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Dedicated to Teachers

Building Meaningful Mathematical Thinking for English Language Learners

Math Talk Blog Header #2

Years of research have found that English language learners can learn to solve word problems, even ambitious kinds. They just need many experiences solving, discussing, and writing word problems. However, many teachers and programs for English language learners have avoided word problems and writing even though word problems are small, mostly predictable texts that offer good opportunities for building language skills.


The Children’s Math Worlds (CMW) Research Project found that all English language learners improve greatly because they have many opportunities to hear and speak English when there are sense-making supports in the classroom.


The Sense-Making Classroom

Building concepts in the classroom requires experiences in which students use objects, drawings, conceptual language, and real-world situations, all of which help students build mathematical ideas that make sense to them. However, these meaning-building supports must link to formal mathematics notation, language, and methods to make formal mathematics meaningful to students.


The sense-making classroom requires linking informal foundational mathematics to formal school mathematics using mathematical language and drawings that help students to reflect, abstract, and generalize.


Students of all ages have experiences outside school that relate to mathematical concepts. These experiences can be brought into the classroom and discussed, roleplayed, drawn, and written about.


Problem-Solving that Builds Confidence

Math Expressions works to bring outside experiences into the classroom, starting with what students already know and working from there. With inquiry-based, interactive instruction, Math Expressions provides visual support and word problems about real-world situations.


Coherent learning paths for core math topics that Math Expressions build across grades are supported by specially designed learning tools developed during years of classroom research in many different classrooms with students from many different backgrounds.


With Math Expressions, students learn a core word problem-solving strategy:

  1. Read the problem
  2. Understand the situation
  3. Make a drawing if it will help


From Meaningful Math Drawings to Math Talk Learning Zones

While math drawings enable everyone to follow the thinking of a student and facilitate sense-making by all listeners, a Math Talk Learning Zone helps build meaning by using senses such seeing, hearing, speaking, and gesturing. Sharing such concept-building experiences helps the classroom community grow, and it creates a common mathematical language, both formal and informal, that facilitates student-to-student talk.


Math Expressions systematically supports students engaging in Math Talk in the classroom and the Teacher Editions advise teachers on how to build such a classroom. Students from Grade 1 to Grade 5 move rapidly from manipulatives to math drawings that are related to their numerical solution methods. These math drawings enable everyone to follow the thinking of a given student and facilitate sense-making by all listeners.


To learn how Math Expressions systematically supports sense-making with meaningful math drawings and engaging Math Talk in the classroom, download the program overview for more on information on active instruction and proven results.

Topics: English Learners, Mathematics, Math, Math@Heinemann, Heinemann Math, Math Expressions, Teaching Math

Date Published: 05/03/23

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