Connecting Math and Science for All Students
Cawley, John F., Foley, Teresa E., Teaching Exceptional Children
Hands-on Contextualized Highly interactive Interconnected Systematic Engaging Interesting Understandable
The words in our little list have a sort of progression. We go from hands-on activities that have context, and we end with engaged students who understand the material we are presenting. What could be better? Sounds easy, right? Well, many teachers may find that they need another word on the list, "systematic," to ensure that all students "get" the connections between math and science and improve their understanding.
This article describes a way to provide systematic connections between mathematics and science through several hands-on lessons, word problems, and opportunities for problem-solving. The article also describes the benefits to all students of linking mathematics and other school subjects.
Special Education Connections
Special education has an extended history of curricular connections. Seguin (1907) commented as far back as 1866: "Teaching facts is not so fruitful as teaching how to find the relations between a single one and its natural properties and connexions" (p. 64). Ingram (1960) and Duncan (1943) suggested that subjects should not be taught alone, but in connections to other subjects. Ingram employed a "unit method" in which students would study a common topic such as "Raising Chickens"; and all skills and processes would be integrated into the topic to ensure that the student recognized the relationships between the subject and its applications.
Other researchers (e.g., Engelmann, Carnine, & Steely, 1991) described how to teach arithmetic computational relationships and their connections within the context of solving word problems in mathematics. Hasselbring and Moore (1996) used contextualized learning environments to teach mathematics to students with learning difficulties. Gersten and Baker (1998) described how to integrate scientific concepts into situated cognitive activities through explicit instruction.
Cawley and Parmar (1993) developed two comprehensive problem-solving programs that integrated mathematics and science within the context of language comprehension and arithmetic. The two programs begin with counting and extend through division and cover a grade span approximating 4 years. The programs are nontraditional in that they engage the student in contextualized problem-solving activities and seek to develop computational proficiency through problem-solving. All activities are "hands-on" and highly interactive. They all take place within science settings (e.g., the matter laboratory; the weather map) and develop proficiency with computation via problem-solving activities.
Our problem-solving programs take advantage of the structure and sequence of math curricula and inject science topics into the lessons. We thus can make interesting and meaningful connections between mathematics and science. This article outlines three mathematics ideas. These are the interrelationships between multiplication and division, ratio, and proportions. The topics cover a grade range of Grades 3 through 8. Each of these topics represents important mathematics principles, as follows:
* The multiplication and division relationship is important as a means of describing multiplication and for using the relationship between factors to define division as a search for the missing factor.
* Ratio is important as a constant (i.e., pi as derived from circumference/ diameter); as a variable for making comparisons (e.g., Which is larger/ smaller: 2/4, 3/8, or 4/8?); and as a guideline for developing mixtures and solutions (e.g., customized paint orders),
Proportions are important for comparing two ratios and for preparing combinations of products (e.g., If 1 ounce of weedkiller is added to a gallon of water, how many ounces of weed killer must be added to 4 gallons of water?). Many adolescents and adults have difficulty with proportional reasoning (AAAS, 1993), as do students with disabilities (Brownell, Mellard, & Deshler, 1993). …