Thursday, October 17, 2013

An Inquiry into Math Instruction

Over the past several years I have had the desire to be a better teacher of mathematics.  Math was never a passion of mine but I didn't dislike it either.  I think starting off my career teaching solely reading left me a little behind. 

Today I am going to share with you my personal inquiry into math instruction.

Last year, I posted about Number Talks. I am still using number talks in my classroom everyday and feel that it has really helped my students with mental math.

This year in my hunt for more literature on math I came across Math Exchanges.
Math Exchanges
This very smart woman outlined how to begin small group meetings in your math workshop.  Now I've held math groups before BUT not like this.  I didn't know what to talk about...I mainly worked on areas that the students weren't strong in or tried to push my advanced students further. 
Kassia explains her easy to use method {trust me!} and how it helps students' development of mathematics.  In these math exchanges with students she describes her process that really works around different kinds of word problems.  My interpretation is below:
Math Exchanges
            *Without the numbers in the problem, read the problem to the students several times, ask,
               “What is going on with _____?”,
*Let students think, retell the problem and talk about what they are thinking with the group.
*Write the numbers in the problem, have the students retell the story again in own   
  words, and have a conversation
*Use retelling language
*Give students time to work and think on their own
-Students may talk to someone else in the group, spend time watching another student work, use math tools (teacher does not interrupt but writes down notes on what students are doing)
             * Time for sharing and reflecting
                          -sit in a circle
                          -no hand raising, listen to the friend speaking…if there is a pause in the
 conversation you may respond, agree, disagree, add on to the ideas of other
Retelling Language
Who can tell us what is happening in this story?
What do we know about what is going on?  What don’t we know yet?
What are we trying to figure out?
Which number do you think will be bigger?  Why?
Language for helping a student get started on solving a problem
*So, what are you thinking about trying/doing first?
*What strategies or tools have you used before that might help you with this problem?
*Is there a friend's strategy that you have used before that you would like to try?
In the book she refers to the CGI Problem Types.  Her word problems stem from these problems and she selects things that are relevant in the students' lives.  Below is a link to Teacher Tipster's pdf.

Kassia's book put math into a perspective I could understand.  Throughout the book you feel like she's a friend speaking to you.  And she constantly ties it back to what she knows about reading and quotes some of the great ones (Regie Routman, Ellin Keane, etc.).  It's an easy and quick read with a lot of bang.
So after reading that I started my math exchanges and noticed that my students had no fact fluency.  I started reading up and found some really interesting and helpful articles.  (The two in reds are my favorites!)
* A chapter from Mastering the Basic Facts in Addition and Subtraction:
*Promoting Meaningful Mastery of Addition and Subtraction:
*Why Children Have Difficulties Mastering Basic Number Combinations and How to Help Them:
*Teaching without Telling: Computational Fluency and Understanding Through Invention:
The article above helped me see that guiding my math instruction wasn't as nearly as difficult as I thought.  The article refers to Kathy Richardson's idea of The Hiding Assessment.  Click on the pictures to download the information on the Hiding Assessment.
I assessed the students in my classroom for their fluency and based off the number that they show fluency I can find their instructional level.  The instructional level is the number at which they showed fluency, the number lower and the number above.  If a child scored a three they would be working with the facts within 2, 3, and 4.  The goal by first grade is to have fluency with facts within 10.  As you can see there is a definite range in my class.  The students scoring like scores will be grouped into partnerships.  (*During Math Exchanges forming groups (produce change and growth in students’ thinking) should be flexible, responsive to specific needs, and students interact with all kinds of mathematicians.*)
Tonight I will leave you with some anchor charts that we have used in math lately.  Later this week I plan to post about my Guided Math Group Binder and Resources that have helped me in my math instruction.

Sleep well my friends,

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