Leading Math Success

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Leading Math Success

• Attaining Mathematical Literacy
• in the Windsor-Essex Catholic District School
  Board
• October, 2004

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EVERYONE is capable of becoming mathematically
literate

• All students can learn mathematics with enough
  support, resources and time and we must ensure
  that they do.

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Students at risk need the BEST of what we have
to offer!

• We may use the best strategies to benefit all
  students, but we MUST use them to support
  struggling students.

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What Research is Telling Us!

• 1. Effective teaching and learning begins with
  the needs of adolescent students
• 2. Students must have a solid conceptual
  foundation in mathematics in order to apply their
  knowledge and continue to learn mathematics
• 3. Effective instructional strategies in
  mathematics emphasize the ability to think, to
  solve problems, and to build ones own
  understandings
• 4. An effective learning experience is one that
  connects mathematics with the lives of adolescent
  students

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Effective teaching and learning begins with the
needs of adolescent students

• Research Finding 1

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The Reality of the Adolescent At Risk Learner

• I cant do math and you cant make me.
  Im out of here!
• Solving problems in math class involves risk
  taking. Students do not want to be embarrassed
  in front of their peers and will not take risks
  unless they feel valued and supported.

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The Reality of Teaching the Adolescent Struggling
Learner

• Grade 7 Teacher
• I wish they all came in ready, eager and excited
  but thats not the case.

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What can we do?

• We can respond by ensuring that students feel
  safe to take risks and participate during
  mathematics learning. Sometimes just showing up
  takes courage.
• Remember, recognition by peers and social status
  are extremely important to them

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What can we do?

• It is important to model the belief that ALL
  students can learn mathematics
• Be sensitive to and avoid verbal and non-verbal
  ways that adults communicate low expectations for
  at-risk students.
• Kids are very attuned to adults attitudes
  toward them. They can tell when you have low
  expectations for them, and it can hurt them
  pretty badly. Littky, 2004

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• It is important that we help ALL students feel
  confident about their ability to learn
  mathematics.

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Our MESSAGE To Our AT RISK Students

• We will not give up on you, nor will we allow you
  to give up on yourself.

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Students must have a solid conceptual foundation
in mathematics in order to apply their knowledge
and continue to learn mathematics

• Research Finding 2

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TIMSS

• Third International Mathematics and Science Study
• Largest and most ambitious international
  comparison of teaching conducted
• Randomly selected nationally representative
  samples from countries around the world of 8th
  grade lessons in math and science. These lessons
  were videotaped
• In particular, they studied
• Ways in which classrooms were organized
• Kinds of math problems presented to the students
• Ways problems are worked on during class

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Question What is the difference between high
achieving vs. lower achieving countries?

• Found a great deal of variation in the emphasis
  given to problems designed to teach skills vs.
  problems designed to teach conceptual
  understanding (problems where students have
  opportunities to connect math facts, ideas and
  strategies)
• Relative emphasis on conceptual problems varied
  among the high achieving countries.
• 54 of the problems in Japan were conceptual
• 13 of the problems in Hong Kong were conceptual
• BUT when they took a closer look, they found a
  similarity among the high achieving countries
  that distinguished them from the rest
• High Achieving Countries included Hong Kong,
  Japan, Netherlands, Switzerland and the Czech
  Republic

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A KEY difference between high achieving vs. lower
achieving countries

• The lower achieving countries when working on
  conceptual problems (making connections) teachers
  almost always stepped in and did the work for the
  students or ignored the conceptual aspect when
  discussing it
• Teachers in high achieving countries differed
  from each other in how many problems of this kind
  they presented. BUT when such problems were
  presented they where presented in such a way that
  students studied the connections or relationships
  embedded in the problem.

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What is the difference between high achieving vs.
lower achieving countries?

• Example Find a pattern for the sum of the
  interior angles of a polygon.

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• Method 1 Teachers ask students to measure the
  angles of various triangles, quadrilaterals, and
  pentagons, finding the results of 180 degrees,
  360 degrees and 540 degrees respectively. Then
  they might ask students what patterns they see,
  whether they could predict the sum of the
  interior angles of six-sided figures, and,
  eventually, whether they could develop a rule for
  the sum of angles if one knew the number of sides
• Method 2 Teachers could simply say, There is
  an easy way to calculate the sum of the interior
  angles of a polygon just count the number of
  sides, subtract two and multiply by 180. Sum
  180(n 2).
• Teachers in the high achieving countries
  implemented at least some of these problems in
  the first way rather than the second.

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Conclusion of the TIMSS Study

• Efforts should focus on ensuring students have
  opportunities to solve challenging problems that
  require them to construct math relationships.
• Avoid stepping in and giving the answers, instead
  provide students with opportunities to think more
  deeply about mathematical concepts and then
  discuss these concepts or relationships.
• Source Journal of Staff Development, Volume
  25(4), 2004.
• A World of Difference

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Effective instructional strategies in mathematics
emphasize the ability to think, to solve
problems, and to build ones own understandings

• Research Finding 3

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Math and Sense Making

• Learning to Read goal bring meaning to the
  printed page
• Learning Math goal bring meaning to
  mathematical symbols, concepts and skills
• Learning Math has to be grounded in sense making.
• There are two distinct aspects of learning math
• Making sense of math ideas and skills that are
  rooted in logic
• Learning the terminology and symbols we use to
  describe math

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Math and Sense Making

• When teaching a lesson, keep in mind whether the
  lesson is based on a logical structure or social
  convention.
• Implications for Teaching
• When a lesson addressed a social convention, it
  makes sense for the teacher to impart the
  knowledge. Memorization may be necessary.
• When ideas being taught are based on logic
  teaching by telling is not appropriate. Students
  need to understand and make sense of the idea.

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Making Sense of Pi

• Source Journal of Staff Development, Vol 24(4),
  2004.
• A can of Coke leads to a piece of Pi

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An effective learning experience is one that
connects mathematics with the lives of adolescent
students

• Research Finding 4

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• Highly effective teachers place
• emphasis on making connections.
• If students lack a deep-seated understanding of
  math concepts they can accurately and quickly
  solve routine problems but they are unable to
  apply their knowledge to new and different
  problems
• They can get the correct answer but they dont
  understand why they work.

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Making Connections

• It is only when we connect something new to
  something we already understand that we actually
  learn.
• Our Goal is for students in our classes to attain
  mathematical literacy.
• the ability to put mathematical knowledge and
  skills to functional use rather than just
  mastering them within the school curriculum

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The Power of Manipulativesto Make Connections

• Manipulatives provide alternative ways for
  students to see and think about math concepts.
• Manipulatives serve as the bridge between the
  concrete and the underlying math concept
• Provides an opportunity for students to talk
  about their learning. If students cannot talk
  about their learning they do not own it.

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Teaching is a Cultural Activity

• Teaching can only change the way culture
  changes..
• gradually, steadily over time as small changes
  are made in daily and weekly routines
• Your MISSION Should you Accept It
• Spend some time each week planning how to
  implement a few mathematics problems to engage
  students in thinking about key mathematical
  relationships

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• Teachers must be agents of change that they did
  not experience as students.
• Anderson and Piazza, 1996.

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A Closing Thought from our Favourite Doc!

• Unless someone like you cares a whole awful lot,
  nothing is going to get better. Its not.
• Dr. Seuss