This study aims to investigate students' computational thinking (CT) through mathematical tasks integrated with programming in Scratch. Participants completed four tasks that required students to solve coding problems, which were focused on prime numbers and the prime factorization algorithm. The study was designed as a case study and the unit of…

A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…

This article explores three attributes of teachers' understanding of fraction magnitude: the accuracy and reasonableness of teachers' estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of…

According to NCTM's "Principles and Standards for School Mathematics" (2000), the act of estimating is reflective of students' mathematical intuition and number sense. Students with more developed number sense are better able to judge the reasonableness of their results. To promote estimation, Jennifer Marshall explored incorporating…

This paper introduces a percentage activity based on the context of "Black Friday" discounts. The aim of the study was to reveal the existing and new conceptions of the 7th grade students regarding the topic of percentage calculation. The activity was designed considering the students' prior knowledge in the concept of "Ratio and…

Teachers do not directly implement new teaching materials, but rather adapt them. For changing teaching practice, research requires more insights into these adaptions. This study draws on the Theory of Instrumental Genesis to describe the ways teachers adopt the percentage bar model to create different learning opportunities. The results of the…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

With the understanding of importance of pedagogical content knowledge, professional noticing has become one of the research subjects of the mathematics educators for the last 10 years. This qualitative study which explores secondary school students' solution processes regarding the concept of equation ,one of the main components of algebraic…

This study revealed how students' understanding of negative numbers and identified their difficulties related with the concept of integer and its counting operation as part of identifying epistemological obstacles about negative numbers. Even though teachers have explained counting operation procedure of integer, but there was concept…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

In Maori medium schools, research that investigates children's mathematical computation with number and connections they might make to mathematical ideas in other strands is limited. This paper seeks to share ideas elicited in a task-based observation and interview with one child about the number ideas she utilises to solve a problem requiring…

While previous work in the domain of proportional reasoning has primarily focused on the coordination of integer quantities, this study investigates how students coordinate fractional quantities. Fine-grained analysis of two seventh graders' responses to a set of systematically designed proportional tasks, shows how their knowledge of…

In the authors' examination of various instructional programs, they observed that most provide all the necessary data to solve proportion problems, employ compatible numbers that are usually unrealistic, present numbers (data) in the order in which they are to be manipulated, discuss contexts that cannot be easily replicated, and present…

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…