A Design Research Project: Investigating an Integrated Mathematics Instructional System (IMIST) Focused on Inquiry Learning and Proficiencies in Symbolic Literacy, Conceptual Literacy, and Problem-solving for High School Mathematics
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2019
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Abstract
The combination of stakeholders’ concerns about mathematics education in the United States – students’ lack of proficiencies, problem-solving skills, and preparation for 21st century careers in stem fields – together with the conflict between educators using different and often fragmented curricula and instructional methods (traditional versus reform-based) suggested a need to develop an integrated framework to help teachers design curricula that used the best research-based practices to improve students’ achievement, engagement, and proficiencies in mathematics. This study was the second phase or enactment phase of a design research project that examined prototypical units for Algebra 2 and geometry. This study investigated the IMIST (Integration of Mathematical Inquiry, Symbolic literacy, and Technology) instructional system developed using principles from design thinking, a design pattern approach, and activity theory as a possible solution to help educators design curricula to meet the learning needs of students and to support students’ development of strong mathematical foundations in symbolic literacy, conceptual literacy, and problem-solving applications. The research questions for this study examined the impact of two IMIST units on students’ overall achievement and mastery of symbolic, conceptual, and problem-solving literacies; on students’ attitudes, engagement, and confidence in mathematics; and reports of their experiences using the IMIST unit learning activities.The IMIST system framework used unit learning objectives to identify authentic, contextual problem-solving applications with supporting symbolic and conceptual learning activities to build and scaffold learning needed for deep understanding of mathematical language and applications. Thirteen students, ages 10 to 15, participated in four separate case studies: two individual, one paired, and one small class. The treatment for each case study was a packet of learning activities designed and written by the researcher to support the learning objectives of a unit on quadratic functions for Algebra 2 students and a unit on right triangles and right triangle trigonometry for the geometry student. The instructor provided online or in-class lessons and discussions that introduced student-centered activities with summaries, reviews, and practice. Formal data collection instruments included demographic surveys, Math Attitudes and Perceptions Surveys, assessment data, pre-intervention interviews, and post-intervention interviews and surveys. The researcher kept a journal with observations and students’ comments as well as annotated class notes written during online and face-to-face classes to capture students’ questions and comments during discussions. A cross-case data analysis was developed to examine similarities and trends relevant to the study’s research questions. Data analysis of the individual and small class case studies examined students’ achievement scores overall and in the core literacies linking their comments from interview and survey data to support and explain their learning outcomes. Similarities and trends in students’ reports provided insights into the impact of the IMIST unit on attitudes and confidence as well as evaluations of learning experiences. The data analysis of the case studies and cross-case analysis identified themes describing how students learned using the IMIST unit activities.