Leveraging Meaning

By Wendy Ward Hoffer, 2019 CCIRA Featured Speaker

“To think inclusively and to think for one’s self is very difficult…Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal and the facts from the fiction.”

– Dr. Martin Luther King, The Purpose of Education, 1947.

Dr. King’s words rang true in the days of the Civil Rights Movement, as they ring true today: the purpose of education is to generate a nation of thoughtful, thinking citizens.

How? P. David Pearson’s research, also from the last century, lights the way to supporting all learners’ cognitive acuity and understanding. In 1983, he and his colleagues investigated how proficient readers make sense of complex texts. They found astonishing congruency between the responses of participants in their study. Turns out, we humans pick from a pretty short list of strategies when we are processing information. We tend to:

  • Draw on background knowledge
  • Ask questions
  • Infer
  • Visualize
  • Determine importance
  • Synthesize, and
  • Monitor for meaning

After Pearson’s research was published, some smarty pants teachers got a hold of it and decided, “If that’s what all the successful grown-ups are doing, let’s go teach those strategies to the kids.” And so they did. Hence, the wonderful and amazing work of Ellin Keene, Cheryl Zimmerman, Cris Tovani and so many other empowering teachers who highlighted how these strategies can help learners comprehend text.

More good news: these strategies aren’t just for fiction or even just for narrative text. We do use these thinking strategies to make sense of everything: graphs, pictures, word problems, facial expressions, clouds in the sky. They transfer and apply, hence the good value in teaching these to all learners.


Let’s take math, for example, where we are recovering from decades of algorithm-focused instruction that sidelined understanding in favor of tricks, like “copy-dot-flop” as the means to divide fractions. How might a thinking strategy leverage deeper understanding of that concept? Let’s visit a PEBC lab classroom where the host teacher is inviting learners to visualize and represent the meaning of ¾ divided by 1/3:

“With your partner, come up with as many ways as you can to represent ¾.”

Students scramble to record thinking in their math notebooks: sketches of pizzas, measuring cups, along with coins and division problems fill their pages. Then the teacher calls the group back and gathers everyone’s thinking on the board. She reminds the learners, “Your job is to select the representation that is both accurate and makes sense to you.”

“Now, turn and talk to your partner: what would it mean to divide ¾ by 3?”

After some conversation, the class discusses as a whole and agrees that if you divide ¾ by 3, you would have ¼. Students show this in a variety of ways using the models of ¾ they already created. “Now, what would it mean to divide that same ¾ by 1/3?”

Again, students are invited to discuss with peers, to use their representations to make sense of this problem. Consensus emerges: a little more than two one thirds fit inside three fourths.


As the conversation continues, the teacher challenges the group to represent other fraction division problems as they grow their understanding of this concept. The class closes with a reflection: how do visualizing and representing help us understand? Learners have a lot to say!

This is but one example of how a thinking strategy can leverage understanding in math. There are so many more! The wonderful news is that these strategies many literacy teachers know well can be equally useful to math learners when we bring them to work in authentic ways.

In order to meet Dr. King’s purpose, to raise a nation of thinkers, we must make make conceptual understanding – not just coverage of content – our target; then, intentionally design learning experiences that support students in developing tools to help them make meaning.

To learn more along these lines, attend the June 24 – 25 PEBC Minds on Math Institute; check out Minds on Mathematics, my book on math workshop; or come to one of my sessions at CCIRA, “Math Workshop” Thursday at 10:30 or my keynote, “We Teach Who We Are,” Thursday at 4:30. I look forward to talking with you more about how we leverage meaning for each and every learner.

Wendy Ward Hoffer  is the author of four books about teaching math and science for understanding: Science as Thinking (Heinemann, 2009), Minds on Mathematics (Heinemann, 2012), Developing Literate Mathematicians (NCTM, 2016), and Cultivating STEM Identities (Heinemann, 2016). She works with teachers at all levels to support learners’ understanding of math and science at the Public Education Business Coalition (PEBC) Follow her @wendywardhoffer

Author: CCIRAblog

Check out CCIRA's website today at ccira.org

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