By Jennifer Wilson and Liz Ramirez
We want to acknowledge that we are all in different situations that shape how we respond to the call to adapt our teaching to fit a model for distance learning. This impacts the access we have to our students for the remainder of the school year.
Our hope is that we find the grace to give each other space to make sense of how we will cultivate agency, mathematical understanding, and language in these times.
We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful opportunities for students to engage in sense-making and to use language to negotiate meaning with their peers. This calls for a language-rich environment where there’s space for all students to participate in argumentation and explanation.
What do these conversations look like now that we are no longer sharing physical space together? And how do we support our multilingual students who are gaining proficiency with English?
In this series of posts, we will consider how to “strengthen the opportunities and supports for helping students to describe clearly their mathematical thinking to others, orally, visually, and in writing” by looking at three Math Language Routines (MLRs). You can learn more about the MLRs here. Let’s begin by exploring an example of MLR3 Clarify, Critique, Correct.
MLR3 Clarify, Critique, Correct
As we prepare to enact this activity, we can anticipate the kinds of responses our students might give. One response to this prompt may be:
“9 is 50% of 4.5 because 9 times is 4.5.”
At first glance, we may focus on how correct this response is. Yet, this statement is a window into current student understanding. Let’s consider, What happens when we pay attention to language? In doing so, teachers have an opportunity to learn more about student thinking, and students have an opportunity to re-engage and examine a mathematical idea more deeply.
The MLR3 Clarify, Critique, Correct routine invites students to examine a mathematical statement such as the anticipated response above that includes conceptual (or common) errors in mathematical thinking as well as ambiguities in language. Then asks students to:
Clarify: Why do you think the student wrote this?
Critique: What changes do you suggest? Why?
Correct: Improve the response.
More than just error analysis, this routine purposefully engages students in considering both the author’s mathematical thinking as well as the features of their communication.
By engaging in this process, students have another opportunity to recognize the distinction between 50% and one-half. This growing attention to precision in language translates to students’ deeper understanding of mathematics.
What might this look like during distance learning?
Here’s an activity from Algebra 1 Unit 4 Lesson 10.
In a typical classroom setting, students would have time to think quietly and talk with a partner. During that time the teacher elicits evidence of student thinking to use during the activity synthesis. How can teachers orchestrate an experience where students get to share and consider each other’s thinking during this time of distance learning?
One option is to make use of the support for English Language Learners provided for this activity.
|Support for English Language LearnersReading, Writing, Speaking: MLR3 Clarify, Critique, Correct. Before students share their descriptions of the possible output values of A, present an incorrect response and explanation. For example, “The outputs of A are numbers from 0 to 50 because I looked on the vertical axis and saw that the graph reaches up to 50.” Ask students to identify the error, critique the reasoning, and write a correct explanation. As students discuss with a partner, monitor for students who clarify that the output values are not restricted by the graphing boundaries shown. This helps students evaluate, and improve upon, the written mathematical arguments of others, as they discuss the range of a function.Design Principle(s): Optimize output (for explanation); Maximize meta-awareness|
We can use this response in two ways.
- If teachers and students are meeting together virtually, the teacher can display the sample response as part of the synthesis and ask students to Clarify, Critique, Correct in the group chat.
- If teachers are unable to meet with students virtually, the teacher can include the same response for students to Clarify, Critique, Correct as part of the assignment.
1c. Here is one student’s incorrect response for #1b. “The outputs of A are numbers from 0 to 50 because I looked on the vertical axis and saw that the graph reaches up to 50.” Identify the error, critique the reasoning, and write a correct explanation.
What comes next for the synthesis depends on the distance learning configuration.
- Maybe the teacher will give feedback to each student’s corrected response, focusing on the language the student used.
- Maybe students will review each other’s corrected statements in a shared virtual document.
Creating a Task using MLR3: Clarify, Critique, Correct
Let’s go back to our question, what happens when we pay attention to language? Consider the following responses one teacher received when they invited their students to Clarify, Critique, Correct the sample response.
Take a moment to look at these two student responses.
Student A’s Response
Student B’s Response
By focusing on language, the teacher has created an opportunity for students to go beyond just describing all possible output values of A. Students are given an additional opportunity to explore the connection between the context, the domain, and the impact on the range of function, and then share their understanding in the corrected explanation.
We would love to learn alongside you. How have you used MLR3 with your students during distance learning? Share your Clarify, Critique, Correct prompt, and, if possible, student work, using #LearnWithIM.