Wednesday, June 27, 2012

Small Groups and Number Talks

Rather than spending the summer months on vacation, I made the decision to teach summer school.  Although spending the summer teaching is an exhausting task, it does have its benefits.  The main benefit is the chance to actually take time to think about and refine my practice as a teacher.  This is exactly what I'm doing as a fifth grade teacher in Palo Alto's Elementary Math Summer School.

Small group number talk focused on ways to represent a mixed number.
Our entire staff of summer school teachers has made the commitment to teach small groups and give daily number talks.  Small group teaching is exactly as it sounds.  It's teaching a group of two to five students in a small chunk of time as opposed to a large group of students in a longer chunk of time.  By doing this, we're able to easily, informally assess student learning, make quick teaching decisions, and truly target each child's needs.  Conducting a number talk in a small group is a powerful way to assess, build, and then extend students' thinking about numbers, which is the basic foundation from which all math learning is based.

A number talk is a five to fifteen minute conversation and think-time based on a number or number problem.  Basically, the teacher presents the group or class with a number, a number sentence, or a problem involving numbers.  Students mentally find solutions and share.  Learn more about number talks at Math Perspectives.  There are numerous benefits to doing this in small groups.  First, students tend to feel safer in small groups when thinking and sharing ideas.  Also, all students are given multiple chances to share ideas.  This happens rarely in whole group lessons.  Plus, students feel more secure when asking questions or requesting clarification with fewer classmates listening. 

In the featured number talk, I showed my students the mixed number, 13/4.  I asked them to think about as many ways as possible to represent this number.  Keep in mind, the students in my class at math summer school are the entering fifth graders in the school district who need the most help and guidance with math, especially number sense.  This particular task was a challenge!   I grouped my class homogeneously, meaning they were in groups with others at or close to the same level of understanding.  I met with my highest-need group first.  Their thinking is represented in green.  Next, I met with my group whose understanding was only slightly higher.  Their thinking is represented in blue.  

Completed Number Talk Chart

As you can see, each group thought about multiple ways to represent this number.  Every student shared at least one idea.  Plus,  each student's level of understanding about mixed numbers, decimals, and fractions increased!   Once a number talk is complete, the chart is displayed in the classroom for at least a few days.

This week and next, we're working on fractions in summer school.  Last week, we focused on thinking about, reading, writing, and manipulating larger numbers.  One particular number talk was extremely effective in helping students understand different ways to represent a large number.  We focused on the number 24,685.  Again, I homogeneously grouped students.  The blue responses show my first group's thinking.  The green writing shows the thinking of my students categorized as mid-level.  The final group with the red writing shows my students with the highest level of number sense skills. 

Many ways to represent 24,685

I was especially impressed with the responses from my final group.  As they came over for their number talk, I told them to look over the other groups' already written responses.  I then told them to take a couple minutes to think of different ways to represent 24,685.  At first, they looked at me as if I was asking them to do the impossible.  Then, they stepped up to the plate and truly stretched their thinking.  I wrote down their six responses (seen in red).  They had many more solutions as well, but I ran out of room on the chart.

Teaching lesson to take away:  If the bar is raised in a safe environment, students will always rise to the occasion and exceed our expectations!

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