Historical Research: How to Fit Minority and Women’s Studies into Mathematics Class Ask middle school students to name their favorite musicians, athletes, or actors, and they will tell you everything about them: statistics, hair color, who they are married to, where they live, their accomplishments, and more. Students are exposed to celebrities every day through television, movies, radio, and the Internet. Isn’t it time we expose our students to some mathematical heroes? Margaret R. Sáraco, [email protected] .nj.us, teaches sixth-, seventh-, and eighthgrade mathematics at Mount Hebron Middle School in Montclair, New Jersey. She is interested in helping students discover real-world applications of mathematics. 70 The Heroes and Heroines of Mathematics In February and March, educators teach history lessons on African Americans and women in our various subject areas, which take the form of PowerPoint presentations and discussions. However, there is little opportunity for students to research these important historical figures, because of all the material that teachers are expected to cover and skills that the students are expected to learn during the school year. It is impossible to add one more Mathematics Teaching in the Middle School ● Vol. 14, No. 2, September 2008 Copyright © 2008 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM. item to our agendas. Or is it? I would argue that students should not learn mathematics in a vacuum. In every other subject in their middle school studieslanguage arts, social studies, science, art, and music—students study the people who made and make significant contributions to the field. However, I was not surprised when I asked my students to name some mathematicians from history; they had difficulty coming up with five names. And of those five mathematicians named, none were female or minority. If students can find themselves reflected in the pages of history, they may be inspired to pursue a career in mathematics. By researching men and women who have made contributions to the field of mathematics, our young scholars may find a role model. In so doing, we may be able to stem the tide of the shrinking number of students entering the field of mathematics by helping them become interested in its history. Photographs by Alex Polner and Margaret R. Sáraco; all rights reserved a Margaret R. Sáraco Vol. 14, No. 2, September 2008 ● Mathematics Teaching in the Middle School 71 Photographs by Alex Polner and Margaret R. Sáraco; all rights reserved Further, the study of mathematics history is imbedded in our national and state-based mathematics standards. NCTM discusses the importance of reaching across other disciplines in understanding mathematics. Many mathematicians who have become part of the chronicles of history are also scientists, physicians, and business executives, among other professions. NCTM’s Communication and Connections strands and New Jersey’s Mathematical Process strand instruct us to teach our students to recognize recurring themes across mathematical domains; recognize that mathematics is used in a variety of contexts; trace the development of mathematical concepts over time and across cultures; recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and recognize and apply mathematics in contexts outside of mathematics (NCTM 2000; State of New Jersey Department of Education). 72 Getting Started To fit mathematics history into the middle school classroom, I started with an idea and a grant proposal. Through grants made possible by the Montclair Fund for Educational Excellence (MFEE) and the Montclair State University Network for Educational Renewal (MSUNER), history books were made available to students in class. Although it would be difficult to fit additional work into a seventy-minute block in which I see my students every other day, I wanted to create a unit plan that would use minimal time in the classroom but would require more preparation of students and teacher. The unit, titled “Minorities’ and Women’s Presence in Mathematics: A Historical Perspective,” is a yearlong project that can be adapted to many different learning and teaching styles. For instance, I repeat this project annually with my students who loop (students and teachers who move to the next grade level together). Attention to these mathematicians need not be reserved for one month Mathematics Teaching in the Middle School ● Vol. 14, No. 2, September 2008 per school year. The project described here begins in September and continues through May. Students research their mathematician and create oral presentations about one notable individual. Each class hears between fifteen and twenty presentations on different mathematicians, depending on the number of students in