Compare and Contrast in Math

Compare and contrast is something often used in Social Studies, English, or other subject but it is not something used as often in math, not because its too hard but because most math teachers have not been trained to use it.

The closest thing we have is the Vann Diagram but its not exactly a compare and contrast exercise.  So with a bit of thinking and working, it can be used in the math class but not for every topic.

First its important to know that when compare and contrast is used, it can strengthen the student's memory, help develop higher order thinking skills, improve comprehension, precision and helps build good work habits.

Lets look at some ways to use compare and contrast in math.

1.  Compare and contrast inequality signs.  Many students have difficulty in distinguishing between less than, more than, greater than or equal and less than or equal.  Requiring them to fill out a chart comparing similarities and contrasting or finding differences can help them put into words their understanding.

2.  Compare and contrast place values such as tenths and tens, thousands and thousandths, so students learn to tell the difference between decimal values and whole number values.  They are very similar but with a small difference.  Some of my students arrive in 9th grade not knowing their place values which hurts them at times.

3. Long division and synthetic division in Algebra.  Although they appear different, the methods share quite a few similarities.  Using a compare and contrast will show students their similarities and differences.  In addition, they can see that it doesn't matter which method used, the answer is the same.

4. Compare and contrast distributive property with binomial multiplication.  It doesn't really matter what method you use to complete binomial multiplication but it still involves distributing terms, just like we teach when using distributive property.

5.  Compare and contrast Greatest Common Factor with Lowest Common Multiple. I can tell you, my students are having so many problems with this topic so completing a compare and contrast in the hopes they can learn to distinguish between the two.

6.  Compare and Contrasting congruent with similar triangles since both share similar methods of proof. 

7.  Compare and contrast bisectors with medians and altitudes because students often have trouble remembering the differences among them.

8. Compare and contrast area with surface area.  I realize one is 2 dimensional while the other is 3 dimensional but they do share similarities.

Any two math topics which have similarities and differences can be used in a compare and contrast exercise.  Let me know what you think, I'd love to hear.  Have a great day.