The aim of this paper is to identify errors and misconceptions that student demonstrated when learning linear independence and linear dependence concepts. A case study is presented involving 73 in-service mathematics teachers at a university in Zimbabwe who were studying for a Bachelor of Science Education Honors Degree in mathematics. Data was…

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises…

The aim of this study was to examine the proportional reasoning skills of seventh-grade students before and after the implementation of STEM activities involving proportional and non-proportional relationships. Case study, one of the qualitative study methods, was used in the research. The data for the study was obtained from eight students. Seven…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

This study enquires into the embodied processes of children in solving multiplication tasks, considering how such processes can expand access to spatial reasoning skills and simultaneously develop students' understanding of multiplication. The analysis focused on four Year 2 students as they completed two embodied tasks. The aim was to understand…

Several working memory processes have been hypothesized to influence different arithmetic operations. Working memory has been compartmentalized into a number of different sub-processes, such as phonological memory and visuospatial memory that are believed to have unique contributions to the performance of two distinct arithmetic operations:…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing…

Numeracy is one of the essential competencies that the objectives of teaching math to primary students should be towards. However, many research findings show that the problem of "innumeracy" frequently exists at primary schools. That means children still do not feel at home in the world of numbers and operations. Therefore, the paper…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

Preparing students to become self-regulated learners has become an important goal of primary education. Therefore, it is important to investigate how we can improve self-monitoring and self-regulation accuracy in primary school students. Focusing on mathematics problems, we investigated whether and how (1) high- and low-performing students…

In the context of a multiplicative problem, our study investigated young children's ability to visualise and draw equal groups. This paper reports the results obtained from 18 Australian children in their first year of school (age 5-6 years). The task "12 Little Ducks," taught by their classroom teacher, provoked children to visualise…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

CBM for mathematics assesses growth in accuracy and fluency of basic math skills using content from a student's curriculum. CBM for mathematics can include single-skill measures (SSM), skill-based measures (SBM), and general-outcome measures (GOM). Past research on growth rates in CBM for mathematics has focused on GOMs and has relied on…