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Sunday, March 27, 2016

Why Don't We Get Math?

     We are less than a week away from the launch of our new book study of Minds on Mathematics.  I had a few minutes today to dig into the book and wanted to share some of my thoughts about the introduction.  

Why Don't We Get Math?

-Cultural: It's Okay Not to Get It
   This is the one I see the most in my school and in my life.  I see over and over again an acceptance among adults that math is hard and it is okay not to get it.  I know of several well educated adults who almost brag that their fifth grader does math they don't understand.  I have never heard a well educated adult bragging that they couldn't read at a fifth grade level.  As the author states, "this social acceptance of mathematical illiteracy is a huge barrier to our children's progress and preparation for life beyond our classrooms." 

- Pedagogical: Math is Memorizing
    When I was in elementary school math was all about memorizing.  The parents of my students are very much in the same place.  For some of us, memorizing worked.  For others it didn't even come close.  No matter where parents fall on this spectrum, most parents believe that math is memorizing.  They want to help when their student is struggling but their idea of helping is to remind kids of the steps to a procedure.  

- Individual: Math Ability is Innate
    This is true even in my own family.  I remember being good at math from an early age and my Mom always being surprised and wondering where my math ability came from.  More than any other subject in school, people seem to have this idea that math skills are inherited or passed down genetically.  This is where the excellent research on growth versus fixed mindset can really help understand how ability is the product of effort.  

Minds-On Math Workshops

Minds on math workshop aims to challenge these beliefs and provide students with a "learning experience in which students are challenged to grapple with their thinking and understanding about math in light of new information and challenges, to make meaning for themselves." Minds on math workshop is about leaving behind decontextualized arithmetic and giving the kids a change to construct meaning for themselves.

After reading the introduction, I can see this book aligns well with what I am already doing and the things I have experienced as a math teacher over the past 10 years.  I am excited to read more and further refine my teaching practice!  Want to join me? Check out the posting schedule below!  Need more information, get it here

Thursday, March 24, 2016

Fluency with Comparing Fractions

   I spend a lot of time in grades 3-5 working on developing strategies for comparing fractions.  I have written before about the 5 strategies my students use to compare fractions.  I also shared my favorite free computer game for kids who are working on fluency with comparing simple fractions.  Today I was working with an intervention group of fifth graders and had a few minutes at the end of our session.  I knew that I needed something quick and fun so I grabbed my regular old deck of playing cards.  
   We split the deck and each flipped two cards and made a fraction.  The first card flipped became the numerator and the second card the denominator.  This allowed us to make all kinds of fractions.   The person with the largest fraction won all of the cards.  Some of our fractions were less than one, some were equal to one and some were more than 1.  It was a great way for students to practice comparing fractions.  Out of the 5 strategies for comparing fractions, I saw students use comparing to a benchmark most frequently during this game.  It was a great way to reinforce the idea of one half, one whole and improper fractions.  I also saw students using common numerators to compare fractions and quite a bit of unit fraction reasoning.  My favorite use of unit fraction reasoning was when a student used the idea of unit fractions and the distance from one to compare 10/11 and 11/12.  "They are both missing one piece.  11/12 is missing 1/12 and 10/11 is missing 1/11.  Since 11/12 is missing a smaller piece, it is greater."         

     After a bit, we changed up the game and had each person flip 2 cards, use their smallest card as the numerator and their largest card as the denominator.  This made all our fractions less than or equal to one.  It made it so that the fractions were a bit closer together and required more critical thinking.  After a few minutes playing that way, we reversed it and had folks put their higher card as the numerator and the lower one as the denominator.  This was a great way to really reinforce the improper fraction, mixed number connection.  

This entire game took under 10 minutes and was a great way to reinforce some big fraction ideas!  I love how it requires no prep and is easy to differentiate!  By pulling out some of the cards in the deck, I could make this game based on friendlier fractions which would be great for third and fourth graders.

