The Effect of Computer-based
  Mathematics on Problem Solving
       Proponent: Daisy T. Emanuel
          3rd Grade Teacher, Sadie Tillis
• Many people regard mathematics as the
  crown jewel of sciences.
• Yet mathematics has historically lacked
  one of the defining trappings of science:
  – laboratory equipment
Physicists




A new particle accelerator, the Large Hadron
Collider, in Geneva, Switzerland.
Astronomers




Celestron Astromaster 70az Telescope
Mathematicians




Archimedes     Albert Einstein
Mathematicians




Leonhard Euler   Carl Friedrich Gauss
Mathematics
   Mathematics concerns not the physical
landscape but an idealized, abstract world.
   For exploring that world, mathematicians
have traditionally had only their intuition.
Erika Klarreich Study (2004)
   Computers are starting to give mathematics the
lab instruments they have been missing.
   Computers’ power is enabling mathematicians
to make quantum leaps into mathematics.
   Computers take only seconds to calculate and
create beautiful graphics of three-dimensional
shapes.
   Computers can solve complex problems and
computers can remediate students in
mathematics.
Knowledge of Teaching with ICT
              “He who can does,
            and he who understands
            teaches.”
            - Dr. Lee Shulman
               President Emeritus of the
            Carnegie Foundation for the
            Advancement of Teaching
            (1997-2008)
Knowledge of Teaching with ICT

    In the 80′s, Lee Shulman introduced the
concept of pedagogical content knowledge to
differentiate it from content knowledge and
knowledge of general pedagogy.
    Pedagogical content knowledge or popularly
known as PCK is teachers’ knowledge of how a
particular subject-matter is best taught and
learned.
Pedagogical Content Knowledge

   Most important elements of its description:
1. knowledge of interpreting the content;
2. knowledge of the different ways of representing
   the content to the learner; and
3. knowledge of learners’ potential difficulties,
   misconceptions, and prior conceptions about
   the content and related concepts.
Concept Map
                                                                                                        2 positive
  2 numbers
                                        a number is                                                      numbers
      with                Opposites                       it is multiplied   it is divided by
                                        taken away                                                      are added
   different              are added                      by any number        other number
                                         from itself
   signs are
  multiplied                                                                                            2 positive
  or divided          r
                                                 results when                                   r       numbers
                                                                                                            are
                      e                                                                         e       multiplied
                                       less            Zero        less
                      s                than                        than                         s       or divided

   a larger           u                                                                         u
  number is           l     Opposite of                                Counting                 l       2 negative
  subtracted                                                                                             numbers
    from a            t      Positives                                 Numbers                  t           are
   smaller                  (Negatives)                               (Positives)                       multiplied
   number                                                                                               or divided
                      w                         consists of                                     w
                      h                                                                         h        a smaller
                      e                                                                         e       number is

                      n                 Set of Integers                                         n
                                                                                                        subtracted
                                                                                                           from a
                                                                                                           larger
 a negative and a                                                                                         number
positive numbers                              closed under
  are added, the                                                                                    a negative and a
negative is farther                                                                                 positive numbers
 from zero on the                                                                                    are added, the
    number line
                           Addition              Subtraction            Multiplication              positive is farther
                                                                                                    from zero on the
                                                                                                       number line
Concept Map
                                  Set of Integers
             can be
         represented by                                    Source of
                                                        difficulties and
                                                        misconceptions
Number    + and –         Tables and
 Line      chips           patterns


                                         Rules on                             Signed
                                                            Failure to     numbers have
  Quantitative relationship            operations are
                                                            relate to      no meaning or
                                       never learned
   involving directions or                 using
                                                             whole          do not make
     ideas on opposites                                     numbers            sense.
                                       memorization.
Knowledge of Teaching with ICT

• It is not a question of whether schools should
integrate these technologies in its curriculum.
• ICT courses have been offered as a subject in
many schools.
• Use of technology in teaching traditional
subjects like mathematics.
• Does knowledge of technology equip teachers
to use it to teach effectively?
Integrating ICT in Teaching
• Some mathematics teachers jumped to it
  right away, used technology in teaching.
• Some teachers are still in testing-the-water
  mode.
• Some, until now, are still totally in the dark,
  sticking to their old method despite the
  availability of technology, oblivious to the
  reality in today’s ICT – driven world.
ICT – driven World
• The students are the natives and the
  teachers are the migrants.
• The way students learn are influenced
  by their experiences with many forms
  of technology and the way these tools
  think and do things.
Printing Machine

           When the pen and
        the printing press were
        invented, everybody
        thought that they will
        give an end to illiteracy.
           It didn’t take long for
        us to realize that it didn’t
        and can’t.
Using Computer to Teach

