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Response: Ways to Teach Common-Core Math to ELLs

This week's question is:

What are the best strategies for teaching Common Core math to English language learners?

I can speak from experience in saying that Common Core has not made it any easier to teach English Language Learners in English classes, but that's only part of it -- Math teachers have to apply the Common Core math standards to ELLs in their classes, too.

Today, educators Bill Zahner, Ben Spielberg, Gladis Kersaint, Denisse R. Thompson, Maria Montalvo-Balbed, and Denise Huddlestun share their suggestions for how teachers can best handle this challenge. You can also listen to a ten-minute conversation Ben, Gladis and Denisse R. Thompson and I had on this topic at my BAM! Radio Show.

In addition, you might also be interested in two collections of previous columns from this blog:

Teaching Math & Science

Teaching English Language Learners

And here's one final resource I'd like to share: The Best Resources For Teaching Common Core Math To English Language Learners.

Response From Bill Zahner

Bill Zahner is an assistant professor of mathematics education at San Diego State University. Zahner's research examines how linguistically diverse students learn important mathematical concepts through engaging in discussions with peers and in whole-class settings:

Many teachers of English Language Learners (ELLs) are concerned about the CCSSM practice standards. Making valid mathematical arguments is difficult for almost everybody, so how can a student who is learning English construct a viable mathematical argument? Below I describe 8 research-based suggestions for teaching Common Core math to ELLs. This is not an exhaustive list, but I hope it gets you started.

  1. Maintain a focus on mathematical concepts

Like all students, ELLs learn math best when they engage with and make sense of important mathematical ideas. Sometimes, in the name of expedience, we teach routines and procedures for producing answers, and hope understanding of ideas will come later (I've done this before big tests). However, considerable research has shown that, with appropriate support, a) ELLs can engage in challenging, conceptually focused mathematics, and b) students who learn concepts and big ideas alongside skills and procedures are better at applying their knowledge.

  1. Ask reasoning questions, listen to all of the ways your English Learners are communicating mathematically and build on student ideas when they do share.

It is important to ask questions that engage ELLs in reasoning. Instead of asking "what did you get?" try asking "how did you solve that?" When they answer, engage with the mathematical content of what your ELLs say (rather than grammatical correctness). Talk moves like revoicing are one way to build on student ideas while guiding the talk toward a mathematical goal.

  1. Seize opportunities to teach language in your mathematics class, incorporating language when it is meaningful

I once observed an expert algebra teacher in a class where 1/3 of the students were ELLs. The lesson revolved around a problem involving weighing 5 things in pairs. The teacher anticipated that the commutative property of addition was likely to come up when solving this problem. However, rather than present the commutative property of addition at the start of the lesson, she waited until that property was needed to answer a question arising from the students' problem solving discussion. Then she pounced on the term. She introduced the formal language and highlighted how it helped set up the problem. My takeaway was that the teacher did not avoid technical vocabulary, but instead she anticipated when it would be needed, and introduced the new terminology when it would be useful.

  1. Simplify Language when Possible, while Keeping Mathematics Intact

Sometimes the unfamiliar context in word problems causes ELLs to give up on problems they could solve. One researcher found that fourth grade ELLs struggled on a combination problem about inside and outside chores, but were able to solve a mathematically equivalent problem about pens, pencils, and notebooks. This example highlights that when selecting problems from a textbook or writing problems from scratch, teachers should be careful to identify when the language of a math problem is unnecessarily complex.  This article has some good tips on simplifying language in mathematics.

  1. Create multiple ways for students to engage in a problem

A math problem that is good for ELLs will include multiple points of entry and multiple ways students can participate in solving the problem. For example, one problem that I created for an article on group work with ELLs allows students to participate in a group's mathematical investigation of ratio, proportions, and unit conversions by gathering data, plotting points, observing patterns, and describing relationships.  For ELLs who are just learning English, allowing non-verbal ways for students to contribute to their group's mathematical activity is an important way to create access.

  1. Encourage students to use and connect multiple representations--graphs, equations, stories, diagrams

The CCSSM include content standards that explicitly call for connecting representations. This is good for ELLS because they benefit from opportunities to use multiple representations in their mathematical reasoning. In one major experimental study, students from regions with a high proportion of ELLs significantly benefitted from using a curriculum and dynamic technology that highlighted connections between graphs, tables, equations, and story problems involving motion.

