liebster award

liebster award

Wednesday, June 29, 2016

My Favorite Math Problem



I had a number of  great math ed professors,  Dr. Brumbaugh is one.  Sadly, I do not recall the name of the one whose materials I still, over 20 years later, look through for inspiration and help. (btw...UCF  Go Golden Knights)

He made every one of his students submit 3 original problems.  They had to be unique, which at the time meant that the problem, or one like it, could not be found within the class materials.  The materials for this class were not a textbook, but a copy of 2 binders that the local Kinko's had.  You walked in and told them you were in professor's class and they sold you 2 binders full of previous student's submissions as well as whatever the professor had added to them.

I was working with 5th graders and I wrote a problem that my students solved with little assistance in about 5-10 minutes.

We had to present our favorite problem in front of the class.  My turn came up and I presented my problem, but because it was the last one of the day (and the professor had a thing about promptness) I didn't get to complete giving the explanation.  He said that we should do the problem and bring a solution to class on Tuesday.  It was Saturday (this being the lab for the Tue/Thur class).   By Tuesday I had well over a dozen students ask me for help.

I've found that 5-6th graders rarely take more than 15 minutes to figure it out, whether they get the correct solution or not.

High school'ers take 30-45 minutes and rarely get a correct solution.

College people, especially those with STRONG math backgrounds fill pages and pages with work and get to the right answer, but are uncomfortable with the answer they have.

I call it the bionic bee problem.  It hinders the student in that the more math they know, the more math they try to apply to finding a solution to it.

I love it for the same reason I love www.mathwithbaddrawings.com , its all about a bad drawing and a great story.

I wish I had his ability in my blog....  maybe I till see if I can draw something and add it later...

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There's this bee.  Not a normal, everyday bee; one which has been bionically enhanced by a secret governmental agency.  Or maybe the illuminati.  It has been enhanced to have perfect reflexes and the ability to fly at 200 mph.  

In order to keep the bee from getting splatted, it is gyroscopically synchronized to turn 180 degrees in case of an imminent collision, returning exactly in the direction it was coming from.   

For some reason the bee has been released on a straight railroad track, well ahead of an oncoming train.  The train is travelling at 77 mph, so there is no way it should be a threat to the bee.  

**At this point I ask if anyone has any questions.  Invariably the question of why it was released in front of a moving train comes up.  I tell them, "hey, its not like the (FBI, CIA, NSA, Etc) tell me why they do anything"  Why do you think they released the bee on a straight section of railroad tracks?

A signalman accidentally transfers another train onto the same straight segment of tracks, this time 300 miles up the track.  This train is travelling 73 mph right toward the bee and the other train.

I'm happy to say that just as the two trains collided together, the bee falls out of the way, exhausted but safe.  Which is good, do you know how much bionic bees cost?

My question to you is, how far will the bee have flown when the trains crash together?

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For high school students used to Algebra, that the tool they use.
College students use Calculus, and sometimes Algebra as well.

For them I add...

What will the flight of this bee look like (zig-zagging back and forth between the two trains).  

I've never typed it out and given it to students.  I may, depending on the class and usually only at the middle school or below level write everything on the board.  (the bee, tracks and trains always get drawn).




Sunday, June 26, 2016

8th grade Transformations

CSS.MATH.CONTENT.8.G.A.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


Not one of the best units for my students this year.  It was basically where we started the year (which in hindsight might need to be modified).  Translations were easy enough.  Students could easily see that when a shape is moved that the basic shape remains the same, but the location changes.  

Dilations, rotations and reflections, however, were not as easy.  The first problem I came across was that students had difficulty picturing that a 1x1 square that doubled in size (becoming a larger square) didn't have an area of 2.  Even after drawing many examples in their notebooks, I still had students who struggled with seeing this.  

Next, I noticed students confusing how a polygon would look when rotated.  A triangle with an acute angle pointing in one direction in the original image should end up with its acute angle facing another direction, but this wasn't the case with many of the students. Reflections were confusing as well.

I am thinking that I will start off next year looking at shapes (capital "T" comes to mind) and go through the transformations (without dilation) before even introducing the idea of graphing this shape.  (which explains why I keep asking everyone where the district die-cut press has gone)  I figure if the students can keep picturing what happened to the "T" it might give them a visual cue to when there is a problem with their doing these transformations on a graph.  

I also will be stressing the graphing aspect of this more next year.  The way this has been done has been with the graphing being an after-thought more than a goal.  I think seeing the changes and coming up with ways of describing these changes (either by verbal or symbolic description) adds necessary depth to the topic. 


Friday, June 17, 2016

Remediation is hard

i wish I had a magic wand,  a perfect solution....the WAY!

It would be so much easier....

Remediation is a matter of understanding the student,   It's a matter of knowing how best he/she/ze will see the concept most clearly.

I've known teenagers for whom subraction still makes no sense.   Division, fraction and number sense confusion is so common as to assume that it's confusion should be expected.

I love my kids, but I ache that I cannot possibly help all of them have experiences to clarify all the misconceptions, never mind successfully develop a full understanding of all the current grade level standards as well.

I do know that disruption and sleeping as well as not doing the work is definitely positively correlated to not participating, not doing homework and not answering questions in math class.

Motivation is a killer for students.  Often-times a student's home life can make our best efforts feel like standing still.  We are not alone in this, the students feel it as well.

It's true that math is sequential, and it builds upon itself.  It's also true that many of our students memorize steps, not understanding the why.  The good news is that continuing to build basic skills and remediating misconceptions does slot in lost concepts and I've seen students with that "ah-ha" look in their eyes.

6th through 8th graders have learned the 4 basic arithmetic operations, they need opportunities to hone these skills and practice them.  My 6th graders practice divisibility, factor trees, do kenken, review vocabulary and skip-count (to practice multiples/multiplication and learn to see linear/arithmetic progression, though I don't share the motivation with them).

My 8th graders need to better explain their thinking (yes, Mathematical Practice #3, construct viable arguments - I'm looking at you).  They need to work on being better at showing their work/thinking so that in time they can be better at those explanations.