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Exploring the impact of Stein et al.’s levels of cognitive demand in supporting students’ mathematics heuristic problem-solving abilities
By Robert Wakhata
The present study explored the impact of Stein et al.’s levels of cognitive demand (LCD) on evaluation and instructional methods in applying the knowledge of equations and inequalities to learn the topic of linear programming (LP). The framework provided by Stein et al. was used to map students’ LP cognitive demands. Students’ specific proficiency levels in solving LP tasks using Stein et al.’s LCD hierarchical framework were investigated. A mixed-method approach with a pre-test and post-test pre-intervention pilot study involving a non-equivalent control group design was applied. The participants were 175 grade 11 students from Mbale district, eastern Uganda. Two pre-interventional LP tests (pre-test and post-test) were administered to the students to examine their cognitive demands. This was followed by an intervention involving application of Stein et al.’s LCD in learning LP. The results showed that before pre-intervention, the performance of urban school’s average post-test scores was higher than that of the rural school. Students from the rural secondary school improved greatly relative to their peers from the urban school. Moreover, only 25.1% of students performed at the highest level of Stein et al.’s LCD (doing mathematics). The post-test scores were better relative to the pre-test (M = 56.51 ± 20.88 vs. 42.23 ± 22.49; p < 0.05). Overall, there was a statistically significant difference between students’ average grades in the pre-interventional pre-test and the post-test (Cohen’s d = 0.81 > 0.5), 95% CI [−18.00, −10.56]). Holding other factors constant, the significant differences in students’ scores were mainly due to the application of suitable tasks which were later mediated by the application of Stein et al.’s LCD instructional approach. This study, therefore, recommends that mathematics educators should effectively apply Stein et al.’s LCD to vary mathematics tasks given to students. This approach enhances students’ cognitive levels, supports students’ heuristic problem-solving abilities, critical thinking skills, and application of mathematics in real-life. Copyright © 2023 Wakhata, Mutarutinya and Balimuttajjo.
Relationship between active learning heuristic problem-solving approach and students’ attitude towards mathematics
By Robert Wakhata
The study explored the direct relationship between active learning heuristic problem-solving approach and students’ attitude towards mathematics, using linear programming (LP) word tasks. Two instruments were used for data collection: the Attitude towards Mathematics Inventory-Short Form was adapted (with α =.75) as a multidimensional measurement tool, and a validated standardized active learning heuristic problem-solving tool. A quantitative approach with a quasiexperimental pre-test, post-test, and non-equivalent control group study design was adopted. A sample of 608 grade 11 Ugandan students (291 male and 317 female) from eight secondary schools (public and private), four from central Uganda, and the remaining four from eastern Uganda participated. Data were analyzed using PROCESS macro for SPSS (v.4). The results revealed a direct significant positive relationship between active learning heuristic problem solving approach (ALHPSA) and students’ attitude towards solving LP word tasks (ATLPWTs). Thus, the ALHPSA positively and directly impacted on students’ ATLPWTs. The findings can be explained by theoretical, conceptual, and/or psychometric factors. Overall, the results indicate beneficial practical implications that support the theoretical framework for enhancing the learning of mathematics using word problems in Ugandan secondary schools and beyond © 2023 by the authors; licensee Modestum. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/)
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