John Hattie - Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning

• John Hattie
• Douglas Fisher
• and Nancy Frey

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Effective teaching is the non-negotiable core of any mathematics program. As mathematics educators, we continually strive to improve our teaching so that every child develops the mathematical proficiency needed to be prepared for his or her future. By mathematical proficiency, we mean the five interrelated strands of conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).

There is a plethora of research-based recommendations about instructional practices that we should employ to build students proficiency, such as peer tutoring, using worthwhile tasks, building meta-cognitive capabilities, using manipulatives, project-based learning, direct instruction... the list goes on and on. But which practices have a strong research foundation? And which are likely to produce the most significant pay-off in terms of students learning?

Several recent reports indicate considerable consensus about the essential elements of effective mathematics teaching based on mathematics education and cognitive science research over the past two decades. The National Council of Teachers of Mathematics (NCTM) publication Principles to Actions: Ensuring Mathematical Success for All describes effective teaching as teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically (NCTM, 2014, p. 5). It also identifies the following eight high-leverage teaching practices that support meaningful learning:

1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning and problem solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual understanding.
7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking.

The 2012 National Research Council report Education for Life and Work identifies the following essential features of instruction that promotes students acquisition of the 21st century competencies of transferable knowledge, including content knowledge in a domain and knowledge of how, why, and when to apply this knowledge to answer questions and solve problems (p. 6) in mathematics, science, and English/language arts:

• Engaging learners in challenging tasks, with supportive guidance and feedback
• Using multiple and varied representations of concepts and tasks
• Encouraging elaboration, questioning, and self-explanation
• Teaching with examples and cases
• Priming student motivation
• Using formative assessment

These features are strikingly similar to the NCTM effective teaching practices described above.

Consensus on these effective practices, while critically important, leaves open the questions of their relative effectiveness, the conditions in which they are most effective, and details of their implementation in the classroom. Visible Learning for Mathematics addresses these questions and more, which makes it an invaluable resource for mathematics educators at all levels.

First, Visible Learning for Mathematics extends John Hatties original groundbreaking meta-analysis of educational practices in Visible Learning (2009) to specific mathematics teaching practices. The book goes beyond identifying research-based practices to providing the relative effect a teaching practice has on student learningthe effect size. For example, the second effective teaching practice calls for implementing tasks that promote reasoning and problem solving. In