A Conversation About Statistics Before College

Barriers and Opportunities for Statistics in Secondary Education


To broaden the conversation about statistics education before college, we asked some luminaries in the statistical education world to provide short answers to the following questions:

What are the greatest barriers and threats for statistics in secondary education?

What are the most promising opportunities (e.g., new forms of technology, innovative approaches to teacher training, and faculty development), and what is needed to take advantage of these opportunities?

Interested in adding to the discussion? Comment below.

Al Coons
Buckingham Browne & Nichols School

(1) Barriers and Threats
There is a growing consensus among secondary-school and college professors that an understanding of statistics is as important as or more important than calculus. Yet, one of the barriers for teaching statistics in secondary education is a disconnect between the value of AP Statistics and college admissions methods.

Bob Hayden recently wrote, “I suspect AP courses are not judged [in admissions] based on their value in college or in real life but rather on their ability to screen students. As long as high schools are more selective in who they point toward AP Calc than AP Stats[,] the colleges are likely to follow suit and see AP Calc as the more demanding course, and hence a better predictor of success in college.”

It is not just which course students are advised to take by their mathematics teachers for the succeeding year. College counselors honestly advise some students that taking calculus rather than statistics might provide some advantage for acceptance at some colleges. Our college counselors suggest that this does not happen often, but there is no way of knowing when this little bump may make all the difference. Given the competitiveness of college admissions, it is hard for most students to ignore this advice, even if they see statistics as more useful in their future.

(2) Opportunities
We already have technologies and modern curricula that allow statistics to be taught in engaging, connected, and comprehensible ways. This is perhaps best reflected by how most AP Statistics courses are taught. The question is whether teachers are aware of and willing to use these approaches and whether teacher training reflects them.

Most secondary mathematics teachers value statistics. Yet their interest in and the quality of teaching statistics is uneven at best. While new teachers often have taken more statistics classes than their predecessors, the courses that they experienced—the ones they are most likely to model their teaching on—often did not align with contemporary standards. Both college and in-service teacher training need to reflect a data-driven, student-centered approach using calculator/computer technology such as applets. This will enhance understanding and reduce drudgery, and add to the enjoyment of the study of statistics.

Further Reading
Robert W. Hayden. May 7, 2015. AP Statistics Community Discussions.

Allan Rossman
Cal Poly – San Luis Obispo

Whenever I give presentations for pre-college students or teachers, I often think of the wonderful but unfortunate adage: “Most people use statistics as a drunk uses a lamppost: more for support than for illumination.” My goal is to refute this saying by leading students and teachers to realize that the discipline of statistics provides a powerful tool for shedding light on important questions about the world. I try to engage students in this discovery, using only very simple statistical tools, such as these three well-known examples:

  • Draft lottery: Students examine a scatterplot of draft number vs. sequential date for the results of the 1970 draft lottery. Then they calculate the median draft number for each month, and they spot an obvious trend not revealed in the scatterplot.
  • Sex bias in graduate admissions: Students calculate acceptance rates for men and women from the famous data set from Berkeley in 1973. Then they calculate acceptance rates for each program separately, finding that the initial finding of apparent discrimination goes away or is even reversed.
  • AIDS testing: Students determine the conditional probability of having AIDS given a positive result for the ELISA test by creating a two-way table of data from a hypothetical population based on the given base rate, sensitivity, and specificity. They discover, to their great surprise, that most of the positive test results are false positives.

In my view, the biggest barrier to achieving this goal (leading students to realize how illuminating statistics can be) involves teacher preparation: We often don’t teach our college courses, especially those taken by math majors who become secondary teachers, with this goal foremost. Too often, we unwittingly convey the impression that statistics is a collection of number-crunching methods rather than a tool for illuminative thinking.

But there are many promising opportunities. Illuminating examples are easier to find than ever, for both college and secondary teachers, as data abound everywhere. (Frankly, I don’t particularly care whether students scrape the web or dig into a paper almanac, as long as they engage with data for the purpose of illumination.) The ASA is helping to make such examples available, and the pre-K–12 GAISE Report and new Statistical Education of Teachers (SET) report provide considerable guidance. Most promising are the creativity and dedication of the growing community of pre-college teachers who focus on statistics, many of whom I have been fortunate to meet through my involvement with the AP Statistics program.

Amelia McNamara
Smith College

(1) Barriers and Threats
For me, a student only truly experiences statistics and data analysis when they are able to ask and answer questions that interest them using data. To do this, I believe they need to be using a statistical software tool designed for working with data. The challenges to providing this authentic experience at the secondary-school level are threefold and inextricably intertwined.

