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The Death March to Calculus (Disclaimer: I stole the title.) Derek Webb Bemidji State University [email protected]. A Timely Aside. Hypothesis: Public school teachers and their unions are responsible for educational failures in mathematics. - PowerPoint PPT Presentation

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Page 1: A Timely Aside

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Page 2: A Timely Aside

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The Death March to Calculus

(Disclaimer: I stole the title.)

Derek WebbBemidji State [email protected]

Page 3: A Timely Aside

A Timely Aside

Hypothesis: Public school teachers and their unions are responsible for educational failures in mathematics.

Lets investigate this hypothesis using statistical thinking.

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Page 4: A Timely Aside

A Timely Aside

Hypothesis: Public school teachers and their unions are responsible for educational failures in mathematics.

Are all schools unionized public schools?

- No, there are lots of private non-unionized schools

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Page 5: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

Can we compare student performance in the public unionized schools to student performance in private non-unionized schools?

Yes, but I can’t because I am biased.

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Page 6: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

The National Center for Educational Statistics (NCES) did such a comparison in 20061.

1. NAEP (2006). Comparing Private Schools and Public Schools Using Hierarchical Linear Modeling. U.S. Department of Education, NCES 2006461.

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Page 7: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

NCES is the primary federal entity for collecting and analyzing data related to education in the U.S

NCES brought us NAEP – National Assessment of Educational Progress

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Page 8: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

Findings: In grades 4 and 8 (The only ones examined), students in private schools scored significantly higher than students in public schools in mathematics.

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Page 9: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

But wait, what about controlling for individual student and school characteristics?

In statistical terminology these characteristics are called confounding variables.

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Page 10: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

Many confounders were accounted for such as gender, race/ethnicity, disability status, student identification as an English language learner, school size, location, and the composition of the student body

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Page 11: A Timely Aside

A Timely Aside Hypothesis: Public school teachers and their

unions are responsible for educational failures in mathematics.

After accounting for confounders, students in public schools scored significantly higher than students in private schools in mathematics in 4th grade

There was no statistical difference in 8th grade.

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Page 12: A Timely Aside

A Timely AsideConclusions:

Find another scapegoat – unions are not it.

Statistical literacy is extremely important – one of the main points of the rest of my talk.

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Page 13: A Timely Aside

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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Page 14: A Timely Aside

What’s Happening in 8-12 Math Today?

Students can be classified into two groups: Students able to succeed in calculus in a traditional

teaching environment – about 15% All the rest – about 85%

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Page 15: A Timely Aside

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

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Page 16: A Timely Aside

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…

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Page 17: A Timely Aside

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

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Page 18: A Timely Aside

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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Page 19: A Timely Aside

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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Page 20: A Timely Aside

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….)

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Page 21: A Timely Aside

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.”

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Page 22: A Timely Aside

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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Page 23: A Timely Aside

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.”

Olivia Webb in second grade…

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Page 24: A Timely Aside

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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Page 25: A Timely Aside

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

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Page 26: A Timely Aside

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

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Page 27: A Timely Aside

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…

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Page 28: A Timely Aside

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.”

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Page 29: A Timely Aside

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.”

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Page 30: A Timely Aside

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.”

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Page 31: A Timely Aside

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)

Mike Shaughnessy, one of the authors, is the current president of NCTM and is at this conference.

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Page 32: A Timely Aside

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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Page 33: A Timely Aside

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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Page 34: A Timely Aside

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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Page 35: A Timely Aside

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.

Page 36: A Timely Aside

Statistical Thinkingvs.

Mathematical Thinking Statistics is, by and large, a probabilistic or

stochastic way of thinking.

Why is this important?

Page 37: A Timely Aside

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)

Page 38: A Timely Aside

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)

Page 39: A Timely Aside

Statistical Thinkingvs.

Mathematical Thinking Mathematical thinking is deductive: the

inference of particular instances by reference to a general law or principle.

“General to specific”

Page 40: A Timely Aside

Statistical Thinkingvs.

Mathematical Thinking Statistical thinking is inductive: the inference of

general conclusions or laws from particular instances.

“Specific to general”

Page 41: A Timely Aside

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)

Page 42: A Timely Aside

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)

Page 43: A Timely Aside

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 Scie

nces class