My NCTM Experience Part 3: Number Talks

  When I saw sessions on number talks in the program,  I knew that I wanted to go to one of them.  We are planning a statewide book study for that will launch at the KATM conference next year, and the 4-10 book topic is on number talks.  I've looked over a copy of the book that we're planning to use, so I know the basic idea of a number talk, but really wanted more information about putting it into action.

       The idea of a number talk is fairly simple: you give students a problem and give them time to work the problem mentally....no pencil, no paper, no calculator.  Then have a discussion about different ways that students solved the problem.

        I was eager to try this idea in my classroom but somewhat reluctant to give up the time (isn't it always about time!).  After attending a session on number talks in middle school, I was convinced that I wanted to make this part of my classroom.  It seemed like a fairly easy idea to implement and one that could really be the center of lots of good discussions.

       The session that I went to for math talks was a good introduction.  We watched some video clips of the instructor doing number talks in a classroom and analyzed them.  One of the most helpful things that we did was practice recording the thinking of our partners.  Some of the ideas were easy to record, but others were a bit challenging.  It was definitely helpful to spend some time thinking ahead about some of the best ways to record strategies to help students understand abstract representations.

         So this week, I actually tried out a number talk for my warm up the last two days, and it was awesome!  I will definitely be incorporating number talks into my warm-ups a couple of days a week from now on.  The conversations we had around different ideas was phenomenal.   My first piece of excitement came from the wide variety of hands that I had in the air of students eager to share their strategies....and some of them were kids that definitely do NOT make a habit of raising their hand.   I have one kid that has been completely disengaged since spring break....like this kid's goal for state assessment was "To try and stay awake".....and he has had his hand in the air the last two days, sharing his ideas.  Is that not amazing???!!  :)

       The other thing that was so exciting was the huge variety of strategies.  The first problem I picked was 18 x 5, which I think was a suggestion I got from the session.  It was a great problem and it led to lots of different strategies.  Our discussion has included some of the following strategies:

• 10*5 + 8*5 = 50  + 40 = 90
• 20*5 - 2*5 = 100 - 10 = 90
• (2*9)(5) = (2)(9*5) = 2(45) = 90
• (9*2)(5) = (9)(2*5) = 9(10) = 90
• 18 + 18 + 18 + 18 + 18 = 90
• 18 + 18 = 36, 36 + 36 = 72, 72 + 18 = 90
• counting up by multiples of 5
• counting up by multiples of 5, starting at 60 since they knew that 5 x 12 -= 60

I was very pleased with this many strategies coming to the surface on our very first attempt!  And this one number talk brought up important ideas and vocabulary such as distributive property, associative property, and the commutative property.  

        So on day 2, I chose the problem 15 x 8.  I intentionally chose a problem that had an even number and a multiple of 5, hoping to encourage rearrangement of factors to get to a multiple of 10.  Again, I had tons of hands in the air and a wide variety of strategies.  As with the first problem, I had a variety of strategies used.  The most common ones were probably these:

• 10*8 + 5*8 = 80 + 40 = 120
• 15 * 2 = 30, 30 x 2 = 60, 60 x 2 = 120
• 15 + 15 = 30, and there are four groups of 2 15s, so you would have 30 x 4 = 120

My favorite one, however, was the very last one of the day.  It came from a student that had already shared one strategy, and as he looked at the wall, he said, "Or you could use a clock.  The 15 is like 15 minutes, and there is 4 of those in an hour.  So it would take 2 hours to have 8 sets of 15 minutes, and I know that 2 hours is 120 minutes."  I mean seriously.....could I have asked for anything more!  What awesome, creative reasoning!

          So, after 2 short days, I am quickly a believer in number talks in the middle school classroom.  I can definitely see a ton of advantages to making these a part of my classroom from day 1 next year.

I've also gotten interested in using visual models during number talks.  I think it is a great way to introduce students to some mental models that can be very powerful, such as the area model, number lines, money and clocks (as mentioned above!).  If number talk slides that already visual models of several strategies might be helpful, check these out in my store!

My NCTM Experience Part 2: Jo Boaler

       The very first day of the NCTM conference, I was so excited about all of the sessions that I forgot to leave myself time to eat lunch.  That's not even true--I knew that I hadn't left a lunch break but I just couldn't help myself!  Jo Boaler was speaking at 12:30 and I was NOT going to miss that.  It as well worth it (and I did manage to find time to eat a quick sandwich after Jo spoke).

     Earlier this year, I read Mathematical Mindsets and it was a truly amazing read.  Listening to her talk was equally amazing.   Jo talked about many of the points from the book but I also had a few different take-aways.  Here are some of the most important points I took away from this hour.

1.  "If you're not struggling, you're not learning."--I talk a lot about making mistakes with my kids at school, and I think I have done a decent job of helping them realize that mistakes are a good way to learn.  But this phrasing helps me realize I need to take that message a step further...I need to normalize the struggle, and not just the mistakes (or right answers).