class. This is an ideal project for an interdisciplinary unit. Mathematics teachers can team with a social studies teacher because of the historical element or with the language arts teacher because of the writing and researching involved. Science is a natural overlap, because many mathematicians are also scientists. At Mount Hebron Middle School, the Science and Technology magnet school for our district, our students take a technology class as a core subject and have access to a computer lab. For this project, students are required to use the Internet and find at least one online source that is helpful to them, so they are allowed to conduct some research online at school. If these resources are not available at your school, this project can be completed without the online research component. (However, you will probably be satisfying your state’s mathematics and technology requirements by having students work on this project using the Internet.) You can also ask the school media specialist or librarian to help obtain resources for this mathematics project. This staff member can also assist the students, by class or individually, when researching their topics. (This individual may also be a good resource when investigating grant money for future projects.) Setting up the Lesson I begin in September by introducing the project to my students. They pick a number out of a hat to determine the order of their presentations. The due Fig. 1 This rubric sets the parameters for grading. Mathematics History Project Rubric Student’s name ___________________________________ Teacher’s name _______________________________ Category 4 3 2 1 Research subject Student shows a full understanding of his or her research topic. Student shows a good understanding of his or her research topic. Oral presentation Student is completely prepared and has rehearsed the presentation. Student is mostly The student is Student is unprepared. prepared but needs more somewhat prepared, but practice rehearsing. it is clear that rehearsal is lacking. Question and answer Student is able to accurately answer most questions about his or her research topic. Student is able to answer some questions about his or her research topic. Student is able to Student is unable to answer a few questions answer any questions. about his or her research topic. Biographical form Form is complete; contains two citations from book sources and one online source. Form is partially complete; contains two citations from book sources and one online source. Form is partially Form is not complete. complete; contains two or fewer citations from book and online sources. Poster Poster is extremely well Poster is well constructed. constructed. dates and the time-to-begin-research dates are posted on a big calendar by their name. Students choose a mathematician to research from a list of 150 mathematicians generated from book resources compiled for the project. Students are assigned a female or a minority mathematician to research. At first, I was going to limit their research subjects to African American and female mathematicians. However, while doing my own research, I discovered many mathematicians who have been delegated to the outskirts of society based solely on race, ethnicity, or gender, so I widened the search. The challenges I face with a middle school population are (1) the reading difficulty of the material and (2) the level of complexity of the mathematicians’ discoveries or inventions. I sometimes suggest particularly accessible mathematicians to various students. Another approach Student shows some understanding of his or her research topic. Poster is not well constructed. is to assign a research subject and a specific discovery or invention. For example, someone could research Benjamin Banneker and his invention of a wooden clock that ran for fifty years. Each student is required either to submit a one-page written report or complete the Mathematicians Biography Form (see activity sheet 1), according to skill and grade level. The report assignment requires that the bibliography include at least two books and one Web site reference. Students give a five- to ten-minute oral presentation to the class, which includes a brief question and answer session about the mathematician they researched. Additionally, each student produces a poster or other visual aid about their mathematician. A “Famous Mathematicians from History” bulletin board displays all the projects to date. Students are given a rubric designed for this project (see fig. 1). Vol. 14, No. 2, September 2008 ● Student does not show any understanding of his or her topic. Form is not complete. The grade for the project is equivalent to one test grade. Helping Students Research THEIR MATHEMATICIAN