I would accomplish teaching mathematical concepts by employing an engineering team of students to work on a project in bridge design. They would make their own decisions about what they would want to study: bridge design, bridge failure, or some component of a bridge such as symmetry. A laboratory report would be essential to the project including hypotheses and a description of the mathematical concepts employed.
A laboratory report is essential because it takes the student to the next level showing their comprehension of the initial mathematical concept(s) learned or applied. The most important element of the report is the hypothesis or problem statement. This is where students demonstrate taking mathematical concept(s) learned to the next level. For example, if a team of students successfully derived the parabolic equation of the main cable of a suspension bridge (see activity 1), then, a hypothesis may be to lengthen the span of the road and see how this effects the original equation or derive a new equations to the lengthening or contraction of the road in order to find patterns. However, students can be creative and do develop their own curious ideas.
Teachers would provide background information about design, materials, and types of bridges (see appendix 2) in group discussion. Alternatively, teachers may have students research aspects of bridges using books and/or media. Teachers would be observant of student choices and query their choices individually. Then students would report out explaining how their choice would help the team. Teachers would also assist by providing guidance and needed information in a timely manner as students are working to move the project along or by asking questions. Inquiries would consist of asking students about what they are thinking about, what they plan to accomplish it, or lead them to explore other solutions. For example, if students are working with several equations, then asking the students about relationships and patterns between equations or to another concept might lead them to a solution. The emphasis is to lead the students and not provide answers. Teachers would always be available to answer student questions and act as moderators throughout the process. Students make all decisions whether they are successful or not. The emphasis is on what they have learned during this process.
This atmosphere of team work is student driven and would enable students to learn to work together, learn from each other, work toward a common goal, and accomplish a task together in addition to learning mathematical concepts and the connection of mathematics to the real world. Other benefits would be it would teach students patience, focus, perseverance, and to enjoy or have fun in the process.
