31 Jul To Run Small Groups or Not…

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Should I run my math classroom using small group instruction?  When should I do them?  Every day?

I get these questions A LOT.  I find the teacher universe is divided on this topic of the whole group vs. small group and with most things in life, my answer is BALANCE.  I believe mathematics standards call for a balanced approach.  I have seen both small group and whole group done very well and I’ve seen them both done very poorly.  For both small and whole group, we need to consider the following:

The three pillars of recent standard revisions call for equal time and intensity on three things:

1. Conceptual Understanding.  Do students understand the how, the why, and the whens?  Are they actively building number sense through mathematical discovery and discourse? 
2. Mathematical Reasoning based in problem-solving.
3. Procedural fluency.  Being able to carry out mathematical tasks, including but not limited to computational tasks with efficiency, effectiveness, and flexibility.

Are both of your structures (small and whole group) providing an equal focus on these there pillars?  Maybe your whole group focuses on the first 2 and your small group focuses on the last one.  Either way, there should be a balanced approach.

The Principles to Action (NCTM) suggest the following actionable goals for all mathematics teachers to run effective math instruction:

• Establish mathematics goals to focus on learning 
• Implement tasks that promote reasoning and problem-solving.
• Use and connect mathematical representations.
• Facilitate meaningful discourse
• Pose purposeful questions 
• Build procedural fluency from conceptual understanding
• Support productive struggle in learning mathematics
• Elicit and use evidence of student thinking

So we if we are to incorporate everything above, is it in small groups or the whole group? My answer: both.  Start in the whole group and refine in a small group. But both should be allowing student-centered discussions and equal access to quality grade-level materials.   

 I grew up in math classrooms where the teacher did all of the work. They had the math knowledge, they told me what and how to do the math. I became an EXPERT rule follower.  But, I never really understood the math and because I wasn’t fast, I relied on my ability to follow rules to get me by. Because our testing systems were all based on multiple-choice, algorithms and timed tests, I did ok.  I was never really asked to explain the math, I was just asked to DO the math. This led to many many issues for me growing up. I was an intervention math kid who somehow faked my way through AP Calculus in high school. Let’s just say the standards of mathematical practice were not ones taught during my schooling nor during the first few years of my teaching career (sorry kids). 

Fast forward.  Now we still have whole group instruction- a stand and deliver gradual release approach- as it was when I was in school, but the standards require us to shift to an approach that fosters more reasoning and conceptual understanding.  Because of this,  we also have this new wave of the small group, math workshop that is supposed to offer students more choice, more engagement, etc.  The intentions with the push toward the small group is a pure one. Many moved to small group/workshop believing we weren’t differentiating in the whole group. Although I believe we weren’t getting whole group right, it didn’t mean it wasn’t possible to differentiate.  Many went to small groups, but, I find the actual math instruction in many of our small groups is still direct (just in a small group instead of a large group), is less (10-20 minute rotations with the teacher instead of 60) and is filled with a lot of fluff activities that lack rigor, accountability, and reasoning.  Much of our small group instruction lacks mathematical discourse, reasoning, and timely and actionable feedback.

What I fear most in small group work is we tend to do more tracking (ability grouping), over scaffolding (deciding who gets rigorous problems and methods vs who doesn’t), and more direct teaching (not student-centered, not inquiry-based).  If we can eliminate those from being the way small groups always run, then I can get on board with more of a balanced approach. 

Bottom Line: Small group and the whole group can both be highly ineffective. Both small group and the whole group can be very effective when paired together and incorporating all of the principles to action, mathematical practice (or process depending on your state) standards, both whole group and a small group can provide effective differentiation, mathematical reasoning, and solid discourse opportunities.   Let’s not throw one out or the other — let’s change how we do them so that they are more effective.

I’d like to talk A LOT MORE about how to effectively run both, but in this post, I’m going to stick with the WHEN and the WHAT (what we are doing in the whole group vs. small group) and we will tackle the HOW another time.  

