The Death March to Calculus (Disclaimer: I stole the title.) Derek Webb Bemidji State University [e-mail]

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The Death March to Calculus(Disclaimer I stole
the title.)Derek WebbBemidji State
Universitydwebb_at_bemidjistate.edu
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Arthur Benjamin

• Short Bio
• Professor of math at Harvey Mudd College
• Mathemagician taking the stage in his tuxedo to
  perform high-speed mental calculations
• Published Secrets of Mental Math and award
  winning book Proofs That Really Count The Art of
  Combinatorial Proof

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Whats Happening in 8-12 Math Today?

• Students can be classified into two types
• Students able to succeed in calculus in a
  traditional teaching environment
• All the rest

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Whats Happening in 8-12 Math Today?

• Students able to succeed in calculus typical
  curriculum
• 8th Grade Algebra
• 9th Grade More Algebra
• 10th Grade Traditional Geometry (think Euclid)
• 11th Grade Pre Calculus
• 12th Grade Calculus

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Whats Happening in 8-12 Math Today?

• All the rest typical curriculum
• 8th Grade Algebra (failures occur)
• 9th Grade More Algebra (failures mount)
• 10th Grade Traditional Geometry or more
  algebra, but slower pace
• 11th Grade Consumer math, financial math,
  algebra 4000, etc
• 12th Grade no math at all, consumer math II,
  finite math IV, etc

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Whats Happening in 8-12 Math Today?

• Students deemed able to succeed in calculus
  dropout rate Half at each grade level.
• For example 8th grade class has 512 students
• 9th grade in death march to calculus is 256
• 10th grade in death march to calculus is 128
• 11th grade in death march to calculus is 64
• 12th grade in death march to calculus is 32

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Death March to Calculus Where did the title
come from?

• Math Horizons February 2010 published by the
  Mathematical Association of America
• Article by Richard Rusczyk
• Founder of Art of Problem Solving (AoPS) math
  education textbook company
• Director of the USA Mathematical Talent Search
• Co-creator of Mandelbrot Competition national
  competition covering all non-calculus areas of
  mathematics. Open to all students grade 12 down.

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Death March to Calculus Where did the title
come from?

• In the article Richard states
• The standard curriculum in the U.S. is a death
  march to calculus
• This is a sham on a lot of levels.

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Death March to Calculus Where did the title
come from?

• In the article Richard states
• Students who will not go into math-related
  fields dont get exposure to the only areas of
  math that will be helpful to them.
• (By the way, this is most students.)

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Death March to Calculus Where did the title
come from?

• In the article Richard states
• They dont develop number sense through number
  theory, and dont develop an understanding of
  risk through a study of probability.

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Death March to Calculus Where did the title
come from?

• In fact, most students get little or no
  statistics or probability. If they do, it is
  often crammed in at the end of 9th grade.

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Death March to Calculus Where did the title
come from?

• In the article Richard states
• The curriculum is simply outdated. I think the
  ineffective use of technology in the classroom is
  indicative of another major failing in the
  curriculum an emphasis on facts rather than on
  strategies for solving problems.

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What do most students need?

• Bemidji State University study
• Based on 5 years of data (2001-2006)
• 78 of all graduates across all programs need one
  or more statistics courses.
• 12 of all graduates across all programs need one
  or more calculus courses.
• More info here

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Whats Happening in Math Education PreK-12?

• 2004 report Ready or Not Creating a High School
  Diploma That Counts from the American Diploma
  Project lists the following quantitative
  competencies needed for high school graduates to
  succeed in postsecondary education or in
  high-performance, high-growth jobs centers
• Number Sense and Numerical Operations
• Algebra
• Geometry
• Data Interpretation, Statistics and Probability

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Whats Happening in Math Education PreK-12?

• Advanced Placement Statistics
• First exam in 1997 7,667 students took exam
• In 2010 129,889 students took exam
• Fastest growing of all AP exams
• Would a High School ever consider offering AP
  Statistics and not AP Calculus? Maybe they
  should.
• More info at the Statistics Teacher Network
  Issue 76

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Whats Happening in Statistics Education PreK-12

• The Mathematical Education of Teachers (MET -
  2001) Report by the American Mathematical Society
  and the Mathematical Association of America
• Sees statistics as the topic in which current
  and prospective teachers need the most help with
  content and pedagogy
• Quotes from the report

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Whats Happening in Statistics Education PreK-12

• The Mathematical Education of Teachers (MET)
  Report by the American Mathematical Society and
  the Mathematical Association of America
• Statistics is the science of data, and the
  daily display of data by the media
  notwithstanding, most elementary teachers have
  little or no experience in this vitally important
  field.