The first challenge is a lack of curriculum; without lesson plans and support resources, it is difficult for in-service teachers to integrate material into their existing courses.

Second is professional development. Most teachers have had at most one noncomputerized mathematical statistics course, and they lack confidence in their data-analysis abilities. There is a clear need for more training. Even with the right resources, it is hard to find sufficient time to get teachers up to speed with statistical thinking and the corresponding technology.

Finally, “data science” requires a computational tool, and it is still not clear what the tool should be. The argument can be made for TinkerPlots or R within RStudio, but counterarguments are easy to come up with for either tool. In particular, the ease-of-learning/flexibility-of-use tradeoff is very clear.

(2) Opportunities
One project attempting to answer these challenges is Mobilize, an NSF grant-supported program I am involved with. Mobilize has produced a variety of curricula at the high-school level, including a six-week data analysis unit for use within a computer science class; two shorter units that can be added into Algebra I and Biology; and (our newest offering) a yearlong introduction to data science course. Over the years, we have offered professional development to hundreds of high-school teachers, and the experience of iterating through teaching methods and statistical programming tools has motivated me to look for better technological solutions.

I believe a next generation of statistical programming tools (likely, blocks-programming—based with textual code layered below) will emerge in the next five years. Of the tools currently available, I am closely watching the development of projects that are pushing the boundaries for integration of text, code, and reproducible output (such as Jupyter and RMarkdown) and those that make it easier to generate data visualizations, whether static (Lyra) or interactive (Shiny).

At this point, these tools are not appropriate for novices, but are making it possible for proficient programmers to create “microworlds” (to borrow a term) that learners can explore.

Alison Gibbs and Bethany White
University of Toronto and University of Western Ontario

Many of the major challenges for teaching statistics in Canadian secondary schools are universal. Statistics is scattered throughout the mathematics curricula, competing with mathematics topics and ultimately limiting the progression toward inferential reasoning. The greatest barrier for statistics in secondary education in Canada is limited teacher preparation. It is not uncommon for programs not to include a statistics course at all, let alone one on how to teach statistics.

An added complication is that curricula are under the purview of provincial governments. The tremendous variation across provinces makes it difficult to develop “one-size-fits-all” teacher training programs in statistics education. How can teachers teach statistics effectively without a foundation in statistics and an awareness of common misconceptions?

Historically, Canada’s national statistics agency (Statistics Canada) was the Canadian leader in supporting statistics education in schools (Townsend, 2011). Statistics Canada’s Education Outreach group had a mandate to develop statistical literacy. During its 15 years of operation, it developed a wealth of online resources (including the Canadian Census At School project), and resource teachers were available to support statistics learning in schools. Sadly, this program was disbanded in 2012, shortly after the misguided federal decision to replace the mandatory long-form census with a voluntary survey.

Rich sources of data and excellent programming relevant to teaching statistics in secondary schools are available online. The flexible nature of online formats increases the accessibility of these resources. Because these are not tailored to specific provincial mathematics curricula, though, there is an enormous opportunity for partnerships between teachers and local statistics faculty. Statisticians can work with teachers to design activities to progress their students beyond creating basic descriptive statistics.

There has been some progress. For instance, the Canadian Census at School program is now operated by volunteer members of the Statistical Society of Canada, so it remains a rich opportunity to embed statistics into classes in a way that’s relevant to students. We’ve also seen innovative examples of how complex statistical concepts can be introduced at appropriate levels; for example, the R Tricks project and a recent project exposing students to Big Data questions in an offshoot of the 2015 Fields Institute Thematic Program on Statistical Inference, Learning, and Models for Big Data.

We still have work to do, though. To really advance K–12 statistics education in Canada, statisticians must take a prominent role in teacher training, the development of statistics classroom activities, and decisions about curricula.

Further Reading
Townsend, M. 2011. The national statistical agency as educator. Statistical Journal of the IAOS 27:129-136.

Chris Wild and Maxine Pfannkuch
University of Auckland, New Zealand

(1) Barriers and Threats
There has never been a bigger buzz about data, the power of data, and the usefulness of people who can extract nuggets of insight from data than there is right now. Ironically, at this very time of explosive growth, the biggest long-term threat to statistics in secondary education is the erosion of its relevance due to narrow, historically entrenched notions of what it can and should do. In the U.S., even the AP Statistics flagship has been leapfrogged in expansiveness of data vision by the newly minted AP Computer Science Principles course.