I’d also like to clarify that when I say small group I don’t just mean centers.  I think we need to be WAY more flexible with what we mean by a small group and not get so stressed out by it.  It might mean:

•  ½ my class is with me at the front, and the other half is at their seats working.  
• Students are in small collaborative groups around the room and I’M doing the moving around— group to group to confer, reteach, etc.  
•  I have choice stations that are intentionally working on the three pillars of need (conceptual understanding, reasoning or procedural fluency) and various kids are around the room and I call a few at a time, based on my data to come to meet with me for 5 minutes or 30 minutes. 
•  I run actual rotations and meet with every kid in a day for the same amount of time.
•   I might meet with one group of students at the end of the day for 10 minutes and not meet with anyone else. 

Let’s agree on one thing: let’s be flexible with the term small group.  Doing a variation of the approaches above seem to me to allow student needs to drive my structures.  There are pros and cons to each of these groupings. I need different structures depending on the group of kids, the content we are working on, the length of time I have, etc.   So, when I say small group, I mean all of the above as options. 

I’ve done it all. I’ve done the whole group every day.  I’ve done all math workshop every day (workshop meaning more of a rotation feel, where I have a mini-lesson, then meet with small groups of children for about 10-15 minutes, sometimes the other kids do the same thing, sometimes it’s choice-based– I’ve done both). I moved to a workshop model with the intent of differentiating better, personalizing more, and engaging students better.  I’ve swung with the pendulums based on what is the ‘new thing.’ I realized quickly that I could differentiate, personalize, and engage students in the whole group too, without sacrificing math talk and strong math community- it was about refining my skills as a facilitator and teaching THROUGH math talk and visual representations.

After 17 years, I have concluded that BALANCE is the answer.  I know that many of you, like me, are TYPE A and like structure and predictability.  You want to know that you’ll spend 15 minutes in a mini-lesson, 45 minutes in small groups and all will be well.  You want to know that Mon-Wed- Fri is the whole group, Tues/Thurs small. I no longer work within these structures, only because I follow the phases of the learning path to determine when small groups will be. With intentional planning, you could possibly find a more structured routine approach.  When I ran my mini-lessons in math workshop, it was stressful to get in an entire lesson of content in 15 minutes. I ended up doing all direct instruction (just telling them what to do and how to do it). There wasn’t time for anything else! There was very little math talk and I had to oversimplify most of my ‘stations’ just so kids could do them independently.

Because of this, I’m going to tell you I think there is A LOT not ok with this small group structure (specifically the math workshop) in an everyday format, at least until we refine what it looks like. There are some days I need the full 60 minutes to engage students in inquiry, discussions, reasoning, and various methods.  Other days, 15 might work because I’m not building onto the previous day’s work.

90% of teachers are like me and are/were doing a direct instruction approach when they  do their ‘mini-lesson.’ Most mini-lessons I watch (and I did for years), involve the teacher TELLING students how to do the math of the day, giving directions for stations, and then releasing them to stations, workbooks, etc.  The teacher then resumes additional direct instruction, heavily guided and scaffolded in small groups. It doesn’t involve much student thinking or reasoning (there isn’t time for that!).

The whole group I’m suggesting involves an inquiry approach in which students are doing 70% of the talking (teachers 30%).  Students are doing a lot of drawing, defending, connecting, and reasoning. In this type of a whole group, engagement and efficacy are high.  Students believe in themselves, take risks, try new things and persevere. It’s not about the time. Sometimes this is 15 minutes, sometimes 60. It’s about students building understanding, not about me getting them to centers. If I’m rushing to get to centers, I can’t possibly be doing a good job orchestrating discussions and building reasoning and conceptual understanding. 

 If we do small group EVERY day, like in a workshop model, we are likely robbing students of many of these experiences because our limited time with students (because we are trying to get to everyone)  tends to cause us to do way too much guiding, scaffolding, etc. for certain groups which is only increasing are most at-risk student’s achievement gaps. Our small groups tend to be ability grouped which intentionally or unintentionally is causing major math mindset issues (lack of growth mindset– I’m always in the blue group because I don’t get math), and are short in time which means we take over the thinking and do a lot of telling and a lot fewer students are talking or reasoning.  That, and we dumb down the materials. Grouping students, scaffolding, etc. is not a BAD thing, there is a time and a place for both, but every day in the workshop model is not BALANCED and becomes a BAD thing if not done well.

