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Creating Mathematical Magic In The Classroom


a shift in curriculum toward a deeper study of mathematical ... a shift in assessment practices toward student evaluation that ... puzzles/brain teasers ... – PowerPoint PPT presentation

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Title: Creating Mathematical Magic In The Classroom

Creating Mathematical Magic In The Classroom
Changes in Mathematics Instruction
  • a shift in curriculum toward a deeper study of
    mathematical ideas and concepts and their uses in
    todays world
  • a shift in learning toward more active student
    involvement with mathematics
  • a shift in teaching toward classrooms as
    stimulating learning environments in which all
    students are given the opportunity to reach their
    mathematical potential and
  • a shift in assessment practices toward student
    evaluation that is based in many sources of

Building a Teaching Bridge from Reading to Math
Effective Reading Instruction
  • Reading is more than pronouncing words..
  • We want student to develop good decoding skills.
  • We include comprehension from the very start.
  • We ask child to make predictions about what might
    come next in story.
  • We use a variety of teaching strategies-shared
    reading, guided reading, independent reading, and
    read alouds.
  • We want student to read fluently.
  • We want our students to love reading.

Effective Math Instruction
  • Therefore, math instruction should consist of
    more than simply calculating numbers
  • We want student to develop good strategies for
    solving problems.
  • We include conceptual understanding from the very
  • We ask child to use mental math to estimate
    before calculating problems.
  • We use a variety of teaching strategies-whole
    group instruction, flexible group instruction,
    and small group instruction.
  • We want students to be mathematically fluent.
  • We want our students to love math.

  • ...instruction can emphasize conceptual
    understanding without sacrificing skill
  • ...understanding does not detract from skill
    proficiency and may even enhance it.

Hiebert (2000)
NCTM Principles and Standards
Investigations In Number, Data and Space
  • NCTM Standards Based Resource
  • Students are striving to
  • Justify their reasoning
  • Communicate mathematically
  • Represent their thinking
  • Make connections to other content areas and
    the world around them

  • Offers students meaningful mathematical problems
  • Emphasizes depth in mathematical thinking rather
    than superficial exposure to a series of
    fragmented topics
  • Communicates mathematics content and pedagogy to
  • Substantially expands the pool of mathematically
    literate students

Calendar Math
  • Analyze data
  • Identify patterns including multiples and factors
  • Explore whole numbers and parts of a whole
    (fractions, decimals and percents)
  • Use mental math to estimate reasonable answers
  • Share strategies for arriving at an answer

In the classroom, students are
  • working in a variety of groupings
  • considering own reasoning and the reasoning of
  • communicating orally and through
  • pictures, numbers and words
  • working on a small number of problems during a
    class session, sometimes on a single problem for
    several sessions
  • using more than one strategy to double check
  • using cubes, blocks, measuring tools, technology,
    and variety of other materials to solve problems.

Goals of Instruction
  • To develop confident and competent lifelong
    learners who embrace mathematical challenges.
  • To assist children in acquiring strategies to
    build new learning skills and to grow as
  • To aid children in making meaningful mathematical
    connections to their world.

Mathematical Proficiency
  • Conceptual Understanding A web of connections.
  • Procedural Fluency Using basic skills such as
    facts, procedures, and formulas quickly and
  • Strategic Mathematical Thinking Formulating,
    representing, and solving problems and
    reflecting, explaining, and justifying their
  • Productive Disposition Viewing mathematics as
    understandable and worthwhile.

Adding it Up, 2001
Emphasis on Understanding
  • Typical of Japanese Math Instruction
  • Teachers pose a complex thought-provoking
  • Students struggle with the problem.
  • Various students present ideas or solutions to
    the class.
  • Class discusses the various solution methods.
  • The teacher summarizes the class conclusions.
  • Students practice similar problems.
  • Source Third International Mathematics and
    Science Study unpublished tabulations.
    Videotape Classroom
  • Study, UCLA, 1996.

Emphasis on Skill Acquisition
  • Typical of U.S. Math Instruction
  • Teacher instructs student in a concept or
  • Teacher solves example problems with the class.
  • Students practice on their own while the teacher
    assists individual students.
  • Source Third International Mathematics and
    Science Study unpublished tabulations.
    Videotape Classroom Study, UCLA, 1996.

Traditional Problems
  • What is the cost of 5 cans of beans if each can
    costs 0.79?
  • What is the cost of 16 boxes of cereal if each
    box costs 2.69?
  • How much change will Sally get if she pays for 8
    pounds of chicken that costs 1.89 per pound with
    a 20 bill?

