Instructional Features that Promote Mathematical Reasoning, Flexibility, and Transfer

Instruction is a central lever for promoting student learning in mathematics. Broadly construed, instruction encompasses teachers’ pedagogical moves (e.g., questioning, feedback), the selection and sequencing of curricular content, task design, and the use of materials that support mathematical activity. Different instructional features influence learning in different ways, such as by enhancing relational reasoning (Richland et al., 2012), deepening structural knowledge (Mulligan et al., 2020), and promoting flexible transfer and the generalization of knowledge (Goldstone & Day, 2012). Despite existing research in the teaching and learning of mathematics, there is a need for further study into the ways that instruction shapes children’s learning beyond performance accuracy and retention. Investigations into how instruction can support different forms of mathematical reasoning can extend theoretical perspectives in educational psychology and yield actionable implications for classroom practice.

Goldstone, R. L., & Day, S. B. (2012). Introduction to “New conceptualizations of transfer of learning.” Educational Psychologist, 47(3), 149-152. https://doi.org/10.1080/00461520.2012.695710

Mulligan, J. T., Woolcott, G., Mitchelmore, M., Busatto, S., Lai, J., & Davis, B. (2020). Evaluating the impact of a Spatial Reasoning Mathematics Program (SRMP) intervention in the primary school. Mathematics Education Research Journal, 32, 285-305. https://doi.org/10.1007/s13394-020-00324-z

Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189-203. http://dx.doi.org/10.1080/00461520.2012.667065

The aim of this Research Topic is to expand current understanding of how specific instructional features shape students’ mathematical thinking. Although reasoning, transfer, and generalization have long been recognized as central to mathematics learning and achievement, current research provides limited insight into which instructional factors promote these outcomes and how they support students’ developing mathematical cognition. The question of how instructional decisions influence deeper and more durable forms of mathematical understanding remains largely unanswered.

The collection of articles in this Research Topic will address this gap by bringing together research that rigorously examines the mechanisms through which specific instructional features, such as pedagogical moves, task structures, sequencing decisions, and representational supports can foster students’ conceptual knowledge and flexible reasoning strategies. By foregrounding the connections between instruction and student thinking, the collection will contribute to current theoretical perspectives on mathematics teaching and learning and will also move the field toward pedagogically relevant guidance for educators. Insights from these studies have the potential to inform classroom practice by clarifying the instructional affordances of particular strategies, materials, and curricular designs, thereby supporting teachers in intentionally adapting instruction to achieve targeted mathematical outcomes.

We welcome original research and review articles investigating how specific instructional features shape children’s mathematical development and learning. This Research Topic focuses on mathematics learning among children from preschool through Grade 8. Studies involving diverse populations—including typically developing learners, students with mathematics difficulties, multilingual learners, and those from varied educational contexts—are encouraged. We are especially interested in work that identifies the mechanisms through which instructional features influence forms of mathematical reasoning. Both quantitative and mixed methodologies are welcome.

Areas of interest include, but are not limited to:

Instructional factors:

• External knowledge representations

• Mathematical vocabulary

• Textbook design, content, and sequencing

• Characteristics of word problems

• Types of feedback

• Task design and cognitive demand

• Instructional analogies

• Use of manipulatives and digital tools

• Cognitive alignment

• Scaffolding and cognitive supports


Mathematical outcomes:

• Problem solving

• Analogical and relational reasoning

• Structural knowledge

• Spatial reasoning

• Conceptual understanding

• Fluency and flexibility

• Transfer and generalization of learning