Nowa Techie

Mathematical Language Routines (MLRs) play a crucial role in enhancing students’ comprehension and communication skills in mathematics. Developed to meet the diverse language needs of learners, these frameworks have become an invaluable tool in promoting a deeper understanding of mathematical concepts. In this series, we will explore each MLR in detail, starting with MLR 1: “Stronger and Clearer Each Time.”

MLR 1: “Stronger and Clearer Each Time” focuses on refining students’ ideas and communication through various activities. By incorporating writing, listening, explaining, and integrating new language, students are encouraged to continually improve their understanding of mathematical concepts. This routine, often conducted in pairs, provides students with the opportunity to collaborate and build upon each other’s ideas, fostering a culture of shared learning and growth.

Throughout this series, we will delve into the different structures and strategies that can be employed within MLR 1, unveiling how this routine nurtures students’ confidence and fluency in mathematics. Join us as we explore the remarkable impact of MLR 1 and its profound influence on students’ language development and mathematical achievements.

The purpose of this routine is to foster the refinement of students’ verbal and written output through structured conversation and revision. By engaging in this process, students can enhance both their thinking and their expression of it.

In this routine, students initially work individually or in groups, gradually progressing towards partner work. This approach allows students to acclimate to the task and build their confidence. For those who may be less familiar with writing, explaining, and refining their thoughts, supportive strategies can be implemented to ensure their success.

Once the structures are in place, it is crucial for students to recognize the ultimate goal, which is either a deep understanding of the concept or the ability to articulate it like an expert. The listener’s role becomes significant as they ask clarifying questions, enabling a comprehensive understanding of the speaker’s thoughts. Simultaneously, the speaker benefits from this exchange, refining their thinking more clearly.

To encourage thorough responses, it is valuable to have students switch partners multiple times during the routine. By engaging in back-and-forth conversation, with equal emphasis on speaking and listening, students not only refine their thoughts but also strengthen their language and reasoning skills. The iterative nature of this process reinforces the importance of pressing for details and encourages the continual refinement of ideas.

Convince Me That, by Daniel Kaufmann, is a highly effective protocol that teachers can implement in their math lessons to foster deeper understanding and engagement among students. To successfully introduce and implement this routine, educators can follow these step-by-step guidelines:

1. Introduce the Problem: Begin by presenting a math problem along with its solution to the students. For instance, students can be asked to explain why 3 x 4 equals 12.
2. Form Partners or Small Groups: Divide the students into pairs or small groups to facilitate collaborative learning. This structure encourages peer interaction and promotes the sharing of ideas.
3. Restrict Algorithmic Thinking: Emphasize that students should focus on concrete or pictorial methods rather than relying on algorithms. This restriction encourages students to think deeply about the problem and explore alternative approaches.
4. Initiate Individual Thinking: Give students time to think individually about the problem and develop their own explanations for the solution. This step helps to build independence and promotes critical thinking skills.
5. Structured Pairing: After individual thinking, partners or group members should share their explanations with each other. This process enables students to refine their understanding through constructive discussions and peer feedback.
6. Revise Written Responses: Encourage students to revise and improve their written explanations based on the feedback received during the structured pairing phase. This step promotes self-reflection and reinforces learning.

To facilitate the refinement process and prompt students effectively, here are some examples suitable for Math Learning Routine (MLR) 1:

• “Convince your partner why the sum of any two even numbers is always even.”
• “Explain to your group why dividing by zero is undefined and cannot result in a finite number.”
• “Justify why the product of any number and zero is always zero.”

These prompts stimulate students to think critically, apply their knowledge, and refine their explanations. By implementing the Convince Me That routine with these strategies and prompts, educators can foster deeper conversations, encourage active learning, and enable students to demonstrate a more profound understanding of mathematical concepts.

For a more detailed explanation and implementation guidelines, you can refer to Chapter 19 of The EduProtocols Field Guide Math Edition. This invaluable resource offers comprehensive insights and practical tips for effectively utilizing the Convince Me That routine in math classrooms.

In conclusion, the implementation of MLR 1 has proven to be highly beneficial for students. It provides them with a structured platform to refine their thinking, improve their communication skills, and deepen their understanding of the subject matter. By engaging in the collaborative and iterative process of MLR 1, students are empowered to develop clearer and more coherent responses.

We invite you to stay engaged with our series and continue exploring the world of Mathematical Language Routines. The second routine in our series, MLR2: “Collect and Display”, has a specific purpose. It aims to capture students’ oral words and phrases and transform them into a stable, collective reference. The main goal is to preserve the language that students use and use it as a reference point for developing their mathematical language.