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History of Statistics

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While an introductory statistics class is required for many college degrees, there are varied opinions on its purpose in a program of study. Students may see it as a roadblock impeding their progress toward graduation while others may see it as a way to develop necessary skills to participate fully in society. In the 2016 GAISE College Report, the committee composed of Carver et. al identifies two main purposes for introductory statistics courses: to develop students' statistical literacy and to teach students introductory statistical methods. With an abundance of information and misinformation available, statistical literacy is the ability to interpret and evaluate statistical information presented in the plethora of contexts encountered in everyday life. Those who take introductory statistics to gain prerequisite skills for careers in specific fields should gain an understanding of not only how to use statistical tools, but also in which context each tool is applicable. In either case, context is vital to the usability of content from an introductory statistics course. Among strategies for emphasizing context is to use the history of statistical topics within the course.

While many have agreed that history should be included in statistics education, there is less of a consensus about how history should be included. According to Dennis (2000), teachers should not simply include a biography of the statistician, which may leave out key details for connecting the history to the content. Instead, the story should lead to a specific result that supports learning outcomes. There are textbooks which include little to no history, and others whose contents are significantly made up of history. Some textbooks simply include biographies at the beginning of chapters, and others cover history as stand-alone chapters. Part of the discrepancy among method ideas is caused by limited research in statistics education, no doubt owing to the relatively short history of statistics as a discipline. Ben-Zvi and Garfield (2008) describe the development of statistics education research starting in 1944 when the American Statistical Association started the Section on Training of Statisticians which became the Section on Statistical Education 29 years later. As late as the 1970's, resources began to be developed to aid statistics teachers in engaging and interesting their students.

Because of the recent emergence of statistics education as a discipline, referring to mathematics education research can provide useful support. According to Karaduman (2010), including the history of topics covered in a math class helps students to know that math is not a finished process. It helps connect math to other disciplines and improves students' attitudes toward math. It also helps to include multiple cultures' contributions in addition to those of well-known and ordinary people. Bidwell (1993) compares teaching math to bringing students to an island where students stay for an hour before returning to the rest of their day. When it is so isolated, students fail to see its value. Using history can help students make connections and humanize math. Understanding the history of math explains many of the whys about procedure, notation, or other conventions.

dice on a book

Several studies have been conducted to attempt to understand the influence of history on math education, many of which study affective outcomes (see Lim and Chapman, 2015). Some of the previous studies were limited by allowing students to opt-in or had a limited sample size. Any change in attitude would be hard to determine if it is due to using history, or simply because it is a new approach. Lim and Chapman conducted a study which relied on a main lecture where all groups were present, and then split up into four groups for tutorial lessons outside of lecture where two were taught historical topics that matched up with the topics discussed in the main lecture. The classes taught using history would include biographies of related mathematicians, historical motivations for topic development, and historical problems and solutions to fit the topic curriculum (2015, p. 196). Researchers found a significant difference between the control and experimental classes at the midpoint of the study showing that those in the class using history were better able to understand the reason for their behavior within the classroom, but this difference was not significant at the posttest. The results concluded that the difference in mathematics achievement was statistically significant between the two groups not only in the middle of the study but also at the end. They indicate that more research should be done to determine a significant difference in attitudes between groups using history and those without.

Katz (1986) used the history of mathematics to motivate and excite students (p. 13). He found that much of the historical information could be easily incorporated into mathematics the way it was typically taught, but some topics required reshaping before including history. While using history required more work, he found that this change was valuable. A historical lens allows students to master skills and connect mathematical subjects with aspects of society. History can show the tools that great mathematicians had at their disposal to make their discoveries, or how later work reinforced earlier theorems (for example, Pascal's triangle supports the idea of combinations). He writes that a historical point of view not only, help[s] the student understand the development of the subject, but it also provides him with ways to connect mathematics and other aspects of civilization as he masters the skills necessary to apply the techniques on his own (p. 19).

From research about the use of history in math classes, we see suggestions that are also applicable in an introductory statistics class. Bidwell (1993) discusses ways to use history. One is through anecdotal display, meaning displaying pictures of famous mathematicians or calendars with their birthdays. Another way is to inject anecdotal material as the course is presented. This means that the teacher interjects biographies and historical contexts as they teach new material. The Mathematical Association Committee report of 1919 recommends this approach, including having their portraits hanging on the walls and some explanation being given of the effect of mathematical discoveries on the progress of civilization (Fauvel, 1991, p. 3). While this may not answer, When am I ever going to use this? it answers a related question, When would someone ever use this?. Seeing the usefulness of statistics can help improve student attitudes and motivation.