To get involved and help students with the research process, create lunch or study groups with several students every month. This is an opportunity to teach them how to help each other and that research can be fun. In addition, five minutes during class or lunch can be reserved for one-on-one conferences on students’ progress. Although this sounds like a lot of time, if different students work on their project throughout the year, and you have 100 students, you will be seeing approximately 10 students each month. Teachers must be knowledgeable about the subjects they are assigning, which requires preparation. Before the school year starts, decide which Mathematics Teaching in the Middle School 73 Fig. 2 Famous women and minority mathematicians ANCIENT WORLD Female Mathematician Hypatia EIGHTEENTH CENTURY Minority Male Mathematician Benjamin Banneker Female Mathematicians Maria Gaetana Agnesi Émilie de Breteuil du Châtelet Sophie Germain Caroline Herschel Mary Fairfax Greig Somerville NINETEENTH CENTURY Minority Male Mathematicians Edward Alexander Bouchet Patrick Francis Healy Kelly Miller James Joseph Sylvester Female Mathematicians Mary Everest Boole Susan Cunningham Ruth Gentry Ellen Amanda Hayes Sofia Kovalevskaya Christine Ladd-Franklin Ada Lovelace Maria Mitchell mathematicians you would like to assign. It could be as few as 20 and as many as 100. Take some time to read about the mathematicians and build your knowledge base. The summer before I began this project, I read numerous biographies, which I enjoyed immensely. Every year that this project takes place, you will have done a lot of the background work. The hardest part of a new lesson is the first year of implementation. If you have little preparation time, try a limited version. When students ask for extra-credit projects, assign them a person from the list of “Famous Minority and Women Mathematicians” (see fig. 2). In addition, for students working on this project who 74 Mary Frances Winston Newson Charlotte Angas Scott Alicia Boole Stott Mary Watson Whitney TWENTIETH CENTURY Minority Male Mathematicians Manuel Berriozábal Albert Turner Bharucha-Reid David Harold Blackwell Elbert Frank Cox Philip Emeagwali Jonathan David Farley Lee Lorch Ronald Elbert Mickens Luna Isaac Mishoe Luis Ortiz-Franco Srinivasa Ramanujan Abdulalim A. Shabazz Richard Tapia William Vélez Jesse Ernest Wilkins Jr. Scott Warner Williams Female Mathematicians Elayne Arrington Lida Kittrell Barrett Dorothy Lewis Bernstein Lenore Blum Marjorie Lee Browne Fan King Chung are looking for extra credit, have a list of other famous mathematicians ready, such as Fibonacci, Ptolemy, Pythagoras, and so on. Save these projects over the summer and post them in the fall; they make wonderful bulletin board displays for September’s Back-toSchool events. the Mathematicians’ Library on Wheels Book Cart The success of this project requires that books be purchased for classroom use. The Resources section at the end of this article lists some books you may want to purchase. Some books contain general information; other books about individual mathematicians are excellent resources for middle school students. Mathematics Teaching in the Middle School ● Vol. 14, No. 2, September 2008 Christine Mann Darden Mary Lovenia Deconge-Watson Etta Zuber Falconer Lillian Moller Gilbreth Meredith Charles Gourdine Evelyn Boyd Granville Euphemia Lofton Haynes Grace Brewster Murray Hopper Fern Hunt Katherine G. Johnson Eleanor Green Dawley Jones Barbara Lee Keyfitz Vivienne Malone-Mayes Cleopatria Martinez Susie Johnson McAfee Shirley Mathis McBay Fanya Montalvo Cathleen Synge Morawetz Caryn Navy Emmy Noether Kathleen Adebola Okikiolu Edna Lee Paisano Theoni Pappas Mina Rees Ida Rhodes Julia Bowman Robinson Myra (and David) Sadker Pauline Sperry Olga Taussky-Todd Anna Johnson Pell Wheeler Grace Chisholm Young However, if your budget is limited, start with these titles. Make sure you include several books to reach students at their particular reading skill level. Once you assemble your book cart, make it available in your room to your students at all times. Although sharing resources with other teachers is preferable, the students are better served if the books and materials are available in your classroom only. When students complete an assignment, they should be able to work on their mathematician from the book cart available in your room. At Mount Hebron, we have regularly scheduled DEAR (Drop Everything and Read) periods; I sometimes offer a book to a student who has forgotten it that day. What a pleasure Student Responses and Results I am thrilled by my students’ investment in the project and their reactions to the mathematicians they present. One question that comes up in every