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!
Jennifer, My principal just had "teacher leaders" in our school meet with him the last week of school about this very subject...writing in all disciplines. Florida and Utah are two states that are no so fond of Common Core and are aligning standards in a different way. Supposedly we are using the same testing company and need to improve writing within our school. I'm the math lead that has to promote, teach, and explain our new focus to the department in the fall. I've done some of this with Pre-Calc students and will definitely check out your Geometry things to share with our teachers in August. Thanks for the lead, Jean
ReplyDeleteThanks for your comments Jean - I hope these activities will be helpful!
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