Research indicates that teachers may hold biases against multilingual learners (MLs). However, there is limited research regarding how teachers notice MLs' mathematical thinking. Given the complexity of teacher noticing and multilinguality, the lead researchers developed the Equitably Attending to and Interpreting a Student's Mathematical Thinking…

Fifth-grade students applied quantitative reasoning in exploring the flow times of three simulated lavas of different viscosities down the slope of a hand-made volcano. After modeling the lava flow times for 6 km down the volcano slope, students used their quantitative models to predict the evacuation times for villagers living 10 km down.…

Very young preverbal children (aged around 12 months) actively engage with their environment, whether at home, on outings, or in early learning centres. Their engagement with their environment can occur in many different ways involving physical and mental activities. In an early learning centre, there are many activities that very young preverbal…

This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world…

Research Findings: The present study analyzes whether child factors are linked to variations in teacher cognitive activation (CA) among individual children in math-related activities within Chinese kindergarten classrooms. The findings show that teachers tend to provide direct CA with high concreteness and that child engagement with tasks is…

Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school…

A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12…

Individuals' perceptions or beliefs about their mathematical aptitude are commonly classified as mathematics self-efficacy. Conversely, metacognitive awareness is characterized as a phenomenon that presents itself in a variety of ways as people engage with objects and circumstances in their everyday lives. The objective of this quantitative…

This article deals with giving a perspective of mathematics to students whose majors are not related to mathematics. A course named "Mathematical View" was specifically designed and implemented for this purpose. The course was given to students majoring in the Turkish Language and Literature Department at Duzce University who opted to…

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

Using an actor-oriented perspective on transfer, we report a case of a student's transfer of covariational reasoning across tasks involving different backgrounds and features. In this study, we investigated the research question: How might a student's covariational reasoning on Ferris wheel tasks, involving attributes of distance, width, and…

In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We used Epistemic Network Analysis to consider the teachers' knowledge organization and connections between knowledge resources as a way to make sense of his understanding. Then, we examined how his understanding was reflected…

Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students in a ten-session teaching experiment. The students successfully reinvented four basic counting…

Children (n = 747; 6.5 years) were assessed on domain-general processes and mathematics and reading-related competencies (start of first grade), addition retrieval (end of second grade), and calculations and word reading (end of third grade). Attentive behavior, reasoning, visuospatial memory, and rapid automatized naming (RAN) indirectly…