I base my “to do small groups or to not do small groups…”  mostly on the learning path, following an inquiry-based approach to mathematics. The whole group for the purpose of this post IS NOT about the teacher doing an I do, we do, you do approach.  This is a direct teaching approach. This is the approach done by most teachers I see. But it doesn’t have to be. I’m suggesting a YOU DO, WE DO, I DO approach which is an inquiry approach. Take a look at this video well done by Mike Flynn that helps explain this approach:   

I think this approach CAN work in both small and large group instruction. In this model, students are the guides, they are at the center. 

There is a learning progression for inquiry-based mathematics classrooms.  My favorite researcher, Dr. Karen Fuson, calls it her Learning Path. Basically, it means we teach mathematics in a student-centered approach via a strong and healthy math talk community. 

Phase 1: We launch a problem.  No instruction, students just produce student-generated ideas. (YOU DO.  Student-generated ideas…students are doing the initial thinking, exploring, trying).  We are sending the message that they ARE mathematicians without a teacher telling them.  They CAN trust their mathematical intuition. They CAN figure the math out.

Phase 2: The teacher observes and monitors what students come up with and takes the generated methods while adding on, connecting, etc. to more desired methods.  Students are fully engaged in active reasoning, defending, error making/correcting, idea revising, etc. In this phase, the teacher is ensuring students know how to DRAW, TALK, and MODEL mathematics. (WE DO, the teacher and students are working together to do the talking, connecting, and adding on. There is explicit teaching in this phase as there are DEFINITELY desired methods, drawings, etc. that we are pushing kids to). 

 If students can draw it out, a visual representation, talk about it (defend, reason, explain) and model (like with math models, or concrete tools), then students are ready to start practicing.  If they can’t? They stay in phase 2.

If they can?

Then I push them to phase 3: Procedural Fluency. In most textbook lessons, this is when the workbook tends to get used a lot. (I personally don’t use the workbook at all during phase 1 or 2 or very limitedly. I use the problems, etc. but I post them on the board.  Workbooks are distracting for everyone.) I build fluency now with those skills. This includes building fluency withdrawing, talking, and modeling. I may do this through workbooks, technology, games, etc. Remember, to be fluent, a student must be efficient, effective and flexible.  So, there have to be some reasoning components to this practice. We aren’t just drilling and doing what calculators can do. (I Do= as the teacher, I’m now orchestrating the room– maybe everyone is practicing, maybe I’m reteaching, running small groups, etc.I’m choosing what methods need to be emphasized, etc.). THIS IS WHEN I DO SMALL GROUPS.  Some are practicing in partners, individuals, etc and others are in maybe a group with me. 

The problem is we often keep the whole class together and push everyone to phase 3.  So now we have kids working problems in workbooks who have NO BUSINESS in a workbook.  If they can’t draw, talk and model, save the workbook. Pull some small groups and keep those kids actively working in phase 2.

I differentiate the process (how students are showing the work), the content (some students may need fewer digits, or may need a scaffold of some sort to access the content such as a number line), or the product (some students may do the workbook page, others may practice on their whiteboards, others may practice by developing sample errors to defend, etc.). So, each station may have the same objective, but what students do there may vary based on the individual. This is based on Carol Ann Tomlinson’s work– the guru of differentiation if you’d like to do some additional reading.

Small groups tend to work for me when I’ve spent a day or a half-day on building good understanding (drawing, talking, modeling) that now I’m ready to do some small group work to help those still in phase 2 and to confer and push those in phase 3. I can often do this in mixed performance groups (read Juli Dixon’s FANTASTIC book, Making Sense of Mathematics for Teaching the Small Group on this topic:).

Small groups work for me when I need students to do exploration or the ‘launch’ activity in collaborative groups or partner work.  

Small groups work for me when I need to dive deeper into student thinking and do some conferring.  I think of this as I think of conferring for writing. I need time to really look at student work and listen to them discuss it with me. 

Small groups work for me when I’m in a reteaching cycle.  We’ve completed a quiz or unit assessment and we need to go into reteaching/extending for a couple of days. Small groups don’t ONLY have to be after a formal assessment.  They can be after your formative assessments tell you to slow down for a day. This could be a great small group day so that we are being PROACTIVE instead of reactive and only reteaching after large chunks of time go by.

