This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Background/purpose: This study aimed to develop and validate a causal model of factors influencing the mathematical reasoning ability of Grade 6 students in Thailand. Materials/methods: The sample consisted of 530 students selected through multi-stage random sampling. Research instruments included a basic mathematics knowledge test, a mathematical…

This dissertation study investigated secondary mathematics teachers' designing and enacting lessons to draw on students' multiple mathematical knowledge bases. The ultimate objective of incorporating open spaces in mathematics lessons is to support students from culturally and linguistically diverse backgrounds in developing mathematical…

Effective personalization of education requires knowing how each student will perform under certain conditions, given their specific characteristics. Thus, the demand for interpretable and precise estimation of heterogeneous treatment effects is ever-present. This paper outlines a new approach to this problem based on the Leave-One-Out Potential…

Prior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students' mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom…

The COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

Background: Although research on mathematics learning programs has taken off in recent years, little is known about how different person characteristics are related to practice behaviour with such programs. When implementing a mathematics learning program in the classroom, it might be important to know whether students with specific…

Effective personalization of education requires knowing how each student will perform under certain conditions, given their specific characteristics. Thus, the demand for interpretable and precise estimation of heterogeneous treatment effects is ever-present. This paper outlines a new approach to this problem based on the Leave-One-Out Potential…

A multiple regression analysis was conducted to investigate what variables may predict the student's self-perceived proficiency in mathematics. Hence, this quantitative cross-sectional survey design aimed to explore the factors predicting the student's self-perceived proficiency in mathematics using gamified instruction. Two hundred twenty-five…

This paper introduces a system that supports student-centered online one-to-one tutoring and evaluates the practical value of the system by running an experiment with 64 experienced mathematics teachers and 810 students in Grade 7. The experiment lasted for 50 days. A comprehensive evaluation was performed using students' academic performance…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

This research aims to explore the secondary school sixth and seventh graders' length measuring estimation skills developing activities related to the daily life objects. The study is in a qualitative multiple case study model. The universe of the research consisted of the sixth and seventh graders. The sample of the research consisted of 85…