I have been thinking about students understanding math…I remember taking calculus in college. I suppose that the TA and the professor talked about the derivative being the slope of the tangent line to the curve at a given point. I memorize definitions of things pretty well, so I am betting that if the professor told me that, then I "learned" it.
But, I also remember starting to teach calculus. All of a sudden it hit me - OHHHHH the derivative is the SLOPE of the TANGENT LINE!!! I'm not sure if I can adequately express this in words, but it was an AHA moment. Even though I memorized the definition, I didn't truly understand what anyone was talking about. I could repeat the definition back, but I hadn't internalized the definition.
So, what I have been thinking about is HOW to get students to internalize definitions.
One thing I came up with is asking students to write about math. I am thinking that if students have to write a paragraph about a certain subject, teachers could check for misconceptions about a given topic.
I am still developing this idea, but here is an example of what I have come up with so far. This is specifically on the topic of medians and altitudes in geometry.
Give students a list of words - For example: median, altitude, slope, midpoint, perpendicular, right angle, etc - and a diagram. Then, students must use all of the words in their own paragraph.
For students a little less sure about the relationships in math, or not as advanced in their writing skills - make up a paragraph for them and then leave the important words out. Have them cut and glue the important words into the paragraph into the correct place.
Writing practice AND a chance for students to practice the math concepts they have learned in a little bit different way - Awesome :)
If you like this idea - check out my new
Writing about Geometry - Medians and Altitudes activity in my Teachers Pay Teachers Store.
Or, if you are one of the few, the brave, the proud calculus teachers out there - check out my
Writing About Calculus - Limits and Continuity
More Writing about Math activities to come - Stay Tuned!