Hipotenusa: Journal of Mathematical Society

Can Growth Mindset Affirmation be Advantageous for More-knowledgeable Learners?

2025-02-24T23:42:35+00:00

Growth mindset is known as a believe that intelligent can be learned. Learning anxiety might occur due to self-doubt that one has an ability to learn, such as in a complex topic in mathematics. Therefore, it is assumed that a positive affirmation that directs growth-mindset might be used to manage anxieties in learning mathematics. This study was aimed to investigate that beside the worked example might increase extraneous cognitive load for more knowledgeable learners, it might also be possible it affects anxiety. A total of 128 Indonesian junior high school students were randomly placed in four experiment groups by using the 2x2 factorial design (with vs. without growth mindset affirmation) x (worked example vs. problem solving based instruction) to examine the instruction on transfer abilities, cognitive loads, and level of anxieties. Using ANOVA(s), findings support the expertise reversal effect that the worked examples were disadvantageous for more knowledgeable learners. The data reveals that they also experienced significantly higher anxiety during learning compared to the counterparts. Nevertheless, no effects were found in favor of the growth mindset affirmation.

Critical Thinking Abilities of Prospective Mathematics Teachers Based on Learning Styles

2025-09-10T02:59:15+00:00

This research attempts to describe the critical thinking abilities of prospective fifth-semester mathematics education teachers at PGRI University Semarang through a qualitative approach. The researcher, as the primary instrument, employed a learning style questionnaire, a Group Theory critical thinking test, and an interview guide with purposively selected subjects. Data were analyzed through flow diagrams which included data reduction, data presentation, and drawing conclusions. Data credibility is obtained through triangulation of sources and time. The research result show that the average critical thinking ability test for visual and audotory styles is relatively higher than for kinsestetic learners. At the stages of focus, reasoning, and inference, all three stylesthe stages of saturation, clarity, and overview, a clear distinction emerges, with the visual style demonstrating greater effectiveness by producing answer that are both accurate and complete, unlike the auditory and kinesthetic counterparts. The ability of the three learning styles to express valid arguments to clarify the truth of the answers they make is still very low. Providing training with open-ended problem-based questions and problem-based learning as well as honing the arguments of prospective mathematics teachers are the alternative solutions chosen to improve critical thinking skills.

Augmented Reality Enhanced Inclusive Learning Model (AR-ILM): Supporting Mathematical Literacy Development for Students with Disabilities

2025-09-11T06:45:31+00:00

Mathematical literacy plays a vital role in daily life, particularly in identifying, reasoning, communicating, problem-solving, and representing mathematical ideas in real contexts. However, for students with intellectual disabilities, developing mathematical literacy remains a significant challenge. To address this issue, innovative scaffolding through interactive and visual media is required. This study aims to develop NEIMoL media assisted by Augmented Reality (AR) that meets the criteria of validity, practicality, and effectiveness in improving mathematical literacy among students with intellectual disabilities. The research employed Plomp’s (1997) development model, which includes five stages: initial investigation, design, realization, testing and revision, and implementation. Data were collected through expert validation, observations, interviews, questionnaires, and mathematical literacy tests. Instruments included expert validation sheets, teacher and student response questionnaires, and pre-test and post-test assessments. The validation results showed the media to be “Very Valid” with an average score of 4.1 (on a scale of 5). Practicality was rated positively, with a score of 3.7, and both teachers and students expressed favorable responses. Effectiveness was demonstrated through an N-Gain score of 0.7175, categorized as high improvement. These findings indicate that AR-assisted NEIMoL media is valid, practical, and effective in supporting the mathematical literacy of students with intellectual disabilities.

Development of a Flipbook-Based E-Module on Linear Programming for Mathematics Education Students

2025-09-30T05:01:09+00:00

This study aims to develop a flipbook-based e-module on linear programming material for students that meets the criteria of validity, practicality, and effectiveness, making it suitable for learning. This study uses the Research and Development (R&D) method with the ADDIE development model which includes five stages, namely: Analysis, Design, Development, Implementation; and Evaluation. The research instruments included an expert validation sheet, a student response questionnaire, and a learning outcome test. The e-module's validity was assessed by subject-matter, media, and language experts using a 1–5 Likert scale, yielding an average score of 126 (max 135), indicating very high validity. Practicality was measured through student responses on ease of use, display, and learning benefits, with 52.5% rating it as very practical and 47.5% as practical. The e-module's effectiveness was assessed based on student learning outcomes, with a mean of 90.25 and 97.5% achieving scores above the Minimum Completion Level (≥75). The results indicate that this flipbook-based e-module is valid, practical, and effective for use in linear programming lectures. Consequently, this e-module has the potential to improve the quality of mathematics learning, particularly in understanding linear programming concepts, and to encourage student independence in learning through an interactive, accessible presentation of materials.

