The outdoors can offer children a rich space for learning and inspires authentic mathematical opportunities. The author describes the experiences her kindergarten students have when when they spend many hours each day, exploring their vast play yard and engaging in play-based activities typically done inside a classroom. She also chronicles the…

Research has demonstrated that providing labels helps children notice key features of examples. Much less is known about how different labels impact children's ability to make inferences about the structure underlying mathematical notation. We tested the impact of labeling decimals such as 0.34 using formal place-value labels ("3 tenths and 4…

Background: A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. Aims: This study aimed to examine both mother-child and…

Desmos Battleship is an engaging activity in which students can improve their visualisation skills, and deepen their understanding of linear functions and circles by making connections between algebraic and graphical representations. The Desmos Battleship activity was used in a Saturday STEM (Science, Technology, Engineering, and Mathematics)…

Snowflakes falling in Brisbane, Australia would likely make news headlines during any season of a given year, even during winter. Year 8 students at Ormiston College which is located in Brisbane, have made their own snowflakes--of a kind. Using the programming language Scratch, all Year 8 Mathematics students wrote code to construct Swedish…

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

Conversation Analysis uncovers features of talk-in-interaction during "real life" conversations. When these phenomena are repeatedly observed in the data, conclusions can be drawn regarding the function of the phenomena as elements of talk. In this project, we drew on a corpus of video-recordings collected in five different early…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

In this qualitative research, we studied difficulties that undergraduate students face while learning the concept of inner product space. Participants were 35 first-year mathematics students from Yildiz Technical University in the 2011 and 2012 academic years. We asked participants to solve 5 inner product space questions. Data were jointly…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

This research examined the effects of two instructional treatments on training performance in solid volume measurement and potential effects on solving capacity and displaced volume problems by two related studies. Fifty-three fifth-graders from a public elementary school in Taipei, Taiwan, participated. In the Phase 1 study, the children (n = 27)…

Students' self-assessment of language features in their oral explanations of a mathematics task was supported by language learning progressions. Learning progressions map a continuum of knowledge or skills development as they increase in sophistication over time. Learning progressions can be a framework to support formative assessment by both…