Geometric Reasoning to Reinventing Quadratic Formula: The Learning Trajectory on Realistic Mathematics Education Principles

City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://mtrj.commons.gc.cuny.edu/

Y

33

Foreign Countries; Junior High School Students; Middle School Mathematics; Geometry; Geometric Concepts; Learning Trajectories; Mathematical Concepts; Mathematical Formulas; Instructional Design; Learning Activities; Student Educational Objectives; Mathematics Instruction; Thinking Skills

2573-4377

This study aims to establish a knowledge base on how to support students in learning. We develop an initial hypothetical learning trajectory by formulating learning activities and predicting the development of students' thinking and understanding. The methodological framework employed in this study is design research, which seeks to generate actionable knowledge for achieving various educational goals through design. The design process incorporates the Hypothetical Learning Trajectory (HLT) thought experiment and the teaching experiment based on the six Realistic Mathematics Education (RME) principles. By integrating individual learning activities with the context and principles of the RME approach, students can construct their knowledge and rediscover the quadratic equation formula. Through comparing the HLT with observed learning outcomes, we redesign the process, revise our HLT, and provide answers to research questions regarding the attainment of specific learning objectives. Similar to our retrospective data analysis, we create a revised HLT to reinforce the concept of the completing the square and reinvent the quadratic formula.

As Provided

2024

EJ1442295