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Enhancing Learning
   Mathematics

       Teh Kim Hong , Suriah Abd Manap
           Mathematics Department
 Every classroom includes a mix of
  learners, therefore diversity is
  expected.
 Examples of diversity:

   - learning styles    - gender
   - hemispheric mode - poverty
   - learning modality - culture
   - special needs       - antiracism
   - human rights
   Due to diverse background, not all
    learners benefit from conventional way of
    instruction.
   Some content taught in school are not
    appropriate for all learners.
   Therefore learners respond differently to
    various instructional approaches
   No single way of teaching works for
    everyone.
 All persons deserve to be treated
  with dignity;
 All are treated equal in rights and
  responsibilities regardless of race,
  disability; gender, age. Religious
  belief,place of origin.
 Teacher must know how to
  accommodate the differences in
  learning preference of students.
Learning Styles
 Is the unique way how people
  (students) learn.
 Teachers should have a repertoire of

  teaching methods from which to
  choose at times, and can fit
  individual differences.
McCarthy’s learning styles
   Imaginative learners
    – perceive cognitively and then
      process the information reflectively
    - They listen, share and try to
      integrate school experiences with
      self-experiences.
   Imaginative learners do not simply accept
    things as they are presented. They are
    curious people. They want to see how
    things work together to produce an overall
    result. Imaginative learners understand
    that there are many facets of any concept
    and are not satisfied until they have
    examined them all. In addition to
    discussions, an effective way to teach an
    imaginative learner is through the use of
    role-play and case study. These learners
    do not respond well to long lectures,
    memorizing, or working alone.
Analytic learners
 Perceive abstractly and process
  information reflectively
 Like details and ideas, prefer

  sequential thought, and value ideas
  more than people
   Analytic learners are opposite from
    imaginative learners. They like the lecture
    format, viewing the teacher as the
    primary information provider. It is the
    student’s job to analyze the information
    and pass judgment on it. These learners
    value facts, figures, and the way it "should
    be." In addition to lectures, they enjoy
    debates, information sheets, and guest
    experts. They don’t enjoy group activities
    unless there is opportunity for an
    exchange of ideas.
Common Sense Learners
 Perceive abstractly and process
  information actively.
 They prefer concrete problem solving

  and are pragmatic learners
 They like doing experiment.
   Common sense learners are not
    satisfied with the theoretical. They
    want to test ideas to see if they are
    workable. They are the problem
    solvers in our groups. They like to
    move while they learn. Being hands-
    on learners, they want to see results.
    The best way to teach these
    individuals is through practical
    demonstrations, testimonies, and
    projects.
Dynamic Learners
 Perceive concretely and process
  information actively.
 Integrate experience and apply and

  value new learning
 Like trial-and-error learning

 Good at taking risks
   Dynamic learners look at things with an
    eye to the future. They are creative and
    have a "what if" mentality. They are risk
    takers. The past is important only insofar
    as it leads to the future. Dynamic learners
    tend to be leaders. They also see the
    humor in situations. Flexibility is an
    important aspect of their learning style.
    They are typified by having many projects
    started but few finished. These learners
    want a teacher who will facilitate rather
    than dictate. They enjoy drama, creative
    writing, or art projects that allow them to
    express themselves.
Left Mode Learners
 Analytic/ deductive – prefer logic
 Rational and respond to verbal
  instruction.
 Solve problems logically and

  sequentially by looking at parts.
 Prefer established and certain
  information and conventional
  classroom.
Right Mode Learners
Right mode learners
 - intuitive / deductive
 - like open-ended, random
    experiences
 - want instruction to be
    demonstrated
 - like synthesizing, experimenting
    and prefer experiential approach
What do schools emphasize ???
Learning modality preferences
 Sensory preferences influence the
  ways in which students learn.
 Result of experience, culture, race,

  gender and handedness.
 3 preferences

  - visual /spatial
  - auditory/ Pattern
   - tactile/ moving/touching
Visual/Spatial learners
 Learn by watching, seeing or
  imagining ,
 often think in pictures and images,

  write things down to remember.
 They may say ”I see, I get the
  picture”.
   These learners need to see the teacher's
    body language and facial expression to fully
    understand the content of a lesson. They
    tend to prefer sitting at the front of the
    classroom to avoid visual obstructions (e.g.
    people's heads). They may think in pictures
    and learn best from visual displays including:
    diagrams, illustrated text books, overhead
    transparencies, videos, flipcharts and hand-
    outs. During a lecture or classroom
    discussion, visual learners often prefer to
    take detailed notes to absorb the
    information.
Auditory Learners
 Learn through listening and
  verbalizing.
 When learning, vocalize silently and
  even move their lips, memorize
  through auditory repetition.
 Solutions may be tried verbally and
  by talking through.
 They may “I hear “, “that sound