Assessing the Competence of Prospective Mathematics Teachers in Technology-Enhanced Differentiated Instruction for Inductive Learning

2025-11-20T23:56:37+00:00

The demands of 21st-century pedagogical competencies necessitate that Prospective Mathematics Teachers (PMTs) be proficient in the integrated application of technology and differentiation. This study aims to assess the competence of PMTs in implementing technology-enhanced differentiated instruction within an inductive learning framework, evaluated through seven key elements referencing the frameworks of Prince & Felder and Tomlinson. Utilizing a descriptive qualitative approach, this study analyzed in-depth peer teaching video recordings from the entire cohort of 15 students in a mathematics education program. The novelty of this research lies in its focus on the integrated operationalization of these three complex pedagogical elements. Data analysis was conducted rigorously using the interactive model of Miles, Huberman, and Saldana, supported by source triangulation to ensure the credibility of the findings. The results indicate that PMTs achieved high competence in inductive learning and differentiation (implemented by 93%–100% of PMTs). However, the implementation of technology-enhanced learning showed significant variance, being adequately achieved by only 67% of PMTs. It is concluded that while PMT training is robust in instructional design and differentiation strategies, the integration of technological tools requires further optimization and focused development to meet the demands of 21st-century skills.

Development of English-Based Electronic Module on Three-Variables Linear Equations System for Mathematics Education Students

2025-11-20T03:53:25+00:00

Many Mathematics Education students face difficulties in learning systems of linear equations in three variables, particularly when the material is delivered in English. This study aimed to develop an English-based electronic module that meets the criteria of validity, practicality, and effectiveness. Using the ADDIE development model, the product was evaluated by two validators (material expert and media expert) and implemented with 35 students enrolled in the selected topics in school mathematics course. The validation results showed that the module achieved an average validity score of 91.11% for content feasibility and 88.57% for language feasibility, indicating a ‘very valid’ category. Student responses indicated that the module was practical, with an overall practicality score of 74.17%. Effectiveness testing demonstrated that 77.14% of students met the Minimum Competency Criteria (MCC), placing the module in the effective category. These findings suggest that the English-based electronic module is feasible for use in supporting students’ conceptual understanding and strengthening language-based mathematical literacy, particularly in learning systems of linear equations in three variables.

Integrating Mathematical Patterns in Muslim Fashion Design: a 4D-Based Edupreneurship Innovation

2025-11-27T04:47:24+00:00

The purpose of this study is to develop an innovation "Mathematical Patterns in Muslim Fashion" an innovation in Muslim clothing design using mathematical patterns and to test its feasibility, practicality, and effectiveness for the development of student edupreneurs. The method used in this study is research and development with 4D model, namely define, design, develop, and disseminate. The subjects of this study were students of Mathematics Education at IAIN Kudus who took the Entrepreneurship course in the even semester of the 2022/2023 academic year. The data collection technique in this study used a questionnaire that included feasibility, namely from expert validation, practicality, namely from student responses, and the effectiveness of using Muslim clothing design innovations using mathematical patterns as student edupreneur development. The results of this study are "Mathematical Patterns in Muslim Fashion" Muslim clothing design innovation using mathematical patterns is feasible with material experts with very good criteria, designer validators with good criteria, and edupreneur expert validators with very good criteria, practicality obtained 96%, and effective with very good criteria used as student edupreneur development.

