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The Death March to Calculus (Disclaimer: I stole the title.) Derek Webb Bemidji State University [email protected] Arthur Benjamin. Short Bio: Professor of math at Harvey Mudd College Mathemagician taking the stage in his tuxedo to perform high-speed mental calculations

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The Death March to Calculus(Disclaimer: I stole the title.)Derek WebbBemidji State [email protected]


Arthur benjamin
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


What s happening in 8 12 math today
What’s 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


What s happening in 8 12 math today1
What’s 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


What s happening in 8 12 math today2
What’s 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…


What s happening in 8 12 math today3
What’s 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


Death march to calculus where did the title come from
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.


Death march to calculus where did the title come from1
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.”


Death march to calculus where did the title come from2
Death March to Calculus – Where did the title come from?

  • In the article Richard states:

    “Students who will not go into math-related fields don’t get exposure to the only areas of math that will be helpful to them.”

    (By the way, this is most students….)


Death march to calculus where did the title come from3
Death March to Calculus – Where did the title come from?

  • In the article Richard states:

    “They don’t develop number sense through number theory, and don’t develop an understanding of risk through a study of probability.”


Death march to calculus where did the title come from4
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.


Death march to calculus where did the title come from5
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.”


What do most students need
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


What s happening in math education prek 12
What’s 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


What s happening in math education prek 121
What’s 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


What s happening in statistics education prek 12
What’s 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…


What s happening in statistics education prek 121
What’s 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.”


What s happening in statistics education prek 122
What’s 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.”


What s happening in statistics education prek 123
What’s 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.”


What does the nctm recommend
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.


What does the nctm recommend1
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)


What does the nctm recommend2
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)


What does the nctm recommend3
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)


Statistical thinking vs mathematical thinking
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.


Statistical thinking vs mathematical thinking1
Statistical Thinkingvs.Mathematical Thinking

  • Statistics is, by and large, a probabilistic or stochastic way of thinking.

    Why is this important?


Statistical thinking vs mathematical thinking2
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)


Statistical thinking vs mathematical thinking3
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)


Statistical thinking vs mathematical thinking4
Statistical Thinkingvs.Mathematical Thinking

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

    “General to specific”


Statistical thinking vs mathematical thinking5
Statistical Thinkingvs.Mathematical Thinking

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

    “Specific to general”


Recommendations
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)


Recommendations1
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)


Recommendations2
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


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