Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

Recent multiplication with regrouping research shows that the combination of the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) has been effective in several studies. More evidence is needed to demonstrate CRA-SIM's effectiveness across settings and students. Therefore, the purpose of this study was to…

Division by zero is often unclear and confusing, and teachers at various grade levels may encounter difficulties in conveying this concept to their students. The concept of dividing by zero plays a crucial role in developing an understanding of certain mathematical concepts, such as rational numbers and the relationship between multiplication and…

This study investigated whether strategy accuracy and flexibility on various types of complex multiplication problems could predict college GPA concurrently and longitudinally in 164 college engineering students. Additionally, it sought to answer whether low- and high-achieving students would show unique patterns of strategy flexibility, accuracy,…

The purpose of this study was to examine four pre-service middle and high school mathematics teachers' understanding of the directly and inversely proportional relationships presented through hands-on and real-world missing-value word problems. The problems included single and multiple proportions, and the PSTs were provided with plastic gears and…

Instruction of multiplication facts has been and continues to be an essential part of mathematics curriculum for students in the intermediate grades with the majority of initial instruction at third grade. Teachers often comment that this is a topic that students struggle to master and that they frequently use fluency drills and fact flash cards…

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the…

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to…

Reports show that only 40% of 4th-grade students are proficient in math and American students are failing to demonstrate proficiency in key areas of mathematics (National Center for Educational Statistics 2011). Improving students' fluency of basic math multiplication facts has been recommended as a way to increase math proficiency…

This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…

Mathematical argumentation and proof has long been identified with algebraization. Much literature discusses the relationship between the two, but with little specificity on how particular semiotic features in argumentation relate to coordination in early algebra. Further, there is a particular lack of research on this topic in the…

A multiple-baseline across participants design was used to investigate the effect of the Cover-Copy-Compare (CCC) intervention on multiplication-fact fluency for students with emotional and behavioral disorders (EBD). Although CCC is a well-researched intervention for mathematics, limited research has been conducted with students with EBD even…

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that…