Day 28- One size DOES NOT fit all!

This was my classroom today.

Nice and clean and ready for Parent Night  at 5pm. But where, do you ask, were the students? They were split between the other teachers of my fabulous team while I was in a Math Professional Development.

I know what you're wondering. "But Mrs. Delk, you already know everything. What else could you possibly need to learn?" Well my friends, the times, they are a' changing. And math is no different!

No longer are we teachers impressed with mere rote memorization of math facts! Gone are the days of math drill and kill sheets! No, my friends, we have reached an enlightened stage in our development of mathematical practices! We teachers now want our students to THINK about math!

Not only THINK about it, but begin to REASON. We want students to fly past REASONING and go straight into forming CONJECTURES and GENERALIZATIONS! I want my students to JUSTIFY their answers and buck their minds against the system of rote memorization! ARE YOU WITH ME?!?!

 (sound of crickets in the background)

I might have come on too strong. Let me try again.

Do you remember when you were in school and the teacher was in the middle of a particularly difficult lesson in Algebra, then he or she turned and said, "Let me show you an easy way to do this," then he or she popped out an equation that you were supposed to memorize and not ever think about again after the test?

OK, you're with me now! If you're anything like me, I knew that as soon as my teacher said those words, I was toast. Every time I heard those words my next thought was, "Easy for who?" Memorizing equations was not my strong point. Some students I noticed nodded their heads and cheered that now there was an easy way to do math. I was jealous of those students. However, I didn't question the teacher and her tricks of the trade. I did my best, passed the test, and graduated out of the class as quickly as possible.

Well, this Math Professional Development was all about how we need to buck the mathematical system- just a little bit. Do students need to know their math facts? YES! Do they need their math facts and mathematical knowledge later in life? YES!
BUT- Do we teachers need to change the way we teach those skills? YES! YES! YES!

Play a little game with me. Look at this picture, then answer the question under it.

How many do you see?

(pause for answers)

Raise your hand if you said 10. 

OK, chances are if you answered 10, it was because you noticed that there are 10 cubes put together to form this long. (notice the mathematical teems used. By second grade, students are expected to know these terms)

OK, now raise your hand if you answered 1.

Chances are if you answered 1, it was because your mind processed the picture as containing one item in it.

So, who is right? BOTH! This picture contains one set of 10, and ten sets of 1s. It probably would have been easier if I had shown this picture instead...

But what's the fun in that? Your brain saw the picture the way it wanted to see it. If you answered 1, and that was not the answer I was looking for, I would have given further directions to take the cubes apart and count them. But that was not the point of the game. I merely wanted to point out that your point of view might not match the others around you.

The same is true in any classroom. In fact, the same was true with a library full of teachers today. We were given the long, and asked: What would students already need to know to be able to count the cubes? It sounded easier than it really was. Look at the picture again.

 

In order for a student to be able to correctly count these cubes, the student needs to know that...

1. Arrangement of the cubes don't matter. Put together, broken apart, sideways, tall-ways, doesn't matter, The answer stays the same.
2. Numbers come in a sequence. 1...2...3...and so on. 
3. Unitizing- they are counted by their units
4. Cubes are counted once and only once
5. You can count them forwards and backwards, doesn't change the answer
6. The last number you say is the total

All that! Just to count cubes! That's pretty big stuff for a 5 or 6 year old! And once the student knows all those things, then we work on the student being able to find answers the best way for him or her.

Time for another game! Are you excited?! This one is fun. Just go with it. This game is called:

Watch the video and count the dots.

How many dots did you count?

This game only has one answer: 9. Raise your hand if you got the right answer. (pause) Good for you! When we did this activity today I was feeling pretty good about myself. A task was presented, and I completed it to perfection. Go me!!

But wait- it can't stop there can it? Did you know the human brain works by trying to form patterns? Chances are, when you looked at the dots, your brain "saw" them in a pattern in order to count them. 

Check out the patterns our minds created today. (and these are for real)

Counting down the pyramid, groups of 3

 

Another group of 3s, pairs of 2 with 1 left over

Counted 5 (like a domino) with 4 points, counted around like a baseball field

Did we all come up with the same right answer? YES! Did we all use the same way to solve the problem? NO! There's a chance you used a different strategy at home! 

So is it any wonder why teachers are now having to change the way we look at our students and the way we teach math? My strategy to solve a problem might not be yours! My easy way might not be your easy way! In math, ONE SIZE DOES NOT FIT ALL! 

So teachers- buck the old math system you knew before and embrace the New Math! A Math where we listen to our students justify their answers (right or wrong)! Where we have more than one representation of how to solve problems! Where we embrace the use of manipulatives and honor private think time! Where students feel comfortable enough to form conjectures and generalizations free from worry about being wrong!

And Parents- encourage your student to share his or her way of solving a problem! Ask your student if he or she can create a picture, use their words, use numbers- and see if they can use numbers in more than one way. Don't freak out about wrong answers! Yes, your child will have to get the right answers on the test, but wrong answers are a spring-board for new learning. Ask your student to share how they got that answer and you can see where their brain was taking them, and then direct them on the right path. Be proud of their brain, not just the right answers.

 

Hmmm... my brain hurts. Now that I'm feeling developed professionally, I can't wait for tomorrow!

p.s. like the cute pics? All thanks to Google Images!