Math and Science Integration F. Mumba University of Virginia MSP Workshop 2014

Main Themes What is math and science integration? Types of mathematics and Science Integration Nature and Extent of M-S integration

Integration of Mathematics & Science Activity 1 What is math and science integration? Why should we promote math and science integration?

What is integration? The expression “integration of science and mathematics” is used in different ways. We need to understand different ways in which the term integration can be used and how they apply to the teaching of science and mathematics. Integration deals with the extent to which teachers use examples, data, and information from a variety of disciplines and cultures to illustrate the key concepts, principles, generalizations, and theories in their subject area or discipline (Banks, 1993).

Types of Integration Activity 2: How many different types of Integration do you know? In your groups come up with different types of integration you can use to integrate math and science.

Activity 3 Read examples and identify them with a type of integration Hint- Look for main elements in the examples.

Type of integration  Discipline specific  Content  Process  Thematic (Miller, Davison, & Metheny, 1993).

Discipline Specific Integration Involves an activity that includes two or more different branches of mathematics or science. For example, activities involving algebra and geometry in mathematics and activities infusing biology, chemistry, and physics in science. Requires a problem where students reach an informed decision based upon data analysis from all the disciplines and their use of critical thinking and problem solving skills.

Content Specific Integration Involves choosing an existing curriculum objective from mathematics and one from science. An activity is planned which will involve instruction in each of these objectives. It is content specific because it conforms to the previously developed curriculum, infusing the objectives from each discipline. In this type of integration, the challenge to the teacher is to weave together the existing programs in science and mathematics with objectives from two separate and distinct curricular.

Process Integration Another approach to integrating mathematics and science is through the use of real-life activities in the classroom. By conducting experiments, collecting data, analyzing the data, and reporting results. Students experience the processes of science and perform the needed mathematics. In small groups, they formulate questions, identify a problem, decide how to collect data, collect it, and then interpret these data.

Thematic Integration Begins with a theme which then becomes the medium with which all the disciplines interact. For example, the theme could be oil spills: in mathematics you would be working with volume, surface area, and cost of cleanup; in science, you would be working with density and environmental aspects of oil spills. Thematic unit goes beyond integration of mathematics and science by including all other disciplines typically found in elementary and middle schools. For example, this unit would include an investigation of the economic and social implications of oil spills. While science and mathematics integration is important, integration of individual disciplines is subsumed under the integration implied by the investigation of the thematic topic.

What does it really mean to integrate science and mathematics? Whether the integration of science and mathematics occurs within the disciplines or is infused with the disciplines, integration will provide for a more reality-based learning experience. Four different types of integration. Each provides approach to integrating math and science disciplines.

Activity 4 In your group, select one activity in your science textbook and identify the type of M-S integration in that activity. Provide reasons for your classification.

Extent of M-S integration? Attention must be paid to not only "what" is being integrated but also to "what extent" each subject is being integrated. Integration doesn’t only involve mixing of disciplines but also whether the mixture is doing justice to the curriculum for each discipline. Are the activities meaningful and appropriate for the grade level they are being taught. In this context the term "meaningful" is used to describe activities that are relevant, engaging, and address Science Standards. "Appropriate for the grade level" refers to concepts and activities that are part of the school district curriculum scope and sequence.

Model of integration We need specific model to characterize the nature of the relationship between the mathematics and science being taught and the curricular goals for the disciplines.

ABC DE Activity 5

M. A. Huntley, 1998, School Science and Mathematics, 98, p. 322.

How do I Locate an activity on this Model? Involves answering the following questions: 1. What are the major mathematics and science concepts being taught in the activity? 2. Are these concepts worthwhile? That is, are they key elements of the curricula and meaningful to students?

Activity 6 Lesson on Observation of the properties of magnets Lesson on Fractions in third grade Lesson that includes concepts from the other discipline that are not at the same grade level are classified as or Mathematics and science content are both part of the curriculum for a particular grade level and the instruction is delivered in a meaningful way, the activities created are classified as

Activity Locate Sample lessons on the model

Sample Lesson 1 A math and science integrated activity where the mathematics content objective is measurement and the science content objective is the study of dinosaurs. To understand the nature of integration of this activity, it is necessary to determine the appropriateness of the mathematics and science content for the grade level that the activity is to be presented. For example, if dinosaurs are taught at one grade level and the measurement objectives are part of the curriculum at a lower grade level, the activity is considered to have a science focus on the continuum. If dinosaurs are part of the curriculum at the same grade level that the measurement objectives are taught, the activity is considered "balanced" on the continuum.

Sample lesson 2 The study of simple machines in science and proportions in mathematics. Groups of students are given meter sticks, a fulcrum, and various metric weights. After balancing the lever, the students are asked to determine the relationship between the masses of the weights and their distances from the fulcrum. After the students have worked on the relationship, the teacher can help the students arrive at the formula for a lever and its proportional relationship. Assuming the mathematics objectives are appropriate for the grade level at which the science activity is presented, this activity represents a high degree of integration where relevant mathematics content blends with meaningful science activities. The physical science domain provides abundant opportunities for balanced mathematics and science integration (e.g., density, buoyancy, force, and motion).

Sample Lesson 3 A typical middle school science activity may involve students exploring the concepts of specific gravity, buoyancy, and Archimedes’ principle. In this activity, students weigh various objects and calculate the volume and mass of the water displaced by the object. They then calculate the specific gravity and make a table of the results. This activity is considered to have a science focus because the purpose of the activity is to teach students about specific gravity, buoyancy, and Archimedes’ principle and involves the mathematical procedures of calculating volume, mass, and specific gravity. Moving beyond the mathematical procedures of merely calculating volume, mass, and specific gravity and seeking a conceptual understanding of the relationship of the ratio of the mass of objects to the mass of the water displaced (e.g., the rate at which the surface area of a ball of clay and the water it displaces changes as its shape is changed and the resulting effect on the specific gravity of the objects) is a much richer, more meaningful mathematical activity. In this instance, both the mathematics and science being taught are meaningful and appropriate (that is, they represent good instruction and are meeting curricular goals). In its new form, this activity is transformed and moved along the continuum to a more balanced integrated activity.

Activity 7 Resources for Integrated Math and Science

Summary Types of integration of math & science lessons. Nature and Extent of math and science integration? Resources for Integrated Math and Science.