Higher Order Thinking Problems
  • Hot dogs come in packages of 8 hot dogs for
  • hot dog rolls come in packages of 6 for 0.90 and
    12 for 1.50
  • hamburgers come in packages of 8 patties for
    4.00 and
  • hamburger buns come in packages of 8 for 1.00
    and 12 for 1.65.
  • You expect that 24 students and 6 adults will
    come to the picnic you are planning. You also
    expect that most-but not all-students will have a
    hot dog and most of the adults will have a
    hamburger. Decide how many packages of each you
    should buy, find the cost of the food, explain
    why you made your decisions, and show how you
    arrived at the cost.

Questioning Students...
  • Can you explain how you solved the problem?
  • Why did you do it that way?
  • How did you prepare for the assignment, the test,
    the activity?
  • Do you like mathematics?
  • Do you like multiplication?

Self Assessment
  • How did you do with this assignment?
  • What does someone need to know to be able to do
    this work?
  • What was easy for you in this assignment?
  • What was difficult for you in this assignment?

Throughout The School Year
  • Your child will be solving problems that take
    considerable time, thought, and discussion.
  • Children are expected to think about the problems
    in their own ways, and to be able to talk and
    write about their solutions.

How You Can Help Your Child
  • Play games with your child including higher level
    thinking games such as
  • chess
  • checkers
  • puzzles/brain teasers
  • simple card games
  • While playing talk about the strategies used to
    solve problems and make winning moves.
  • Children enjoy these kinds of activities while
    enhancing mathematical thinking.

Do Mathematics Together!
  • Everyday situations
  • Count, count, count!
  • Classify (toys, silverware, laundry)
  • Find 2 and 3 dimensional objects
  • Set the table (positional language)
  • Count and make change

Family Ideas
  • Use sharing to reinforce division and fraction
  • Incorporate measuring into daily activities
  • Baking, gardening, crafting
  • Use rulers, measuring cups, scales
  • Numbers are everywhere! Look for them on
    mailboxes, route signs, in newspapers

Link Mathematics with Daily Life
  • Everyday people face situations that involve
  • Deciding which route to take to a destination
  • Estimating the cost of groceries
  • Developing a schedule
  • Determining the percent off at a great sale

Learn About Math Related Careers
  • Math is the foundation for a wide variety of
    interesting careers.
  • Many jobs our children in the primary grades will
    experience have not even been invented yet!
  • It is imperative that our students be able to
    think and apply their knowledge to a variety of

Support Homework!
  • Be aware of what is happening in the classroom
    and have ongoing dialogue
  • Play the games which support the math program.
    They are essential!
  • Support student learning by review homework
    assignments and basic facts
  • Dont do homework for your child.

Be Positive About Math!
  • Acknowledge the fact that math can be
  • Persistence and hard work are keys to success.
  • Struggling at times in math is normal and is
    actually necessary to and valuable in
    understanding mathematics.

Attitude Increases Ability
  • A positive attitude is the essence of productive
  • A childs level of confidence determines his/her
    ability to obtain and retain new learning.
  • In social circles you never hear -I really do
    not comprehend what I read.
  • Accept mathematical challenges!

We need to do something
  • According to a survey conducted on behalf of a
    leading Fortune 500 Company.
  • 84 of students surveyed would rather do one of
    the following than their math homework clean
    their room, eat their vegetables, go to the
    dentist or take out the garbage
  • Only 1/3 of students surveyed reported liking
    math a great deal.
  • 43 of students reported having a difficult time
    understanding the mathematics they are taught in
  • By eighth grade, as many as 45 are turned off to
    math, describing it as BORING!

Have High Expectations
  • All students are capable of doing challenging
  • All students are expected to know basic facts and
    be able to apply them correctly in a variety of
  • All students are expected to communicate

Purpose of Games in Investigations
  • Games are a central part of the mathematics in
    the unit, not just enrichment.
  • Games develop familiarity with the number system,
    such as 10s, 100s, and 1000s and provide engaging
    opportunities for practicing computation.
  • Playing games encourages strategic mathematical
    thinking and demands that students find an
    optimal way (rather than just any way) of solving
    a problem.
  • Games are played often throughout a unit and
    throughout the year to develop fluency with
    numbers. It is expected that students will play
    games many times.
  • Games provide a school to home link. Parents
    learn about the mathematical thinking their
    children are doing by playing games with them at
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