The biggest barrier is the pitifully small market share statistics gets in the curricula of almost all countries. It is not getting the exposure deserved by the benefits it can bring to society and the future lives of students. Historical market capture by others has crowded us out and, as they say, possession is nine-tenths of the law. Other barriers are a lack of teachers who were educated in statistics at college and university and inadequate professional development to help them “up-skill” and modernize.

Then there are inertial, attitudinal barriers. With statistics education needing to expand its scope, we prioritize by considering what machines can do versus the thinking that is inherently human. Anything that is purely procedural can be taken over by computers; the subject needs to become much more conceptual with much more focus on bigger pictures. We have to wean ourselves off our heavy concentration on soon-forgotten procedural details.

Conceptual approaches also require that students write. Math teachers “didn’t sign up” to teach how to write and mark “essays.” Math teachers’ and students’ extreme discomfort with uncertainty and ambiguity is another barrier. This becomes insidious in the attitudes where “easy to teach” and “easy to assess” gets to trump “actually worth learning.”

Then there is an attitude that teachers cannot teach things they did not themselves learn in college or university. Its corollary is, “teachers can’t learn to teach new things.” This is paralyzing, and more so since most university study in statistics has not actually prepared people to teach modern data-driven, conceptual approaches to statistics. Also paralyzing is the attitude that says we cannot start change until everything has been worked out and is in place. In some arcadian Neverland, this might be ideal but, in the real world, resources for development do not begin to flow and new textbooks do not begin being written until we are staring down the barrel at changes that will hit us “tomorrow.”

All of these things can conspire to have us still teaching 1950s statistics in the 2050s, albeit to dramatically shrunken numbers as other disciplines expand to fill the data void and become the go-to disciplines for turning data into insight.

(2) Opportunities
Data are currently seen as exciting and valuable, and the people who know how to gain value from it are highly sought after. There has never been a better time for getting attention and market share for teaching modern, accessible, data-centric statistics.

Statistics education has an opportunity to help students come to a much broader appreciation of what data is and what it can do for them and society. It has an opportunity to help students to make better sense of their world using data, to be not-easily-misled, and to prepare for a burgeoning job market. It has an opportunity to harness the power of visualization to greatly enhance the statistical understanding of a much wider spectrum of society. It has an opportunity to harness computational power to finesse away tedium, unnecessary difficulties, and mindless procedural busywork so we can concentrate on turning data into insights. Modern approaches to statistics give math teachers an opportunity to teach an area that is not only important but also palpably real and palpably relevant.

Our teachers are perceptive citizens of a fast-changing world where they expect rapid technological advance to continue to profoundly affect the way people work and live. They do want to prepare their students for this world. They do want to make a difference. When given license to break free of rigid historical shackles, many are incredibly creative and incredibly innovative in response to new challenges.

Let’s trust in the capabilities of our teachers to learn new things, seize the opportunities, and break down the barriers, casting those barriers aside to advance into a brave new world.

Long live the data revolution!

Dick De Veaux and Paul Velleman
Williams College and Cornell University

Kelly is proud to land a summer internship right after graduation from high school. Her boss, noting the 5 on her AP Statistics test, asks her to look into the factors associated with customers who leave in favor of competitors. He has a database of about 3 million customers with demographic, sales history, and personal data. Kelly reaches for her TI-83, but soon realizes that, even with the data connector, her calculator is the wrong tool. She remembers how to test the difference between two groups and something about regression, but there are so many variables here, not just the two she worked with in class.

(1) Barriers and Threats
The course that we have been teaching is rapidly becoming irrelevant. Most of our students will not be statisticians, so we hope to teach them to think statistically. But how do statisticians think? One important component is that we deal with several—sometimes many—variables at once, and we use computers to deal with large amounts of data. Yet, after a full year, AP students have hardly been exposed to any analyses with more than two variables or a few hundred cases.

We are told that it isn’t practical or affordable for statistics classes to use computers, but the fastest-growing AP course last year was Computer Science, where students work regularly on computers.

(2) Opportunities
There is no reason to link the AP Statistics course to a particular piece of outdated technology. The AP Computer Science and the future Computer Principles courses use … computers. Open-source statistical software is readily available and becoming increasingly easy to use and master. Students who lack access to computers can at least learn to read and understand output from common statistics software.

The main impediment to implementing changes to the AP Statistics course is that most of the teachers have never actually done a statistical analysis and, thus, prefer to emphasize the small sample, computational, and probabilistic topics in the curriculum rather than statistical modeling. Let’s free the AP course from its technological and probabilistic shackles and rethink a course in statistical thinking and modeling better suited for the 21st century.

Donna LaLonde
American Statistical Association

(1) Threats and Barriers
The 2010 Elementary and Secondary Education Act Reauthorization stated: “The goal for America’s educational system is clear: Every student should graduate from high school ready for college or a career.”

