Year: 2017

Author: Haryanto, Bakir, Vosniadou, Stella, Darfiana, Nur

Type of paper: Abstract refereed

The purpose of this research is to measure students' levels of fraction learning progression from a cognitive interview. The proposed model hypothesizes five levels of fraction learning progressions, which are structured into two dimensions of knowledge: conceptual and procedural knowledge. These five levels (from lowest to highest) are: 1) no understanding of fractions; 2) part-whole; 3) improper fractions and fractions as measure; 4) unbounded infinity; and 5) density. Fifteen Junior High School Students participated in the cognitive interview. The tasks were given adaptively to each participant. For the first task, all participants received the same item, but for the next task, the participants received different tasks depending on their answer in the first task. If their answer was correct they received a higher level of task derived from the hypothetical model. If their answer was not correct, then they received another question from the other competencies within the same level or below. The interview for each participant terminated after 30 minutes, or when there was evidence to confirm the levels of the proposed model.
In order to measure the level of students' fraction learning progression, we hypothesized that the process of the cognitive interview discussed above can be considered as a process of updating the belief (probability) regarding the students' level in the proposed model. The belief about the students' level is updated when there is a new information from the student answers. Based on the above, we used a Bayesian approach to model the conditional probability of students' responses. This conditional probability is constructed to update the belief about the level of students' learning progression. This study limits the discussion about measuring the level of students' learning progression within the dimension of conceptual or procedural knowledge. A further study is required to estimate students' level of learning progression based on the joint of the two-dimensional knowledge.