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Saturday / February 24

How Can Teachers Make Mathematics Learning Visible?

Most people think of us as literacy educators, which we are. Our professional lives have been shaped by the role that language plays in learning. We believe that human beings learn through language – listening, speaking, reading, writing, and viewing. And this applies to all content areas. We do NOT believe that all teachers are teachers of reading, but rather that language impacts the learning we all do.

As background, or perhaps evidence, that we have something to say to mathematics educators, Nancy taught elementary school for many years.  She was rated as highly effective in her instruction, especially in the area of ensuring that students mastered mathematics content. Doug has a master’s degree in statistics, actually bio-statistics, and has taught stats to high school and college students.

Despite our backgrounds, we probably would not have written Visible Learning for Mathematics without our collaborators. In fact, it was Will Mellman who pushed us to write this book. Will was a math and science supervisor (and now a principal) and he wanted to know what works in mathematics education. Who doesn’t, right? We all know that mathematics knowledge is a gatekeeper. Students who do not master mathematical concepts are less likely to graduate from college. And mathematics is a central part of so many careers, and not just accounting!

So, Will’s quest for what works led us to John Hattie’s seminal work. John had summarized data from thousands of studies and millions of students.  His review has been called the “holy grail” of educational research. We believed that this would allow us to figure out what works best and when. Together with well-known mathematics education experts Linda Gojak and Sara Delano Moore, we embarked on this endeavor, working to draw connections between John’s research and what mathematics education-specific research tells us works, and then situating it all squarely in the mathematics classroom through stories and examples, so that we could help teachers really see and feel why the Visible Learning approach makes sense for math.

One of the key concepts in this book is about the level of learning students need to do. We have organized information about surface levels of learning and compare that with deep learning and transfer of learning. Importantly, surface does not mean superficial. Unfortunately, a lot of people don’t value surface level learning, which we see as a big mistake. At the surface level, students meet concepts and ideas. Over time, they use those concepts and apply what they have learned. But what’s even more important is that the instructional strategies that teachers use to develop students’ surface level understandings don’t work very well at the deep or transfer levels. And what works at the deep level doesn’t really work well for surface level learning. We’ve come to learn that matching the right approach (be that instructional strategy or classroom experience) for the right type of learning is what makes the difference when it comes to impact on students’ learning.

As we wrote this book with our amazing collaborators, we were continually confronted with the question about direct versus dialogic approaches to mathematics instruction. We consulted a number of professional resources as well as the meta-analyses that John had reviewed. In the end, we agreed that there is a need for both. We believe that timing is important, not to mention the sequence of lessons. When teachers know who their students are, what they need to learn, and what they have already mastered, they can identify specific instructional moves that will close the gap. Sometimes, that means that the teacher uses a more direct approach. Other times, it means that students need to engage with others. To our thinking, it’s about being strategic rather than adhering to one philosophy over another.

What’s more interesting, at least to us, is the use of rich mathematical tasks that require students to mobilize their understandings and their resources and bring all that they have to bear on the situation. These rich mathematical tasks require that students collaborate with their peers and that they draw on past experiences and previous instruction. Mathematics classes should be filled with language – the language of learning.

Then teachers can determine what students know and use that information to determine the impact that they have had on learning. This will take us full circle, as teachers who know the impact that have on students’ learning allows them to identify future learning experiences to further close the gap. When this happens, proficiency in mathematics is heightened and students are able to apply their knowledge in a wide range of situations. Lucky us to have been part of the translation of John’s database into guidance that math teachers can use to validate and extend their instructional repertoires.

Written by

Douglas Fisher, Ph.D., is Professor of Educational Leadership at San Diego State University and a teacher leader at Health Sciences High & Middle College. He is the recipient of an IRA Celebrate Literacy Award, NCTE’s Farmer Award for Excellence in Writing, as well as a Christa McAuliffe Award for Excellence in Teacher Education.

Nancy Frey, Ph.D., is Professor of Literacy in the Department of Educational Leadership at San Diego State University. The recipient of the 2008 Early Career Achievement Award from the National Reading Conference, she is also a teacher-leader at Health Sciences High & Middle College and a credentialed special educator, reading specialist, and administrator in California.


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