Overview

Session Focus

This session focuses on the role language plays in accessing, understanding, and expressing mathematical ideas, and on instructional strategies that support all students in making sense of mathematics. You will explore instructional strategies for supporting multilingual learners and consider how these strategies may also benefit students who are native English speakers. You will also learn about a routine for helping all students make sense of story problems.

As we have explored in previous sessions, effectively supporting all learners begins with making sense of the mathematics. When teachers take time to make sense of the mathematics for themselves, and anticipate how students will respond to an activity or problem, they are able to more effectively assess student understanding and differentiate their instruction to meet all students' learning needs.

When making sense of the mathematics is at the heart of the work for students, they are more likely to see themselves as active agents of their own learning and develop a positive mathematical identity.

Understanding and expressing mathematical ideas, can present different kinds of challenges for students. Read the following problems. Think about what each problem is asking and consider what kinds of challenges related to language each problem might present for students.

Select one of the problems shown above. What role does language play in understanding the problem? Jot down some notes about possible challenges students might encounter accessing the problem and expressing their solutions. You will return to these notes in Activity 2.

Activity 1: Strategies for Supporting English Language Learners

This activity focuses on supporting multilingual learners in math class. You will explore eight instructional strategies that can be used to help students who are learning English access and express their mathematical ideas. While specifically designed for multilingual learners, many of these strategies can also be used to support students who are native English speakers.

The linguistic demands of math lessons can present specific challenges for multilingual learners. Watch as Professor Judit Moschkovich discusses what students who are learning English need in order to successfully engage in math activities and discussions.

Note: Professor Moschkovich references her paper “Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for multilingual learners” in this video. This reading is optional unless you are taking this course for graduate credit.

Reflect on the ways in which Professor Moschkovich’s key points about multilingual learners can also relate to what other groups of students may need in the math classroom.

The 8 Strategies for Supporting English Language Learners

Read about the 8 Instructional Strategies for Supporting English Language Learners pictured in the image above. 

If you work with students who are learning English as a second language, which of these strategies do you currently use? Can you envision using some or all of these strategies to support the math learning of students who are native English speakers?

Watch as Chris Confer facilitates an introductory discussion with third graders about comparing and finding the difference.

Which of the 8 strategies does Ms. Confer utilize during the introductory discussion? How do these strategies, along with other teaching moves, effectively support students learning English in Ms. Confer's class?

Read 4th grade teacher Ms. Lloyd’s reflection on her work to create a supportive environment for Hedson—an English language learner with significant academic and social challenges. Her goal is to help Hedson share his ideas during math class.

What does Ms. Lloyd do to make Hedson feel comfortable in the classroom while at the same time supporting his mathematical growth? Which of the 8 instructional strategies does Ms. Lloyd use? Are there additional strategies she could consider using to support Hedson?

Share an example from Ms. Confer's classroom or from the Case of Hedson in which you saw the teacher enact one of the 8 strategies on the Multilingual Learner Forum.

Activity 2: Building Meaning for Mathematical Language 

This activity focuses on ways to support students in building meaning for mathematical language. You will be introduced to a set of questions to consider when assessing students’ understanding of mathematical language and when introducing math vocabulary. You will also be introduced to a routine to support students in making sense of story problems and on exploring how math learning can support literacy and language development. Building meaning for mathematical language is critical for students to be able to effectively solve problems and communicate their thinking.

In their book, Teaching Math to Multilingual Students Grades K-8: Position English Learners for Success, authors Chval, Smith, Trigos-Carrillo and Pinnow provide questions to assess students’ understanding of math language and for making decisions about how and when to build meaning for mathematical vocabulary.

-Chval, Smith, Trigos-Carrillo & Pinnow
Teaching Math to Multilingual Students Grades K-8: Position English Learners for Success

Assessing Student Understanding

Building Meaning for Vocabulary

You can ask your students the following guiding questions: What does the word or phrase mean to you? Have you used this word or phrase before? When have you used this word or phrase? What do you think of when you hear this word/phrase? Can you draw or make a list of what you think of when you hear this word/phrase? What does this word/phrase mean in your first language?