Small groups ARE FANTASTIC for intervention or WHAT I NEED blocks of time.  I am NOT doing these groups during core instruction.  YES, some students need additional support, different materials, off grade-level instruction, etc.  But, during my CORE, this is not my focus. I will provide necessary access so all students can access the content, but I’m not running small groups during core instruction time so that every kid is getting their level of mathematics.  I definitely think some of this is happening naturally as I provide scaffolds and accommodations, but as a basic rule of thumb, I really work hard to provide EQUAL access to high-quality standards, curriculum, and instruction to ALL students during core instruction.  Response to Intervention is necessary but it is NOT happening when I’m teaching my core standards. Everyone is working on grade-level standards during my core math block, they may just be doing it differently (see paragraph above on process, product, and content). 

So, when do we do small groups?  

• When you are moving into phase 3 of a concept or skill.  Sometimes this happens the same day as phase 1 and 2, sometimes it happens the same day, the next day, or at the end of the week.
• When you are in a reteaching cycle 
• When you have orchestrated a whole group convo on a skill or strategy and now need to check in with individual students and have smaller circles for conversations.
• When you want groups to collaboratively explore (phase 1) then you bring them together in a whole group to discuss (phase 2), then they go back into small groups to build fluency. 

I’ve reinserted the Principles to Action with some guiding questions you can ask yourself as you reflect on the structures you are using to teach and the structure you are considering using.

Principles to Actions: Ensuring Mathematical Success for All (NCTM) 

• Establish mathematics goals to focus learning

Are your goals specific, actionable and rigorous?  Do you have any time-filler activities that lack purpose, rigor or focus?  Could students answer the question of what they are expected to know, understand and do?

• Implement tasks that promote reasoning and problem-solving.

Students need time to try what they think will work, get feedback, and revise.  They need time to reason with others (not just 3 others in a small group– the sample size of good thinking is too small). Are your launch questions or station questions more than computational questions? Are students having to justify and defend their ideas?

• Use and connect mathematical representations.

Connecting representations is a key part of what the teacher is doing during phase 1 & 2.  Practicing the representations, explaining and defending fit well in small group and the whole group.

• Facilitate meaningful discourse

Like legit discourse.  Not one person sharing and everyone else acting like they care.  I mean true mathematical discourse in which all students have a voice and are actively sharing and thinking.  How many conversations are students having and I mean ALL students? If you were to put a percentage on it would you say 50/50 (50 teacher, 50 students? 90/10 (90 teacher/10 students (this is a very average ratio if you are doing an I do, we do, you do approach))?  Current research calls for 70/30 (70% students, 30 % teacher).

• Pose purposeful questions 

Is your instruction in whole and small group too direct? Are your questions open or closed?  If they are open, you are allowing for many methods, ideas, and strategies. If they are closed you get yes, no, or one-way ideas. It’s tough to build on these.  Posing purposeful questions is what makes phase 2 work so you can go into phase 3. Do these same high level of questions also exist in your small group?

• Build procedural fluency from conceptual understanding

If you choose to have students practice in stations, is there a balanced approach amongst them?  Are there stations where students have to draw, talk, model as well as practice and develop fluency with these skills?

• Support productive struggle in learning mathematics

Are you over scaffolding for students in a small or whole group?  When students struggle do you offer a solution or do you ask a purposeful question?  When students struggle do their hands immediately go up to be rescued? If yes, you probably need to work on refining your “You do, We do, I do” approach as you are most likely doing too much “I do, we do, you do.”

• Elicit and use evidence of student thinking

Are you using student-generated ideas/evidence to orchestrate the discourse and build/connect ideas?  Or do you use your examples and direct teaching to show kids what to do? Do you build on what students say to help them to the next stage in understanding?  

Just have balance.   

I really believe both small group and the whole group are important to student learning. 

How have you found a balance?  What is working for you?  What isn’t?  Where do you need additional support?

I’d love to continue the conversation online.  Comment below or let’s connect on FB (Empower Consulting page) or Twitter (@sekiebler).

Are you looking for more support with launching the whole group using an inquiry approach and then orchestrating an effective conversation before you head into small groups?  Register for my FREE webinar where I’ll outline the key steps to taking any textbook lesson and transforming it simply into a powerful learning experience.

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