This article is based on a talk by Alan Schoenfeld, professor in the School of Education, for the GSI Teaching & Resource Center’s How Students Learn series in Spring 2011.

On this page:
Key Learning Principles
Research Fundamentals
Applications to Teaching
Further Reading

Also available:
Video and full summary of Alan Schoenfeld’s talk “Learning to Think Mathematically (or Like a Scientist, or Like a Writer, or…)”

Key Learning Principles

  • Students learn content, but they learn most effectively when they also learn disciplinary and professional frameworks for analysis and application of content knowledge.
  • Students need to learn problem-solving strategies for situations that have no obvious solutions or explicit procedures laid out.
  • Metacognition, the ability to analyze one’s own critical thinking process and to adjust it when necessary, is an essential element of robust learning.

Research Fundamentals

Disciplinary and professional frameworks: Students, particularly undergraduate students, are not simply amassing facts; they are acquiring “disciplinary habits of mind” that provide them with the analytical framework and context in which to use their knowledge. Although we typically realize that the content of our knowledge makes a difference to our ability to solve problems, we don’t always consider how we know it or recognize our interpretive filters. When working with students, we need to be able to evaluate the interpretive filters they have developed. That is, being a good teacher means more than being able to explain the same thing in multiple ways — good teachers need to recognize how students know the material and form strategies for intervening when their understandings falter.

Problem-solving strategies: Most disciplines students encounter in college involve some kind of problem solving activity — attempts to confront situations that do not have obvious answers or obvious procedures to find answers. As researchers in our disciplines, we can usually identify problems fruitfully and can apply appropriate strategies to define and resolve a problem. Our students often do not yet have this kind of knowledge, so they need to learn relevant problem-solving strategies.

Also called “heuristics,” problem-solving strategies can be identified in every discipline. For example, in writing and composition, in which students must improve a paper from one draft to the next, the heuristics may include guidance to outline the first draft, identify topic sentences in all the paragraphs, and question the basic argument and rhetorical structures. In mathematics, heuristics include approaches like drawing a diagram of a problem, looking at individual cases, solving an easier related problem, and establishing sub-goals. Students can be taught these strategies.

Metacognition: In order to solve problems effectively, we must control, monitor, and self-regulate our thinking. This awareness of how we know and apply our knowledge is known as metacognition. What we know matters, but awareness of how and when we use our knowledge matters even more. In mathematics, a student may pick a formula to work through a problem and pour copious amounts of energy into calculation, not realizing after coming up with an implausible answer that the formula he chose doesn’t fit the nature of the problem. A student tasked with writing a book review may not stop to consider the difference between a book review (an academic genre) and a book report (a schoolish genre) and write the wrong kind of paper. Or students may have only limited strategies for preparing to take a midterm exam, receive a disappointing grade, and not understand why their preparation strategy was not adequate.

Keeping a writing or study log, writing a brief few sentences about how they think their paper turned out, and learning to use heuristics are some of the ways in which students can learn metacognition and become more self-regulated in their intellectual work.

Applications to Teaching

Teaching Metacognition, from Carleton College’s Geoscience Department (applicable to all disciplines)

Exam Wrappers, from Carnegie Mellon’s Eberly Center for Teaching and Learning

Teaching Problem Solving, from Vanderbilt University’s Center for Teaching

Further Reading

Please note that some links may require Library proxy access. Please see the Library’s page Connect from Off Campus.

Brown, John Seely, Allan Collins, and Paul Duguid (Jan.-Feb. 1989). “Situated Cognition and the Culture of Learning.” Educational Researcher 18.1: 32–42.

Clauss, Jon and Kevin Geedey (June 2010). “Knowledge Surveys: Students’ Ability to Self-Assess.” Journal of the Scholarship of Teaching and Learning 10.2: 14–24.

Halpern, Diane F. (Winter 1999). “Teaching for Critical Thinking: Helping College Students Develop the Skills and Dispositions of a Critical Thinker.” New Directions for Teaching and Learning 80: 69–74.