Nowa Techie

Welcome to the fourth installment of our series, where we delve into the fascinating realm of Mathematical Language Routines (MLRs). In our previous discussions on MLR 1: Stronger and Clearer Each Time and MLR 2: Collect and Display, we explored the crucial role they play in cultivating critical thinking skills and fostering a deep understanding of mathematical concepts. Let’s continue our journey toward mathematical success by exploring the next MLR in line.

MLR 3: Critique, Correct, and Clarify is a routine designed to enhance mathematical writing and discussions. The primary purpose of MLR 3 is to foster a culture of critique and improvement in mathematical conversations. By engaging in this routine, students are encouraged to actively evaluate, correct, and articulate mathematical concepts with clarity. Through collaborative groups or partner talks, students can refine their thinking as they work together. To introduce this routine, teachers can model it by providing a predetermined piece of writing for critique, ensuring that it includes common errors and vague language to encourage more precise language. This approach empowers students to identify and rectify mistakes while enhancing their ability to clarify their ideas effectively.

Beginning this routine can be tricky, especially since it involves critiquing and correcting another person’s work. However, there are strategies that can help create a safe space where students feel comfortable critiquing and correcting each other’s mathematical reasoning.

At the middle school and high school levels, it is a bit easier as students change classes, and using an example from another class can happen – with names removed.

For elementary-level students, making up a problem/solution that they can use to critique is advisable. It’s important to ensure that the problem/solution contains common errors related to the content being studied.

Once this routine is established, it will become easier for students to seek out peer feedback. Teachers play a crucial role in creating a safe environment where students feel encouraged to seek out one another for critiquing. By implementing these strategies, teachers can foster a supportive and collaborative atmosphere for students to improve their mathematical reasoning skills together.

One Math EduProtocol that works well with this MLR is Nacho Problem. This EduProtocol was developed by Ligia Ayala-Rodriguez with the intention of addressing common errors exhibited by students. The main concept behind Nacho Problem is to task students with identifying and explaining the errors they encounter. Let’s take a look at an example to better understand how it works:

Second-Grade Nacho Problem Example

Ms. Daines needs to drive to San Jose which is 109 miles away. Along the way she stopped in Salinas which is 48 miles away. When she began driving from Salinas, how far away was Ms. Daines from San Jose? The work was provided but no explanation was given. This allowed for students to critique and analyze the provided work, find the error, and clarify their reasoning. 

In this example, which was taken from an introductory lesson using Nacho Problem, the wording is kept basic and straightforward. However, as students progress with this EduProtocol, their written expression and complexity will naturally grow.

The beauty of Nacho Problem lies in its simplicity and effectiveness. By encouraging students to find errors and explain their reasoning, it promotes a deeper understanding of mathematical concepts. So, if you’re looking for an educational approach that fosters critical thinking and problem-solving skills, Nacho Problem is definitely worth considering, but not your only option. Sometimes, always, never is another good approach to this MLR.

Incorporating MLR 3 into your math class can greatly enhance your students’ understanding and written communication skills, which are vital for their success. This instructional approach can be implemented as early as kindergarten, allowing students to develop the valuable ability to analyze others’ work critically. This fosters a deeper comprehension of mathematical concepts and empowers them to ask more precise and insightful questions. In our next discussion, we will explore MLR 4: Information Gap, where students are encouraged to engage in critical thinking by identifying the necessary information to solve word problems.