By Jennifer Wilson and Liz Ramirez
Imagine a learning environment where every student not only understands and uses mathematics but also enjoys the process. This vision extends beyond mere calculation to a space where learners actively make sense of mathematical concepts and articulate their understanding through collaborative language. Creating language-rich classrooms empowers all students, especially those developing their English proficiency, to participate in mathematical discussions, argumentation, and explanations.
But how do we cultivate these rich conversations in today’s learning environments, particularly when physical classrooms may be replaced by digital spaces? And crucially, how do we best support our multilingual learners as they strengthen their English skills alongside their mathematical prowess?
This article, part of an ongoing series, delves into strategies to “strengthen the opportunities and supports for helping students to describe clearly their mathematical thinking to others, orally, visually, and in writing,” specifically through Math Language Routines (MLRs). For those new to MLRs, a comprehensive overview is available here. Previous articles in this series explored enhancing access and MLR 3 Clarify, Critique, Correct.
Here, we focus on MLR 5: Co-Craft Questions, a powerful routine for fostering both mathematical thinking and English Work Learning Collaboratively.
Unpacking MLR5: Co-Craft Questions for English Language Learners
The Co-Craft Questions routine is strategically designed to immerse students in a mathematical context before they feel pressured to find solutions. This approach intentionally creates a supportive space for students to generate the language of mathematical questions themselves, a critical aspect of english work learning in a collaborative setting.
Implementing Co-Craft Questions: A Step-by-Step Guide
- Engaging Hook: Begin by presenting a compelling context or problem stem. This could be a captivating image, a short video clip, or a list of intriguing facts related to a mathematical concept.
- Individual Question Generation: Students individually take time to formulate potential mathematical questions that arise from the presented context. This encourages initial engagement and personal interpretation.
- Collaborative Question Comparison: Students pair up to share and compare the questions they have written. This peer interaction allows for language negotiation and the refinement of ideas. Selected questions are then shared and discussed with the whole class, broadening perspectives and fostering a sense of collective inquiry.
- Question Revelation and Focus: Finally, reveal the specific question(s) students will be working on for the lesson. Alternatively, the teacher can select from the rich pool of student-generated questions, making the learning process even more student-centered and relevant.
Let’s illustrate this with an example from Geometry Unit 5 Lesson 11.
Imagine presenting students with the image below and the prompt: “The building on the left side of the picture is called the Cayan Tower. What mathematical questions could be asked about the tower?”
Cayan Tower in Dubai, UAE
Cayan Tower in Dubai, UAE: A visual prompt for mathematical question generation in collaborative english work learning.
When using this prompt, teachers can anticipate a diverse range of student responses, showcasing varied levels of mathematical thinking and english language development. Examples might include:
- “How tall is the building?”
- “How many floors does it have?”
- “What are the building’s dimensions?”
- “Does the twist affect the interior space?”
- “How long would window cleaning take?”
- “How is the twisting structure engineered?”
- “Are all the floors the same size and shape?”
The true power of MLR 5 emerges when we consciously focus on language. By collectively examining the questions generated by peers, the class engages in a valuable reflection on the language inherent in mathematical inquiries. This is particularly beneficial for English learners, as it directly addresses english work learning needs by enhancing their awareness of mathematical question structures. This routine provides essential space for students to connect contextual understanding with relevant vocabulary, and to recognize the patterns and formats of mathematical questions firmly rooted in real-world contexts.
The following table outlines specific support strategies for English Language Learners within this activity, emphasizing the integration of speaking and reading skills through MLR5 Co-Craft Questions:
| Support for English Language Learners: Speaking, Reading: MLR5 Co-Craft Questions. Use this routine to heighten awareness of the language used when discussing cross-sections and volume, particularly in the context of the Cayan Tower. Before presenting pre-determined questions, show the image of the Cayan Tower alongside the statement: “The building on the left side of the picture is called the Cayan Tower.” Instruct students to individually write down potential mathematical questions about the tower. Encourage students to then compare their questions in pairs before a whole-class discussion. Actively listen for and amplify questions that naturally lead to discussions about cross-sections and volume of the Cayan Tower. For example, highlight questions like, “What is the area of the base of the Cayan Tower?” and “What is the volume of the Cayan Tower?” This approach to english work learning integrates key Design Principle(s): Maximize meta-awareness; Support sense-making. |
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By leveraging these student-generated responses, educators can effectively guide student interest towards the intended learning objectives, such as applying knowledge of prisms and cross-sections within a meaningful, real-world scenario. This fosters deeper learning and enhances english work learning through contextual application.
Adapting Co-Craft Questions for Distance Learning and Collaborative English Work
MLR 5 is remarkably adaptable to both synchronous and asynchronous distance learning environments, maintaining its effectiveness in fostering english work learning and collaborative skills. Regardless of the format, it’s crucial to provide opportunities for students to review, compare questions, and reflect on their learning experience.
In an asynchronous setting, students might submit their questions via a digital platform. The teacher can then compile and share these questions later through a document or video. This asynchronous sharing provides students with additional time to interact with and thoughtfully reflect on the diverse range of questions generated, further enhancing their english work learning experience.
Consider the following example from a 5th-grade virtual class meeting. In this teacher’s second virtual session with the group, the primary goal was to cultivate a strong sense of mathematical community within the digital space, facilitating collaborative english work learning.
The class utilized an activity from IM Talking Math K–5 (IM Talking Math 6–8 resources are available in English here and Spanish here).
The session began by displaying an image of gloves and posing the same open-ended question: “What mathematical questions could be asked about the gloves in this picture?” Students were encouraged to share their questions in the chat box, creating a dynamic space for collaborative english work learning.
Here are a few examples of student responses:
Evelyn: How many are there?
Taner: How many pink and white gloves are there? Solve and show your work with a model and equation.
George: Are there different colors and materials?
Observing the variety in responses, the teacher prompted a deeper reflection by asking, “What makes a question mathematical?” This question sparked a class discussion focused on the nature of mathematical inquiry within english work learning.
Students were drawn to Taner’s question, referencing previous classroom tasks and demonstrating an emerging understanding of mathematical problem-solving. When the teacher then asked, “What makes Evelyn’s question mathematical?” students collaboratively recognized that the gloves could be counted to find a numerical answer.
Turning to George’s question, the teacher again probed, “What makes this question mathematical?” After a moment of thoughtful silence, students highlighted that they could categorize and count the gloves by color, and potentially even by material. This collaborative exploration of question types significantly enhances english work learning by focusing on mathematical language.
By intentionally emphasizing language, the teacher effectively guided students beyond simply answering pre-set questions. This interactive conversation provided a valuable platform for students to deeply engage with the context and develop a refined sense of the types of questions that invite mathematical exploration and quantitative reasoning. This set the stage for the teacher to then pose a more targeted question: “Explain where you see the equation 9×2×5=9×10 in the picture.”, seamlessly transitioning from question generation to problem-solving within the framework of english work learning.
Next Steps for Collaborative English Work in Math
We are eager to continue learning alongside you. How have you implemented MLR5 Co-Craft Questions with your students, especially in distance learning environments? We invite you to share your Co-Craft Questions prompts and, if possible, examples of student work, using #LearnWithIM on social media. Your experiences and insights are invaluable as we collectively refine strategies for effective english work learning in mathematics.
Special thanks to Vanessa Cerrahoglu and her students for generously sharing their learning experiences with us.
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