I see students working in groups all the time… Students working collaboratively in pairs or small groups having rich discussions as they sort shapes by specific properties, students identifying and extending their partner’s visual patterns, students playing games aimed at improving their procedural fluency, students cooperating to make sense of a low-floor/high-ceiling problem…..

When we see students actively engaged in rich mathematics activities, working collaboratively, it provides opportunities for teachers to effectively monitor student learning (notice students’ thinking, provide opportunities for rich questioning, and lead to important feedback and next steps…) and prepare the teacher for the lesson close. Classrooms that engage in these types of cooperative learning opportunities see students actively engaged in their learning. And more specifically, we see students who show Agency, Ownership and Identity in their mathematics learning (See TruMath‘s description on page 10).

On the other hand, some classrooms might be pushing for a different vision of what groups can look like in a mathematics classroom. One where a teachers’ role is to continually diagnose students’ weaknesses, then place students into ability groups based on their deficits, then provide specific learning for each of these groups. To be honest, I understand the concept of small groups that are formed for this purpose, but I think that many teachers might be rushing for these interventions too quickly.

First, let’s understand that small group interventions have come from the RTI (Response to Intervention) model. Below is a graphic created by Karen Karp shared in Van de Walle’s Teaching Student Centered Mathematics to help explain RTI:

As you can see, given a high quality mathematics program, 80-90% of students can learn successfully given the same learning experiences as everyone. However, 5-10% of students (which likely are not always the same students) might struggle with a given topic and might need additional small-group interventions. And an additional 1-5% might need might need even more specialized interventions at the individual level.

The RTI model assumes that we, as a group, have had several different learning experiences over several days before Tier 2 (or Tier 3) approaches are used. This sounds much healthier than a model of instruction where students are tested on day one, and placed into fix-up groups based on their deficits, or a classroom where students are placed into homogeneous groupings that persist for extended periods of time.

Principles to Action (NCTM) suggests that what I’m talking about here is actually an **equity** issue!

We know that students who are placed into ability groups for extended periods of time come to have their mathematical identity fixed because of how they were placed. That is, in an attempt to help our students learn, we might be damaging their self perceptions, and therefore, their long-term educational outcomes.

###### Tier 1 Instruction

While I completely agree that we need to be giving attention to students who might be struggling with mathematics, I believe the first thing we need to consider is what Tier 1 instruction looks like that is aimed at making learning accessible to everyone. Tier 1 instruction can’t simply be direct instruction lessons and whole group learning. To make learning mathematics more accessible to a wider range of students, we need to include more low-floor/high-ceiling tasks, continue to help our students spatalize the concepts they are learning, as well as have a better understanding of developmental progressions so we are able to effectively monitor student learning so we can both know the experiences our students will need to be successful and how we should be responding to their thinking. Let’s not underestimate how many of our students suffer from an “experience gap”, not an “achievement gap”!

If you are interested in learning more about what Tier 1 instruction can look like as a way to support a wider range of students, please take a look at one of the following:

- How do we meet the needs of so many unique students in a mixed-ability classroom?
- Differentiated Instruction: comparing 2 subjects
- Differentiating Mathematics Instruction

###### Tier 2 Instruction

Tier 2 instruction is important. It allows us to give additional opportunities for students to learn the things they have been learning over the past few days/weeks in a small group. Learning in a small group with students who are currently struggling with the content they are learning can give us opportunities to better know our students’ thinking. However, I believe some might be jumping past Tier 1 instruction (in part or completely) in an attempt to make sure that we are intervening. To be honest, this doesn’t make instructional sense to me! If we care about our content, and care about our students’ relationship with mathematics, this might be the wrong first move.

So, let’s make sure that Tier 2 instruction is:

- Provided after several learning experiences for our students
- Flexibly created, and easily changed based on the content being learned at the time
- Focused on student strengths and areas of need, not just weaknesses
- Aimed at honoring students’ agency, ownership and identity as mathematicians
- Temporary!

If you are interested in learning more about what Tier 2 interventions can look like take a look at one of the following:

Instead of seeing mathematics as being learned every day as an approach to intervene, let’s continue to learn more about what Tier 1 instruction can look like! Or maybe you need to hear it from John Hattie:

Or from Jo Boaler:

###### Final Thoughts

If you are currently in a school that uses small group instruction in mathematics, I would suggest that you reflect on a few things:

- How do your students see themselves as mathematicians? How might the topics of Agency, Authority and Identity relate to small group instruction?
- What fixed mindset messaging do teachers in your building share “high kids”, “level 2 students”, “she’s one of my low students”….? What fixed mindset messages might your students be hearing?
- When in a learning cycle do you employ small groups? Every day? After several days of learning a concept?
- How flexible are your groups? Are they based on a wholistic leveling of your students, or based specifically on the concept they are learning this week?
- How much time do these small groups receive? Is it beyond regular instructional timelines, or do these groups form your Tier 1 instructional time?
- If Karp/Van de Walle suggests that 80-90% of students can be successful in Tier 1, how does this match what you are seeing? Is there a need to learn more about how Tier 1 approaches can meet the needs of this many students?
- What are the rest of your students doing when you are working with a small group? Is it as mathematically rich as the few you’re working with in front of you?
- Do you believe that all of your students are capable to learn mathematics and to think mathematically?

