Learning transfer has been studied for over a century, though studies are primarily through the lens of the researcher or an expert. The purpose of this project was to better understand the student perspective in transfer by examining how they approached transfer tasks and how these approaches related to classroom instruction. The Actor-Oriented…

The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

Teachers and caregivers use children's books (i.e., trade books) to support mathematics learning in school and home settings; shared book reading offers a unique opportunity to support students' understanding of operations and schema development. No prior studies have examined the representations of addition, subtraction, multiplication, and…

The concept of fractions given in learning is the concept of part of whole and part of unit. The development of student's concepts of fractions can be built through fraction schemes. A partitive fraction scheme is a scheme that estimates the size of the fraction in the form of non-units to the whole that is not partitioned. The concept of…

Numerous studies have shown a significant positive relationship between the mental representation of hands in young children and their calculation performance. The literature indicates that certain components of manual motor skills may be critical to the quality of this relationship. The main objective of this study is to measure the benefit of an…

Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…

This study assessed the effectiveness of modified schema-based instruction (MSBI) in teaching students with autism spectrum disorder (ASD) how to solve additive compare word problems. The study was conducted in Spain, and it involved three students with ASD who were 6, 7, and 9 years of age. A single-case, multiple-baseline across-students design…

Children and young people live in a world that is constantly changing. In order to master their lives successfully, they will need many skills and competences. These include mathematical competences, which they should build up from primary school age. This article deals with the question of how mathematics lessons should be designed in order to…

It is important for teachers and researchers to have access to evidence-based practices that target teaching specific content area skills, such as mathematics, to students with ASD (Hume et al., 2021). Previous literature reviews targeting mathematics interventions for students with ASD (Barnett & Cleary, 2016; Gevarter et al., 2016; King et…

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

This study analyses the view of students' mental models in solving mathematical problems. The study employed a literature review using well-accepted and robust guidelines. Data were collected by searching books and articles of journals. Data analysis techniques were done qualitatively. The finding of this study showed that the mental model is…

Background: Many studies have shown that ambitious, "student centered" approaches to STEM instruction benefit K-12 student learning. However, relatively little research has systematically investigated the learning processes that support teachers to skillfully enact these challenging pedagogies. In this study, we used a mixed-methods,…