Imagine you are cooking a cheese sauce with someone, and you say "now dump in the cheese", when in all actuality you meant for them to sprinkle it in slowly and stir it as it dissolved. They follow what you said and dump it all in at once. Depending on the recipe, you may have just ruined the entire batch, ending with a lump of warm cheese and NOT a sauce that you can pour over your pasta. My point... language in any field is very important. Misuse, or misunderstanding can result in unintended (possibly useless) results.
I have an uncommon perspective on math education. I teach undergraduate and graduate level math classes, I observe and help student teachers in their 7-12 math classes, and I have preschool and elementary age kids at home and I stay very involved in what they are learning. In other words, I see bits and pieces of the entire spectrum of math education.
Many people struggle with math. I'm not here to answer why. But there are some "Common misconceptions" and "Common language" issues that in the long run can set you and your child up for a lot of mistakes not just on math tests, but in life. Learning something correctly the first time is easier than relearning. So, this series of posts is going to discuss some of these issues that I've personally either had to struggle to correct in my students, or seen other teachers struggle to fix.
I'm also happy to hear debate and discussion on these ideas. So comment away.
Future post topics will probably touch on
- Dividing "by" vs "into"
- Causation vs. correlation
- A banana is a fruit
- THE equation of a line
- Using intuitive, common words in math and when that can get us in trouble.
- "A line segment is a line" and other self-referential definitions.
- Straight (?) lines
- What exactly is an angle?
- Is a sphere just a 3D circle? Is a cube a 3D square?
- What exactly is a cylinder?
(please feel free to send me topic suggestions or write a guest post!)
Stay tuned.