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Math In The Science Classroom

Math In The Science Classroom. Guidelines for Preventing Math Errors. Keep track of all information (paper trail). Use visual keys, such as arrows. Keep track of units. State answer clearly, WITH UNITS. Check that your answer makes sense.

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Math In The Science Classroom

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  1. Math In The Science Classroom

  2. Guidelines for Preventing Math Errors • Keep track of all information (paper trail). • Use visual keys, such as arrows. • Keep track of units. • State answer clearly, WITH UNITS. • Check that your answer makes sense.

  3. You have a bowl with 2 oranges and 3 apples. If you reach into the bowl without looking, what is the probability that you will grab an orange? Or is it 2/3?

  4. Errors vs. Misconceptions

  5. Examples of Math Misconceptions • 1/3 vs. 1/8 - which is bigger? • Belief - Larger denominator is bigger. • 2.36 vs. 4.2 - which is bigger? • Belief - Numbers with more digits are bigger. • g vs. mg - which is bigger? • Belief - More letters mean bigger units.

  6. Examples of Math Misconceptions • Numbers with more digits are bigger • 2.36 vs. 4.2 • More letters mean bigger units • g vs. mg • Multiplication by 10 adds a zero • 2.36 x 10 = 2.360

  7. Powers of Ten – Gahh! Distances Dilutions Environmental Science

  8. Statistics:Correlation vs. Causation • Belief: Fluoridated water causes cancer. • Nations that add fluoride to their water have a higher cancer rate than those that don't. • Belief: Marriage is bad for your health. • In Alabama, counties with higher divorce rates generally have lower death rates.

  9. Probability Misconceptions • Genetic probabilities • Health probabilities

  10. Mammography Statistics • The probability that a woman has breast cancer is 1%. • If a woman has breast cancer, the probability that she tests positive is 90%. • If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9%. A woman has a positive mammogram. What is her risk of actually having breast cancer? A. Out of 10 women with a positive mammogram, ~9 have breast cancer. B. Out of 10 women with a positive mammogram, ~1 has breast cancer. C. The probability that she has breast cancer is about 1%.

  11. "There are three kinds of lies: lies, damned lies, and statistics." Sounds more impressive than cutting the risk from 2.8% to 1.5%, doesn’t it?

  12. And then there’s the Hadron Collider…

  13. Graphing Difficulties

  14. Graph Interpretation Problems • Graph vs. picture • Slope vs. height • Disconnect from data tables

  15. What type of graph should I use? • Line Graphs • Plot related data points. • Bar Graphs • Emphasize individual data points. • Pie Charts • Compare parts, or percents, of a whole.

  16. What’s wrong with this graph? • Inadequate (and inaccurate) title • Axes poorly labeled – units? • No grid • Inappropriate scale

  17. What’s wrong with this graph? • No title • Axes poorly labeled – units? • Not well-gridded for interpretation • Should this be a straight line?

  18. Worst Graph Ever?

  19. Best Pie Chart Ever?

  20. The Case of the Missing Workers Measurements Graphing

  21. What do we need to know? • Where is the ulna? • How will we measure it? • How will we analyze the data?

  22. I have not failed. I've just found 10,000 ways that won't work.  - Thomas A. Edison

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