Learning in the Classroom: Implications for Middle School Math Teachers

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Learning in the ClassroomImplications for
Middle School Math Teachers
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Key Questions

• What is the relationship between learning and
  instruction?
• How can the research on student learning
  influence teachers instructional practices?
• What role do math teachers play in the
  teaching-learning process?

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Educational Psychology is

• The application of psychology to the study of

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What is learning?

• Definition
• Critical components to this definition
• Learning is a process, not a product
• Learning involves change in knowledge, beliefs,
  behaviors, and attitudes
• Learning is not something done to students, but
  rather something students do themselves

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What do we know about learning?

• Research has found
• The brain plays a role
• Learning is based on associations
• The learning environment makes a difference
• Learning occurs in cultural and social contexts
• People learn in different ways
• People think about their own learning, and their
  feelings matter

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Educational Practitioners Common Questions About
Learning

• Why cant students apply what they have learned?
• Why do students cling so tightly to
  misconceptions?
• Why are students not more engaged by material I
  find so interesting?
• Why do students claim to know so much more than
  they actually know?

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What is instruction?

• Definition
• Critical components to this definition
• Manipulating what the learner experiences
• Intention on changing the learners knowledge

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• Things You Should Know
• About Your Students and How They Learn

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Prior knowledge and beliefs affect learning,
usually for the better, but sometimes for the
worse.

• Background

• Instructional Implications

• Activating prior knowledge
• Accurate, but insufficient prior knowledge
• Inaccurate prior knowledge

• Administer a diagnostic assessment
• Look for patterns of error in student work
• Explicitly link new material to knowledge from
  the present and previous course(s)
• Use analogies and examples taken from students
  everyday experiences
• Ask students to justify their reasoning

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As information processers, learners can only
process a limited amount of information at once.

• Background

• Instructional Implications

• Cognitive Overload
• Intrinsic, extraneous, and germane cognitive load

• Manage intrinsic load, minimize extraneous load,
  and promote germane load

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Using worked examples in teaching can have
positive academic and cognitive outcomes.

• Background

• Instructional Implications

• Enactive vs. vicarious learning
• Scaffolding
• Worked examples

• Replace some practice problems with worked
  examples
• Sequence worked out examples by backward fading
• Provide explanations of each step in a worked
  example
• Ask learners to generate explanations of each
  step in a worked out example

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As information processers, learners need time to
process incoming and outgoing information.

• Background

• Instructional Implications

• Think-Time and wait-time
• Definition
• Benefits
• Categories of silence

• Provide students time to process information and
  complete cognitive tasks
• Deliberately and consistently wait in silence for
  3 to 5 seconds
• Ensure that students also preserve the
  disturbance-free silence

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To develop mastery, students must acquire
component skills, practice integrating them, and
know when to apply what they have learned.

• Background

• Instructional Implications

• Mastery learning
• Definition and assumptions
• Development of mastery
• Component skill development
• Integration
• Application

• Diagnose, weak or missing skills and provide
  practice
• Encourage practice to increase fluency
• Discuss conditions of applicability
• Provide opportunities to apply skills

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Goal-directed practice coupled with targeted
feedback is critical to learning.

• Background

• Instructional Implications

• Deliberate, goal-directed practice
• Effective feedback
• Content
• Timing

• Build in multiple opportunities for practice
• Set expectations about practice
• Look for patterns of errors in students work
• Prioritize and balance your feedback
• Provide feedback at the group level
• Require students to specify how the feedback was
  used

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Learners are more likely to devote time to
activities that have value for them.

• Background

• Instructional Implications

• Attainment value
• Intrinsic interest value
• Extrinsic utility value
• Cost

• Link academic tasks to students espoused
  interests or everyday activities
• Establish the relevance of academic tasks to
  students short-term and long-term goals
• Dont take the value of the academic task for
  granted
• Provide authentic, real-world tasks

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Learners achievement goals influence their
cognitive processes and behavior.

• Background

• Instructional Implications

• Performance goals
• Learning goals
• Work-avoidant goals

• Avoid focusing students attention on how they
  appear to others
• Acknowledge that learning requires exerting
  effort and making mistakes
• Use a variety of motivational strategies to get
  students truly engaged

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To engage voluntarily in activities, learners
want their chances of success to be reasonably
good.

• Background

• Instructional Implications

• Self-efficacy
• Sources of self-efficacy information

• Provide opportunities for students to be
  successful
• Engage in effective modeling practices
• Set proximal rather than distal goals
• Challenge underconfidence
• Foster competence and confidence

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When learners think their chances of success are
slim, they may behave in ways that make success
even less likely.

• Background

• Instructional Implications

• Self-handicapping
• Indicators of self-handicapping

• Attribute success to effort and ability, failure
  to controllable conditions
• Demonstrate the effect of effort
• Break tasks into more manageable parts
• Provide explicit strategy training

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To be motivated to pursue specific goals,
students must hold positive outcome expectations.

• Background

• Instructional Implications

• Outcome expectations
• Positive and negative outcome expectations
• Expectancies are shaped by our experiences

• Provide early success opportunities
• Educate students about the ways we explain
  success and failure

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Summary

• Learning is a process, not a product.
• Instruction is the deliberate arrangement of
  learning conditions designed to support the
  internal processes of learning.
• Planning instruction is a strategic, thoughtful
  process
• The learner should always be considered when
  designing instruction.

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• For more information
• Kamau Oginga Siwatu, Ph.D.
• Assistant Professor of Educational Psychology
• College of Education, Box 41071
• Texas Tech University
• Lubbock, TX 79409-1071
• Office telephone [phone] ext 431
• Office facsimile 806/742-2179
• Email kamau.siwatu_at_ttu.edu
• Webpage http//www.webpages.ttu.edu/ksiwatu