Background: National and international assessments show South Africa's underperformance in mathematics. As many learners already fall behind in the early grades, where foundational number sense should be established, addressing the challenges of number sense in the Foundation Phase (FP) is important. Research recognises the need to better develop…

In the realm of mathematics education, geometry problems assume a pivotal role by fostering abstract thinking, establishing a connection between theory and practice, and offering a tangible portrayal of reality. This study focuses on comprehending problem-solving methodologies by observing the eye movements of 45 primary and multi-year grammar…

In this paper it is investigated if the mental computation strategies in the research literature are enough to satisfactorily categorize the mental computation strategy use by preservice elementary teachers (PETs) in subtraction on two-digit natural numbers. The PETs' use of mental computation strategies is measured operationally with a written…

Given the connection between problem-solving and computational thinking (CT), studying the connections between these two constructs is critical. This study focused on students' computational problem-solving strategies, specifically how they applied conditional logic to solve CT-related puzzles within a game-based learning environment called…

Background: There is a concern in South Africa that pre-service teachers do not have the required knowledge to teach mathematics in primary school and to develop learners' number sense. In this study, pre-service teachers taught the mental strategy of bridging through ten through a structured teaching sequence from the Mental Starters Assessment…

The purpose of this quantitative, quasi-experimental nonequivalent control group study was to determine if there is a difference in mathematical fact fluency among third-, fourth-, and fifth-grade students with varying practice methods and spacing intervals while controlling for pre-test scores. The study filled the literature gap by examining the…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

This longitudinal study was conducted in order to determine and improve the mental addition strategies of students in their 2nd and 3rd years at elementary school. The first part of the study used the qualitative research method of case study, while the second part adopted the single group pretest-posttest quasi-experimental design. The study…

As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

Strategies are an important component of self-regulated learning frameworks. However, the characterization of strategies in these frameworks is often incomplete: (1) they lack an operational definition of strategies; (2) there is limited understanding of how students develop and apply strategies; and (3) there is a dearth of systematic and…

We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…

In this study, we explore the application of process mining techniques on assessment log data to explore problem-solving strategies in Algebra. By analyzing sequences of student activities, we demonstrate the significant potential of process mining in identifying problem-solving strategies that lead to successful and unsuccessful outcomes. Our…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…