The purpose of this study was to understand children's operations on fragmenting schemes while they are engaged with three different visual models, including circle, rectangle, and length model. This study was a sequential explanatory mixed method, which included two phases that happened sequentially with the dominant use of the quantitative…

The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

Much research has examined the reciprocal relations between a child's spontaneous focus on number (SFON) in the preschool years and later mathematical achievement. However, this literature relies on several different tasks to assess SFON with distinct task demands, making it unclear to what extent these tasks measure the same underlying construct.…

To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

The teacher's job is to prepare learning plans, create modules, implement, assess, and evaluate. The fact that teachers don't have modules yet. As a result, the mean logarithmic learning outcome of 74.80 is below the standard of 75. It is urgent to research because there is a gap between theory, expectations, and reality. The aim is to produce a…

In this commentary, I reflect from a neurocognitive perspective on the four chapters on natural number development included in this section. These chapters show that the development of seemingly basic number processing is much more complex than is often portrayed in neurocognitive research. The chapters collectively illustrate that children's…

This study aims to analyze the problem-posing skills of primary school mathematics teacher candidates with problem-posing experience and their views on problem posing. The case study, one of the qualitative studies, was used in the study. The study group is ten prospective elementary mathematics teachers who were selected using the purposive…

Research findings have established common student misconceptions for literal symbolic representations of variables but lack corresponding findings of when or how these misconceptions arise. This article reports findings from an exploratory study of U.S. grade 4-6 students' conception(s) for various representations of unknown addends commonly found…

Students' difficulties understanding the meaning of logarithms could stem in part from differences between teachers' and students' views of them. The purpose of this article is to unpack some specialized content knowledge for teaching logarithms. The author discusses the history of logarithms to show why they can be understood as repeated…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

In this work we will analyze the relation between registers of representation and the construction of the fraction concept. Ninety-six students from first year of compulsory secondary education participated in the study, and performed equal share tasks in the context of Egyptian fractions (unit fractions with different denominators). The aim was…

It has been stated that a criterion of a threshold concept is that it is troublesome or difficult to understand. However, not all difficult concepts are also threshold concepts. This article explores this difference through the context of students' difficulties in learning prosthetics and two models of describing threshold concepts. Students and…

This study explores the similarities and differences between English and Arabic numeral-based formulaic expressions, and difficulties that student-translators have with them. A corpus of English and Arabic numeral-based formulaic expressions containing zero, two, three, twenty, sixty, hundred, thousand…etc., and another corpus of specialized…

The study focuses on the effect of the lexical-syntactic structure on the patterns of errors by Arab first graders in tasks involving reading two-digit number and writing two-digit numbers to dictation. Children made few change or omission errors, indicating that they had little problem with the lexical aspects of the counting system. However,…

The use of different registers to represent mathematical concepts enhances understanding. For example, rational numbers can assume pictorial, symbolic and natural language representations and this kind of change improves learning. Based on these assumptions, a teaching experiment for the learning of rational numbers by 2nd grade students was…