Math can be a challenging subject for many students, but the right approach can make all the difference in helping them gain deep conceptual understanding. To help students reach grade-level proficiency in math, it’s essential to use strategies that encourage active learning, critical thinking, and collaboration. Here are three effective approaches to help students truly start understanding math.

1. Stop "Telling" and Start Asking Students Focused Questions

One of the most powerful ways to encourage understanding is by shifting from a "telling" approach to an "asking" approach. Instead of simply explaining concepts to students, start asking them focused questions that guide them to think critically about the problem at hand. Questions like, “What happens if we add these two numbers?” or “How can we break this problem into smaller parts?” prompt students to explore concepts independently, allowing them to make connections on their own. 

This method encourages deep thinking and helps students develop problem-solving skills, as they actively engage in figuring things out rather than passively receiving information.

2. Flip the "I Do, We Do, You Do" Model

Traditionally, the "I do, we do, you do" model involves teachers first demonstrating a concept (I do), then the teacher leads a guided practice with students (we do), and finally having students apply it on their own (you do). 

However, flipping this model can foster more meaningful learning. 

Start by having students attempt a problem on their own first (you do), allowing them to engage with the concept independently. 

Then, collaborate together to discuss strategies and solutions with a partner or group (we do). 

The teacher then facilitates a discussion of various strategically selected solutions (I do). This flipped approach ensures that students are actively involved in their learning and can better understand why certain methods work, leading to greater retention and comprehension.

Note:  the “We and I” are completely different in the RED Hot flipped model.  

Instead of “We” doing guided practice led by the teacher demonstration, We are now collaborating, sharing our ideas, and perhaps coming up with a blended solution.

Instead of “I” the teacher “going over” the “correct” solution, the teacher facilitates a discussion where students do the talking. They get to do the “telling” about what they discovered and how they thought about the problem.  Various solutions are shared, and the teachers asks questions to help students make connections for deeper understanding.

3. Share Student Solutions Strategically to Build Understanding

Let’s go a little deeper with how to do this “strategic” sharing. One of the most effective ways to reinforce math understanding is by allowing students to share their solutions and articulate their thinking to the class. Rather than presenting only the “correct” answer, highlight a variety of student solutions and approaches. 

This strategy not only celebrates diverse thinking but also helps students see different ways to approach a problem. When students observe their peers solving problems in different ways, they gain new insights and methods for solving similar problems themselves. 

Sharing solutions strategically fosters a collaborative learning environment where students feel more comfortable contributing their ideas and learning from each other.  You can select several students to share their work starting with simple strategies to more complex ones.  

Another way to show multiple representations is following CRA Sequencing.  Begin with a concrete example.  ( The student may have used manipulatives in their solution.) The next share then includes a visual representation. ( The student used a diagram, drawing or other visual representation.) And then introduce an abstract representation of the solution. (The student used numbers and math symbols.)  

As students share different examples, you help them make connections with questions such as 

• How are they the same? 
• How are they different?
• Who has a similar solution?

Conclusion

By focusing on asking thoughtful questions, flipping the traditional teaching model, and sharing student solutions strategically, you can create a more engaging and effective learning environment that fosters a deeper understanding of math. 

These approaches not only help students reach grade-level proficiency but also cultivate critical thinking and problem-solving skills that will serve them throughout their academic careers and beyond. With these strategies in place, students will be empowered to take ownership of their learning and approach math with confidence.