Book Study Launch

Looking for some motivation as the school year comes to a close?  Want to try a new structure for math class this spring and/or next school year?  Join us for a 5 part book study on Minds on Mathematics: Using Math Workshop to Develop Deep Understanding.  You can read all about it here!   

Monday, March 21, 2016

Minds on Mathematics: Math Workshop Book Study

How is your professional reading coming?  Mine has taken a big hit over the past few months.  I find I am most inspired when I am reading a really good teaching book and have been putting it on the back burner for way to long.  I have been keeping up with my monthly issues of Teaching Children Mathematics and a few of my favorite teaching blogs but haven't had my nose in a really good math book in almost 3 months!  Last year, I read 14 professional books that I can remember and this year I am at 0.  With that in mind, I am putting my professional reading on the top of my priority list.  I think the end part of the school year is a great time to read a new book and try new things.  It is the time of year I sometime struggle with finding the joy in teaching and it is easy to get bogged down in testing and administrative tasks.  Reading a good book keeps me motivated!  Chatting with all of you about what I am reading really keeps me motivated and pushes me to try what I am reading in the classroom.
I am happy to announce that I will be hosting a new book study starting in 2 weeks!  I am going to be taking a look at Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8.  

You can read more about the big ideas in this book here or read the introduction and chapter 1 here.  

I will be posting on Saturday mornings.  
Here is the posting schedule:

Hope you can join me on my journey to learn more about math workshop!  

Jelly Bean Math

The countdown to Easter (and the spring testing season) has begun!  Today, I planned a quick little project with a group of 10 second graders that was super engaging and a great way to practice estimating, counting, comparing numbers and early division concepts.
It all started with little Dixie Cups of jelly beans (I used these ones).  I put the kids in 3 groups.  I gave each group a little cup of jelly beans and posted these directions on the SMART board.

Want to try this with your students? Grab these directions from Google Drive.

Two of my groups had 3 kids in them and one group had 4 kids.  I gave the groups with 3 kids 45 jelly beans and the group with 4 kids 60 jelly beans.  

I have really been working on independence with these kids and tried my best to step back and observe and not take over!  

I saw so many things that made my math heart happy!

Kids organizing and recording estimates
One group organized all their beans by color and then decided it would be much more efficient to put them in groups of 10.  The other groups went for groups of 10 from the get go. 
When each group had figured out how much they had, it was quite easy for them to figure out how much they were off by.  These kids are so flexible and fluent with double digit subtraction

Dividing the jelly beans equally between each group member was fun to watch.  Each group started by giving everyone 10.  Two of the groups were convinced that there would be a leftover bean that would have to be cut up.  The rationale was that because 15 is odd, there will be a leftover.  They were surprised to find that there was none left!  The main strategy for sharing out the beans was to give each person 10 and then share them out 1 by 1 until they were gone.

This part took a total of 14 minutes (including a few minutes of eating the beans!)

Then I pulled the group together and had each group share out how many beans their group got and how many each person ended up with.  There was some outcry over one group getting 60, but it provoked an interesting discussion about how each kid ended up with 15.

I then presented them with this problem."There are 10 second graders in this room and I gave you each 15 jelly beans.  How many jelly beans did I give out?"  I gave kids a minute to think at the circle then sent them off to grab a white board and show me what they knew.  I chose this problem because last winter when I was reading Children's Mathematics I became very intentional about making sure kids have the chance to solve Base 10 Story Problems.  Since 10 kids were in this group, I thought it would be interesting to see who used base 10 knowledge to solve this problem.  I gave out 10 groups of 15 but some kids used the idea of that being the same as 15 groups of 10.  
This student used base 10 knowledge to solve the problem (and the distributive property!)
Another student who used base 10 knowledge
This student added 45+45+60.  They used the number of jelly beans each group had.

Total time for this was 25 minutes.  We had a lot of fun, the kids got some good practice and I got to learn some new things about what strategies my students have.  How are you working on estimating and counting in your classroom?  Want to try this out?  Grab the directions from Google Drive