Mathematical Knowledge for Teaching and Design Thinking: A Case Study of Elementary Teachers at a STEM School



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This exploratory case study explores the connection between elementary teachers’ mathematics knowledge for teaching in the domain of algebraic reasoning and their implementation of Design Thinking as an innovative active learning instructional strategy. Scaffolding on Shulman’s conceptualization of pedagogical content knowledge, mathematical knowledge for teaching (MKT) refers to measurement as a means to decipher specialized teacher effectiveness for teaching K-12 mathematics (Hill et al., 2005). As an innovative STEM instructional strategy, Design Thinking (DT), is an iterative process of phases that provide a real-world solution-based approach to solving problems (Ejsing & Skovbjerg, 2019; Kelley & Kelley, 2013; Lewrick et al., 2018; Luka, 2019; Painter, 2018). Three elementary teachers bounded together created the case for this exploratory case study. The research design includes data collection completed in three phases for each participant within six weeks. The procedure for data collection for each participant included: (1) Participant completion of an MKT and DT questionnaire, (2) participant semi-structured pre-interviews, (3) observation of an algebraic reasoning DT unit of study, (4) collection of participant DT implementation reflection, (5) participant semi-structured post-interviews, and (6) collection of student artifacts at the completion of the algebraic reasoning DT unit of study. Bounding the three elementary STEM teachers, as the exploratory case, data collection included six different data sources for this study an MKT and DT (1) questionnaire, (2) observations, (3) teacher reflective journaling, (4) pre-and post-interviews with each participant, (5) student artifacts, and (6) researcher journal. Some of the data for the case study was collected using four different instruments: (1) an MKT and DT questionnaire, (2) an observation protocol, (3) a semi-structured pre-interview protocol, and (4) a post-interview protocol. Data analysis included descriptive, open, axial inductive, and deductive coding to develop categories of triangulated convergence between teachers’ MKT and DT implementation. The study’s findings affirmed teachers MKT connected to DT as an innovative student-centered teaching and learning methodology and provided contextualized information and strategies for keeping the subject meaningful and relevant. Also, the researcher confirmed the impact of teacher mindset and instructional beliefs anchored to implementing student-centered visible learning, strategic questioning, and tasks to engage students in higher cognitively demanding problem-solving tasks. Recommendations for future research include (1) quantitative data validation, (2) student perspective of DT, and (3) statistical connections to student achievement. In addition to benefitting instructional leaders and educational practitioners, this study’s findings can also benefit curriculum development of STEM-integrated learning standards and resources to support the school-to-career STEM pipeline.



STEM Education, Design Thinking, Mathematics Knowledge for Teaching