Book Review: Mathematical Thinking and Communication

Sometimes having a blog pays off and you get advance copies of upcoming publications. This is one of those times…

The good people at Heinemann sent me a book entitled, Mathematical Thinking and Communication: Access for English Learners by Mark Driscoll, Johannah Nikula, and Jill Neumayer Depiper. If you are regular reader of this blog (and why wouldn’t you be?) you may be thinking, “English learners? I thought this blog was about students with disabilities, why are we talking about English learners?” That is a good question, faithful blog reader, so I’ll address it first.

There is a well documented disproportionate representation of English language learners in special education. Amanda Sullivan notes this may happen because”both underreferral and overdiagnosis occur because of misunderstanding of the educational needs of students identified as ELLs (Case & Taylor, 2005), poorly designed language assessments (MacSwan & Rolstad, 2006), and weak psychoeducational assessment practices (Figueroa & Newsome, 2006).”

ELL special ed disproportionate table

Taking this into consideration, the following review is going to focus on the pedagogical framework highlighted in Mathematical Thinking and Communication: Access for English Learners. Even though most English learners do not share the same cognitive challenges that some students with disabilities do, they do share challenges relating to expressive and receptive language and communication. Thus the strategies to create access for communication of mathematical thinking can be shared by teachers of all learners.

The book highlights a four-prong design framework for creating access for English learners:

  • Challenging mathematical tasks
  • Multimodal representation
  • Development of mathematical communication
  • Repeated structured practices

Challenging mathematical tasks refers to instruction that allows students to engage in the strands of mathematical proficiency (adaptive reasoning, strategic competence, conceptual understanding, productive disposition, and procedural fluency). Multimodal representations refers to the use of not only auditory modes of communication, but also visual and kinesthetic modes as well. Development of mathematical communication highlights the need to scaffold communication for students who struggle with language, whether through learning a second language or cognitive challenges. This can be done through sentence frames or graphic organizers. Finally, repeated structured practices is the idea that routinizing the classroom environment can allow students to focus more on communicating their mathematical thinking rather than social-emotional considerations.

Unlike most professional development, Mathematical Thinking and Communication does practice what it preaches. It uses visual and structured methods for helping teachers create access for English learners throughout the book. This is a great resource not only for teachers of students learning a second language, but also special educators working with students with communication challenges.

Check it out and then come back here and let me know what you think!

3 thoughts on “Book Review: Mathematical Thinking and Communication

  1. Disproportionality in special education and communication for ELL is an extremeley important and interesting topic to read about! I am a second year in college and I have been at a teaching placement for the past three months in Oakland. I work in a seventh grade math class where the demographic is predominantly black and Latino students. It is not a special education class, but I feel that many of the points made in the essay and articles are relevant. There are several English Language Learners in my classes that are at a disadvantage when it comes to learning the material because the resources that they need (other Spanish speakers, a supportive and accessible curriculum, etc.) are limited. In my teaching program, they attempt to address the issues and challenges that might arise in classrooms that have culturally and linguistically diverse students. However, it is not a simple solution, especially for prospective teachers who are not bilingually proficient like myself. (One instance, my teacher who is bilingual was absent so I was in charge and I had a difficult time helping students who couldn’t speak English well.) I would want to address this in my future classroom by creating an atmosphere that allows all students to be comfortable in their surroundings to focus on the math, as the articles described.


    • Thank you for your comment, Caeli. I’m sorry it’s taken me so long to respond, but it deserved some thought!

      I agree that creating an atmosphere of access and cultural relevance is a step in the right direction in the effort to curb the disproportional representation of English learners in special education.

      Have you read any of Rochelle Gutierrez’s work? She says we should shift from focusing solely on learning English to what it truly is, emerging bilingualism. Here is her talk from ShadowCon at NCTM in San Francisco.

      Enjoy and good luck!


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