Sunday, May 29, 2016

...My {Math} Life Is A Lie (2)

I can't even believe how great this book is (and I'm a math-y... not a read-y) Mathematical Mindsets.  I have easily spent over two hours of outside class time reading, highlighting, rereading, note taking, and side-researching everything the book talks about... and I haven't even gotten to the good stuff! All of the "which I write about in Chapter yada yada" that she has said so far.

Why has my whole life been a lie, you wonder?  Well, that is because "math education" or math in schools today (and in my day) is not actually what math is! Timed tests, repetitive procedures, rules and memorization, all of it... We've been forced to think that that is what math is, and it's not!  I'm here to tell you [or at least pass on from Jo] that we need to take back math.  As math teachers, elementary teachers, mathematicians... all of us.  We need to put the conceptual process back into math so kids, students, adults, anybody can explore math and realize that it is about more than just answering as fast as you can and using rote procedures.

Math is patterns!  I feel like most (if not all) math can relate back to patterns.  The book talks about how babies and infants (which I think are the same thing... no?) are obsessed with math and patterns.  I didn't even think about this!  So we just shove math at kids from the time they are born all the way through preschool and they love it.  They just manipulate, create, build, learn and conceptualize and then as soon as they get to kindergarten we say "Math is a test and you have to be the fastest or you suck at math."  Math trauma anyone?  Math anxiety anyone?

I don't know about you, but the school I taught at had a SCHOOL WIDE GOAL for timed tests.  Like hearing that the first time, made my heart hurt.  But now, with Jo B in my life, I literally want to die thinking about it.  #stopthetimedtests #mathisnotarace Another thing I heard all day long was "[the students] HAVE to know their facts first or they won't understand this"... the lie detector determined that that is ALSO a lie Jerry.  I know how you're feeling right now, breathe through it.  Jo B herself did not memorize any facts growing up and she went to become a famous mathematician and author.  This is crazy, right?

So HOW do we teach math facts then.  HOW do we teach math if we can't use the same rote methods that really haven't been working for years.  Number sense - of course!

What is number sense you might ask? Teaching kids to memorize numbers right? Wrong-o.  Teaching kids to be flexible with numbers, to PLAY with them, that's right I said PLAY with numbers... while learning.  It can happen people.  This website tells us that the five components of number sense are: number meaning, number relationships, number magnitude, operations involving numbers and referents for numbers, and referents for numbers and quantities.  Basically what you need to know about number sense is that it's the foundation for math and it helps kids make sense of math.

I bet if you talk to someone who specializes in ELA or who has seen a dynamic reading program they will tell you all about the fundamentals of phonics and how phonemes has revolutionized learning to read.  Well, guess what?  Number sense will do that same thing for math and your kids will LOVE it.  What it comes down to is that kids need to be able to learn numbers without structure, without rules, and without stress!

The other step towards freeing students of math anxiety by doing the REAL math is to do so much modeling our faces fall off.  And I don't mean stand up there and talk at the kids and show them method after method after method.  I mean put that pencil in their hand, that array on their desk, those chips or coins or blocks or whatever in front of them and let them do it THEIR way.  Then, you have 26 little modelers in the room who will completely engage their classmates by showing their thinking, their process, and their creativity.  Exploration is the answer, what was the question?

Sunday, May 22, 2016

Math Toys (1)

So since I've been introduced to this Math Toybox... I've been addicted to these Pattern Blocks.  I started a tessellation in class and spent a good chunk of time continuing it.  The problem is, I will be honest, I think at some point I didn't copy it correctly so it's really (maybe) not a true tessellation... very sadly.  But overall, it looks totally awesome! In addition to it being very addicting, time consuming, and fun... this could also be an awesome tool to use in the classroom! (Everything I do gets connected back to the classroom some how :-P )  One of the things that I love most about this website is that it defies the teacher complaint of manipulatives.

"They take too long to get out" - This takes about 33.4 seconds to load on a classroom iPad/computer/laptop/chromebook/smartboard/whatever!
"The kids play with them and don't do what they're supposed to" mixed with "They're too distracting" - This is on the interweb so you can easily have them "put it away"  or out of sight and pull it right back up!

Manipulatives are SO beneficial to math.  Don't believe me?  Well I did a little research...

By using manipulatives in mathematics, it allows children to be create their own models and commit it to memory.  If we think about the popular "gradual release model", we think about how first the teacher models a new skill.  After that, the teacher will walk through the skill supporting students and asking for them to support her.  Then, the students are to explore and practice the skill on their own.  Just like the practicing of the skill, students must also be practicing new concepts.  And by practicing, many students learn best by using their hands to discover and manipulate.  This is even more important in today's instantaneous environment for students to be required to explore the process before getting to the solution and a "rule" for solving a problem.

This ties in with the book I'm reading, "Mathematical Mindsets."  So far, Jo (Boaler, the author) has talked in depth about the negative attitude toward mathematics that so many people have.  This is including the influence that is being put on students in and outside the classroom.  Where I'm going with this (and Jo) is that overcoming the instantaneous environment that society has created for today's student ties in with Jo's focus on utilizing the growth mindset specifically focusing on mathematics.  Empowering students to learn their own process is key for encouraging growth mindset and also in encouraging a love and understanding of math!

Tuesday, May 10, 2016

What even IS math? (0)

What a fabulous question.

At first, my answer is what I knew math to be growing up.  Which is what I consider a system of rules, equations, formulas, etc.  I always loved my math, and my brain loved math (even thought I'm a girl!) I loved math every single day until it was conceptual and applied.  This is how we teach math today.  When I was growing up it was about "knowing your facts" and memorizing formulas or using a "formula sheet" and just plugging in numbers.

Math is SO. much. MORE!  As a classmate described working in math, he says doing math involves wearing a tool belt.  If you think about when you're working on a project (or a problem) and you use different tools for different things.  The tools are put in place to make the project easier or faster.  Sometimes you have to try to different tools if you are inexperienced with the project until you find the right tool that works.  Sometimes you have a new project and you have to learn what tools to use to do the project.  This is how math works.

Math also explains the things that are going on around us.  Like when I go to the grocery store and I need to know how much food I can buy.  Well, first I have to know how much money I have.  To figure out how much money I have, I have to know how many hours I worked and how much money I made for each hour I worked, or the total amount of money I made.  Doesn't make sense?  Okay, well I want to play outside with my friends after school.  But my mom says I need to do chores for 45 minutes and then I need to do my homework for 20 minutes and I also have to read for 30 minutes.  And if I want to play with my friends the whole time then I won't be able to watch my normal 30 minutes of TV, but if I want to do both then I'll have to factor that in too.  So how long can I play outside in order to make sure I get all my things done... well that's do some math! Now you're getting it!

Math can be proven... and it has been.  That's why when we are working with problems today, we get to utilize our tool belt! Because there is proof in the proofs :)