The effect of the Addie instructional design on mathematical modeling, communication, logical thinking and motivation of grade 9 students

Mathematics education aims not only for students to memorize formulas but also to become individuals who can use these formulas effectively, generate creative solutions to problems, have developed communication skills, and relate mathematics to other fields and everyday life. Therefore, this research aims to evaluate the impact of the ADDIE skill-based instructional design, prepared for ninth-grade students, on the mathematical skills included in the secondary education mathematics curriculum. The research adopted a multi-phase mixed-method design. It consists of three main stages. In the first stage, a sequential explanatory design was used in the development of measurement tools, and data triangulation was employed during the needs analysis process. In the second stage, which includes the design and development steps, a pilot implementation was conducted to identify and receive feedback on any deficiencies in the design. In the third stage, the implementation and evaluation of the design were carried out using an embedded design. The quantitative section employed a quasi-experimental design with pre-test, post-test, and retention test (2x3) including experimental and control groups, while the qualitative section was conducted using a case study design. The study's population and sample consisted of 9th-grade students and mathematics teachers teaching at this grade level in Anatolian high schools in Aydın province, which admit students based on non-exam secondary education success scores and are affiliated with the Ministry of National Education. In the study, the Mathematical Communication Self-Efficacy Scale and Achievement Test developed by the researcher were used during the needs analysis and the evaluation process of instruction. Additionally, the Mathematical Modeling Self-Efficacy Scale, Logical Thinking Test, and Mathematics Motivation Scale were utilized. A semi-structured student interview form was employed to examine the effectiveness of the design. During the needs analysis and the evaluation of the design's effectiveness, the Modeling Competencies Assessment Rubric and the Mathematical Communication Skills Level Scoring Key were used. The third phase of the research was conducted with 58 ninth-grade students from an Anatolian high school, with 29 students in the experimental group and 29 in the control group. Both groups took a pre-test before the six-week implementation of the ADDIE-based skill-oriented instructional design, a post-test after the implementation, and a retention test six weeks after the post-test. During the study, a heterogeneous focus group selected from the experimental group participated in modeling activities and rubric evaluations before, during, and after the design implementation. While the experimental group received the ADDIE-based instructional design, the control group followed the ongoing program. Quantitative data were analyzed using SPSS and AMOS, while qualitative data were analyzed through descriptive analysis. The results of the needs analysis indicated that students' mathematical process skills were insufficient. However, analyses conducted after the implementation showed a significant difference between the experimental and control groups in terms of mathematical achievement and mathematical communication self-efficacy, indicating that the objective was achieved. While there was a significant difference between the groups regarding mathematical modeling self-efficacy and logical thinking skills, the objective was not met. No significant difference was found between the groups concerning mathematical motivation. Rubric evaluations of the modeling activities revealed that the objective was met in terms of modeling skills but not in terms of mathematical communication. Both types of evaluations showed a consistent increase throughout the implementation process. The least improvement was observed in the "Verification" sub-skill, one of the sub-dimensions of modeling skills. Additionally, post-implementation student interviews indicated that students developed different perspectives, found group activities enjoyable, improved their quick decision-making skills, appreciated the opportunity for everyone to express their ideas, and felt that they could explain themselves better mathematically.