The lack of consensus on both the intellectual content and accurate assessment of “readiness” is a barrier. Regardless of how readiness is defined, teachers must be equipped with the resources to create student-centered learning environments.

It is risky to endeavor to teach new content in new ways. We need to be willing to commit resources to a thoughtful and sustained effort of professional learning. This will require a substantive, ongoing commitment to professional learning communities, as well as access to the tools and technology required to design and implement active learning.

(2) Opportunities
Public schools across the country have developed “one-to-one” initiatives or “bring your own device” initiatives to provide access to technology. This is an opportunity as long as access isn’t confused with innovation. Models such as Substitution Augmentation Modification Redefinition (SAMR) that challenge us to think critically and creatively about our content and pedagogy in a technology-rich environment hold great promise.

As we continue to make progress in overcoming the access barrier, we need to be focused on developing and supporting resources for effective teaching. Well-organized and continually curated repositories will be effective in supporting professional learning, if we are able to encourage collaboration. This will require a commitment to nurturing the teacher network so professional community is not confined to physical location.

Further Reading
Elementary and Secondary Education Act Reauthorization. 2010.
Substitution Augmentation Modification Redefinition.

George W. Cobb
Mount Holyoke College

I could easily spend some of the meager 400 words allotted me by complaining, or alternatively, I-could-try-to-deceive-the-word-count-software-by-eliminating-the-spaces-between-my-words, but instead I’ll squander a sentence on self-justification: To stay within prescribed limits, I’ve resorted to what our colleague Edward Tufte has justifiably condemned as The Cognitive Style of PowerPoint (2006) … Next slide, please …

Curricular lineage. As my former Dean Don O’Shea used to say, liberal arts colleges are the places where research from universities is first brought into the undergraduate curriculum. I suggest in addition that, as the upper-division college curriculum changes to reflect the cutting edge, the introductory course changes, albeit more slowly, and secondary-school courses tend to follow.

Changes in practice. Statistics at the graduate level has been changing rapidly, much more so than mathematics or history. We now have exact inference based on randomization, Bayesian hierarchical models using MCMC, and algorithmic methods that are free from dependence on probability models. Not to mention graphics, diagnostics, and reanalysis.

(1) Barriers and Threats: Supply and Resistance
A short supply of secondary teachers who know the practice of statistics. The accelerating demand for courses in statistics (and its more fashionably named/disguised relatives) outstrips the supply of teachers with firsthand knowledge of contemporary data analysis.

Resistance and residence. Computers have made statistics less dependent on mathematics, and thus less attractive to teachers who, by inclination, training, and experience, think of themselves and their colleagues as mathematicians. We statisticians know that “statistics is not mathematics” but, as our practice evolves, the gap between the two subjects becomes increasingly obvious. Will statistics at the secondary level continue to find an intellectual and institutional home in departments of mathematics?

(2) Opportunities and Strategies: Appeal, Access, and Openness
Broader appeal. Big Data! Bioinformatics! Business analytics! Beneath the veneer of hype, data science can be made broadly relevant and attractive.

Broader accessibility. Computers have made statistics less dependent on mathematics, and so much more broadly accessible to high-school students.

Openness. My experience with high-school teachers has led me to admire their openness to new ways to think about what they do, and their dedication to what is best for their students. All of us who care about statistics, its teaching, and its learning should applaud and support that commitment.

Conclusion: The future looks good.

Katherine Halvorsen
Smith College

The opportunities for exposing students to statistics in primary and in secondary schools may be unlimited. In primary school, as soon as students learn to count, they can start collecting data and learning to display their data on pictographs, bar charts, and line graphs. Later on, in elementary school, when they learn fractions, followed by decimals and percents, they can use circle graphs to display data that describe the parts of a whole.

In middle school, where the Common Core introduces the Statistics and Probability domain, wider opportunities open up. Students learn what distinguishes statistical questions from other kinds of questions, such as deterministic questions and broad research questions. They learn to describe data distributions along with center, shape, and spread. In seventh grade, students learn to draw random samples and why random sampling is important. They compare two populations by comparing the distributions of sample data from each population. In eighth grade, students use scatterplots to display bivariate data and learn to look for trend and outliers. They begin to discuss association between two variables and distinguish association from causation.

In high school, students learn to display categorical data in two-way tables and discuss possible association or trend. High-school statistics emphasizes linear models for quantitative data and discusses interpretation of the slope and intercept. Students also learn to distinguish experimental studies from sample surveys and other observational studies, and they learn how randomization is used in each type of study. They also discuss what types of conclusions can be drawn from each kind of study. They begin to address questions of inference and learn about confidence intervals for means and for proportions. They see statistical tests in the form of randomization tests.

