Ac 2008-1824: Integrating Algebra and Engineering in the Middle School Classroom

The Building Math curricula project was originally titled “Integrating Algebra and Engineering in the Classroom.” It resulted in the development of three middle school instructional units that uniquely integrates inquiry-based mathematics investigations and engineering design challenges. The engineering design challenges provide meaningful and engaging contexts to learn and use mathematics, and to develop students’ teamwork, communication, and manual skills. The mathematics investigations yield useful results to help students make informed design decisions. In particular, special focus was given to the development and use of algebraic reasoning. This paper seeks to answer the questions: “What algebraic learning is evidenced in the student work and classroom videos collected in the pilot studies?” and “How was the engineering design is informed by the mathematics research phase of design challenge?” The major finding claims that when engaged in Building Math design challenges, middle school student at different grade levels use algebraic reasoning when analyzing changing rates of an exponential function, interpret slope in a meaningful context, and use a mathematical model to make reasonable predictions. They then use this understanding to inform their engineering designs to meet the criteria and constraints of the challenge. Algebra and Engineering There is widespread consensus that algebra is important as a “gatekeeper” to higher levels of math and careers in science, technology, math, and engineering fields (Moses, 1993 1 ; Pelavin & Kane, 1988 2 ). Also, prominent organizations such as the National Academy of Engineers and the International Technology Education Association have been calling attention to the need to increase technological literacy for all people, even those who may not enter or are not in quantitative professions. “To take full advantage of the benefits and to recognize, address, or even avoid the pitfalls of technology, Americans must become better stewards of technological change” (Pearson, 2004 3 ). The Building Math project sought to address the demonstrated needs described above by developing activities that integrate algebra and engineering. This was not an easy endeavor, as existing activities tended to emphasize one subject over the other, or require a team of teachers (i.e., technology, science, and math) to coordinate over a fairly lengthy period of time. After several iterations of implementing activities in pilot classrooms, activities that successfully integrated algebra and engineering had these qualities: (1) the activities are embedded in some greater context that makes the design work have a purpose, and (2) the activities make mathematics a necessary means to designing an effective product or process. For example, in the Amazon Mission unit (consisting of three week-long design challenges that can be done throughout the year), students read a one page introduction that invites students to imagine that they are planning to visit an indigenous people group in the Amazon rainforest. Students learn that many Yanomami people suffer from malaria and that their first design challenge is to design a prototype of a medicine carrier that can keep the medicine insulated within a temperature range. Students analyze a graph showing the change of temperature over time that models the performance of an existing poorly functioning medicine carrier. They then conduct hands-on controlled experiments to learn about the insulation performance of different materials, collect data and create graphical representations to make predictions and inform their designs. This is the first of three design challenges in the Amazon unit that utilize the same storyline. The storyline describes needs or problems for which students need to engineer solutions, and the math investigations support and inform the designs. This is in contrast to many traditional engineering design challenges where students are simply told to design an object like a bridge or tower without any real-world context that expresses a need for a bridge or a tower. This is also in contrast to open-ended design challenges where students are simply given materials to tinker with, usually by trial and error, until they find something that “works.” Building Math design challenges are research-based – the math investigations develop a base of knowledge that students draw upon to make design decisions. Other guiding principles for designing the units included: (1) activities should be relatively short (maximum 1 week), (2) math topics should be appropriate for and important ones in middle school, (3) students work in groups, (4) algebraic relationship and reasoning are highlighted, (5) students build a product or design a process that can be tested, (6) there are quantitative methods of measuring performance, (7) students use the 8-step engineering design process during challenges (see Figure 1), and (8) a variety of solutions are possible. These principles are in line with five strategies for contextual learning used by nationally recognized science and mathematics teachers as identified by The Center for Occupational Research and Development (CORD) 4,5 and Crawford 6 • Relating – learning in the context of one’s life experiences or existing knowledge • Experiencing – learning by doing, through exploration and discovery • Applying – learning by putting the concepts to use • Cooperating – learning in context of sharing, responding and communicating with other learners • Transferring – using knowledge in a new context The three Building math units are described in Table 1. Table 1: Overview of Building Math Units Unit Name and Storyline Grade Level Engineering Design Challenges Math Content Everest Trek: Students imagine that they are climbing Mt. Everest. 6 • A coat • A bridge to cross a crevasse • Graphing