Teaching Developmental Math

throughProjects and Rich Problems

Michael C. BurkeCollege of San Mateo

TMP-RPM Summer Math InstituteSleeping Lady Mountain Retreat, Leavenworth, WA

August 24, 2010

burke@smccd.edu

. Focus on Problems

In the final analysis, the best measure of the quality of a course will reflect the quality of the work that the students in the course actually produce. And the work that the students produce is largely the work they are asked to produce.

What problems do we ask our students to solve?

Klamath River Salmon

It’s not (only) about the fish …

Klamath River Salmon

This river is remarkably clear and crouded with salmon in maney places, I observe in assending great numbers of salmon dead on the shores, floating on the water and in the Bottom which can be seen at the debth of 20 feet, the cause of the emmence numbers of dead salmon I can’t account for so it is … The number of dead Salmon on the Shores & floating in the river is incrediable to say – and at this Season they have only to collect the fish Split them open, and dry them on their Scaffolds on which they have great numbers … great quants. of salmon on scaffolds drying.

Journal of William ClarkOctober 17, 1805Lewis and Clark Expedition

Klamath River Salmon: Data and Graph

250000

200000

150000

100000

50000

0

count

2015201020052000year

Inriver Salmon Run, Klamath River

Overview

1. Introduction

2. Exercise: Klamath Salmon

3. Overview

4. Exercise: George Will, Al Gore, Arctic Sea Ice

5. Exercise: Moose, Malthus, World Population

6. Thoughts: Using This Material

7. Thoughts: Ideas that Are Central to My Work

8. Conclusion

Initial Focus

My initial focus was relatively narrow. I saw the data-based assignments as an interesting supplement to my mathematics classes. In particular, I wanted to:

• ask my students to use a spreadsheet to examine functions from numeric, geometric and analytical points of view

• offer my students genuine applications of mathematics

• teach through interdisciplinary problems, so that my students would see that knowledge is not constrained by disciplinary boundaries

• ask my students to write about mathematics because I had the conviction that writing about mathematics would help them to clarify their mathematical thoughts

First Steps

For the past few years, I have been designing, and assigning, data-based integrative writing assignments in my mathematics classes.

Each assignment presents the students with a data set about an important issue. Students are asked to analyze the data mathematically by constructing a mathematical model, and then to use a spreadsheet to implement the model.

They are to produce a written paper in which they present their model (with a table and a graph), and then use this work as a basis for any conclusions that they reach.

Central Questions

As I became involved with this work, I became increasingly interested in questions of a completely different type -- questions such as:

How do we know that something is true?

How do we make a decision?

How do we even know what we really think?

To think about how these questions play out in the real world, we look at a case study: Al Gore and George Will on the topic of global warming.

An example of developing assignments:

We will now look at Al Gore and George Will on the topic of global

warming.

1

2

1

2

Al Gore’s use of the slide:Al Gore's Presentation

1

2

2

1

1

2

Totals: 7 cooling / 20 neutral / 44 warming

The WACPack Version

The English Teacher’s Version