It is important to note that the Common Core is intended for all students, not just the college preparatory group. The pre-college curriculum includes most of the topics taught in the AP Statistics syllabus that is now taught in many high schools and that is modeled on the standard introductory college statistics course. For states and for schools across the country, the introduction of statistics into the elementary and secondary curriculum means a large investment in teacher training and new technology and textbooks.

In spite of the hurdles to be overcome, this new curriculum offers great opportunities for collaboration among science, social studies, and math teachers to introduce statistical thinking; even data collection and analysis in many areas of study beyond the mathematics classroom.

Sandra R. Madden
University of Massachusetts, Amherst

(1) Barriers and Threats
The two greatest threats are a) misguided curriculum expectations and materials, and b) teachers without a strong understanding of statistical big ideas. The Common Core State Standards for Mathematics (CCSSM) have essentially stripped statistics from the pre-K–5 curriculum. Against the ASA’s advice that students should begin to experience formulating statistical questions; designing ways to collect, analyze, represent; and interpret data to answer the questions with emphasis on the development of informal inferential reasoning, the CCSSM postpones statistical exploration until grade 6 and then crams statistical content into an already-crowded mathematical curriculum. Given that statistical ideas develop through experience over time, this undermines optimal development for students, nearly guaranteeing a superficial student experience involving emphasis on procedures over conceptual understanding and statistical reasoning.

Most secondary mathematics teachers have minimal preparation for teaching statistics, with few opportunities to learn about how to support statistical learning. When their own learning has been dominated by procedural and theoretical exercises at the expense of experiencing the wonder of asking important questions and engaging in a statistical process, teachers lack the foundation and rely on their frequently lackluster textbooks, typically devoid of opportunities for statistical inquiry.

The Advanced Placement (AP) curriculum is dominated by techniques and procedures that should be given new life, particularly to include randomization testing. There is a dramatic difference between calculating and comparing means from two groups versus coming to understand the behavior of differences of measures of centers as empirical sampling distributions during randomization testing. Curricular experiences for most have concentrated on the former at the expense of the latter. Teachers and their students should be invited into the powerful and magical world of statistical exploration. This includes use of tools to support investigations that are worthy of their time and curiosity.

(2) Opportunities
Supporting teachers to develop facility with new statistical modeling and reasoning tools takes time, but is essential at all levels. Simulation and resampling methods and resampling approaches can be accessible to teachers and students when tasks, tools, and learning environments are carefully designed.

Learners benefit most when they construct the technological models they are exploring, rather than sliding virtual variables in models constructed by someone else. It is demystifying to build and explore a working model of a phenomenon and often leads to conceptual insights not within the view of the learner when exploring a pre-existing model.

Dynamic technology scaffolding (DTS) is a curriculum design principle that supports learners’ facility with tools while simultaneously supporting their statistical development. Through a sequence of experiences, the learner engages with physical modeling of a phenomenon, then explores a pre-existing model of the phenomenon, and finally constructs their own working model.

Learners become statistically empowered as their facility with learning tools grows. They begin to pose and explore their own questions, rather than waiting for a teacher or textbook to direct them. Tools that can be adapted to students’ constructions pay enormous dividends over time. When learners express their understanding through the use of a tool, their knowledge of the content and the tool become visible. Building the capacity of more knowledgeable others is at the heart of our most pressing need and greatest promise.

Sharon Hessney
Mass Insight Education

(1) Barriers and Threats
The greatest barriers to high-school statistics are students, teachers, and curriculum/assessment writers thinking that computing statistics is statistics. We statisticians know that statistics is the understanding of data in context. Context requires gathering data and analyzing data appropriately.

We statisticians know that this requires experience with critical thinking in many contexts. Although secondary teachers and students experience with computation, they need to learn to experience data in context. Shifting the focus of statistics will encounter three barriers: time, funding, and a desire to think quantitatively differently.

All of that will need a changing force to grab the limited education resources there are for each of these.

(2) Opportunities
The most promising opportunities in statistics are the relatively easy-to-use statistical software packages that can be used on many devices, not just computers. From calculating means to performing randomization tests, for example, software can reduce the time spent on calculation and increase the time spent on understanding how statistics “work” Software allows us to explore the statistical “forest” rather than thinking the computation “tree” in front of us is all there is.

Training teachers to use this software and obtaining the funds to provide the software and platforms are barriers to broad integration of software into the statistics curriculum.

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