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Whats Happening in Statistics Education PreK-12

• The Mathematical Education of Teachers (MET)
  Report by the American Mathematical Society and
  the Mathematical Association of America
• Of all the mathematical topics now appearing in
  the middle grades curricula, teachers are least
  prepared to teach statistics and probability.

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Whats Happening in Statistics Education PreK-12

• The Mathematical Education of Teachers (MET)
  Report by the American Mathematical Society and
  the Mathematical Association of America
• Statistics is now widely acknowledged to be an
  extremely valuable set of tools for problem
  solving and decision making. But, despite the
  production of interesting statistics materials
  for the schools, it has been hard to find room
  for the subject in (high school) curricula
  dominated by preparation for calculus.

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What Does the NCTM Recommend?

• The NCTM also recommends that students be
  engaged in meaningful activities involving data
  and chance from preK through 12.
• NCTM publication Focus in High School
  Mathematics Reasoning and Sense Making
  Statistics and Probability (2009)
• One of the authors is the current president of
  NCTM.

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What Does the NCTM Recommend?

• In our increasingly data-intensive world,
  statistics is one of the most important areas of
  the mathematical sciences for helping students
  make sense of the information all around them, as
  well as for preparing them for further study in a
  variety of disciplines.
• NCTM publication Focus in High School
  Mathematics Reasoning and Sense Making
  Statistics and Probability (2009)

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What Does the NCTM Recommend?

• Achieving competence according to the standards
  set forth in Principles and Standards for School
  Mathematics (NCTM 2000) depends on a thorough and
  deep understanding of the foundations of
  statistics and probability.
• NCTM publication Focus in High School
  Mathematics Reasoning and Sense Making
  Statistics and Probability (2009)

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What Does the NCTM Recommend?

• Statistical reasoning is also inherently
  different from mathematical reasoning, and
  effective development of it requires distinct
  exercises and experiences.
• NCTM publication Focus in High School
  Mathematics Reasoning and Sense Making
  Statistics and Probability (2009)

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Statistical Thinkingvs.Mathematical Thinking

• Mathematics is, by and large, a deterministic way
  of thinking and the way mathematics is taught in
  schools in America entrenches students into a
  deterministic way of viewing the quantitative
  world around them.

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Statistical Thinkingvs.Mathematical Thinking

• Statistics is, by and large, a probabilistic or
  stochastic way of thinking.
• Why is this important?

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Statistical Thinkingvs.Mathematical Thinking

• Science entered the nineteenth century with a
  firm philosophical vision that has been called
  the clockwork universe By the end of the
  nineteenth century, the errors had mounted
  instead of diminishing By the end of the
  twentieth century, almost all of science had
  shifted to using statistical models Popular
  culture has failed to keep up with the scientific
  revolution.
• - David Salsburg The Lady Tasting Tea (2001)

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Statistical Thinkingvs.Mathematical Thinking

• Statistics has its own tools and ways of
  thinking, and statisticians are quite insistent
  that those of us who teach mathematics realize
  that statistics is not mathematics, nor is it
  even a branch of mathematics. In fact,
  statistics is a separate discipline with its own
  unique ways of thinking and its own tools for
  approaching problems.
• - J. Michael Shaughnessy, Research on Students
  Understanding of Some Big Concepts in Statistics
  (2006)

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Statistical Thinkingvs.Mathematical Thinking

• Mathematical thinking is deductive the inference
  of particular instances by reference to a general
  law or principle.
• General to specific

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Statistical Thinkingvs.Mathematical Thinking

• Statistical thinking is inductive the inference
  of general conclusions or laws from particular
  instances.
• Specific to general

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Recommendations

• Consider integrating more statistics and
  probability into the curriculum at all grade
  levels across the entire academic year.
• Consider offering AP Statistics and AP Calculus
  or, if your school is too small, just AP
  Statistics
• Consider quality alternative courses for the
  students that should not be in the Death March to
  Calculus path. (this is most students)

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Recommendations

• Consider alternative courses for the students
  that should not be in the Death March to Calculus
  path. (this is most students)
• Courses should be engaging
• Activity based where possible
• Focus on discrete math, statistics, probability,
  and number sense, (not traditional algebra) and
  make use of spreadsheets (not calculators)

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Recommendations

• Have a meaningful 12th grade math class for those
  students not in AP Statistics or AP Calculus
  REMEMBER, this is most students.
• One option is Introduction to the Mathematical
  Sciences class