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#mtbos, Teaching Philosophy

Math Creates Flow!

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Of the many ways to measure a Math lesson,  one is flow.  The 75 minute blocks at my college can feel like a long time to be doing Math.    Therefore, I try to have a variety of modalities within a lesson to capture students’ attention and to provide opportunities to learn and do Math.

The best flow experience I witnessed in my classroom was an activity (on Graphing Functions) starting at 1:58 which was 17 minutes before class ended.  I had thought they would first work independently and then work in pairs.

1:58 handout given students have alone time to think and work while I visit deskside
2:05 students are working independently while I circulate around
2:10 students are still actively learning solo
2:15 class has officially ended — do I tell them?
2:20 they are STILL working — so engrossed
These students may have another class at 2:30 — our room is about to be taken over by the teacher and students waiting patiently outside the door.
2:23 Drat! I have to break the magic and tell them that class is over

At the end, I was delighted that students were totally in a flow state.  They lost all sense of time while they were learning and doing Math.  My only regret?
WHY DIDN’T I THINK TO HAND THIS OUT AT 1:45???

brain puzzler, brain teaser

October 2019 Brain Puzzler Solution

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Q:  How many factors of 155^9 are perfect squares and/or perfect cubes?

A: 37 factors of 155^9 are perfect squares and/or perfect cubes.

155 is a composite number composed of 5 x 31.
Therefore
155^9 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 31 x 31 x 31 x 31 x 31 x 31 x 31 x 31 x 31

25 Perfect Squares:
1: 1 is both a perfect square and a perfect cube.
4:  Perfect squares with just 5s = 5^2, 5^4, 5^6, 5^8
4:  Perfect squares with just 31s = 31^2, 31^4, 31^6, 31^8

Combining the 5s and the 31s Perfect Squares
4: 5^2 x 31^ 2, 5^4 x 31^2, 5^6 x 31^2, 5^8 x 31^2 
4: 5^2 x 31^ 4, 5^4 x 31^4, 5^6 x 31^4, 5^8 x 31^4 
4: 5^2 x 31^ 6, 5^4 x 31^6, 5^6 x 31^6, 5^8 x 31^6 
4: 5^2 x 31^8, 5^4 x 31^8, 5^6 x 31^8, 5^8 x 31^8 

12 Perfect Cubes:
Perfect cubes with just 5s = 5^3, 5^6 (already counted above), 5^9  (2)
Perfect cubes with just 31s = 31^3, 31^6 (already counted above), 31^9 (2)

Combining the 5s Perfect Cubes and the 31s Perfect Cubes
5^3 x 31^3, 5^6 x 31^3, 5^9 x 31^3  (3)
5^3 x 31^6, 5^9 x 31^6 (2)
5^3 x 31^9, 5^6 x 31^9, 5^9 x 31^9  (3)

documentation, Kahoot

Kahoot Student Survey: Which is better? A positive or negative slope?

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Kahoot is amazing for compare/contrast and for taking the temperature of the class.  The anonymity helps students express their thoughts without judgment.

Those who voted “negative” explained that it would be beneficial to lower money owed or cholesterol levels.  The “positive” folks shared their examples of money saved or growth chart of a child.

But without knowing the application, one cannot tell if a positive or negative slope would be better.  In hindsight, this would have been good to revisit right before the midterm exam!  Kahoot link (this is the first of 7 questions).