Kathleen Z. Rooney
The idea of this unit is to teach math around a purpose. The goal is for students to seek out math applications on an "as needed" basis to answer questions about the diseases we are focused on. The students who can utilize this unit will likely be high school students in an integrated math course that exposes students to statistics as well as functions. The goal of the unit is to illuminate the bridge from univariate to bivariate data and integrate the interpretation of statistics with algebraic representations of real life relationships.
Principles of statistics will be used to collect, vet, analyze and display information about Lyme and WNV. Single variable distributions will be evaluated using measures of center and spread. We will apply evolutionary thinking to predicting environmental pressures that affect the health and growth of particular organisms, such as the tick. This leads us to connect two factors, x and f(x), and enter the world of bivariate data. We will test our assumptions using correlation and regression. We can analyze and predict the growth of disease by studying the range of our x variable.
This is an exploration model, with the teacher serving as facilitator and guide. Lessons have concrete tasks to complete. Students will explore materials to seek out information needed to accomplish the tasks. Students will be provided with materials (films, research writings, newspaper articles and websites) and a list of the assignments (assessments) required for each section of the unit. The teacher guides the groups to fulfill the assignments. Following each completed assignment, students will share the information they have collected with the other groups.
Math cannot help but be deep and abstract. Understanding its depth requires a student's ability to apply the tools they have learned. Like reading, it must become a meaningful symbolic language, not simply a page of ciphers and symbols to be manipulated. Great literature is full of nuance, subtexts and symbolism and so too are the nuanced uses of math, and ways to interpret numerical information that we have collected. Once applied in a specific way, students are able to approach synthesis of mathematical ideas by generalizing the application to a broader range of cases. This unit strives to connect the depth of mathematical reasoning with the students' curiosity. The subjects of disease, death, plague and survival capture our collective imaginations and can make for some intriguing examples to explore and analyze. In addition, we focus on two diseases that are geographically and temporally relevant. Restricting our focus to two diseases is intended to make the manipulation of numerical data about the diseases clear. It is an excellent interdisciplinary exploration into the sciences of biology, public health, medicine and environmentalism.
Unit Objectives
Enduring understanding
Math can help us study the process of evolving diseases. The engine of evolution is random mutation, mimicked by probability. The pressure of environment leads to success or failure of a mutation. Statistics helps us look at variation and possibilities and find patterns. Through our study of data and statistical analysis, we may find patterns created by the data. Writing a function that emulates the data we have collected is a powerful tool, known as modeling. When we discover correlations between variables such as environmental influences and populations we can explore these relationships through linear functions. Modeling, combined with evolutionary prediction and analysis can help us to understand and reduce the risk of diseases.
Mathematical objectives
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1.1 Use principles of Statistics to collect organize and analyze information that relates to West Nile Virus and Lyme disease.
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1.2 Sort information categorically and numerically
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1.3 Create a collection of values (distribution) about the diseases of interest that can be analyzed and compared to other distributions using
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a. Measures of center
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b. Measures of spread
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1.4 Using the previous univariate data, suggest a relationship using an independent variable (x) and an x-dependent f(x) variable. Plot as a scatterplot.
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1.5. Using the scatterplot, find the mean of x and mean of f(x). Using that point as a pivot, manually draw a line of best fit.
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1.6 Use a statistics utility to create a regression model for the data. Discuss the relationship between the visual representation (graph) and algebraic representation (equation).
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1.7 Use correlation to test the relationship proposed in 1.5. Discuss correlation and best fit.
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1.8 Use data, regression models and evolutionary thinking to suggest public and personal actions and policies around these two diseases
Biological objectives
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1.1 Analyze historical information about the diseases of West Nile Fever and Lyme disease and their presence in New Haven County and in Connecticut. Create a disease profile for each illness that describes symptoms and outcomes and identifies the pathogen that causes these illnesses.
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1.2 Identify vectors, hosts and reservoirs in vector-based disease systems and create diagrams that follow the life cycle of the disease vectors.
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1.3 Collect information about environmental factors that affect the health of the various organisms in the life cycle of these pathogens.
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1.4 Using evolutionary thinking, predict environmental and social factors that have contributed to the growth of these diseases in our current situation.
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1.5 Test your hypothesis using a scatterplot to visually check for a relationship between the variables you have chosen to investigate.
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1.6 Evaluate and discuss the linearity of the relationship between the variables investigated. Evaluate any outliers or unusual observations.
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1.7 Discuss exponential growth and disease, looking at historical disease models and looking at the mechanics of bacterial and viral reproduction.
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1.8 Use data, regression models and evolutionary thinking to suggest public and personal actions and policies around these two diseases.
Assessments
In relation to each objective in the unit, students will submit the following work as an ongoing assessment of their understanding of and attainment of the objectives. Students will be divided into working groups to research either West Nile Fever or Lyme Disease Students will:
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1.1 Interpret several types of tables and charts with data about our target diseases. Read historical information about the diseases. Create a profile of the disease including symptoms as well as outcomes of these illnesses and describes the pathogen that causes the illness. Shape a targeted question for further research.
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1.2 Construct a pie chart or histogram showing regions of Connecticut and their rates of disease
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1.3 Using Lyme disease incidence in two counties in Connecticut and the rates of West Nile Virus-infected mosquitoes in several Connecticut counties, compare measures of center and spread by using box and whisker plots.
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1.3.2 Create a diagram showing the life cycle of the pathogen that they are studying.
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1.4 Collect data from primary sources (government websites/weather almanacs) related to the life cycle drawing from 1.3. Using the data, your previous graphs, and evolutionary thinking to support your writing, suggest a hypothetical relationship between disease rates increase or decrease and environmental factors and create a scatterplot of the data collected about variable x, and population, f(x).
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1.5 Manually fit a line of best fit. Discuss the slope and approximate fit of the data points and write a descriptive model that includes the hypothesis, research and the mathematical graphic.
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1.6. Use the data from 1.5 and a statistics utility to create a regression model for the data. Predict data points outside of the collected data, using your function and line of best fit. Write a comparison of the line of best fit and the regression model.
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1.7 Perform correlation tests to demonstrate or disprove predicted relationships.
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1.8 Write policy suggestions for New Haven County to reduce future disease cases. Use all of your work from the unit to create a supporting document for your policy suggestions.
