Download The Death March to Calculus

1
The Death March to
Calculus
(Disclaimer: I stole the title.)
Derek Webb
Bemidji State University
[email protected]
2
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
3
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
4
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
5
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…
6
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
7
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.
8
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.”
9
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….)
10
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.”
11
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.
12
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.”
13
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
14
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
15
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
16
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…
17
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.”
18
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.”
19
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.”
20
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.
21
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)
22
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)
23
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)
24
Statistical Thinking
vs.
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 Thinking

Statistics is, by and large, a probabilistic or
stochastic way of thinking.
Why is this important?

Statistical Thinking
vs.
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 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 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 Thinking
Statistical thinking is inductive: the inference of
general conclusions or laws from particular
instances.
“Specific to general”
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)
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)
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