MiamiClassroom

Bidwell's third suggestion is to organize the course material in the same order it was discovered in history, including the discovery process in the course content. As suggested by reshaping the structure of scope and sequence in a math class, some advocate for using history as a backbone structure of a course. Perkins (1995) argues for such a need, quoting Freudenthal (1983) who asserted that any failure in math education is from not realizing that young people have to start somewhere in the past of mankind and somehow repeat the learning process of mankind (pp. 61-62). Those in favor of using the history of math as a backbone argue that students should be taught the same things in the order that they were discovered. Those against say that it would waste too much time in the dead ends mathematics has taken in the past. They argue that there is no reason to spend so much time on processes that didn't work. Their picture of the ideal sequence of topics is to follow logically, where teachers begin with the basics and then build ideas from there without referring to the sequence. One of the issues with this, however, is determining what the basics are. Perkins (1995) does not advocate that all topics in math should follow exactly how they were studied in history, including all dead ends, but that education should follow history, while limiting the sequence using what we know now. Not only can the students benefit from learning the history of math, but Perkins explains that history teaches teachers about what to expect from their students: primitive stages, roundabout ways of approaching ideas, valuing errors, and to be patient (p. 68).

To avoid spending any extra time covering the history of math or an overload of content, Fried (2008) suggests replacing examples commonly used with historical examples, showing the real context of when the idea was first applied, thinking of the history as something to be used rather than studied. When choosing which aspects of history to include, Fried opines that students should observe that mathematics is a creative endeavor, more than just solving problems and understanding mathematical proofs.

Fauvel (1991) gives guidelines for using history in a mathematics classroom quoting G. Heppel in an 1893 talk: (1) The history of mathematics should be strictly auxiliary and subordinate to mathematical teaching. (2) Only those portions should be dealt with which are of real assistance to the learner. (3) It is not to be made a subject of examination (Fauvel, 1991, p. 6). He also compiled a list of ways that history can be included:

Mention past mathematicians anecdotally

Provide historical introductions to concepts which are new to pupils

Encourage pupils to understand the historical problems to which the concepts they are learning are answers

Give history of mathematics lessons

Devise classroom or homework exercises using mathematical texts from the past

Direct dramatic activity which reflects mathematical interaction

Encourage the creation of poster displays or other projects with a historical theme

Setting projects about local mathematical activity in the past

Using critical examples from the past to illustrate techniques or methods

Explore past misconceptions/errors/alternative views to help in understanding and resolving difficulties for today's learners

Devise the pedagogical approach to a topic in sympathy with its historical development

Devise the ordering and structuring of topics within the syllabus on historically-informed grounds (Fauvel, 1991, p. 5)

Some of these ideas have been researched in other studies. Brükler (2003) wrote about using history to help students have a more positive attitude of mathematics, specifically focusing on using anecdotes. She states that one reason anecdotes and quotes are effective is because students are not required to memorize them. She writes Through biographies and anecdotes one can also show that math is not dry and mathematicians are human beings with emotions and normal (or if not exactly normal, then certainly not generally dull) lives (p. 37). She suggests using these as introductions for topics. Included in anecdotes of mathematicians are quotes, many of which emphasize the importance of asking questions and that the answers often don't come easily or right away. Brükler also touches on giving history of mathematics lessons by explaining, in schools we use history of mathematics, and other more or less popular mathematics, chiefly as motivation for a topic or as a help for understanding it, while in the general popularisation the point is less to teach some real mathematics, but more to change the attitude towards mathematics (2003, p. 41).

In his dissertation written in 2000, Marshall referenced the same list above provided by Fauvel. The project used 55 problems based in mathematics history in teaching and found that this improved students' attitudes toward math and reduced math anxiety.

Katz and Michalowiz (2020) created modules for teaching math that use historical information and interaction. One of the opening activities includes a short play to engage students in a read aloud. Students get an introduction to Archimedes and then proceed to do activities related to discoveries attributed to Archimedes. There are similar important figures in the development of statistics whose information is more reliable than mathematical pioneers because their lives were more recent and better documented. Following their contributions can provide students insight into how certain ideas and methods were developed and under what circumstances.

Archimedes, printer's sample for the World's Inventors souvenir album (A25) for Allen & Ginter Cigarettes MET DP838812

As many of the available resources focus on teaching math rather than statistics, the concern among instructors is that it takes a long time for instructors to research the history of each topic taught in class and decide how to incorporate it in the lesson. TRIUMPHS, by the Digital Commons at Ursinus College, is one resource that has some lesson plans including the history of very specific topics. However, there are very few lesson plans published so far, such as topics on data visualization, linear regression, and p-values. Each topic needs to be researched individually, which increases the preparation time needed to include the history of topics as they are taught.

The research on this website offers resources to aid in including the history of statistics within any introductory statistics classroom. This website includes brief histories of major topics and discoveries in the introductory statistics curriculum as well as historical problems that have often inspired the development of statistical ideas and methods prevalent today.