Math In The Science Classroom

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

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?

Errors vs. Misconceptions

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

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

More Math Misconceptions Multiplication creates bigger numbers. Multiplication creates bigger numbers. Multiplication by 10 adds a zero. Multiplication by 10 adds a zero.  2.36 x 10 = Proportion of blue w/ 2 blue and 3 red items Proportion of blue w/ 2 blue and 3 red items  2/3 or 2/5?

Powers of Ten – Gahh! Distances Dilutions Environmental Science

Statistics: Correlation vs. Causation Belief: Fluoridated water causes cancer. 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. Belief: Marriage is bad for your health. –In Alabama, counties with higher divorce rates generally have lower death rates.

Probability Misconceptions Genetic probabilities Genetic probabilities Health probabilities Health probabilities

Mammography Statistics The probability that a woman has breast cancer is 1%. 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 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%. If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9%. 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%. A woman has a positive mammogram. What is her risk of actually having breast cancer?

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

And then there’s the Hadron Collider… Hadron Collider… Hadron Collider…

Graphing Difficulties

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

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

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

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

Graphing Misconceptions Interpretation Interpretation –Graph vs. picture Creation Creation –Title –Choice for x and y axes –Axis labels/units –Scaling –Scales not linear/uniform –Type

Types of Graphs Line Graphs Line Graphs  Plot related data points. Bar Graphs Bar Graphs  Emphasize individual data points. Pie Charts Pie Charts  Compare parts, or percents, of a whole. Histograms Histograms  Show frequency distributions.

Procedure Rubric Is this an experiment? Is this an experiment? –Valid hypothesis - falsifiable! –Identification of variables AND (very important): AND (very important):

Could you personally do this experiment successfully using this procedure?

Math Teacher Estimates of Student Interest and Comprehension of Probability

Worst Graph Ever?

Best Pie Chart Ever?

The Case of the Missing Workers MeasurementsGraphing

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

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