Tuesday, April 17, 2012


What if we could design a project-based class for middle school students that integrated math and science-- that provided context for math and gave instructional minutes back to science?  What if this class capitalized on the natural correlation between the Practices For K-12 Science Classroom and the Standards for Mathematical Practice.  What if students were asked to design investigations, used modeling to move from the concrete to the abstract and then presented their findings for peer review?  What if they used technology to take snapshots of their learning along the way and kept a running journal of the process?

What if...


Anonymous said...

Thought-provoking questions! My school has a "model" similar to what you describe, with math and science paired in the earlier grades. In practice, I have seen it play out quite differently from the philosophy with which it was designed. Mostly, "math" in this situation gets relegated to 'the formulas we use to solve scientific problems.' Your vision sounds much deeper.

Frank Noschese said...

Hi David,

Jane Jackson asked me to post this on her behalf:

Arizona State University offers a summer graduate course for 8th and 9th grade teachers to prepare them to integrate math and physical science.

Methods of Physical Science Teaching II (June 11-29, 2012)
(Physical Science with Math Modeling Workshop II)
* focuses on force, motion, introductory chemistry, nature of science
* aligned with Common Core Standards
* all 8 scientific practices of NRC Framework for K-12 Science Education
* collaboration, creativity, communication, and critical thinking
* systems, models, modeling
* coherent curriculum framework
* literacy in science and math
* Multiple learning styles are addressed.
* Naive student conceptions are addressed.
* authentic assessments
* Details at http://modeling.asu.edu/MNS/MNS.html
* For information: Jane.Jackson@asu.edu

PHS 594/PHY 494 provides a deep understanding of standards-based content in 8th and 9th grade physical science and mathematics. To exemplify effective instruction, the course is taught using a robust pedagogy, Modeling Instruction.

In 2001 the U.S. Department of Education recognized ASU's Modeling Instruction Program as one of two EXEMPLARY K-12 science programs in the nation.

Content of an entire semester course is reorganized around basic models to increase its structural coherence. Participants are supplied with a complete set of course materials (resources) and work through activities alternately in the roles of student or teacher.

The Modeling Method is introduced as a systematic approach to design of curriculum and instruction. The name Modeling Instruction expresses an emphasis on making and using conceptual models of physical phenomena as central to learning and doing science.

Mathematics instruction is integrated seamlessly throughout the entire course by an emphasis on mathematical modeling.

Student activities are organized into modeling cycles that engage students systematically in all aspects of modeling. (Specifics of the modeling cycle are at http://modeling.asu.edu/modeling-HS.html.) The teacher guides students unobtrusively through each modeling cycle, with an eye to improving the quality of student discourse by insisting on accurate use of scientific terms, on clarity and cogency of expressed ideas and arguments. After a few cycles, students know how to proceed with an investigation without prompting from the teacher. The main job of the teacher is then to supply them with more powerful modeling tools. Lecturing is restricted to scaffolding new concepts and principles on a need basis.

David Cox said...

I don't think turning math into the stuff you do to get right answers in science would be very interesting. Surely computational thinking would be a component, but I'm more interested in the entire process of moving from concrete to abstract.

Sounds interesting. And right in the wheelhouse of what I'm talking about. It's almost scary how close these two ideas are.

Frank Noschese said...

Also FYI regarding models/functions in science and math:


1) Linear model:
* Rate of change = constant.
* Common representations are graphs and equations
for straight lines (e.g., velocity, acceleration,
force, momentum, energy).

2) Quadratic model:
* Change (in rate of change) = constant.
* Usual representations are graphs and equations for parabolas (e.g., accelerated motion, kinetic and elastic potential energy).

3) Exponential model:
* Rate of change is proportional to amount.
* Representations include graphs and equations of exponential growth and decay (e.g., population growth, radioactive decay).

4) Harmonic model:
* Change (in rate of change) is proportional to amount.
* Usual representations are graphs and equations of trigonometric functions (e.g., waves and vibrations, harmonic oscillators, situations in electricity and magnetism such as simple AC circuits and LC circuits).