Building Conceptual Bridges in Mathematics: A practice-based Study on Fractions in Grade 4

Fractions are often considered one of the most challenging mathematical concepts for students to grasp. While many pupils become familiar with fractions as parts of a whole, fewer develop the ability to see them as expressions of proportional relationships, since they are often taught separately. This study investigates how teaching focused on ratio as a shared characteristic between fractions and proportionality can support students in grade 4 in broadening their conceptual knowledge of fractions. The study was conducted through a teaching intervention based on structured and conceptual principles, inspired by the Learning Study method and Ma’s (1999) theory of Mathematical Pedagogical Content Knowledge (MPCK). A total of 27 students in grade 4 participated in the intervention, which included a pre-test, three math lessons, a post-test, and a follow-up focus group interview with five students. The data was analyzed using a model categorizing student responses into five components: equal partitioning, equivalence, ratio, multiplicative relationships, and proportionality. The results indicate that while most students initially demonstrated secure knowledge of fractions as parts of a whole (equal partitioning), many struggled with identifying fractions as expressions of constant ratios. After the intervention, a larger number of students were able to describe and apply proportional relationships using fractions in multiple representations, including verbal reasoning, tables, and symbolic form. Findings suggest that conceptual teaching that highlights the relationship between fractions and proportionality focusing on the numerator and denominator, and links this to real-life proportional contexts, can support students in developing an understanding of fractions as ratios. The greatest progression in the student’s results was within the areas of equivalence and ratios. The study contributes to the field by illustrating how teaching that emphasizes conceptual connections across mathematical domains can enhance student’s relational reasoning with rational numbers.