Insights into Design Principles in Mathematics Education: Understanding the 'Why's And 'How's

Designing effective teaching and learning in mathematics is essential for helping students grasp concepts and develop skills. Various interventions are developed, and the effectiveness of these "design"s is evaluated from multiple perspectives, and the success of them is seen holistically as the design itself. With the growing need to understand how designs function in real environments, design-based research (DBR) has gained prominence in mathematics education (Gravemeijer & Cobb, 2013). DBR systematically examines instructional designs, evaluating both theoretical and practical aspects throughout all stages of the learning process (Plomp, 2013). Design principles include research-based arguments and applications from the beginning to the end of design-based research processes (van den Akker, 2013). They serve as a guide containing the necessary information for the designed educational product, which include social norms, learning steps, criteria, guidelines, etc., that act as a bridge between theory and practice (Bakker, 2019). Although design principles cannot guarantee a hundred percent successful application (van den Akker, 2013), they are considered useful for effective and feasible interventions and convey situations that can be generalized when applied in similar environments (Plomp, 2013). Due to the predominantly qualitative nature of design-based research methods, there is a "generalization" problem with findings related to design. Transferring the principles of the design, rather than the design itself, could be a way to solve the generalizability problem (Plomp, 2013). Many AI models (i.e. Magicschool AI platform) require knowledge about the principles of mathematics teaching-learning processes. In this study, the focus is on the processes of determining design principles to better understand the use of design principles in mathematics education research.

Methodology, Methods, Research Instruments or Sources Used

The best method to guide the research question is a Systematic Literature Review. This method aims to gather and synthesize the findings of studies addressing a specific research question using systematic methods. Systematic literature review process was carried out by searching for keywords within the abstracts of the studies. The keywords were determined as mathematics education and design principles but its organization is significant to focus on what is needed. The document search was limited as in the part of abstract "design principles" or “design principle” and in the part of author keywords “mathematics education”. The language was limited to English and the document type was not restricted. The keywords were searched in the Web of Science and Scopus browsers due to their various research collection on education. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), an internationally important guideline for presenting systematic reviews and meta- analysis reports, provided guidance during the data identification process (Page et al., 2021).The data analysis was conducted through content analysis using MAXQDA 22 software. Out of the 52 documents analyzed: 17 documents were obtained from the Web of Science (WoS) database, 20 documents solely from the Scopus database, 37 documents from both WoS and Scopus databases

Conclusions, Expected Outcomes or Findings

The findings include three categories considering how the design principles were defined in the research, how they were analysed/used, and how its contribution to mathematics learning environment were identified in the studies. The analysis has shown that there is no specific definition for design principles used in the literature. On the other hand, the design principles were described with words such as “characteristics of the design”, “inquiry-based”, “features of a design”, and “powerful learning environments”, which are correlated with empirical research process. Another category about how design principles were analysed demonstrated that design principles as a concept were mostly mentioned in design-based research method. Moreover, the studies involved design principles as a tool (design principles were helpful to construct intervention) more than design principles as a goal (the studies aim to develop design principles, and these principles are tested). In studies using design principles as a goal, the method generally includes the following steps: literature review, identification/development of principles, application of them in the design of the study, partial evaluation of the design by participants, and reporting of its effectiveness. In studies where principles are used as a tool, the method generally includes the following steps: examination of the literature, identification of the most current and widely accepted principles, characteristics, or features specific to the topic in mathematics education, and adaptation of design principles. In the third category, the discussion/conclusion sections of the studies were reviewed to understand the contribution of design principles: if the designs achieve the targeted success, the design principles are also deemed successful and the design principles should be applied in other settings to increase their generalizability. In conclusion, the research findings suggest that the flexible nature of approaches based on design principles holds the potential to yield generalizable results in education.