (a) the types of proofs presented in a typical high school geometry textbook and (b) teachers' preparedness…

Build collective teacher efficacy and students' mathematical thinking using the Mathematics in a PLC at Work™ lesson-design process. This second edition of the popular "Mathematics Instruction and Tasks" book guides preK-12 teacher teams in ensuring improved mathematics achievement. Gain new and enhanced understanding of…

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research…

The virtual-representational-abstract (VRA) instructional sequence presents as a viable mathematics intervention for students with disabilities, including students with autism spectrum disorder (ASD). Yet, to date, all research has been conducted face-to-face with students. However, virtual manipulatives provide an opportunity for educators to…

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners' progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

This paper reports on data obtained during semi-structured interviews with students who had recently experienced a guided inquiry approach to learning ordinary differential equations (ODEs) in a service-taught module. Previous research identified the strengths and weaknesses of similar cohorts of students. The results from that research informed…