Consortium for Mathematics and its Applications

Product ID: Biomath
Textbook
High School

Imperfect Testing : Breast Cancer Case Study (Student)

Author: Published by COMAP, Inc. in conjunction with DIMACS, Rutgers University.


What is the BioMath Connection (BMC) Project?

BMC was a pioneering project linking biology and mathematics in the high schools. It provided an opportunity for high school teachers, writers, researchers, and others to get in on the ground floor of developing innovative classroom materials. The materials consist of 20 modules that can be flexibly adapted for use in a variety of courses at a variety of grade levels in both biology and mathematics. The project was run by DIMACS at Rutgers University in collaboration with the Consortium for Mathematics and its Applications (COMAP) and Colorado State University (CSU).



The results of a mammogram, like those of many tests, are not always correct. A false positive test result may create unnecessary anxiety, while a false negative test result may lead to a false sense of security. In this unit, students examine the case of an adult female who learns her mammography test is positive. They then use real data to calculate the probabilities of receiving true (or false) test results and discuss the possible implications of a positive test result, given the properties of the test. These properties, which include sensitivity and specificity, can be used to help determine the rates of incorrect test results. Students also investigate the importance of disease prevalence.
Following a positive mammogram the woman has a genetic test through which she learns she has the BRCA gene mutations associated with breast cancer. The students investigate what it means to have this mutation and how scientists are working on medical treatments that can be tailored to a particular genetic profile. Finally, knowing their mother is positive for the BRCA mutation leads to a dilemma for her daughters. They must decide if they will be tested for this BRCA allele, since results from testing for this allele still do not definitively determine whether or not a woman will develop breast cancer.

Topics
Biology:
Imperfect testing, genetic testing, genetic variation, pharmacogenetics, ethical choices, decision making based on data interpretation, taking perspectives, gold standards.
Mathematics: Probability, conditional probability, Bayes' Rule.

Prerequisites
Biology:
Basic understanding of DNA structure and function; what a gene is and that an allele is a version of a gene.
Mathematics: Ratios and proportions; calculating percentage.

Length
This unit consists of 6 lessons and will take 4-6 class periods (45 minutes each).

©2015 by COMAP, Inc.
BioMath Student Edition
40 pages

Mathematics Topics:

  • Various

Application Areas:

  • Biology

Prerequisites:

Various

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Related Resources

Imperfect Testing : Breast Cancer Case Study (Teacher)

What is the BioMath Connection (BMC) Project? BMC was a pioneering project linking biology and mathematics in the hig...

COMAP, Inc.

COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.


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