The Power of Structured Discussion in Education

In a landscape where student engagement and comprehension remain at the forefront of educational challenges, how can we transition our students from rote memorisation to a profound understanding of mathematical concepts?

The answer lies in creating an environment ripe for structured discussion and comparison—an approach that not only nurtures critical thinking but also fosters a genuine love for learning.

The Compare, Discuss, Make Sense (CDMS) routine is a powerful framework that can reshape our teaching strategies. It provides a structured yet flexible platform for teachers to guide students through inquiry and sense-making, ultimately deepening their conceptual understanding. Through engaging discussions, students can unpack complex ideas, grapple with diverse perspectives, and find joy in mathematical exploration.

The Importance of Discussion and Comparison

Mathematics is much more than a collection of procedures; it’s about understanding the ‘why’ behind those procedures. Engaging in mathematical dialogue allows students to:

– Deepen their understanding of concepts

– Make sense of new ideas

– Learn from diverse perspectives

– Enhance their engagement and interest in the subject

However, facilitating real-time discussions can be a challenge. Teachers often face hurdles such as selecting suitable tasks and establishing routines to foster meaningful conversations. The CDMS routine addresses these issues directly and empowers educators to foster a deeper understanding.

Deconstructing the CDMS Routine

The CDMS routine unfolds in two phases, completed in approximately 20 minutes, yet offers profound insights into students’ understanding.

Phase 1: Comparison (Approx. 8 minutes)

In this initial phase, students analyze and contrast different approaches to solving a mathematical problem:

– Prepare to Compare:

Individually, students explore two distinct problem-solving methods. They are prompted to question the reasoning behind each approach, diving into what is happening in each step.

– Make Comparisons:

The class then collectively discusses these methods, identifying similarities, differences, and the reasoning employed. Teacher-led prompts such as “Why do both methods work?” guide students to articulate their thoughts and connect ideas.

Phase 2: Discussion (Approx. 12 minutes)

Following the comparison, the routine shifts to a deeper conversation:

– Prepare to Discuss:

Students think independently about the questions that arose during the comparison and then pair up to explore their thoughts. They might reflect on how the comparison helps their understanding or how they could apply the methods to similar problems.

– Discuss Connections:

This culminates in a whole-class discussion where students share insights. Here, the teacher plays a pivotal role in facilitating dialogue, ensuring all voices are heard, and prompting deeper reasoning with follow-up questions.

Identifying the “Big Idea”

The CDMS routine concludes with students articulating the main takeaways or the “Big Idea” of the activity. This ensures that the learning objectives are clear, reinforcing student ownership of their understanding.

Practical Application: The Case of Riley and Gloria

Consider two students, Riley and Gloria, who solve the equation 4(x+5)²=64 using different methods. Riley opts for the square root approach, while Gloria divides both sides by 4.

Through the CDMS framework:

– Students independently analyze Riley’s and Gloria’s methods.

– As comparisons unfold, they engage in discussions about the implications of their choices and the mathematical principles at play.

As they discuss connections, they ponder questions such as why one method might be more efficient than another, particularly in varied contexts. The teacher facilitates this exploration, addressing any misconceptions and guiding students toward a deeper understanding of algebraic principles.

Conclusion: A Call to Action for Educators

As educators, we must move beyond mere instruction and foster environments where comprehension reigns supreme. The CDMS routine is a vital tool in helping students transition from memorisation to achieving a true understanding of mathematics. By integrating structured discussions into our classrooms, we not only enhance student engagement but also empower them to become critical thinkers and passionate learners.

Let’s harness the power of discussion and comparison in our teaching practices to unlock the full potential of our students in the realm of mathematics. Together, we can cultivate a generation that not only learns maths but truly understands it.