1 The Death March to Calculus Disclaimer I

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The Death March to Calculus (Disclaimer: I stole the title. ) Derek Webb Bemidji State University dwebb@bemidjistate. edu 2

A Timely Aside § Hypothesis: Public school teachers and their unions are responsible for educational failures in mathematics. Lets investigate this hypothesis using statistical thinking. 3

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 nonunionized schools 4

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. 5

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. 6

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 7

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. 8

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. 9

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 10

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 4 th grade There was no statistical difference in 8 th grade. 11

A Timely Aside Conclusions: Find another scapegoat – unions are not it. Statistical literacy is extremely important – one of the main points of the rest of my talk. 12

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 13

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% 14

What’s Happening in 8 -12 Math Today? § Students able to succeed in calculus – typical curriculum: 8 th Grade – Algebra 9 th Grade – More Algebra 10 th Grade – Traditional Geometry (think Euclid) 11 th Grade – “Pre Calculus” 12 th Grade – Calculus 15

What’s Happening in 8 -12 Math Today? § All the rest – typical curriculum: 8 th Grade – Algebra (failures occur) 9 th Grade – More Algebra (failures mount) 10 th Grade – Traditional Geometry or more algebra, but slower pace 11 th Grade – Consumer math, financial math, algebra 4000, etc… 12 th Grade – no math at all, consumer math II, finite math IV, etc… 16

What’s Happening in 8 -12 Math Today? § § § Students “deemed” able to succeed in calculus dropout rate: Half at each grade level. For example: 8 th grade class has 512 students 9 th grade in death march to calculus is 256 10 th grade in death march to calculus is 128 11 th grade in death march to calculus is 64 12 th grade in death march to calculus is 32 17

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 (Ao. PS) – 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. 18

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. ” 19

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…. ) 20

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. ” § 21

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 9 th grade. 22

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… 23

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 24

What’s Happening in Math Education – Pre. K-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 25

What’s Happening in Math Education – Pre. K-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 26

What’s Happening in Statistics Education – Pre. K-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… 27

What’s Happening in Statistics Education – Pre. K-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. ” 28

What’s Happening in Statistics Education – Pre. K-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. ” 29

What’s Happening in Statistics Education – Pre. K-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. ” 30

What Does the NCTM Recommend? § The NCTM also recommends that “students be engaged in meaningful activities involving data and chance from pre. K 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. 31

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) 32

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) 33

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) 34

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) v v v 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 12 th grade math class for those students not in AP Statistics or AP Calculus – REMEMBER, this is most students. v One option is Introduction to the Mathematical Sciences class