I’d love to continue the conversation. Write a response, or send me a message on Twitter ( @markchubb3 ).

I’m a kindergarten teacher and our district uses EasyCBM as a state test. The reading portion is timed to a minute. In the second month of school if kids can’t say enough letters or sounds in a minute they are considered at risk. This is before they’ve had the opportunity to learn their letters and sounds. So, we are using instructional time to work on making them fluent. That’s not something that students should master in the first weeks of kindergarten. This is my opinion. Thoughts?

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Seems to me that those in positions of authority want data… they want to make the right decisions so they can support teachers and schools appropriately. However, those who are wanting all of this data sometimes neglect to think about the unintended messages being sent to teachers and students.

Your story really illustrates this point. Instead of teachers helping their students fall in love with books, start to make sense of reading materials….. they start off the year by showing you what your students don’t know. The medical model of education is the problem here. Diagnosing and remediating is becoming a real problem because we are constantly being put into a deficit model of thinking!

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Great post! I have been thinking about this concept for the past couple of years. I was really forced to address it when I had a class where 75% of my students feel into the Tier 2 section of the triangle. After engaging the services of a Student Support Tacher, we began co-teaching as an intervention. It has totally changed my practice. We no longer have students working in ability groups, no one is leaving the classroom for support. We just changed the environment of the classroom to respond to the needs of the students. I have learned that by taking the time to plan for all students, removing barriers, moving meaningfully from the concrete to the abstract, I do not need to rush to interventions. I have not been able to articulate what your blog presents so clearly….our students need more meaningful experiences with math. In the end, what I thought was tier 2 intervention just became solid Tier 1 practice. Thanks

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Thank you for the ideas you presented. One thing that struck me is how we rush to intervention after one lesson on the concept. The rushing to intervention made me connect to the belief, long held, that if you get it right away/ fast you are “good at math”. It is like we indirectly support that belief in our actions, which I do believe are well intentioned yet do not allow learning to develop.

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I agree with everything in your blog, love Jo Boalers work and Principals to Action and would love some guidance. I’m a math coach in a district that tracks students starting in fourth grade and “compacts” the curriculum or what I call speed math. In addition to tracking, every grade level has a 30 minute intervention time where targeted students (based on district data) are pulled into a “math lab” for small group instruction. These groups are taught by instructional assistants and a math interventionist oversees the groups and provides ongoing data to district.

All kids are given a computer diagnostic test at the beginning of the year and that’s how the identified kids are grouped. Once in groups, the diagnostic tells them what skills they need to work on and the IA’s are provided with lesson plans. Every kid (regardless of tier) have to spend 45 minutes a week on a computer to work in lessons that are on their individual pathway determined by that same diagnostic test. Kids just finished the middle of the year diagnostic test teachers will analyze data and determine next steps in January. BTW the assessment takes at least 2 hours and yes kindergarten through fifth grade takes it.

This year the district adopted the resource from the same company that does the computer based diagnostic interventions and is used for tier 1.

I’d love some thoughts on how to change perceptions of those that make decisions. Everything I’ve mentioned is out of my control.

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I try to share research or educational leaders’ work with others. This can help make others aware of the issues. However, one of the problems is that faced is the idea of what can be done instead. Personally, I would suggest we spend a lot more time focusing on what good initial instruction looks like. Active learning, visual/spatial components, problem-based instruction…. If we do this, we should need less structured intervention because the teacher’s role moves from discriminating knowledge to noticing student thinking, and interacting in ways that mitigates potential issues.

Instead of changing everything, try to see a path where you could downplay some of the negative pieces here, and emphasize the importance of some of the positive parts.

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There is a huge push for guided math groups to be happening every day during our one hour math block. I see how small group math can be helpful and that data is useful but what I’ve noticed is that my students need math to be more “scientific”. They need to experiment with numbers and problems using hands on manipulatives in scenarios relating to their own lives. By setting up my math class with a mix of skill building and time to apply skills to real world problems, they are having greater success understanding math. This is true for all ability levels who often work in mixed groupings. The oral thinking and problem solving amongst peers solidifies understanding for those who have a stronger understanding and opens a math door for those kids who have difficulty when pulled into a group. Using open ended problems allows every learner to access math learning. Just my observations!

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