  1. Connect to your students' lives

Mathematics is most relevant when it means something for students. Many students, including many ELLs, feel disconnected when math is just about numbers and equations. With support, ELLs can be engaged in seeing the math in their world. For example, one after school program took ELLs out into the community to see how mathematics was used in local shops. This engagement connects to the CCSSM Modeling standards, can spark students' interest in mathematics, and even lead to transformative change over time.

  1. Continue learning & improving

This list is not exhaustive. Learn more by paying attention to your practice, observing and asking questions of your colleagues, reading websites such as Understanding Language (and of course the one you are reading now), and magazines such as the NCTM journals. And, most important, stay connected to your fellow teachers by getting involved with organizations such as the NCTM affiliate Todos: Mathematics for All.



Response From Ben Spielberg

Ben Spielberg has worked as a math instructional coach for middle and high school teachers and has taught middle school math and science.  A Teach For America alum and former member of the Executive Board of the San Jose Teachers Association, Ben currently works on economic and fiscal issues at the Center on Budget and Policy Priorities.  He holds a B.S. in Mathematical and Computational Sciences from Stanford and blogs at 34justice.com:

Successful Common Core math instruction for English Language Learners (ELLs) often includes some form of structured oral language practice.  Like other teaching strategies that work well for targeted student populations, well-implemented structured oral language practice also benefits students who don't fall in the target group (in this case, native English speakers).  As practiced in San José Unified School District (SJUSD), basic forms of structured oral language practice involve two primary features: planned opportunities for verbal interaction and open-ended sentence frames.

1)    Planned opportunities for verbal interaction: The Common Core's Mathematical Practices represent one of its greatest opportunities: to move away from the type of rote memorization commonly seen in mathematics classrooms and towards critical thinking about mathematical concepts.  Unless students have frequent opportunities to speak, however, these opportunities will often fall flat.  Two Mathematical Practices in particular - Mathematical Practice 3: Construct viable arguments and critique the reasoning of others and Mathematical Practice 6: Attend to precision - require extensive verbal interaction.

Opportunities for verbal interaction can be derailed by student confusion (which frequently leads to classroom management issues), and it is very important to plan these opportunities purposefully.  A successful structured oral language practice activity, just like other successful classroom activities, might include strategic student grouping, instructions about which students speak when and for how long, both a small group and large group component, a written component, behavioral expectations, and/or a demonstration of the activity with a model group ahead of time.  The eventual activity the teacher chooses matters far less than that the teacher has considered these factors and made purposeful decisions that he or she believes will maximize learning.

2)    Open-ended sentence frames: We often teach our students content-related vocabulary like variable, parabola, and radius, but we less often provide explicit instruction on "glue" language - the words and framework necessary to articulate ideas.  Students, especially ELLs, may also lack the self-confidence to speak up in class, and appropriately designed sentence frames can provide them with the support they need to overcome both of these obstacles during a planned opportunity for verbal interaction (sentence frames can also be useful during writing exercises).

To be effective, sentence frames must complement cognitive work, not replace it.  Sentence frames that function like fill-in-the-blank exercises do not accomplish this goal.  Consider the following sentence frame that a teacher might use for a lesson on negative exponents:

Sentence Frame 1: A ___________ exponent tells you to multiply the _______________ a certain number of times.

If a teacher uses sentence frame 1, students can only respond with definitions.  While students should certainly be able to articulate the definitions of positive and negative exponents, this sentence frame requires only memorization.  The sentence frame is essentially a fill-in-the-blank exercise, not useless but not in the spirit of the Common Core.

Instead, imagine a teacher using the sentence frame below:

Sentence Frame 2: ___________ is equivalent to __________ because __________________.

Sentence Frame 2 is much more open-ended than Sentence Frame 1.  Potential responses can reference previous learning and include both rough definitions (i.e. "A base raised to an exponent of zero is equivalent to one because of the division rule of exponents") and problem solving (i.e. "4-2 is equivalent to 1/16 because 4-2 is the same as (1/4)2, which is (1/4)*(1/4)").  A teacher teaching this lesson might choose to focus on Mathematical Practice 2: Reason abstractly and quantitatively or Mathematical Practice 7: Look for and make use of structure.

For both English Language Learners and native English speakers, structured oral language practice can be a useful way to foster conceptual understanding while simultaneously building language skill and confidence.  It can help lay the groundwork for the writing and explanations required by the Common Core.  This technique requires practice and considerable planning, but its payoff for students is well worth the investment.


