To: Math faculty and others interested

From: Peter Hayes and Rob Hawley

Re: Report on initial use of Lakeside Indicators in math classes

Sept. 1996

This past year we made an initial stab at helping math students reach academic goals through the work of analyzing and reporting on one of the seven indicators which make up Lakeside's Indicator Project. We've put together and shared this simple report because we think and hope that the work will interest you. Because there is much good potential for further work, both within individual classes and as a cooperative venture within the department, we hope that you might consider whether it might help you reach goals you have set for your students. We are both happy to discuss or help with the work in any way.

Background: An indicator is a small, measurable piece of information which can help us understand the functioning of a larger system. As you may remember, two years ago the school went through a process of selecting and beginning to use seven indicators of the health and functioning of the school campuses and community. The decision was made to work toward integrating the work of tracking and learning from the indicators into the school's existing curriculum. For more information, look at the "Indicators Project" section of Lakeside's web site; it is under "collaborations". Similar indicators projects are being actively used on the city, county, state, national, and global level.

Purposes of Rob's Work:

1) To help two sections of Precalculus students understand periodic functions.

2) To research, analyze, and present information on some aspects of the school's use of natural gas, electricity, and water. Through this, engage students in thinking about and positively shaping how resources are used at the school and beyond.

3) To use the world wide web and related tools to help reach the above goals.

Approach Taken:

1) We agreed on purposes and method, divided tasks, and collected necessary data

2) Rob personally did the exercises that students would be assigned to test data quality and generally see how things would work. Several good examples, ie data sets that exhibited periodic behavior, were identified. This is said with the following caveat: juniors have much less tolerance for and ability to cope with messy data. If data points are missing, seem out of range at all, the students want to say that the entire set of data is invalid - see lessons learned 1.

3) Introduced the work to students in a long period session in the Orchard. Peter gave basic background on indicator projects and their value as well as basic instruction on Netscape. Rob set work into context of the course, was clear in his enthusiam, expectations, and assignments.

4) The classes were split into two groups, each worked a different set of data. See lessons learned 2. 3.

See attached assignment.

Lessons Learned:

1. Use "clean " data to the greatest extent possible.

2. Break class into small groups of 3 or 4 - while it is nice to achieve collaboration at a greater scale, this open ended work is tough for them. The ability to agree upon and follow a strategy for analyzing the data is crucial and smaller groups help.

3. Have groups from the same class work the same data - this gives the opportunity for large scale brainstorming and progress (reality) checks that may help keep everyone moving towards a conclusion.

4. Plan for specific people/groups to take responsibility for posting results. This part of the process was eventually ignored as the assignment took up so much class time.

Next Steps:

I still feel this can be a valuable and effective means for introducing periodic situations. I would like to put together a complete example of the work done last year and provide this as reference for groups working the modified assignment this year.

Lakeside is one of many organizations that have recently undertaken "indicators" projects (Sustainable Seattle, Sustainable St. Louis, Willapa Region, etc.). In each case, the community selects and uses indicators to help understand their progress relative to shared goals. In most cases the overall goal is sustainability.

The Lakeside project has collected data in seven indicators categories; Recource Consumption, Diversity of the Community, Diversity of Participation, Acceptance and Inclusion, Levels of Stress, Curriculum Vitality and Relevance, and Size of the School's Endowment. The idea is that the numbers collected in each of these areas have meaning, that they are indicative or represent something about the sustainability of the community.

Our job is to consider data collected from the Resource Consumption category with the following goals.

1. Describe the particular sets of data in terms of mathematical functions. This will include analysis of features such as maximums and minimums, slopes and also a comparison of Lakeside's numbers with other local communities. We studied Lakeside 's consumption in the following areas and we have determined that.....

2. Use the mathematical model determined in 1. to make conclusions regarding what the numbers say about the health of the community. It may then be possible to make recommendations relating to this indicator and the community's objective of moving towards health and sustainability. Here is what we think the numbers say about Lakeside and what we think should be done in response .

3. Produce a report of your analysis, results and recommendations or conclusions. This report will be incorporated into the Indicators Project and accessible through the Lakeside home page under "Collaborations" (we will discuss how this is done). The importance of the report is that it will document progress towards the project goal and also provide a reference for future analysis of indicators data. It will be critical to provide details of the steps to your analysis so that they may be repeated in the future or modified as necessary. This is the analysis we performed in 1996 along with the results and conclusions from our study... We would modify our procedure next time by....

The class will be divided into two groups, each with specific sets of data to analyze. Both groups will consider and report on solid waste data for 1994-1995. The groups will then consider different sets of utilities data. This second analysis will be completed with reference to related statistics from outside the Lakeside community. Specifically, one group will test electricity usage at Lakeside and for the local region. The other group will study natural gas usage and local heating degree days.

Here are some points to consider as you design and complete your analysis and report.

- Take some time initially to decide as a group how your numbers would work as "indicators". What might they say about the community in general?

- Record your hypotheses prior to starting your statistical analysis...what patterns do you expect the numbers to follow?...what sort of function might be used to model this data? Linear functions of the form f(x) = ax + b and trigonometric functions of the form f(x) = AsinB(x-C) + D may be useful.

- With the above ideas to guide your thinking, perform the data analysis and then carefully record as many meaningful results as possible. As you conduct the analysis, you will notice trends and details about the numbers...record this information.

- Discuss how your results confirm or refute your earlier hypotheses - do different patterns emerge for which there are logical explanations?