Analysis of Higher Order Thinking Skills in a TPACK Based Flipped Classroom Supported by Dynamic Assessment

2025-11-21T00:32:11+00:00

This study aims to identify students’ mathematical higher order thinking skills (HOTS) through the implementation of a Flipped Classroom model grounded in the Technological Pedagogical and Content Knowledge (TPACK) framework and supported by dynamic assessment. A mixed method approach with a concurrent embedded design was employed. The study involved 32 prospective mathematics teachers, divided evenly into an experimental group (n = 16) receiving TPACK based Flipped Classroom instruction with dynamic assessment and a control group (n = 16) receiving conventional instruction. HOTS were measured using a validated essay based test aligned with indicators of interpretation, analysis, evaluation, inference, and problem solving. For the qualitative phase, three students representing high, medium, and low prior ability levels were purposively selected. Data were analyzed using both quantitative and qualitative techniques. Quantitative data were analyzed using paired and independent samples t-tests and N-Gain, while qualitative data were examined using open coding and thematic analysis. Descriptive results showed higher posttest scores for the experimental group (M = 74.3, SD = 10.4) compared to the control group (M = 55.1, SD = 9.0). The independent samples t-test indicated a statistically significant difference between groups (p < .05), with a large effect size (Cohen’s d = 1.65) and a moderate N-Gain of 0.58 in the experimental group. Qualitative findings revealed that the high ability student demonstrated complete alignment with HOTS indicators through coherent modeling and proof strategies, while the medium ability student exhibited accurate procedural reasoning and partial conceptual explanation. The low ability student showed limited abstraction but demonstrated incremental improvement through scaffolded feedback. The combined findings show that integrating TPACK based Flipped Classroom instruction with dynamic assessment supports deeper mathematical reasoning by linking pre class technological engagement with in class mediated learning. This study contributes to the literature by demonstrating how dynamic assessment operationalized within a TPACK aligned flipped environment can strengthen students’ HOTS across varying ability levels.

Enhancing Algebraic Reasoning in The Classroom: The Effects of Search, Solve, Create, and Share Strategy

2025-12-06T08:42:53+00:00

Algebraic reasoning is a fundamental competency in mathematics learning; however, many students experience difficulties in applying algebraic concepts, particularly in quadratic functions. This study aims to enhance students’ algebraic reasoning through the implementation of the SSCS (Search, Solve, Create, and Share) strategy, a structured problem-solving instructional approach that emphasizes systematic exploration, solution development, model construction, and mathematical communication. The study employed a collaborative classroom action research design involving Grade X senior high school students, conducted across two cycles consisting of planning, action, observation, and reflection stages. Students’ algebraic reasoning was assessed using indicators that include pattern recognition, algebraic representation, manipulation of algebraic expressions, and logical justification. Data were collected through algebraic reasoning tests and classroom observation sheets. The findings reveal a substantial improvement in students’ algebraic reasoning abilities, with the mean score increasing from 62.33 in the pre-cycle to 81.25 in Cycle II. Additionally, the percentage of students achieving mastery learning increased from 27.78% to 91.67%. These results indicate that the SSCS strategy effectively supports the development of algebraic reasoning by engaging students in structured problem-solving and reflective mathematical communication.

Mathematics Teachers' Understanding of the Algorithms for Solving Quadratic Function Problems

2025-11-11T08:32:24+00:00

This study investigated secondary school mathematics teachers' understanding of the mathematical concepts underlying the algorithms used in teaching quadratic functions. It examined three constructs: i) why the graph of a parabola is a curve and not a straight line; ii) why the solution of a quadratic equation remains unchanged when the equation is multiplied by -1; and iii) the justification for the counter-intuitive shift of the parabola in horizontal transformations. A qualitative case study design was employed, involving five secondary school mathematics teachers selected through a combination of purposive and convenience sampling. Data were collected using a Subject Matter Knowledge Questionnaire (SMKQ) that focused on teachers' understanding of quadratic functions and their underlying algorithms. Responses were analysed through conventional qualitative content analysis. Findings revealed that while most teachers demonstrated adequate procedural skills, they exhibited limited conceptual understanding of the meaning underlying the algorithms in the constructs investigated. Their reasoning often reflected a focus on knowing how rather than understanding why, indicating a gap between procedural fluency and conceptual depth. The study concludes that strengthening teachers' conceptual understanding of mathematical algorithms is essential for improving instructional quality and learner outcomes. It recommends targeted professional development programmes that integrate both procedural and conceptual aspects of mathematical knowledge.