First let me say, that because I have spent the last 10 years in elementary school (and before that 10 in middle school), much of what I'm going to write is from that perspective but know that this is not exclusive to elementary classrooms and it is something that middle and high school classrooms need to think about as well.
Most of us realize that the way we were taught math (sit and get or chalk and talk) is not effective for most students today (or then for that matter). In a push for differentiated and/or individualized instruction many teachers have ditched the notion of whole group instruction and opted for 5 day a week small group instruction and/or centers (or workstations). I applaud teacher's creativity in trying to help students learn more math content in a student centered conceptual way but....have we increased the application or transfer of that content through the sole use of small group instruction? While we are presenting the material in a more engaging way (games, less worksheets, etc...), are we really teaching kids to understand math and apply or transfer those concepts more than the old traditional ways of math instruction?
The beauty of the Common Core and the thing that I believe ties all of the new standards together, be it Next Gen, C3, Math or ELA CCSS, is teaching in an inquiry based way so that students become problem solvers and critical thinkers. Honestly, if you have attended on of my workshops, you have heard me say at least once (if not a dozen times), "If my kids only take away a few things from math instruction, I hope it is the Math Practices because if they are proficient with those habits of mind they can do anything"!
Consider this, how are we building those Math Practices in small group and centers? I think
some of that can happen there but I think that critical thinking and problem solving is best learned from each other in whole group settings as well as the teacher. Often when teachers group students for centers they are placed in homogeneous groups. But, I contend that students learn these critical thinking and problem solving skills for students of all levels. Some of our "lowest" math students tend to "think outside the box" where some of our "high" math students are very linear in their thinking - both groups of students can benefit from each other.
So I'm not saying do away with small groups....I'm advocating for a BALANCE of whole and small group instruction. There are benefits of both.
What should that whole group instruction look like? It should be filled with things like Number Talks, 3 Act Lessons and other intriguing problems to solve, open-ended problems, Noticing and Wondering, etc... This should be a time where students are collaborating, working together, and sharing. Most importantly this time should end with at least 10-15 minutes of whole group sharing of learning, questioning, and thinking aloud together. Teacher's don't need a page of math problems for this -- they need 1 or just a couple of good ones!
This whole group time should not just focus on the content but the
thinking as well. I worked with a fabulous group of grade 5 magnet students (with a wonderful young teacher) for a 3 Act Lesson this year. These kids had lots of math SKILLS!!! They knew how to do math but, not surprising to me struggled to solve a problem that they generated in a 3 Act Lesson. They were quick to "erase" their thinking if it didn't seem to work out. When I noticed this, we stopped and had a quick whole group discussion about the value of analyzing what went wrong and just setting it aside in case they might need some of those calculations again (this is something we also talked about it in the conclusion of the lesson). These students also did lots of calculations but didn't label much and therefore struggled when they had to explain what they did to remember why they did those calculations. We talked, in the end about how solving this problem was a lot like doing a science experiment - if the math didn't work out we had to analyze what went wrong and then determine another path to take to solve the problem instead of just scrapping everything and doing something different or giving up. Their teacher told me, after the lesson, that his kids didn't so much learn new math that day but they really learned the value of analyzing one's thinking and communicating in a more concise way, their thinking through what they wrote on paper. He told me that the kids really enjoyed the lesson and learned so much that they could apply to future problems.
So, what should the teacher's role in these whole group sessions be? The teacher should be the facilitator and questioner. The teacher doesn't even have to have the "answer" to the problem - the teacher just needs to know how to question kids when they get stuck and when to stop and talk about the problem solving methods (as needed). The teacher also needs to skillfully set up the class to help kids develop those habits of mind - whether to use pairs, small groups, and when to use protocols to cross pollenate those ideas.
One of those ideas that I use to cross pollenate ideas is called "Send a Spy". Often if kids are working in small groups I will stop them and tell the groups that it is time to "send a spy". Sometimes I appoint the spy in each group and sometimes I let the group choose. Each group send their spy to look at the work of other groups as they continue to work. We have rules for this...no one can cover their work, the spies aren't allowed to write or talk until they get back to their group. They only have about 2-3 minutes to do this - I usually play some "spy music", like the Mission Impossible Theme while this is going on. When the music stops they have to return to their group and share what they learned.
These are just some of my thoughts on the structure of math time. Honestly for me, in an elementary classroom I would have 3 days of small group instruction and 2 of whole group each week.
If you want to learn more about teaching problem solving be sure to read Max Ray-Riek's book,
Powerful Problem Solving.
Agree...Disagree with any of this? Want me to elaborate on any of this? I'd love to hear from you! Leave me a comment!
While this phenomenon started as a high school structure, I embrace this as also a very powerful instructional tool at the elementary level (even down to the Pre-K level). I have borrowed and adapted some elementary ideas from Graham Fletcher (out of GA) as well as written many of my own. If you are interested in checking this out, check out my 3-act lesson website: