Learning and teaching mathematics and science

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Learning and teaching mathematics and science

• Helge Strømsø
• Institute for Educational Research
• University of Oslo

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Key findings - 1(Bransford et al. 2000)

• Students come to the classroom with
  preconceptions about how the world works. If
  their initial understanding is not engaged, they
  may fail to grasp the new concepts and
  information that are taught, or they may learn
  them for purposes of a test but revert to their
  preconceptions outside the classroom.

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• A newspaper is better than a magazine. A seashore
  is a better place than the street. At first it is
  better to run than to walk. You may have to try
  several times. It takes some skill but its easy
  to learn. Even young children can enjoy it. Once
  successful, complications are minimal. Birds
  seldom get to close. Rain, however, soaks in very
  fast. Too many people doing the same thing can
  also cause problems. One needs lots of room. If
  there are no complications, it can be very
  peaceful. A rock will serve as an anchor. If
  things break loose from it, however, you will not
  get a second chance.

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Making and flying a kite
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• Learners often fail to relate what they already
  know to new material unless they are prompted to
  do so.
• (Pressley et al. 1992)

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• Despite instruction to the contrary, students of
  all ages often persist in their belief that
  seasons are caused by the earths distance from
  the sun, rather than the inclination of the
  earths axis relative to the plane of its orbit
  around the sun, which affects the amount of solar
  energy striking the northern and southern regions
  of the earth as it orbits the sun.
• (Gollub et al., 2002)

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Key findings - 2 (Bransford et al. 2000)

• Learning with understanding is facilitated when
  new and existing knowledge is structured around
  the major concepts and principles of the
  discipline.

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• A rich body of content knowledge about a subject
  is a necessary component of the ability to think
  and solve problems in that domain, but knowing
  many disconnected facts is not enough. Research
  clearly demonstrates that experts content
  knowledge is structured around the major
  organizing principles and core concepts of the
  domain, the big ideas.
• (Gollub et al., 2002)

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(Chi et al., 1981)
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• Mostly, their expectations do not match mine.
  Some of them believe that to enter math class is
  to enter an alien universe. Others just expect
  that their tasks will consist of practicing
  ritualistic procedures, after being told exactly
  what to do. Most students simply do not know that
  there are ideas involved in mathematics.
• (Pustejovsky, 2005)

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Key findings - 3(Bransford et al. 2000)

• A metacognitive approach to instruction can
  help students learn to take control of their own
  learning by defining learning goals and
  monitoring their progress in achieving them.

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Metacognition

• Thinking about what one knows, what one is
  currently doing, or what ones current cognitive
  or affective state is.
• (Hacker, 1998)

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• In several experiments, students learned about
  strategies for controlling variables in a complex
  science experiment that was simulated via
  computer. As they studied, some received periodic
  questions that asked them to reflect onand
  briefly explainwhat they were doing and why
  others did not receive these questions. On tests
  of the extent to which students knowledge
  transferred to new problems, those in the
  metacognitive group outperformed those in the
  comparison groups.
• (Lin and Lehman, 1993)

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• In research with experts who were asked to
  verbalize their thinking as they worked, it was
  revealed that they monitored their own
  understanding carefully, making note of when
  additional information was required for
  understanding, whether new information was
  consistent with what they already knew, and what
  analogies could be drawn that would advance their
  understanding.
• (Bransford et al., 2000)

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• I learned how to think like chemist through
  nine years of education and three research
  positions. I thought about what that means,
  though, only when I became a teacher.. I
  realized that to teach chemistry effectively I
  would have to make clear to my students these
  ways of thinking that I myself had internalized
  and was no longer really aware of doing.
• (van Heerden, 2005)

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Designing learning environments 1

• Educational institutions and classrooms must be
  learner centered.
• Teachers must pay close attention to the
  knowledge, skills, and attitudes that students
  bring into the classroom.

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Designing learning environments 2

• To provide a knowledge-centered learning
  environment, attention must be given to what is
  taught, why it is taught, and what competence or
  mastery looks like.
• Knowledge-centered learning emphasize
• teaching of some subject matter in depth,
  providing many examples and providing a firm
  foundation of factual knowledge
• understanding rather than just memorizing
• teaching metacognitive strategies

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Designing learning environments 3

• Emphasize ongoing assessments designed to make
  students thinking visible to both teachers and
  students.
• Formative assessments should provide students
  with opportunities to revise and improve their
  thinking, help students see their own progress
  over the course of weeks or months, and help
  teachers identify problems that need to be
  focused.

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Thank you for your attention!

• h.i.stromso_at_ped.uio.no