class, regardless of the mathematician’s gender, is this: “Were they married, and did they have any children?” I inquire why they deem that so important. Their response in all classes is that they are not sure if they would have time in their own lives to have a family and produce that kind of work. I have found a few students already imagining what it might be like to be a mathematician. Some students ask about the mathematician’s discoveries and inventions or about how and when he or she died. Many students report on inventions or ideas not often discussed in a middle school mathematics class, such as high-end calculus and Boolean geometry. The students find it interesting even if they cannot understand all of it. It is not uncommon for students to complain to me about the inability to find material on their subject. I use this as an opportunity to discuss how some people have been written out of history and suggest that we can help write them back into history by presenting them to our classmates and posting something about them on our history wall. CONCLUSION As with any undertaking, the hardest part is getting started. This article contains the groundwork to get teachers started. The best lessons I have created or worked with are those that are collaborative, and this project encourages students to work together. RESOURCES Baumgart, John K., Duane E. Deal, Bruce R. Vogeli, and Arthur E. Hallerberg, eds. Historical Topics for the Mathematics Classroom. 2nd ed. Reston, VA: National Council of Teachers of Mathematics, 1989. Grinstein, Louise S., and Paul J. Campbell, eds. Women of Mathematics : A Biobibliographic Sourcebook. New York: Greenwood Press, 1987. Johnson, Art. Famous Problems and Their Mathematicians. Englewood, CO: Teacher Ideas Press, 1999. Morrow, Charlene, and Teri Perl, eds. Notable Women in Mathematics: A Biographical Dictionary. Westport, CT: Greenwood Press, 1998. National Council of Teachers of Mathematics. “Focus Issue: History.” Mathematics Teacher 93 (November 2000). Osen, Lynn M. Women in Mathematics. Cambridge, MA: MIT Press, 1974. Perl, Teri. Math Equals: Biographies of Women Mathematicians + Related Activities. Menlo Park, CA: AddisonWesley Publishing Co., 1978. . Women and Numbers: Lives of Women Mathematicians Plus Discovery Activities. 3rd ed. San Carlos, CA: Wide World Publishing/Tetra, 1997. Reimer, Luetta, and Wilbert Reimer. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians. Palo Alto: CA: Dale Seymour Publications, 1995. . Mathematicians Are People, Too: Stories from the Lives of Great MathVol. 14, No. 2, September 2008 ● Photograph by Alex Polner and Margaret R. Sáraco; all rights reserved it is to see students engrossed in a book about a mathematician. ematicians, Volume 2. Palo Alto: CA: Dale Seymour Publications, 1995. Reimer, Wilbert. Historical Connections in Mathematics: Resources for Using History of Mathematics in the Classroom. Fresno, CA: AIMS Education Foundation, 1992. Smith, Sanderson. Agnesi to Zeno: Over 100 Vignettes from the History of Math. Emeryville, CA: Key Curriculum Press, 1996. Spangenburg, Ray. African Americans in Science, Math, and Invention. New York: Facts On File, 2003. . Kid’s Guide to African American History. New York: Facts On File, 2003. Yount, Lisa. A To Z of Women in Science and Math. New York: Facts On File, 1999. references National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000. State of New Jersey Department of Education. www.state.nj.us/education. Ed. note: If you would like to contact the author about the lesson, ideas for changes, or reactions to implementing it, send an e-mail message to [email protected] montclair.k12.nj.us and write “Historical Research Lesson” in the subject line. l Mathematics Teaching in the Middle School 75 activity sheet Name _____________________________________ Mathematician Biography Form Approach this research as if you were a newspaper reporter. Follow the who, what, when, where, why, and how format to look for important information to share with your classmates. 1. Who is the mathematician that you have been assigned to research? 2. What did he or she do? 3. When did he or she live? 4. Where was he or she born? 5. Where did he or she live? 6. Why has his or her work been important to the field of mathematics? 7. How did he or she make the discoveries? 8. List at least three of the major discoveries or inventions attributed to your mathematician: 9. Choose one of his or her discoveries or inventions from above, and explain the discovery or invention in detail. 10. Why did you choose this discovery to discuss? 11. What did you find interesting about this mathematician’s life or work? from the September 2008 issue of

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