               It is not enough to
            know how to use
            ICT just us it was not
            enough to know
            mathematics content to
            teach mathematics so
            that students learn it
            with meaning and
            understanding.
Technological Pedagogical
      Content Knowledge
   A teacher’s knowledge regarding
technology is multifaceted and that the
optimal mix for the classroom is a balanced
combination of technology, pedagogy, and
content.
   It can be used as framework for designing
learning experiences for teachers and for
planning, analyzing and describing the
integration of technology in teaching.
Technological Pedagogical
   Content Knowledge
References
• http://www.learningtoday.com/corporate/mat
  h-software.asp
• http://prime.isthe.com/no.index/chongo/mer
  digit/long-m42643801/prime-c.html
• http://www.tpck.org/tpck/images/tpck/b/b1/
  Tpack-contexts-small.jpg

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Ict integration in teaching

  • 1. The Effect of Computer-based Mathematics on Problem Solving Proponent: Daisy T. Emanuel 3rd Grade Teacher, Sadie Tillis • Many people regard mathematics as the crown jewel of sciences. • Yet mathematics has historically lacked one of the defining trappings of science: – laboratory equipment
  • 2. Physicists A new particle accelerator, the Large Hadron Collider, in Geneva, Switzerland.
  • 4. Mathematicians Archimedes Albert Einstein
  • 5. Mathematicians Leonhard Euler Carl Friedrich Gauss
  • 6. Mathematics Mathematics concerns not the physical landscape but an idealized, abstract world. For exploring that world, mathematicians have traditionally had only their intuition.
  • 7. Erika Klarreich Study (2004) Computers are starting to give mathematics the lab instruments they have been missing. Computers’ power is enabling mathematicians to make quantum leaps into mathematics. Computers take only seconds to calculate and create beautiful graphics of three-dimensional shapes. Computers can solve complex problems and computers can remediate students in mathematics.
  • 8. Knowledge of Teaching with ICT “He who can does, and he who understands teaches.” - Dr. Lee Shulman President Emeritus of the Carnegie Foundation for the Advancement of Teaching (1997-2008)
  • 9. Knowledge of Teaching with ICT In the 80′s, Lee Shulman introduced the concept of pedagogical content knowledge to differentiate it from content knowledge and knowledge of general pedagogy. Pedagogical content knowledge or popularly known as PCK is teachers’ knowledge of how a particular subject-matter is best taught and learned.
  • 10. Pedagogical Content Knowledge Most important elements of its description: 1. knowledge of interpreting the content; 2. knowledge of the different ways of representing the content to the learner; and 3. knowledge of learners’ potential difficulties, misconceptions, and prior conceptions about the content and related concepts.
  • 11. Concept Map 2 positive 2 numbers a number is numbers with Opposites it is multiplied it is divided by taken away are added different are added by any number other number from itself signs are multiplied 2 positive or divided r results when r numbers are e e multiplied less Zero less s than than s or divided a larger u u number is l Opposite of Counting l 2 negative subtracted numbers from a t Positives Numbers t are smaller (Negatives) (Positives) multiplied number or divided w consists of w h h a smaller e e number is n Set of Integers n subtracted from a larger a negative and a number positive numbers closed under are added, the a negative and a negative is farther positive numbers from zero on the are added, the number line Addition Subtraction Multiplication positive is farther from zero on the number line
  • 12. Concept Map Set of Integers can be represented by Source of difficulties and misconceptions Number + and – Tables and Line chips patterns Rules on Signed Failure to numbers have Quantitative relationship operations are relate to no meaning or never learned involving directions or using whole do not make ideas on opposites numbers sense. memorization.
  • 13. Knowledge of Teaching with ICT • It is not a question of whether schools should integrate these technologies in its curriculum. • ICT courses have been offered as a subject in many schools. • Use of technology in teaching traditional subjects like mathematics. • Does knowledge of technology equip teachers to use it to teach effectively?
  • 14. Integrating ICT in Teaching • Some mathematics teachers jumped to it right away, used technology in teaching. • Some teachers are still in testing-the-water mode. • Some, until now, are still totally in the dark, sticking to their old method despite the availability of technology, oblivious to the reality in today’s ICT – driven world.
  • 15. ICT – driven World • The students are the natives and the teachers are the migrants. • The way students learn are influenced by their experiences with many forms of technology and the way these tools think and do things.
  • 16. Printing Machine When the pen and the printing press were invented, everybody thought that they will give an end to illiteracy. It didn’t take long for us to realize that it didn’t and can’t.
  • 17. Using Computer to Teach It is not enough to know how to use ICT just us it was not enough to know mathematics content to teach mathematics so that students learn it with meaning and understanding.
  • 18. Technological Pedagogical Content Knowledge A teacher’s knowledge regarding technology is multifaceted and that the optimal mix for the classroom is a balanced combination of technology, pedagogy, and content. It can be used as framework for designing learning experiences for teachers and for planning, analyzing and describing the integration of technology in teaching.
  • 19. Technological Pedagogical Content Knowledge
  • 20. References • http://www.learningtoday.com/corporate/mat h-software.asp • http://prime.isthe.com/no.index/chongo/mer digit/long-m42643801/prime-c.html • http://www.tpck.org/tpck/images/tpck/b/b1/ Tpack-contexts-small.jpg