Increasing Mathematics Achievement for ALL Students

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Increasing Mathematics Achievement for ALL
Students

• Presented by
• Melisa Hancock
• Teacher in Residence

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History of Mathematics

• 1960s Arithmetic Test A logger cuts and sells
  a truckload of lumber for 100. His cost of
  production is 4/5 of that amount. What is his
  profit?
• 1970s New Math Test A logger exchanges a set
  (L) of lumber for a set (M) of money. The
  cardinality of Set M is 100. The Set C of
  production costs contains 20 fewer points. What
  is the cardinality of Set P of profits?
• 1980s Dumbed Down Math A logger cuts and
  sells a truckload of lumber for 100. His cost
  is 80, his profit is 20. Find and circle the
  number 20.

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History of Math, cont.

• 1990s version An unenlighted logger cuts down
• a beautiful stand of 100 trees in order to make
  a 20 profit. Write an essay explaining how you
  feel about this as a way to make money. Topic
  for discussion How did the forest birds and
  squirrels feel?
• 2004 version A logger sells a truckload of
  lumber for 100. Her cost of production is 120.
  How does Martha Stewart determine that her
  profit margin is 80?
• Teaching in 2010 El hachero vende un camion
  carga por 100. La cuested de production es . .
  . . . . . . . .

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Over The Past Decade. .

• The National Council of Teachers of
• Mathematics (NCTM) has advocated
• for changes in school mathematics
• programs so that ALL students have
• the opportunities to engage in high-
• quality mathematics that will prepare them for
  today and a world tomorrow they can only imagine.

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Principles and Standards for Teaching
Mathematics

• Challenges the traditional emphasis on
  shopkeepers arithmetic and routine problem
  solving. According to this new perspective, the
  global transformation from an industry-based
  society to an information-based one has involved
  a corresponding transformation of expectations
  for mathematical literacy.

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• The mathematical competence necessary for success
  in the information age includes the familiar
  fluency with facts and skills, but it also
  requires sophisticated mathematics reasoning and
  problem solving in a variety of contexts.

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• The perspective articulated in the NCTM Standards
  challenges the widely-held assumption that
  mathematical thinking is accessible to only a
  talented few and emphasizes the importance of
  education ALL students to become mathematical
  thinkers.

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Problem . . .

• Since the mid-1800s mathematics books have been
  developed around the SHOW AND TELL method.
  Unfortunately, mathematics books have changed
  very little today. NCTM Standards have caused
  publishers to use appropriate Standards buzz
  words in their texts, but the focus is still on
  procedural knowledge rather than conceptual
  understanding. Lots of WHAT to do and HOW to do
  it.and very little WHEN to do it and WHY you
  do it!

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NCTM Standards (1989)

• The Learning Principle makes it very clear that
  learning with UNDERSTANDING is both essential and
  possible. That is, ALL children can and must
  learn mathematics with understanding. It is
  impossible to predict the kinds of problems
  students will face in the future. The Learning
  Principle says that understanding is the only way
  to ensure that students will be able to cope with
  these unknown problems in the future.

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• For all the current controversy surrounding
• issues of student achievement and
• accountability, we forget there is far less
• controversy about a shared desire on all
• sides to see more kids learn, to reduce the
• achievement gap, and to improve the
• quality of the complex work of teaching in all
• schools, whether they are affluent or not.
• (Mike Schomoker)

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Visions for Improvement

• State and National standards are not programs to
  be implemented but are visions for improvement in
  mathematics.
• -Deborah Ball

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Mathematical Knowledge

• 1.Conceptual Knowledge (logical relationships,
  representations, an understanding and ability to
  talk, write and give examples of these
  relationships, etc.)
• 2. Procedural Knowledge (knowledge of rules and
  procedures used in carrying out routine
  mathematical tasks and the symbols used to
  represent mathematics)

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Mathematics! Its as easy as Pi!!!!!!

• Using the Link Sheet,
• tell me what YOU know about pi.

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Textbook Selection and Use

• Studies about the influence of textbooks on the
  mathematics curriculum invariably conclude that
  the most important single factor in determining
  what content children are exposed to in the
  classroom is the textbook.

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Think LONG TERM Take A K-12 Perspective

• Textbooks ought to be a major force to encourage
  a coherent program from grade to grade, building
  on past activities and preparing for future
  learning.

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WHERE DO WE BEGIN? First of all.recognizing
how difficult change really is!

• Teachers and administrators must step back and
  take a hard look at what is going on in their
  school. A "no excuses" attitude must prevail.
  Begin by 1) acknowledging that poor student
  achievement is unacceptable 2) accepting
  responsibility for the problem 3) clearly
  stating that ALL stakeholders in the system need
  to be part of the solution and 4) committing to
  long-term efforts and innovations even if
  immediate results are not apparent.

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Challenging Traditional Beliefs

• Meeting the needs of all children requires that
  we challenge and perhaps change many of our
  long-held assumptions about the mathematics
  curriculum and about how children learn
  mathematics.

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Hard Arithmetic is Not Deep Mathematics!

• Problem solving is the cornerstone of school
  mathematics. Without the ability to solve
  problems, the usefulness and power of mathematics
  ideas, knowledge, and skills are severely
  limited. Students who can efficiently and
  accurately multiply but who cannot identify
  situations that call for multiplication are not
  well prepared.
• Unless students can solve problems, the facts,
  concepts, and procedures they know are of little
  use.

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Equity Principle, NCTM

• All students, regardless of their personal
  characteristics, backgrounds, or physical
  challenges, must have opportunities to studyand
  support to learnmathematics. Equity does not
  mean that every student should receive identical
  instruction instead, it demands that reasonable
  and appropriate accommodations be made as needed
  to promote access and attainment for all
  students.

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An Era of ChangeNCTM, 2000

• In this changing world, those who understand
• and can do mathematics will have significantly
• enhanced opportunities and option for shaping
• their futures. Mathematical competence opens
• doors to productive futures. A lack of
• mathematical competence keeps those doors
• closed....ALL students should have the
• opportunity and the support necessary to learn
• significant mathematics with depth and
• understanding. There is no conflict between
  equity and excellence.

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Curricular Focus

• Collaborative adoption process
• Research based
• Aligned to Standards
• Appropriate assessment model
• Commitment to continuous improvement

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Teachers Role

• Every mathematics classroom should provide
  mathematical skills that are a bridge to the
  real-world. This means going beyond memorization
  into a world of reasoning, problem solving and
  communication.

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(When Procedures ARE THE FOCUS)If the only tool
you have is a hammer, everything around you looks
like a nail.

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Conclusions

• The bottom line is that there is just no way to
  create good schools without good teachers.
• -National Commission on Teaching and Americas
  Future, 1996.
• Behind every great teacher is a great
  Administrator!!!!
• High Expectations, A No Excuse Attitude, and
  Support, Support, Support, Support,
  Support!!!!!!!!!!!