  right”,”that rings a bell.
   They learn best through verbal lectures,
    discussions, talking things through and
    listening to what others have to say.
    Auditory learners interpret the underlying
    meanings of speech through listening to tone
    of voice, pitch, speed and other nuances.
    Written information may have little meaning
    until it is heard. These learners often benefit
    from reading text aloud and using a tape
    recorder.
Tactual Learners
 Learn by manipulating and doing.
 Action oriented and like to be

  physically involved.
 Approach problems in a physical way
  or by manipulating models or
  objects.
 Respond to music by moving and

  want to touch picture .
 They may say ”I feel, I like to get
  better handle on the info
   Tactile/Kinesthetic persons learn best
    through a hands-on approach, actively
    exploring the physical world around them.
    They may find it hard to sit still for long
    periods and may become distracted by their
    need for activity and exploration.

Hemispheric Mode
   Left mode learners
     • Analytic/deductive
     • Rational and response to verbal
       instructions
     • Systematic, able to solve problems
       logically
Multiple intelligeces
 Spatial
 Bodily kinetic

 Musical

 Lingustic

 Logical-mathematical

 Interpersonal

 Intrapersonal

 naturalist
   Spatial- ability to perceive the visual
    spatial world accurately and perform
    transformations upon one’s perceptions.

   Bodily-kinetic – expertise in using one’s
    whole body to express ideas and facility in
    using one’s hands to produce or transform
    things.

   Musical – capacity to perceive,
    discriminate, transform and express
    musical forms
   Linguistic – capacity to use words
    effectively, orally and in writing.

   Logical mathematical - capacity
    to use numbers effectively and to
    reason well.

   Interpersonal – ability to perceivee
    and make distinctions in the moods,
    intentions, motivations and feelings
    of others.
   Intrapersonal – self knowledge and
    the ability to act adaptively based
    on the knowledge.

   Naturalist – ability to observe and
    operate hands-on in nature and the
    environment.
“Do Not Teach Like You Have Been Taught”
“if students do not learn the way we teach
   them, then we must teach them the way
   they learn!”.

   Use new pedagogy and instructional
    delivery systems that can keep students
    actively engaged in their learning style
    preferences.
   Whenever possible give students optional
    approaches to tasks.
   Be flexible, be cross culturally and help
    students to acquire the ability to use
    different learning styles.

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Week 16 enhancing learning mathematics

