1. www.BioInteractive.org Math and Statistics in the Biology Classroom Paul Strode Pre-IB/IB Biology/Science Research Fairview High School, Boulder, CO 22 nd year teaching

2. 2002 Going Beyond the Mean: Statistics in the High School and College Science Classrooms Fairview High School 64 students in IB Biology 500 students in the Senior Class (13%) 87% of students may graduate with little, if any training in data and error analysis Math and Statistics in the Biology Classroom

3. Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org 2009-2011

4. Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org 2009-2011

5. Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org 2009-2011

6. Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org 2013

7. Schlotter, N. E. 2013. A statistics curriculum for the undergraduate chemistry major. Journal of Chemical Education 90:51-55. Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org 2013

8. Framework for K-12 Science Education (2011) By grade 12, students should be able to: ● Analyze data systematically, either to look for salient patterns or to test whether the data are consistent with an initial hypothesis. ● Recognize when the data are in conflict with expectations and consider what revisions in the initial model are needed. ● Use spreadsheets, databases, tables, charts, graphs, statistics... Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org

9. Chapter 3: Dimension 1: Scientific and Engineering Practices; Practice 4: Analyzing and Interpreting Data The National Academies Press (2011), p. 3-30 Going Beyond the Mean: Statistics in the High School and College Science Classrooms Math and Statistics in the Biology Classroom www.BioInteractive.org

10. 2013 nextgenscience.org Math and Statistics in the Biology Classroom www.BioInteractive.org

11. MS.ETS1 Engineering, Technology, and Applications of Science HS.ETS1 Engineering, Technology, and Applications of Science 2013 nextgenscience.org Math and Statistics in the Biology Classroom www.BioInteractive.org

12. The College Board (2012), p. 98 The College Board gets a little more specific Math and Statistics in the Biology Classroom www.BioInteractive.org

13. Error bars to indicate uncertainty Mean and Standard Deviation Student’s t-Test Correlation and Regression Impossible! Math and Statistics in the Biology Classroom www.BioInteractive.org

14. ● Calculation of Variance, Standard Deviation, and using 95% Confidence Interval error bars to illustrate uncertainty in summarized data ● The Student’s t-Test to compare two means ● One-Way Analysis of Variance (ANOVA) to compare more than two means ● The Chi-square Test to compare observed with expected distributions ● The Pearson Product-moment Correlation Coefficient (r) and Linear Regression (r 2 ) to determine the strength of a relationship ● But we also must build a solid foundation: The meaning of the hypothesis/explanation in science. The difference between a hypothesis/explanation and a prediction. The null statistical hypothesis (H 0 ) p-values Degrees of freedom (df) We can do ALL of this for SOME of our students and we can do SOME of this for ALL of our students. Math and Statistics in the Biology Classroom www.BioInteractive.org Statistics Modules for 1 st year Biology: YOU → YOU ALL → WE