This study used the RBC+C model to reveal the abstractions of the 6th-grade students in the process of transition to the parallelogram area formula. Also, constructing parallelogram area information was employed as a teaching experiment based on the basic interpretive approach, one of the qualitative research methods. The study participants…

Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet…

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…

Judging the reasonableness of computational results is pivotal for students to understand mathematical concepts. This domain is the most sensitive to the presence of misconceptions in mathematics. Confidence ratings can serve as a measure of the strength of students' conceptual understanding. This study investigated the performance,…

This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…

This paper presents strategies identified in Mexican rural school students in seeking structure on equivalence tasks that involve the equal sign and tasks that do not. The results arise from the pilot study of a research project on the structure of numbers and numerical operations -- a key aspect of early algebraic thinking. [For the complete…

In this article, the authors present a brief description of the different views of the "nature of mathematics" (NOM), share a five-point view of NOM that undergirds the teaching profession's guiding documents, and describe ways of providing opportunities for teachers and students to have conversations in the classroom that build…

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…

This study highlights the importance of an educational design that includes robotics and programming through a visual programming language as a means to enable students to improve substantially their understanding of the elements of logic and mathematics. Gaining an understanding of computational concepts as well as a high degree of student…

State-mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519…

State mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519…

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…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes's method of exhaustion in order to compute the number p. Working in a computer environment, students inscribe and…