When I walk into a K-12 math classroom and I see students sitting passively listening to the teacher talk about math I cringe a little. Rather we want students to be actively, and physically engaged in their math lessons. We want to encourage student-to-student collaboration, students’ critical thinking, and problem-solving. Here is how we get there and why!

The Role of Teacher Table

When we place students into small groups (3-5 students) and engage in a math lesson with them we, the teacher, see and hear so much of what is happening in their brains. What strategy they are using to solve the task, what tools are they selecting, and why? The teacher table is one of the most effective ways to gather formative assessment data that will inform our instruction. Picture this… there are 5 students at your teacher’s table and you are conducting a lesson on operations with decimals. All of the students have a whiteboard and marker along with a 10×10 grid to demonstrate their reasoning. You ask the students to ‘show me’ .03 + .46 =. Each student proceeds to work on their grid and whiteboard to show you their strategy. The conversation might go like this:

Teacher: Sara can you show us how you solved the problem?

Sara: I shaded in 3 boxes in the first column, then shaded in 46 boxes in the rest of the columns.

Teacher: Ryan, can you share what Sara did in your own words?

Ryan: She colored in 3 out of 100 squares in her grid, then colored 46 squares to fill 49 boxes. But I didn’t do it that way.

Teacher: Can you share how you did it differently than Sara?

Ryan: I didn’t use my grid. I added the 100th place, like the 3 and 6 then I added the tenth place to get .49.

Teacher: Colleen do you agree or disagree with Sara and Ryan? Can you show us why?

Notice how the focus is on the strategy and process rather than the answer. Students must attend to what other students in the small group are sharing to make sense of the other students’ strategies and compare it with their strategy. Is this possible in a whole group lesson? It is certainly more challenging to make happen. When using manipulatives in our classroom, it is much easier to monitor the use of the manipulatives with 5 students instead of 25 students. At Teacher Table, we can quickly make note of where each student’s mastery is on our success criteria before moving to the next small group.

Station Rotation: What should I use for my stations?

Unless you have a class larger than 30 students I would recommend maintaining 4 total stations with one of the stations being Teacher Table. Here are some station ideas for your math classroom.

• Fluency Station: It is critical that students in grades K-6 engage in a number sense-focused fluency station each day for at least 10 minutes. Fluency games are the best approach for this station. My favorite games on the Kentucky Mathematics Center website align with Jennifer Bay-Williams’s work. These games can be taught at Teacher Table or as a whole class first to practice them before asking students to work independent of the teacher at a station. You can build a repository of fact fluency games that you can change out every couple of days. 
• Spiral Review: Using the 5 Representations we want to build a station that connects previous learning to new learning.
  • Sample Grade 2: New content is 2-digit by 2-digit addition. My spiral review station is  5-6 numeric problems that are 2 digits by 1 digit where the students are using base 10 blocks to build the problem and solve. Students could build the problem and solution with physical base 10 blocks and then draw their solution on a recording sheet. They should be asked to share their strategy and recording sheet with a partner to encourage the students to communicate and collaborate in the station.

• Connecting Representations Station: Using the 5 Representations we want to build a station that connects representations within the same standard.
  • Sample Grade 5: New content is multiplying fractions using an area model. The connecting representations station uses fraction bars to demonstrate the multiplication of fractions rather than using the area model and shading. This type of station builds conceptual understanding because the students are using a concrete model (fraction bars) and the area model to multiply fractions visually. The two stations together create a more comprehensive understanding of the math content.
  • Sample Grade 8/Algebra 1: New content is addition and subtraction with polynomials. The connecting representations station would ask the students to add and subtract algebraic expressions using algebra tiles (concrete representation) while the teacher table lesson might focus on adding and subtracting algebraically using like terms and the distributive property. Again, the variation in the representations creates a stronger understanding of the math content.
• Play-Based Station: Using play-based activities such as tangram puzzles, magna tiles, pattern block puzzles, etc. is a fantastic way to engage students in the world of mathematics. It is important to change these stations often to avoid overuse and boredom.
• Stations to avoid: We want to limit our use of two very popular stations; technology and independent work. We are missing opportunities for students to interact with each other and learn from each other when we include these stations in our rotation. Rather than ask students to play a game on a tech app, give them a fluency game where they talk through their strategies and process their thinking. Instead of giving students a workbook page to complete individually, provide a set of task cards and a recording sheet where students engage with a partner to complete the activity. When students are together in the classroom we want to maximize student discourse.

Small group instruction with a Teacher Table and Station Rotation is hands down the best research-supported instructional model to build conceptual understanding and procedural fluency for students. This instructional model should be used in all grade levels rather than relegating it to only the primary grades. This is how we begin to shift our math classrooms from passive student engagement to active student engagement.