Multiplicative thinking is a critical stage of mathematical understanding upon which many mathematical ideas are built. The myriad aspects of multiplicative thinking and the connections between them need to be explicitly developed. One such connection is the relationship between place value partitioning and the distributive property of…

Early mathematics education bases a foundation of academic success in mathematics for higher grades. Studies show that introducing mathematical contents in preschool level is a strong predictor of success in mathematics for children during their progress in other school levels. Digital technologies can support children's learning mathematical…

This article aims to describe the mathematical identity of elementary school students during studying mathematics. When studying mathematics, the students often face difficulties in understanding the concepts which results the decrease in their learning motivation. It will lead to the lack of development of their mathematical identity. The…

Elementary school children (ages 7-11) struggle to understand mathematical equivalence, a foundational prealgebraic concept. Some manipulations to the learning environment, including well-structured nontraditional arithmetic practice alone, have been shown to improve children's understanding; however, improvements have been modest. The goal of…

The objective of this study is to produce a vignette in measuring mathematical knowledge for teaching based conceptual (MKT-C). The method of this research is a development research conducted by synthesizing the expert reviews on MKT-C in the knowledge domain of material content which was divided into sub domains: common content knowledge based…

The relevancy of linear algebra (LA) in different areas and also the difficulties faced by undergraduate engineering students studying this content are well known. Grounded on this premise, we aimed at articulating papers related to the teaching and learning of LA in engineering undergraduate programs through a mapping of the main investigations…

Background: The learning of rational numbers is a complex and difficult process that begins in the early grades. This teaching often focuses on the mastery of essential knowledge, including particular skills (e.g. using fractions to describe part--whole diagrams) and interpretations (e.g. sharing), which often results in an incomplete and…

Elementary pre-service teachers in an upper-division algebra mathematics content course explored graphing through the use of Calculator-Based Rangers™ (CBRs). This study explores how they used the "Distance Match" feature of the technology to engage in algebraic thinking. Operating CBR technology, pre-service teachers' perceptions…

Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from…

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…

Experts claim that individual differences in children's formal understanding of mathematical equivalence have consequences for mathematics achievement; however, evidence is lacking. A prospective, longitudinal study was conducted with a diverse sample of 112 children from a midsized city in the Midwestern United States (M[subscript age] [second…

This is a companion piece to "Professional Learning Community: Improving Mathematical Problem Solving for Students in Grades 4 through 8. Facilitator's Guide. REL 2019-002" (ED595201). It contains handouts to accompany each of the sessions included in the facilitator's guide.

A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…

Generative activities have been shown to support students to engage in space-creating play and exercise their conceptual agency to generate a mathematical space (e.g. Stroup et al. 2004), yet these studies implement generative activities only with their resonating counterpart, classroom networks, technological infrastructures that connect…

As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…