What is learning?

“What is learning?” I posed this question to the group of coaches I was working with. I asked them to individually write their definition of learning down on an index card and then share it with a neighbor. The room where became quiet as the coaches contemplated how to put this complex concept into words. Although facilitation of learning is the focus of our daily work, we don’t often talk about what we mean when we use the word “learning” and we don’t all operate from the same internal definition of this term.

How might you define learning? Take a moment to think about how you would explain what learning is to someone else.

After sharing our ideas, we considered John Hattie’s definition of learning. Dr. Hattie is a renowned education researcher and the author of multiple books including Visible Learning for Mathematics: What Works Best to Optimize Student Learning.

According to Dr. Hattie, learning is “the process of developing sufficient surface knowledge to then move to deeper understanding such that one can appropriately transfer this learning to new tasks and situations.” Here’s how he defines surface, deep, and transfer learning:

Surface Learning is the initiation to new ideas. It begins with development of conceptual understanding and then, at the right time, labels and procedures are explicitly introduced to give structure to concepts. Surface learning is not shallow learning. It is not about rote skills and meaningless algorithms.
Deep Learning is about consolidating understanding of mathematical concepts and procedures and making connections among ideas. Students move to deep learning when they plan, investigate, and then begin to make generalizations.
Transfer Learning is the phase of learning in which students take the reins of their own learning and are able to apply their thinking to new contexts and situations.

“What are you thinking?” I asked the coaches. Their eyes were wide; I could tell that these ideas were causing some re-evaluation of their personal definitions of learning.

“Oh my,” one of the coaches voiced, “When I help my teachers plan for instruction, we’ve been focusing entirely on surface and deep learning. We’re not providing students with opportunities for transfer learning. It’s no wonder that many aren’t successful on paper and pencil assessments!”

Others added their own connections, echoing a recognition that we frequently don’t give students learning experiences which allow them to learn how to apply their learning in new contexts. In other words, we don’t finish teaching.

We decided to see what these three aspects of learning would look like in the context of a single curriculum target. We chose an upcoming fourth grade standard and worked together to articulate specific examples of surface, deep, and transfer learning required for mastery of this standard (see chart below). We recognized that our listing of learning targets related to this standard was not comprehensive, but the coaches felt this exercise helped them gain a better understanding of how to help students achieve true learning.

Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
Surface Learning:
Ability to represent and solve multiplication and division problems using manipulative and pictorial models
Automaticity with multiplication facts
Deep Learning:
Representational fluency for multiplication and division situations (ability to flexibly represent multiplication and division with a variety of concrete and pictorial models, equations, contextual and word problems)
Procedural fluency for multiplication and division (ability to solve problems using a variety of computational strategies based on an understanding of place value, properties of operation, and the relationship between operations)
Transfer Learning:
Ability to apply multiplication and division in solving real-world problems.
Ability to make connections from division to fractions and decimals.

The coaches admitted that their own understanding of transfer learning was still very much at a surface level, but they wanted to know more and to be able to use this knowledge in supporting teachers. They felt that this frame for thinking about mathematics learning could be helpful in planning and differentiating instruction and in building teachers’ understanding of the progression of mathematics learning which must occur within and across curriculum standards. They agreed to do the following as their homework prior to our next session together:

  • Have a conversation with someone at their school about surface, deep, and transfer learning and its implications for student achievement in mathematics.
  • Bring back a story about teaching for transfer learning from their work with teachers.

If you’d like to also take on these same homework assignments, I’d love to hear your stories about teaching for transfer learning. Let’s use this learning community to deepen our own understanding of this important lens of learning mathematics.

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