2.  "Math is not about speed, it is about depth and multiplicity of ideas."--Again, this is not a new message for me, but hearing it at this session just helped reinforce how important this is.  According to Jo, much of math anxiety onset begins  with timed tests. Interestingly, she said that math anxiety most affects the high achievers.  This matches with my beliefs....I've always been one to give kids as much time as needed.  Looking at this made me realize that although I have never really associated  speed with being good at math, this is not something that I talk a lot to the kids about.  I need to do a better job of verbalizing this message to my kids....math should be about deep thinking and understanding over speed.

3.  Teach kids to be skeptics--I love this idea.  What a great way to encourage great discussion and listening skills.  Jo gave three levels of being a critic.....convince yourself, convince a friend, and convince a skeptic.  I'm trying to figure out exactly how to incorporate this into my classroom norms for next year, but I definitely love this idea.

4.  Math freedom--This was one of my biggest take-aways.  Jo showed several clips of kids from her summer math camp, and so many of them talked about freedom being the reason that they liked the camp when they didn't like math in school.  Jo expanded on this idea into two types of math freedom:  organizational freedom and math freedom.

• Organizational freedom included several things such as how you handle talking, sharing, recording, spending your time and movement in your room.  I'll be honest....this one gives me pause as a classroom teacher.  I understand that kids like freedom in moving around and how they spend their time....but I also know that in my classroom, structure and procedures have always been a bedrock that help my room run effectively.  I don't want to discount this idea, but I do think it is easier to do some of these things in a summer camp setting versus a regular classroom setting.  This is one I will take some time to reflect on this summer and think of ways that I can use this.
• Math freedom included things like interpretation of problems, how kids see problems, learning new ideas, how we think about mistakes, and ideas about inquiry and creation.  I really loved this idea of math freedom....that kids begin to see math as a subject that is not just a set of rules, but there is freedom about where to start and how to proceed.  I want kids to see that math can be creative in how you think about a problem and that it needs to make sense.

I was so inspired by all of these ideas that since I've gotten back, I've taken Jo's free online course for students call "How to Learn Math for Students".  It had such great messages for students that I'm trying to figure out how to incorporate this awesome material into my classroom next year.  I also enrolled in "How To Learn Math for Teachers and Parents".  This one was not free, but I'm so excited to see what else I can learn.  I've just started the course, and I look forward to all that I will learn.

I'm already starting to have some ideas about how I want to change up some things in my classroom next year.  One definite thing is that I will be starting next year with some form of the free online course.  The other big thing I have been considering is changing up how I do homework.  I really want to make it more self-directed...I think I'll blog more about this idea later as it is still forming in my head.  I just know that I'm wanting to move towards something that is differentiated and puts it to students to examine where there are at and push themselves.

My NCTM Experience Part 1: Dan Meyer

I feel so lucky to have been sent to the NCTM Annual Conference in San Antonio last week by the KATM Board.  I am going to do a series of blog posts about my favorite sessions and biggest conference take-aways.  I'm starting with one of the last sessions that I went to.  

 Last week I sent an email to the generic Desmos email.  Imagine my excitement when I not only got the answer I wanted, but the email came from Dan Meyer!  Yes, I in my own geeky kind of way was soooo excited.  Fast forward to the NCTM conference when I was talking to another math teacher who starts to tell me about someone (can't remember who!?!) and said, "She's my math crush.  Who's yours?"  And while I may not have thought of it in those exact words, I had to admit that it was Dan Meyer.  Now fast forward to the 8 am session on Saturday morning of the NCTM conference....what a way to start my day!

Dan with Kira and me.  He has perfect long arms to take a selfie!

The title of the session was "Math is Power, not Punishment".  The big idea of the session was based around the idea that we need to create intellectual need in our students for what we are teaching them.  As Dan said, "Math is the aspirin, but what is the headache?"  He had some really great, quick activities to illustrate this point.  The most powerful one involved the coordinate plane.  Dan started with a slide of a bunch of dots on the screen and told us each to choose one of them.

         

Then the screen changed....all those dots were there, but there was a bunch of others.  Dan got a couple of volunteers from the audience.  Volunteer #1 had the job of trying to describe which dot was hers to volunteer #2...and let's just say that was a tough job!

Then it was Volunteer #2's turn, and here is what happened.  I thought this was a great illustration of the idea of creating intellectual need.

The examples that Dan used in the presentation were very meaningful for me as a middle school teacher....the need for the coordinate grid, and another activity that looked at the value of combining like terms before solving equations.

This idea is not just powerful for secondary teachers however.  As I left this session with my K-2 Math Enrichment colleague, it got us talking about a lesson she had been telling me about earlier in the day.  She had done a lesson using non-standard measurement units, such as hands, feet and so on. As she and I talked, we realized that this lesson on non-standard measurement units would be a great way to create intellectual need in her students.  See what headaches can be cured by using standard measurement units.

As teachers, we want to help our kids find the easiest way to do things.  But perhaps we are taking some of the value of process away by not letting them experience some of the headaches first.
This is truly a powerful idea....that if kids see the value of what a method saves them it will be more meaningful to them.  Think of all those things you teach.....why did mathematicians invent those things?  What headaches did they help cure?