  • 1. Enhancing Learning Mathematics Teh Kim Hong , Suriah Abd Manap Mathematics Department
  • 2.  Every classroom includes a mix of learners, therefore diversity is expected.  Examples of diversity: - learning styles - gender - hemispheric mode - poverty - learning modality - culture - special needs - antiracism - human rights
  • 3. Due to diverse background, not all learners benefit from conventional way of instruction.  Some content taught in school are not appropriate for all learners.  Therefore learners respond differently to various instructional approaches  No single way of teaching works for everyone.
  • 4.  All persons deserve to be treated with dignity;  All are treated equal in rights and responsibilities regardless of race, disability; gender, age. Religious belief,place of origin.  Teacher must know how to accommodate the differences in learning preference of students.
  • 5. Learning Styles  Is the unique way how people (students) learn.  Teachers should have a repertoire of teaching methods from which to choose at times, and can fit individual differences.
  • 6. McCarthy’s learning styles  Imaginative learners – perceive cognitively and then process the information reflectively - They listen, share and try to integrate school experiences with self-experiences.
  • 7. Imaginative learners do not simply accept things as they are presented. They are curious people. They want to see how things work together to produce an overall result. Imaginative learners understand that there are many facets of any concept and are not satisfied until they have examined them all. In addition to discussions, an effective way to teach an imaginative learner is through the use of role-play and case study. These learners do not respond well to long lectures, memorizing, or working alone.
  • 8. Analytic learners  Perceive abstractly and process information reflectively  Like details and ideas, prefer sequential thought, and value ideas more than people
  • 9. Analytic learners are opposite from imaginative learners. They like the lecture format, viewing the teacher as the primary information provider. It is the student’s job to analyze the information and pass judgment on it. These learners value facts, figures, and the way it "should be." In addition to lectures, they enjoy debates, information sheets, and guest experts. They don’t enjoy group activities unless there is opportunity for an exchange of ideas.
  • 10. Common Sense Learners  Perceive abstractly and process information actively.  They prefer concrete problem solving and are pragmatic learners  They like doing experiment.
  • 11. Common sense learners are not satisfied with the theoretical. They want to test ideas to see if they are workable. They are the problem solvers in our groups. They like to move while they learn. Being hands- on learners, they want to see results. The best way to teach these individuals is through practical demonstrations, testimonies, and projects.
  • 12. Dynamic Learners  Perceive concretely and process information actively.  Integrate experience and apply and value new learning  Like trial-and-error learning  Good at taking risks
  • 13. Dynamic learners look at things with an eye to the future. They are creative and have a "what if" mentality. They are risk takers. The past is important only insofar as it leads to the future. Dynamic learners tend to be leaders. They also see the humor in situations. Flexibility is an important aspect of their learning style. They are typified by having many projects started but few finished. These learners want a teacher who will facilitate rather than dictate. They enjoy drama, creative writing, or art projects that allow them to express themselves.
  • 14. Left Mode Learners  Analytic/ deductive – prefer logic  Rational and respond to verbal instruction.  Solve problems logically and sequentially by looking at parts.  Prefer established and certain information and conventional classroom.
  • 15. Right Mode Learners Right mode learners - intuitive / deductive - like open-ended, random experiences - want instruction to be demonstrated - like synthesizing, experimenting and prefer experiential approach What do schools emphasize ???
  • 16. Learning modality preferences  Sensory preferences influence the ways in which students learn.  Result of experience, culture, race, gender and handedness.  3 preferences - visual /spatial - auditory/ Pattern - tactile/ moving/touching
  • 17. Visual/Spatial learners  Learn by watching, seeing or imagining ,  often think in pictures and images, write things down to remember.  They may say ”I see, I get the picture”.
  • 18. These learners need to see the teacher's body language and facial expression to fully understand the content of a lesson. They tend to prefer sitting at the front of the classroom to avoid visual obstructions (e.g. people's heads). They may think in pictures and learn best from visual displays including: diagrams, illustrated text books, overhead transparencies, videos, flipcharts and hand- outs. During a lecture or classroom discussion, visual learners often prefer to take detailed notes to absorb the information.
  • 19. Auditory Learners  Learn through listening and verbalizing.  When learning, vocalize silently and even move their lips, memorize through auditory repetition.  Solutions may be tried verbally and by talking through.  They may “I hear “, “that sound right”,”that rings a bell.
  • 20. They learn best through verbal lectures, discussions, talking things through and listening to what others have to say. Auditory learners interpret the underlying meanings of speech through listening to tone of voice, pitch, speed and other nuances. Written information may have little meaning until it is heard. These learners often benefit from reading text aloud and using a tape recorder.
  • 21. Tactual Learners  Learn by manipulating and doing.  Action oriented and like to be physically involved.  Approach problems in a physical way or by manipulating models or objects.  Respond to music by moving and want to touch picture .  They may say ”I feel, I like to get better handle on the info
  • 22. Tactile/Kinesthetic persons learn best through a hands-on approach, actively exploring the physical world around them. They may find it hard to sit still for long periods and may become distracted by their need for activity and exploration. 
  • 23. Hemispheric Mode  Left mode learners • Analytic/deductive • Rational and response to verbal instructions • Systematic, able to solve problems logically
  • 24. Multiple intelligeces  Spatial  Bodily kinetic  Musical  Lingustic  Logical-mathematical  Interpersonal  Intrapersonal  naturalist
  • 25. Spatial- ability to perceive the visual spatial world accurately and perform transformations upon one’s perceptions.  Bodily-kinetic – expertise in using one’s whole body to express ideas and facility in using one’s hands to produce or transform things.  Musical – capacity to perceive, discriminate, transform and express musical forms
  • 26. Linguistic – capacity to use words effectively, orally and in writing.  Logical mathematical - capacity to use numbers effectively and to reason well.  Interpersonal – ability to perceivee and make distinctions in the moods, intentions, motivations and feelings of others.
  • 27. Intrapersonal – self knowledge and the ability to act adaptively based on the knowledge.  Naturalist – ability to observe and operate hands-on in nature and the environment.
  • 28. “Do Not Teach Like You Have Been Taught” “if students do not learn the way we teach them, then we must teach them the way they learn!”.  Use new pedagogy and instructional delivery systems that can keep students actively engaged in their learning style preferences.  Whenever possible give students optional approaches to tasks.  Be flexible, be cross culturally and help students to acquire the ability to use different learning styles.