I chose to read the book Flatland, by Edwin A. Abbott for use in future geometry classes. The book is somewhat of a timeless classic in its content and readability. The main character, A. Mathematician, tells the story of his life in Flatland. He describes the people who live in his country, including lines (women), isosceles triangles (soldiers and lowest class workmen), equilateral triangles (middle class men), squares and pentagons (professional men and gentlemen), hexagons and heptagons (nobility), and circles ("priests" of the highest rank of all). A. Mathematician also describes what everyone "sees" in this two-dimensional world. Later on in the book he is introduced to the idea of a third dimension that is beyond the comprehension of anyone who resides in Flatland. The entire plot of the book may be interpreted at different levels. Beyond the obvious geometric lessons being taught to the reader, there are ranks and classes of people and politics behind the interactions of the Flatlanders. There is also a fair amount of belittling of women and the lowest ranking isosceles triangles, which reminded me almost of the 1920's time period.

Edwin A. Abbott, a scholar, educator, theologian and author, was born in London in 1838. He attended "...St. John’s College in Cambridge, where he was elected a fellow at the age of twenty-three. After two years as Assistant Master of the King Edward School in Birmingham, he was appointed headmaster of the City of London School, a prestigious educational posting" (p. 10). He held that position for 33 years. After retiring from that job, he authored several other books before his death in 1926. The preface to the book also states "Flatland may well be Abbott’s attempt to make the Supernatural credible (if not exactly explainable in any strict sense) as a kind of higher-dimensional influence." I think that Abbott tries to rationalize the Supernatural and does so allegorically in this novel. He speaks of what life he knows in English Victorian culture. Abbott succeeded in both instructing and amusing the reader on every page of the novel and always keeps the reader thinking, wondering and learning.

Abbott, Edwin A. (1984) Flatland: A Romance of Many Dimensions. New York:

Penguin Books USA Inc.

I heard about the book from a few friends of mine and they didn’t seem to have too favorable of opinions on it. However, after reading the back cover to find out what it was about, I decided to read Flatland and see for myself. I actually enjoyed it more than I initially thought I would. There was some mild humor in the book, and it was very easy to follow. It required minimal geometric knowledge, so almost anyone could really read the book. Some of the book I took more personally, and I think it’s just because I’m female and respond emotionally to a lot of what I read. Not to sound like a feminist, but I didn’t like how women were depicted in the book, anywhere from where they should "wiggle their posteriors" because they were lines that otherwise wouldn’t be seen easily by all to their low rank in the caste system and how they are treated because of this.

I definitely saw the book representing more than just geometric figures and took more than one meaning from the book upon completion. It was as if these shapes were actual people who could be compared to the society in which we live.

This book would definitely fit best into the high school geometry curriculum. I think that it would work well because the language is pretty simple and the book is relatively short. And there are chapters that could be omitted without losing the overall theme of the book. It really would work on student’s spatial thinking and geometric analysis. It gives students something to think about and sample manipulatives could be very easily incorporated by the teacher to go along with the reading. The unit I would use this novel with would be one relating to shapes, both two- and three-dimensional, what cross-sections look like and things of that nature. There really wasn’t anything that would be inappropriate for high school age students to read. I think that some portions of the book do classify things and make generalizations about groups, and I think that that goes along with judging people in various "groups" at school without knowing anything about them besides their affiliation. So in that aspect, I question the novel, but we could discuss this issue in class and attempt to look beyond it in our reading of the novel.

I would expect all students to participate in each of the following activities. However, if after I collected assignments, I considered there to be room for improvement, I would return it to the student with some suggestions for corrections and ask the student to resubmit the assignment. Students would also be responsible for keeping track of all of these items. Small groups will then submit a portfolio at the end of the unit containing all group work and all members’ individual work as well. I would encourage students to discuss activities with one another to increase understanding and for new and different ideas, yet each must submit an original where appropriate. Copying will not be tolerated.

• Write a paper discussing your understanding of what two-dimensional and three-dimensional space means. Give examples for each. Also, discuss what it would be like to live in a two-dimensional world instead of in three-dimensions.

• Read aloud selected chapters in class.
• Chapter 1--Of the Nature of Flatland
• Chapter 2--Of the Climate and Houses in Flatland
• Chapter 3--Concerning the Inhabitants of Flatland
• Chapter 5--Of our Methods in Recognizing one another
• Chapter 6--Of Recognition by Sight
• Chapter 16--How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland
• Chapter 17--How the Sphere, having in vain tried words, resorted to deeds
• Chapter 18--How I came to Spaceland and what I saw there

• After reading chapter 3, students will work in small groups that the teacher will select. In these groups, students will use Play Dough to create models to represent the characters of the book Flatland. We may then use them as reference in our continued reading and in discussing cross-sections as well. We will see what Flatlanders look like and also Spacelanders.

• Upon completion of chapter 10, we will have been introduced to a few ways in which Flatlanders may identify one another in their daily encounters. Students are to compile a list with brief explanations describing other possible means that may be used in recognizing fellow citizens of Flatland. There is a minimum of five items on any given list. Students may work alone or with one other partner.

• During one class period, anytime after reading chapter 12, reflect on the reading thus far and consider where some of the gaps in the author’s explanations of daily life lie (i.e. "things" existing in this Flatland where three dimensions would be necessary). Write a brief jot list on your own for 10 minutes and then collaborate with three or four other students nearby and share your ideas. We will then discuss this as a whole class and compile one large list.

• If you were A. Mathematician, a resident of Flatland, how would you describe three dimensions to family and friends (who are also Flatlanders)? Begin a list after completing chapter 12 and have the teacher ok it. Make some additions to the same list after reading through chapter 19. What additions or changes did you make? Again, this will begin as an individual project. Then students will collaborate and share their ideas. Finally will discuss these ideas as a whole class.

• Write a new ending to the book. Begin from the point where A. Mathematician returns to Flatland from his adventures with the sphere in Spaceland.

• Write a one-page reaction to the story. Did you like the story? Was the story easy to follow? Could you identify with any of the characters or identify them with someone else? This is by no means an all-inclusive list of what should be included in this reaction, but merely some ideas to get you thinking.

• Create one edition of a weekly newsletter or newspaper that residents of Flatland read regularly. For instance, in Wisconsin we read the Stevens Point Journal or the Milwaukee Journal Sentinal. What kind of information do we obtain from these daily papers? You may take basic story topics from these to keep the Flatlanders informed of the news in their land. Include at least five of the following: news, weather, entertainment, sports, self-improvement, editorials, real estate, and classified advertisements.

• Draw an aerial view of a small portion of Flatland. Include floor plans of home, streets, people and where they are, etc. Pay special attention to the drawings so that all your figures are regular, as all Flatlanders are and that they are similar to what Abbott had described in his book.

This project flowed very smoothly and quickly. The book was relatively easy-reading, so I was able to finish that up in a weekend. Once I had finished it, the ideas just flowed as to activities that I could have students do with the book. It does relate to math in a lot of ways and I tried to get a mix of mathematics and literacy in the lessons to be done throughout the course of reading the novel. I jotted a few ideas down as I read the book and referred to those and also compiled a brief list of ideas that I had for activities. Then I put these into a list form and expanded on them more in depth in the paper.

Rachel Gruhle