The Math Concepts Challenge

Would you help us with an experiment on students' understanding of some basic ideas?

We have questions for your students to consider. To keep your news feed from getting filled with long forms, the form is embedded after a jump so we'll need you to visit each page separately. In order to allow for confidentiality and still allow students to review their answers, please have your students come up with a FakeName and use that FakeName for all fifteen questions.

We think it would be best if you point your students to this form and have them record their thoughts on each question BEFORE any class discussion, perhaps as a homework assignment the evening before, but we'll leave that up to you as a teacher. If students wish to change their thoughts after class discussion, please ask that they submit a new entry.

Thanks!

The Grant Wiggins Math Concepts Challenge ...

Question 1:  "You can't divide by zero". Explain why not.
To the best of your understanding, explain why you can't divide by zero, even though you can multiply by zero.

Question 2 - Equivalence

"Solving problems typically requires finding equivalent statements that simplify the problem." Explain.

Question 3: Invert and Multiply
You are told to “invert and multiply” to solve division problems with fractions. To the best of your understanding, explain why this works and when it works; include any situations for which this instruction doesn't work.

Question 4: Organized list of numbers
Place the given numbers in order from largest to smallest and predict the errors that some of your classmates might make.

Question 5: Multiplication is Just repeated Addition.
Explain why this statement is false, giving examples.

Question 6: Catering the Party.
How many tables will be needed?

Question 7: Most teachers use the mean to assign a grade, but this measure hides information. What information is hidden and what, if anything, should we do about it?

Question 8: Conversion Equations
Create the equations that a website or a calculator might use.

Question 9: Imaginary Numbers
Why were imaginary numbers invented?

Question 10: Conventions
What is the difference between a convention (such as PEMDAS) and a law (such as the distributive property)?

Question 11: Precision and Accuracy.
What's the difference?

Question 12: Undefined Terms in Geometry.
If we can draw them, why can't we define them?

Question 13: Axioms.
What are they and why can we use them?

Question 14: Point Nines
It's that old chestnut:    0.9999999999999 ... 1?

Question 15: Negative times a negative is ... ?
Why do we say that?