Examining Students' Proportional Reasoning Strategy Levels as Evidence of the Impact of an Integrated LEGO Robotics and Mathematics Learning Experience

Abstract

In many school districts in the United States, the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) outline what students should understand and be able to do in their study of mathematics. These standards are composed of content standards and practice standards that must be connected in order to allow students to engage more deeply with the subject matter. Engagement and learning in context can support understanding in a couple of ways. The first is by increasing student motivation and interest in the curriculum itself. The second is by enhancing transfer of learning through the demonstration of connections between abstract mathematics and real-world problems. Students must be prepared to apply this knowledge in multiple external situations, often through creative and personally meaningful situations, as well as to learn to address mathematical problems in a variety of situations and contexts. The presented study used a problem-solving experience in engineering design with LEGO robotics materials as the real-world mathematics-learning context. The goals of the study were (a) to determine if a short but intensive extracurricular learning experience would lead to significant student learning of a particular academic topic and (b) to explore the differences in mathematical problem-solving strategies used by students when solving problems of ratio and proportion in two different learning environments. It was important to first determine if indeed a short-term but intensive extracurricular learning experience could be effective, given the reliance of such an experience as the framework for conducting the educational research. The experimental research explored student learning in mathematics but deliberately limited the specific topic of exploration to integrated concepts of proportional reasoning within LEGO robotics challenges in engineering design. The impact of this experience upon students’ proportional reasoning was measured and is described with a focus on proportional reasoning strategy levels. Two research questions guided this study: Research Question 1: Can a significant change in students’ understanding of ratio and proportion take place during a short but intense learning experience? Research Question 2: How do students’ demonstrated proportional reasoning strategy level use compare for students learning ratio and proportion concepts within the integrated LEGO robotics and mathematics program versus when using a traditional textbook-based mathematics program? A prior study by the author (Martinez Ortiz, 2011) describes the comparison of resulting student group performance based only on correct answers to proportional reasoning questions.