An Angle Inscribed in a Semicircle

While listening to Annie Forest’s vlog at

http://showyourthinkingmath.blogspot.com/2017/04/small-changes-that-make-big-impact.html 

my life kinda flashed before my eyes!

As further background, Mrs. Forest is highlighting an excellent article, titled, “Never Say Anything a Kid Can Say!”  Author: Reinhart, Steven C.;  Source: Mathematics Teaching in the Middle School, v5 n8 p478-83 Apr 2000.  The article is excellent!

The things I learned from my teachers and other teachers that I’ve been using (as a teacher) that I often don’t think about.  I’ll make a short list here.  This probably needs to be further developed at some point.

1. My (late) college math professor, Dr. Mildred Gross, was a very caring person, but not exuberant.  She was small, quiet, and reserved (collected and very organized). When you answered a question, she would often ask, “Why?”  This is the neutral response (which Annie talks about in the vlog) — not telling the student that they are right or wrong.
2. My cooperating teacher, when I student taught, was Mr. Pool. He had a rule of thumb: I like to call on every student every day, so that when they walk out of my classroom, they knew they were there for a reason. This has been a great rule of thumb.
3. Someone told me (it may have been Melfried Olson) that the tutor should avoid picking up the pencil. The student should so all the writing. Good general rule.
4. A Corollary to Never Say Anything a Kid Can Say! is “Never Punch into a Calculator Anything a Student Can Punch.” I’ve developed a rule of thumb for myself when it comes to calculations from a calculator.  I do not even take a calculator to class.  (If using Desmos, I do demo Desmos.)
   In math class when we get down to a step that might require a calculator, here’s how it goes. (This happens an average of 4 times everyday.)

T: OK now we have 2.8x = 18.2

T: Do we have a mental math strategy for that? (3 second wait) I don’t think so. Please put that into a calculator.  (3 second wait) Who has the answer?  (BTW, as the S’s are punching keys, I’m doing a mental estimate 😉

S: 6.5

Then T looks around the room. If at least two other students (with calculators out) give a head-nod, T moves on.  If there are no head nods, T asks, “Does 6.5 agree with the other calculators in the room?”

I use this strategy for the following reasons:

• Keep the students engaged. (I teach college. Sometimes students need to learn that learning is a participation sport.)
• It teaches that we should always ask the question Do we have a mental math strategy for that? (and I teach mental math and if was 2x = 18.2, we would have a strategy)
• Teach them to use a calculator – parentheses, logs, exponents, etc.
• If they can’t put it into a calculator, I’m loosing them and I never want to loose them.
• I do sometime walk around and peek into some calculator.

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