You can use the following guiding questions to decide if you need to build meaning for language and how to do it: What are the most critical words/phrases that I should introduce/initiate (as a teacher)? What is the most natural place for this language to be introduced? How can I build meaning through gestures, written words, images, videos or models? How can I include the language in future problems, activities or thematic projects? How much time should I invest in building meaning for this language?

What connections do you see between these questions and the teaching moves used by Ms. Confer or Ms. Lloyd in the previous activity? 

Making Sense of Story Problems

As you explored in the Overview activity, making sense of and using language to express mathematical ideas can present challenges for all learners. The language demands of story problems are such that many, if not all, students, can encounter challenges in making sense of and accessing the mathematical content of a problem. In order to effectively solve story problems, students need to be able to visualize the situation and context and understand what is being asked. They can then return to the context of the problem as needed, as they proceed with their solution.

The following Story Problem Routine is designed to help students make sense of story problems and select a solution strategy based on their understanding of the situation. Some teachers, particularly in the lower elementary grades, move through the routine as a series of steps, while others select parts of the routine to use with their students in a variety of contexts. One goal of such a routine is for students to internalize these habits of mind and independently apply them to their work.

Read the Story Problem Routine.

Consider which steps of this routine you may already be using in your work with students, and which steps you would like to consider implementing.

Watch as third grade teacher Nikki Faria introduces a multiplication story problem to students. As you watch, think about which parts of the Story Problem Routine Ms. Faria uses with her class.

How does Ms. Faria help her students make sense of the problem? Of the operation of multiplication? How does Ms. Faria use the  context/story as a support?

Exploring Links Between Mathematics and Literacy

Working with students who have a variety of needs is always challenging and is compounded when one of those needs is limited reading ability. Read Maria Martinez-Roberts’ reflection about a 5th grade student who begins the schoolyear as a non-reader, and whose interest and strength in mathematics contributes to the development of his literacy skills.

What experiences have you had teaching mathematics to students with limited literacy skills? In what ways have you been able to connect mathematics and literacy while keeping the focus on making meaning for both?

Return to the notes you wrote about one of the story problems pictured below.

What are some ways that you could support students in accessing and making sense of the problem? Share your thinking on the Math Language Forum.

Activity 3: Supporting Math Learning Closing Reflection

Throughout this course, you have thought deeply about ways to support the range of math learners. Over the past 6 weeks, you have engaged in activities, explored tools, read articles, and discussed:

• Setting up an equitable math learning community
• Facilitating meaningful mathematical discussions
• Using a strength-based approach to formative assessment to support student learning
• Strategies for differentiating instruction
• Student grouping practices
• Supporting multilingual learners

Reflect on your learning in this course. What new and important ideas will you take with you? What strategies or new learning will you integrate into your teaching practice this coming school year?

To complete this reflection, you can:

• Respond to these questions in paragraph form
• Create a bulleted list of new ideas and/or strategies you will use with your students
• Write a letter to yourself stating takeaways from this course that you would like to remember in the future
• Create a representation of your takeaways and next steps

Post your reflection on the Course Reflection Forum.

Forums

• Return to the Multilingual Learner Forum. Read others' responses and respond to at least one post that interests you.
• Return to the Math Language Forum. Look through others’ responses and respond to at least one post that interests you.
• Return to the Course Reflection Forum. Add to the conversation by responding to others' posts.

Key Learnings

• Language plays an important role in accessing, understanding, and expressing mathematical ideas.
  
  
• Instructional strategies that focus on making sense of the language of a mathematical task or problem can support multilingual learners as well as native English speakers.
  
  
• When making sense of the mathematics is at the heart of the work for students, students are more likely to see themselves as active agents of their own learning and develop a positive mathematical identity.