Wednesday, July 11, 2012

Math Exchanges, A Book Report

How do you teach math?  What kind of system do you have set in place for your students?  Do you teach the whole class, small groups, one on one (let's be real.), centers, a workshop approach?  Please do tell! 

I have tried it all (almost).  This next year I am leaning towards a workshop approach.  

This book is a quick read, and one I would recommend to fellow teachers!  I wanted to post about the key learning points to remember.  All credit is due to Wedekind.  All throughout the book, she is connecting her Math Workshop to the structure of Reading/Writing Workshop.  This really helped me to get a picture of what it will look like in my room.  I'm still not sure how it will look, sound, and feel, but I am open to ideas.  Here are a few that I want to implement next year!

1. We are all mathematicians:  Identity-Building Statements 
-Mathematicians are curious.  
-Mathematicians ask themselves questions.
-Mathematicians need lots of time to think, think, think.
-Mathematicians look for challenging problems in their world to figure out.
-Mathematicians persevere.
-Mathematicians make lots of mistakes, but they keep on thinking.
-Mathematicians change their ideas and strategies and come up with new ones.  Then they change their ideas again.  This is part of being a mathematician.
-Mathematicians talk to and question other mathematicians in order to help themselves understand.
-Mathematicians do not always agree!  Disagreeing respectfully is part of being a mathematician.
-Mathematicians work together. They explain their ideas and thinking. They listen to the thinking of other mathematicians.

I found this very similar to What Do Writer's Do anchor chart and Reader's unit of study.  This provides a good outline of broad themes I want my students to take away from during math time.

2. "Math Exchanges emphasize change.  This may sound simple, but the purpose of meeting with small groups of mathematicians is to produce change and growth in their thinking.  Too often, teachers meet with groups for the sake of meeting ('It's time to pull these five kids together!  What should we talk about?')  and without a specific focus.  They may have the vague notion that meeting with small groups of mathematicians (or perhaps only meeting with struggling mathematicians) is a good practice.  Math exchanges put the focus on planned, purposeful exchanges between mathematicians of different abilities." 

I don't even want to admit how many times I have met with a group of students for the sake of meeting.  This paragraph knocked the wind out of me.  Guilty.

3. "As a teacher, it has taken me time to work to a place of comfort with math exchanges.  I started out having math exchanges with two students and working with only one group per day.  Even now at the beginning of the year I may spend so much time focusing on setting up the expectations of a math workshop that I only work with one group per day through October.  I've learned to be okay with this.  I have learned from experience and practiced to trust in teaching deeply within math exchanges.  Students are still learning throughout all the parts of the math workshop.  It is okay to start small.  Give yourself the time to explore how you will best facilitate these math exchanges."

I feel the need to print this up and post it in my lesson plans for the first few weeks of school.  Breathe. Slowly.  Do not rush.  Routines. Routines. Routines. Breathe.  Think baby steps.  My kids need clear expectations and practice before I can expect to pull small groups.  Any other firsties with me?

4. "Even though this is a relatively independent time for thinking (during small group practice), I do not usually discourage children from watching each other or even mimicking what other students do or write.  In the beginning of the year, children unfamiliar with math exchanges may complain, "She's copying my ideas!"  or try to shield their papers from others in the group.  I simply reply with one of the mathematician statements we have practiced: "Mathematicians learn from watching, listening and talking to, and working with other mathematicians."

Why haven't I ever approached it like this? I get so freaked out when they are looking at each others work, but it truly is a natural process mathematicians go through.  Obviously, if a student continues this behavior I would talk to them about it.  The author even suggests stating that you notice the student thinking about the other students ideas and inviting them to ask questions about their strategies.  Brilliant!

5. Say "strike a pose"to get students attention.

6.  No hand raising is allowing during sharing/reflecting whole group or small group teaching time.   Students sit in a circle.  I plan on teaching my students how to be attentive to pauses in the conversations that shows when someone is finished with an idea.  Teaching students how to restate what the previous person said will allow for better understanding and a more direct conversation flow.

7. The last chapter titled "Reflection and Self-Monitoring" had, by far, the most impact on me personally as a teacher.  The author talks about slowing down our thinking in order to go deeper, teaching self monitoring, and the difference between content reflection (how you grew in a specific concept or strategy) and process reflection (how you grew as a mathematician through behaviors and practices). She offers a cute end of year self reflective project and tips on how to be a better reflective teacher.  Journaling about my teaching life-what feel right, what I'm struggling with, what's really going well- I hope those things find a place in this blog.  I also want to find a reflection partner.  Meeting for breakfast (or happy hour!) once a week for intentional teacher talk sounds like a WONDERFUL idea! I will need to be careful not to turn this time into a gripe fest (as it so easily does!) or a gossip fest.  I love the idea of chatting about a book or lesson plans over coffee.  

The last few pages, titled "Living a Rich Mathematical life" really tugged at my heart.  

After trying to sum it up in my own words, I will have to refer back to the book.  She writes it beautifully.

"Regie Routman (2008) writes about the importance of living a life full of experiences that we can take back into the classroom to share with our students.  One particular story Routman tells in Teaching Essentials hit home with me one year in the late fall when I was feeling overwhelmed and not wholly satisfied with my teaching.  Routman writes, 'One of the things I love best in the summer is to make fruit pies and tarts.  When the berries in the Northwest are luscious an the stone fruits are beautifully ripe, I create all kinds of delicious and gorgeous desserts.  It's sheer fun" (2008, 129).  When I first read this I snapped the book shut.  'How does this woman have time for berry picking with all the teaching and writing she does?  Why can't I do that too?'  I demanded.  I opened the book again to reread and found this sentence: 'I am a more interesting person if I have stories to tell that are not just about school' (127).  I ordered this thought and asked myself, 'How can I teach my students to live a rich, full life inside and outside of the classroom if I am not doing this myself?"

My number one goal this year in teaching students is to encourage them to live a rich. full life inside and outside of the classroom.  In order to carry this goal out, I must practice what I preach.

Here's to long, warm, Texas bike rides, sewing it all wrong and taking the thread out stitch by stitch, making new friends, and not having to be perfect!



  1. This sounds like a great book. My district does math work stations and problem solving with lessons and ideas coming from Debbie Diller and Van de Walle. I pull small groups during this time. We have to have 90 minutes of math instruction daily. I love teaching math to my Firsties. =)

    Be sure and add a followers button. Go to the top of your blog and choose design. Then choose layout and the followers is the ninth choice I think. I'll be sure to follow you then. =)

    I would love for you to hop over and visit me when you get the chance. I have shared some *freebies* that I am going to use for math work stations the first couple weeks of school. =)

    Heather's Heart

  2. Heather,

    Thank you for the advice! I have successfully added a follower link as well as a few more gadgets! Thanks for being patient!

    I am enjoying reading your blog! I have been trying to get my hands on a copy of Conscious Discipline as well! That book looks amazing. I have dabbled a little bit on Bailey's website and was impressed.

    Have you ever heard of Whole Brain teaching? I came across it last Spring and was able to try some of the techniques out on my class last year. I would love to know your thoughts on that as well!