Academic journal article The Science Teacher

Giving Meaning to the Numbers

Academic journal article The Science Teacher

Giving Meaning to the Numbers

Article excerpt

Byline: Jeff Marshall, Bob Horton, and Joyce Austin-Wade

When learning, students yearn for meaning, challenge, and relevance. Integrated learning fulfills these desires by limiting the compartmentalization of learning-providing a more coherent learning environment. Too often, mathematics and the physical sciences are taught as separate entities. Yet, many commonalities exist, especially between chemistry and Algebra II and between physics and precalculus (including trigonometry).

I (Jeff) am a science teacher, and my quest to integrate science and mathematics learning began over a decade ago when I participated in a two-year National Mathematics and Science Fellows project sponsored by the National Science Foundation and the Coalition for Essential Schools. As a science teacher, I welcomed the opportunity several years later when a math teacher also had a desire to integrate application-based learning. We created an integrated math/science course that specifically relates physics and precalculus concepts. I collaborated with my coauthor Bob to make sure the mathematics aligned with the most current mathematics standards and concepts.

Context

An alternative education program provided the context for this learning experience, but this course would also work in more traditional settings. In the featured alternative program, students take one or two courses at a time. Upon completion, students start the next course. For more traditional settings where classes are 55 minutes or 90 minutes long, students' classes can be blocked together (e.g., first-period physics and second-period mathematics or vice versa). Blocking student schedules provides longer exploration opportunities and flexibility to reconfigure groups so individual needs are met (e.g., a group of students can work on the computer to learn specific mathematics skills while another group gathers data to be analyzed).

Framework

The National Science Education Standards (NRC 1996) and the Principles and Standards for School Mathematics (NCTM 2000) share a significant number of standards. Figure 1 (p. 38) provides several examples where physics and mathematics standards logically parallel one another. Our integrated course unites recommendations from the College Board for Physics (2006), both the National Science and National Mathematics Standards, and the state standards. Although this is not an Advanced Placement class, being aware of the College Board's expectations helps lay the foundation for those taking a second year of physics.

Given a textbook and a list of standards, teachers too often start at the beginning of the textbook and "cover" as much material as possible until the year ends. To avoid this, our approach when developing the course began by planning backwards. First, we identified the skills and knowledge base in each discipline that students should attain by the end of the school year. Then, we condensed each discipline's list to the most critical things students should know and be able to do by the end of the course (McDonald 1992; Wiggins and McTighe 1998). Figure 2 (p. 39) details the list for physics and precalculus. The core of the integrated course focuses on commonalities and complementary ideas between the two courses. Standards that do not link well between disciplines are taught using an unlinked teaching approach. For instance, proving key trigonometric identities is a mathematical skill that does not have a parallel physics concept. We believe that trying to integrate marginally linked content would ultimately weaken the curriculum for one or both of the disciplines.

Because students receive credit in math and in physics, integrated assignments receive grades for both courses. Each teacher assesses different predetermined aspects of integrated assignments. For example, during inquiry investigations the math teacher places higher value on the data and results section, while the science teacher places greater emphasis on the ability to study a scientific problem, collect meaningful data, and draw accurate conclusions based on findings. …

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