Math In The Science Classroom Guidelines for Preventing Math Errors Keep track of all information...

Math In The Math In The

Science Science

ClassroomClassroom

Guidelines for Guidelines for Preventing Math ErrorsPreventing Math Errors

Keep track of all information Keep track of all information (paper (paper trail).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 Check that your answer makes sense.sense.

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

Or is it 2/3?Or is it 2/3?

Errors vs. Errors vs. Misconceptions Misconceptions

Examples of Math Examples of Math MisconceptionsMisconceptions

1/3 vs. 1/8 - which is bigger?1/3 vs. 1/8 - which is bigger?

Belief - Larger denominator is bigger.Belief - Larger denominator is bigger.

2.36 vs. 4.2 - which is bigger?2.36 vs. 4.2 - which is bigger?

Belief - Numbers with more digits are 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.Belief - More letters mean bigger units.

Examples of Math Examples of Math MisconceptionsMisconceptions

Numbers with more digits are Numbers with more digits are biggerbigger

2.36 vs. 4.22.36 vs. 4.2

More letters mean bigger unitsMore letters mean bigger units

g vs. mgg vs. mg

Multiplication by 10 adds a zeroMultiplication by 10 adds a zero

2.36 x 10 = 2.3602.36 x 10 = 2.360

Powers of Ten –Powers of Ten – Gahh! Gahh!

Distances

Dilutions

Environmental Science

Statistics:Statistics:Correlation vs. Correlation vs.

CausationCausation Belief: Fluoridated water causes cancer.Belief: Fluoridated water causes cancer.

– Nations that add fluoride to their water have Nations that add fluoride to their water have a higher cancer rate than those that don't. 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 In Alabama, counties with higher divorce rates generally have lower death rates. rates generally have lower death rates.

Probability Probability MisconceptionsMisconceptions

Genetic probabilitiesGenetic probabilities

Health probabilitiesHealth probabilities

Mammography Mammography StatisticsStatistics

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 If a woman has breast cancer, the probability that she tests positive is 90%.tests positive is 90%.

If a woman does not have breast cancer, the probability If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9%.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 And then there’s the HadronHadron Collider… Collider…

Graphing Graphing DifficultiesDifficulties

Graph Interpretation Graph Interpretation Problems Problems

Graph vs. pictureGraph vs. picture

Slope vs. heightSlope vs. height

Disconnect from data tablesDisconnect from data tables

What type of graph What type of graph should I use?should I use?

Line Graphs Line Graphs Plot related data points.Plot related data points.

Bar GraphsBar Graphs Emphasize individual data points.Emphasize individual data points.

Pie Charts Pie Charts Compare parts, or percents, of a Compare parts, or percents, of a

whole.whole.

What’s wrong with this What’s wrong with this graph?graph?

Inadequate (and inaccurate) titleInadequate (and inaccurate) title Axes poorly labeled – units?Axes poorly labeled – units? No grid No grid Inappropriate scaleInappropriate scale

What’s wrong with this What’s wrong with this graph?graph?

No titleNo title Axes poorly labeled – units?Axes poorly labeled – units? Not well-gridded for Not well-gridded for

interpretationinterpretation Should this be a straight line?Should this be a straight line?

Worst Graph Ever?

Best Pie Chart Ever?

The Case of the The Case of the Missing WorkersMissing Workers

MeasurementsMeasurements

GraphingGraphing

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 have not failed. I've just found I've just found 10,000 ways that 10,000 ways that won't work.won't work.

  -   - Thomas A. EdisonThomas A. Edison