This study investigated the role of tools in supporting students to reason about even and odd numbers. Participants included Kindergarten, Grade 1, and Grade 2 students (ages 5-8) at two schools in the USA. Students took part in a cross-sectional early algebra intervention in which they were asked to generalize, represent, justify, and reason with…

Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not…

This research aims to determine the metaphorical perceptions of gifted and normally developing students attending primary education regarding solving mathematical problems. In the research, the qualitative research method was employed. In the 2022-2023 academic year, 206 students studying at the primary school level in Turkey were determined…

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

Teaching with analogies is an important pedagogy that helps learners construct abstract conceptions through reasoning with something familiar. Heat concepts were chosen for this study because they have an intangible nature and involve complex mechanisms that often challenge school-aged learners. Learning this kind of complex concept with analogies…

The fact that the mathematics course is abstract, that it is not possible to associate it with daily life, and that it is impossible to concretize abstract expressions causes a prejudice against the this course and leads to a decrease in the academic achievements of students. It is seen that throughout history, various studies have been carried…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

One of the aspects of programming that novices often struggle with is the understanding of abstract concepts, such as variables, loops, expressions, and especially Boolean operations. This paper aims to explore the effects of programming tools with different degrees of embodiment on learning Boolean operations in elementary school. To this end, 67…

Around 6% of U.K. children are underachieving at school relative to their potential (URP). We explored whether difficulties with phonological decoding, short-term memory (STM), and complex grammar may be responsible. We compared school-based reading test data or formal SATs, and verbal reasoning in 2462 children (150 URP and 2312 non-URP children)…

This qualitative study focuses on Grade 6 students' possibilities to engage in disciplinary writing practices in history teaching in a school located in a socially disadvantaged and linguistically diverse area. The aim is to contribute knowledge about how students negotiate different literacy expectations in the teaching. The researcher used…

Historical reasoning, as a disciplinary literacy, aims to develop higher-order thinking in addition to depth of historical knowledge beyond the textbook and memorization of facts. It teaches students to use information across multiple sources to contextualize and corroborate historical accounts, constructing an informed yet critical interpretation…

For several decades, there has been a push to advance students' knowledge and abilities in science, technology, engineering, and mathematics (STEM). One capacity that has been linked positively to STEM achievement is relational reasoning, which involves identifying associations between objects, ideas, and situations. Yet, few studies have examined…

This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

The need for data literacy is an increasingly pressing priority in society, but most of the work in data-centred education has focused on developing skills at the middle school, secondary, and post-secondary levels, with little attention on the potential for engaging elementary-aged students in reasoning with and about data. This paper reports…

Hypothesis-based reasoning with conditionals is a skill that is required for engaging in integral activities of modern elementary school science-curricula. The teaching of this skill at this early stage of education, however, is demanding, particularly in whole school classes in which it is difficult to adapt teaching to children's individual…