Jurnal Pendidikan Matematika Universitas Lampung

Designing a Hypothetical Learning Trajectory Based on Students’ Learning Obstacles in the Transition from Arithmetic Thinking to Algebraic Thinking among Seventh-Grade Students

Mila Agustina — 2026-09-19

This study aims to identify students’ learning obstacles in the transition from arithmetic thinking to algebraic thinking and to design a Hypothetical Learning Trajectory based on these findings through a Didactical Design Research approach in the prospective analysis stage. This research employed an exploratory qualitative method involving 33 seventh-grade junior high school students selected through purposive sampling. Data were collected through diagnostic tests, teacher interviews, student interviews, and document analysis, and were analyzed using the Miles and Huberman model, consisting of data reduction, data display, and conclusion drawing. The findings reveal that students experience ontogenetic, epistemological, and didactical learning obstacles, particularly in understanding variables, coefficients, constants, algebraic term structures, and relationships among verbal, numerical, symbolic, and geometric representations. Based on these findings, a Hypothetical Learning Trajectory was developed, consisting of progressive learning stages from understanding the meaning of algebraic symbols, recognizing structural relationships among algebraic elements, connecting multiple representations, to performing substitution operations. In conclusion, the developed Hypothetical Learning Trajectory is anticipatory and grounded in students’ learning obstacles, providing a systematic and adaptive foundation for mathematics instructional design that supports the development of students’ algebraic thinking.

The Effectiveness of Baamboozle's Assisted Problem Based Learning (PBL) Model on Students' Mathematical Problem Solving Ability

Meida Sari Mutmainnah — 2026-10-25

The abstract must stand alone so that in the abstract there should be no terms or abbreviations that do not have a definition in the abstract as well. This study aims to examine the effectiveness of the Problem Based Learning (PBL) model assisted by Baamboozle in improving students' mathematical problem-solving ability. This study employed a quantitative approach with a quasi-experimental method using a Posttest Only Control Design. The research was conducted at a public junior high school in Purworejo, Central Java, Indonesia, during the second semester of the 2025/2026 academic year. The sample comprised 64 seventh-grade students, consisting of 32 students in the experimental class and 32 students in the control class, selected through cluster random sampling. The experimental class was taught using the PBL model assisted by Baamboozle, whereas the control class received direct instruction. Data were collected through a mathematical problem-solving ability test developed based on Polya's problem-solving stages. The data were analyzed using the Lilliefors normality test, F-test for homogeneity, and independent samples t-test at a significance level of 5%. The results indicated that the mean score of mathematical problem-solving ability in the experimental class was 75.47, compared with 65.13 in the control class. The hypothesis testing yielded t_calculated = 2.2880 > t_table = 1.6698, indicating a significant difference between the two groups. Thus, PBL assisted by Baamboozle was more effective than direct instruction in supporting students' mathematical problem-solving ability.

Problem Based Learning with a Deep Learning Approach and the Mathematical Connection Skills of Vocational High School Students

Dwi Ariani — 2026-10-28

This study examines whether students’ mathematical connection abilities differ between learning through Problem Based Learning integrated with a Deep Learning approach and learning through Discovery Learning integrated with the same approach. The research population consisted of Grade X Automotive Engineering students at a vocational high school during the 2025/2026 academic year. The sample comprised 76 students from two experimental classes, with 38 students in each class, selected through cluster random sampling. After the treatments were completed, data were obtained using a test measuring students’ mathematical connection abilities. Data analysis included the Lilliefors normality test, F-test for homogeneity, and t-test for hypothesis testing. The Lilliefors test showed that both groups were normally distributed, with calculated values of 0,111 and 0,093, respectively, both lower than the critical value of 0,143. The homogeneity test showed homogeneous variances, with a calculated of 1,693, lower than the critical of 1,729. The t-test produced a calculated of 1,911, exceeding the critical of 1,665, indicating a significant difference between the groups. The analysis confirmed a significant difference in students’ mathematical connection abilities between the two groups, with those receiving Problem Based Learning integrated with a Deep Learning approach obtaining a higher mean score than those learning through Discovery Learning with the same approach.