PHS 594/MTE 598

Integrated Mathematics and Science for Middle School (3 semester hours)

Instructor: Rob MacDuff, Ph.D. in mathematics education <macduff@asu.edu>

Teaching Assistant: to be announced

Description: Models and modeling as an integrating theme for middle school mathematics and science.

Course objectives:

(1) Develop a modeling approach to learning arithmetic, pre-algebra and science by creating an understanding of the common models that coordinate these three areas.

(2) Develop student activities that support both math and science (an approach to mathematics that makes it science-friendly).

(3) Explore structures inherent in the real world and conceptual tools used to represent them.

(4) Develop an understanding of learning and how model-based instruction incorporates theories of learning into student activities.

(5) Create learning environments that encourage thinking, reasoning and understanding, with a special focus on proportional reasoning.

Course content:

Utilizing the modeling method of instruction, abstract mathematical concepts such as number, fraction, and ratio will be used to develop mathematical models of physical situations that contain either part/part or part/whole relationships. The development of a solid understanding of number is an essential step in developing the concept of measurement, which is a necessary prerequisite to understanding science concepts.

Math and science standards will be examined to identify alignments among core subject areas. Discovering the commonalities these standards have can point to ways that science instruction can improve student performance on mathematics standard-based assessments, and vice versa.

An emphasis will be placed on the use of activities that create environments for student to demonstrate their thinking, reasoning and understanding.

Basic Models:

The emphasis of this course is to develop mathematical and graphical models that can be used to describe science phenomena. Thus for each of the following models, an understanding of when, why and how each model can be built and used will be developed. The model names reflect the types of activities required to construct the model from a physical perspective.

(1) Partitioning model: Physical situations that are partitioned into equivalent subsets are generally modeled by either products or fractions depending upon whether the system as a whole is considered or just partitions. This model is a common thread in strands 1, 3, 4 & 6 of the Arizona Mathematics Standard.

(2) Grouping model: Physical situations that require grouping as a means of description are generally modeled by division. This model is a common thread in strands 1, 2, 3, 4 & 6 of the Arizona Mathematics Standard.

(3) Counting model: The collection of objects to form groups can be modeled by means of arithmetic. This requires understanding of number as both count and as operator. This model is a common thread in strands 1, 2 & 4 of the Arizona Mathematics Standard.

(4) Measurement model: The difference between number and measure will be explored. This model will be used to address aspects of strand 4 of the Arizona Mathematics Standard.

(5) Coordination model: Different quantities can be associated with one another by some conversion factor. The conversion factor specifies that one quantity is equivalent to another. Mathematically this relationship is referred to as a ratio. This model will be used to address aspects of strand 4 of the Arizona Mathematics Standard.

Punctuality and active participation in class and group activities are crucial to the learning experience. Homework will be assigned from time to time but the emphasis will be on cooperative learning experiences and collaborative curriculum development activities.

All participants will be subscribed to BlackBoard, an online discussion forum hosted by ASU. Each participant will be expected to submit questions or respond to questions. Teachers are encouraged to share their experience in light of what is being taught in class and the course reading material. Assignments will also be posted as a means of compiling curriculum resource materials.

No textbook.