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(Statistics): This is a project I do with my 11th grade students. They study a unit on statistics that deals with mean, median, mode, standard deviation, graphing data, least squares regression lines, correlation, and independence/dependence of two variables. They first study the theory and this takes the first semester. This is a grueling process for girls where they cannot see the end result of this theory. At the end of the first semester the girls write down a topic of interest. Usually this is sports, or medicine, or business, or engineering. Based on their interest the girls either collect their own data or find data on the web that relates two variables…Students gather data and then write a mathematics paper on the relationship between the two variables… The excitement of proving something or using their math skills to prove something is both energizing and brings new life to the theory they have learned all year. Using their skills in an application allows girls to connect the theory with their interest. The paper is like a history paper which has about six sections including an introduction, research, a hypothesis, data collection, an analysis, and thoughts on the process. As they write each section, students work with each other and with me to get feedback on their ideas. They present their ideas to the class and are very engaged when presenting to their peers. This process helps them sort through their ideas collectively.
The girls in my in Honors Pre-calculus class (10th & 11th grade) completed an activity where they needed to model the data from the SARS epidemic that took place in Hong Kong during 2003. The activity took place while they were learning about different types of exponential functions. The girls were presented with a data table that contained two variables; days since March 23, 2003 (the initial diagnosis date) and the total number of cases of SARS diagnosed up to that date. Their task was to fit a model so that they could predict the total number of cases of the disease. The girls put the data into their graphing calculators and produced a scatterplot of the data to get a visual feel for what the data looked like. They broke themselves into small groups to work on the modeling process. After a few moments they realized that the models that they had studied would not fit this data well so they wanted to know about different types of models. In class we spent time discussing the way disease travelled and the fact eventually there could be no more people left to infect. They were presented with a logistic model which is a model used on this type of data. They spent most of the period trying to find an appropriate model that would fit through the data point. Their assignment was to write up their findings and use the model to predict the total number of cases of SARS.

What made this particularly effective was the fact that this did not stop after the class period ended but instead carried on for several days beyond because the girls wanted to explore the model and come up with different ways to assess its effectiveness. They asked for other data to continue exploring the modeling concept with so they were given a data set that looked at the amount of oil produced in the US between 1930 and 1950. This data set led them in several directions including their own research component to find out more about oil production so that they could correctly model the data. Their curiosity led them to a deeper understanding of both the mathematical models and the modeling process itself. The conversations that took place in class were related to the importance of modeling and the mathematics we were learning was much deeper than just the formulas on the pages of their text books. Many of the girls told me that this was the first time in life that the math they were learning had real meaning to them because they saw the real application for the math. The conversations around these two data sets have carried on for several weeks, both in class and during office hours because they want to have more information and to be able to think about the concepts from a different perspective. In the end, each girl needed to turn in two different documents each including a model and an explanation for each of the data sets. Each student’s work exceeded my expectations for the assignment and showed a deep understanding of the mathematics as well as the phenomenon they were trying to model.