Sunday / May 19

Making Mathematics Learning VISIBLE

Most people think of us as literacy educators instead of mathematics educators. 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.

Despite our literacy backgrounds, we probably would not have written Visible Learning for Mathematics without our collaborators. It was Will Mellman who pushed us to write the book.

Will was a math and science supervisor (and now a principal) and he wanted to know what works best in mathematics education. Who doesn’t, right? We all know that mathematics knowledge is a gatekeeper. Students who don’t master mathematical concepts are less likely to graduate from college. And mathematics is a central part of so many careers—not just accounting!

Naturally, Will’s quest for what works led us to John Hattie’s seminal work.

As many of you may well know, John’s Visible Learning research is a meta-meta-analysis of thousands of studies involving millions of students.  It’s been called the “holy grail” of educational research and we believed that this would allow us to figure out what works best and when, specifically regarding mathematics.

Together with well-known mathematics education experts Linda Gojak and Sara Delano Moore, we embarked on this endeavor. We began 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.

Surface, Deep, and Transfer

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.

Direct Instruction vs. Dialogue

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 John Hattie’s Visible Learning research. 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.

We feel so lucky to have been part of the translation of John Hattie’s Visible Learning research into guidance that math teachers can use to validate and extend their instructional repertoires. Read Visible Learning for Mathematics now and discover these strategies for yourself.

Visible Learning books

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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