Response From Gladis Kersaint & Denisse R. Thompson

Gladis Kersaint, Ph.D., is a professor of mathematics education at the University of South Florida.  She focuses on effective mathematics teaching, at-risk students, and use of technology in mathematics. Denisse R. Thompson, Ph.D., is Professor of Mathematics Education at the University of South Florida. She researches curriculum development and research, mathematical literacy, and assessment. They are the two of the three authors of Teaching Mathematics to English Language Learners (Mariana Petkova is the third).

"Best strategies" is a misnomer.  Teachers should use appropriate strategies to meet specific instructional aims and support learners' needs.  Because mathematics is a language, all students are "mathematics language learners." Therefore, instruction must incorporate multiple strategies to build student facility with mathematical language. Because mathematics classrooms are typically the only place students learn and use this unique language, English Language Learners (ELLs) need additional support because they are learning English, while also learning the language of mathematics.

To teach Common Core Math, the Standards for Mathematical Practice (SMP) (e.g., construct viable arguments, critique the reasoning of others) should be the focus of instruction.  Embedding SMPs daily helps develop critical thinking skills and provides opportunities to use mathematical language. The key is to scaffold learning opportunities so ELLs can fully engage in classroom activities and demonstrate knowledge.  The SMP provide the rationale for the strategies recommended below as an overarching instructional approach, and not an add-on solely for ELLs.

  • Establish a language-rich classroom with many opportunities for students to read, write, interpret, and talk about mathematics. Incorporate tasks that require ELLs to use and interpret mathematics language and provide multiple opportunities for sense making. Develop both English and mathematics-specific objectives for most lessons. Build vocabulary knowledge from prior experiences so students can make connections between new and familiar phrases. Have students develop personal mathematics dictionaries.
  •  Express information in multiple ways to provide access to mathematics language (e.g., simplify/elaborate language and examples, use diagrams) and embed clarity checks to ensure understanding.
  •  Provide a "safe" context for ELLS to use and make sense of mathematics language and concepts (e.g., by working in pairs or small groups).
  • Assess mathematics learning in equitable ways (e.g., allow ELLs to use learning tools during assessments such as personal dictionaries, avoid non-essential linguistic complexities, provide test accommodations).



Response From Maria Montalvo-Balbed & Denise Huddlestun

Maria Montalvo-Balbed is a member of the ASCD Professional Learning Services faculty and Director of ELL Programs at Metro Regional Education Service Agency (RESA) in Georgia. She has developed and taught numerous professional development classes in the areas of diversity, cultural literacy development, and authentic engagement of English learners. Denise Huddlestun is Mathematics Coordinator at Metro RESA and works with Montalvo-Balbed to provide professional learning to mathematics teachers:

Culturally and linguistically diverse students are the fastest growing population in the public school system in the U.S. It is critical for content teachers who teach English Language Learners (ELLs) to understand the complexity of learning in a second language.

With the implementation of more rigorous standards requiring students to apply the mathematics they know to solve problems rather than to solve basic arithmetic or computation problems, there is a greater demand for teachers to provide instruction where students develop necessary skills for problem solving. According to the first Standard for Mathematical Practice (SMP), the language demands of mathematics must be considered and addressed as teachers provide learning experiences where students can develop proficiency in making sense of problems and solving them. "No longer should instruction focus on imitating and memorizing what is presented by the teacher, but rather on students' problem-solving strategies, including their ability to generate and define problems as well as their mathematical reasoning and communication." (Barton and Heidema, 2002.)

There are no literacy standards for mathematics. However, the SMPs describe the behaviors of mathematically proficient students that require students to use language skills in reading, writing, speaking, and listening. Teachers of mathematics must attend to the language demands unique to mathematics and intentionally plan to provide opportunities for students to develop the behaviors. The following strategies are beneficial when teaching ELLs mathematics:

  •         Provide teacher think-alouds
  •         Ask guiding questions to help ELLS make sense of problems
  •         Provide models, visuals, and different representations
  •         Provide opportunities for ELLs to translate charts or diagrams into words and explain (construct a viable argument)
  •         Demonstrate relationships and patterns and then provide opportunities for ELLS to look for structure and patterns
  •         Provide sentence strips such as "When I ____, I notice _________" for ELLs to describe the patterns they discover.

Here are two recommended websites for teachers looking for more tips:

Understanding Language -- ELL Math

Teaching Mathematics to English Language Learners - NCTM


Response From Reader

Thanks to Ben, Gladis, Denisse, Maria, Denise and Bill, and to reader Tara, for their contributions!

Please feel free to leave a comment your reactions to the topic or directly to anything that has been said in this post.

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