Creating Mathematical Magic In The Classroom

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Creating Mathematical Magic In The Classroom
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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
  evidence.

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Building a Teaching Bridge from Reading to Math
Reading
Math
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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.

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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
  start.
• 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.

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

Hiebert (2000)
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NCTM Principles and Standards
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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

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Investigations

• 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
  teachers
• Substantially expands the pool of mathematically
  literate students

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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

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In the classroom, students are

• working in a variety of groupings
• considering own reasoning and the reasoning of
  others
• 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.

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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
  mathematicians.
• To aid children in making meaningful mathematical
  connections to their world.

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Mathematical Proficiency

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

Adding it Up, 2001
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Emphasis on Understanding

• Typical of Japanese Math Instruction
• Teachers pose a complex thought-provoking
  problem.
• 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.

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Emphasis on Skill Acquisition

• Typical of U.S. Math Instruction
• Teacher instructs student in a concept or
  skill.
• 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.

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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?

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Higher Order Thinking Problems

• Hot dogs come in packages of 8 hot dogs for
  2.50
• 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.

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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?

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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?

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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.

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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.

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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

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Family Ideas

• Use sharing to reinforce division and fraction
  skills
• 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

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Link Mathematics with Daily Life

• Everyday people face situations that involve
  mathematics.
• Deciding which route to take to a destination
• Estimating the cost of groceries
• Developing a schedule
• Determining the percent off at a great sale

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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
  situations.

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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.

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Be Positive About Math!

• Acknowledge the fact that math can be
  challenging.
• 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.

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Attitude Increases Ability

• A positive attitude is the essence of productive
  learning.
• 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!

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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
  school.
• By eighth grade, as many as 45 are turned off to
  math, describing it as BORING!

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Have High Expectations

• All students are capable of doing challenging
  mathematics.
• All students are expected to know basic facts and
  be able to apply them correctly in a variety of
  situations.
• All students are expected to communicate
  mathematically.

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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
  home.