Flatland Math Project

Group Members: Vincent, Donna & Mandeep

Part 1:  Trying Out the Project

Donna and Vincent were both very interested in trying out this project.  Both of them probably ended up spending more time than Susan suggested they do.  It was interesting to see how visually and conceptually different their end products were from each other. 

Vincent found that it was necessary to read the first half of Flatland in order to understand the general concepts behind the story (such as how Flatlanders “see”).  But he found this first half of the book very dry and not very entertaining to read.  He enjoyed the second part of the book, which told the story.  He found that watching the 30 minute Flatland movie partway through reading the first half of the book helped re-energize his interest in finishing the book.  Vincent thought mostly about how to draw the comic in a way that would convey the story of Flatland to the audience as efficiently as possible.  He concentrated on telling a story in a minimal way that would visually convey the concept of dimensions.  He had a few false starts before he starting drawing a comic that he found satisfying.  He settled on simple black and white line drawings with minimal words.

Donna thought that watching a math movie and reading a math story was in itself a very interesting task.  She was very curious and did not know what to expect.  The book, the film and the movie each had slight variations that became topics of discussion.  Creating a comic strip forced her to really think about the concepts, often going back to the book for reference.  She really enjoyed using colors and shapes, and if anything, spent too much time on the production since it was addicting.  Her comic was created on a computer and she spent a significant amount of time on the visual details of her comic. 

The fact that these two comics turned out so differently demonstrate that students will focus on the different parts that are of interest to them.  We both felt this was an educational experience that students will enjoy.

Vincent's comic is located here: 

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B_WqVw36Np6_ZWUwYjYzNTgtNmY4OS00MGE2LWEyYWUtODQ2YzlkNmQ0OWE3&hl=en&authkey=CIfHqNkO

Donna's comic is located here: 

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B_WqVw36Np6_ZDJhZDJiNDktYzZlZi00NmIxLTg5ZjItYjk0ZmJjODM5Y2U1&hl=en&authkey=CMbM6dcD

Part 2: Looking at the Project with “Teachers’ Eyes”

The strengths of this project are that this is an enrichment assignment which allows students to develop a deeper understanding of geometric shapes and projections.  Having to create a comic telling the story of Flatland gives students the opportunity to apply their understanding of the book and the mathematical concepts discussed in it in a creative manner.  This project also enables students to take part in an inventive hands-on activity that the visual and artistically inclined students in the class will appreciate.   Reading the story of Flatland is also beneficial because it illustrates to students how fascinating and intriguing mathematics can be and encourages them to be imaginative and enquiring about the world and the math around us (ie, could there exist a fourth dimension and if it does, what would it look like?)  It also provides students with an alternative way of looking and comprehending geometric shapes (ie, a circle as a polygon with an infinite number of sides.)

The weaknesses of the project include having the possibility that students may spend too much time coming up with a comic strip and not concentrate enough on the mathematical aspect of this project.  Some constraints within the context of the classroom include there being is a lot of reading required for this assignment and some students may not have strong reading skills and thus may require a lot of time to finish the readings.  This may put pressure on the time constraints for this project.  The first half of Flatland is also very heavy with explanations which may make it difficult for some students (especially ESL and some LD students) to understand the novel and if they’re unable to comprehend the math topics discussed in the book, they will not gain anything from this activity.  Another issue with this project may be that some people (the girls in particular) may take offense at the sexism presented in the novel.  Getting a class set of the books may also be a problem in some schools.

The ways to adapt this project to try to overcome these weaknesses include having emphasis placed on the fact that this is a math (and not an art) project, so it will be mathematical content and understanding (not drawing skills) that will be assessed with this project.  Some strategies to deal with the time constraints of this project include having students read only Flatland for this assignment and, only if necessary, specific parts of Flatterland, Sphereland and/or the Scientific American article on the “planisphere,” with the teacher specifying which parts to read.  There is enough new mathematical material and concepts for students to learn and absorb just from reading Flatland; however, the projects that follow up with readings from these other books could be given bonus marks though.  To deal with the explanation-heavy first half of Flatland, there could be class/group discussions of the readings in class.  Also the project could be adapted to include the viewing of the Flatland movie and film (either during or outside of class) to help reinforce students’ understanding of the mathematical concepts (like dimensions) that are presented in the book.  There could also be a disclaimer before beginning the book and/or discussions while reading the book about the sexism presented in the novel so that students are prepared for it and not taken by surprise.  The teacher could also contact public libraries to try to obtain copies of Flatland if there is not a class set available.

Some ways to modify the project include:

•   Getting the class to write out and then perform a play and/or small skit about the story of Flatland
• Having the class divided into small groups and then having each group make their own movie about Flatland
• Allowing students to use computer graphics and/or photographs of common items and props to come up their comic strip about Flatland
• Having students use a simple, free programming environment of Scratch to create the 2D characters described in the story

Part 3: New Project Idea

Flatland Project – Personifying Shapes

Published by Edwin A. Abbott in 1884, Flatland:  A Romance of Many Dimensions is a satirical novella that tells the story of a world with only two dimensions. The inhabitants of Flatland are shapes, all with interesting characteristics and personalities.  Several films have been created from this original book, including a short film entitled Flatland: The Movie.

For this project, you will need to read the book and we will view the short movie in class.  We will then have a discussion about the concepts in the book.  Following this discussion, you will work in pairs to personify the shape of your choice with the result being a poster to be presented to the class.  You will have 1 full class period to work in pairs on this project.

1.     Read Flatland, available on line via Google Books (cut and paste link below).

http://books.google.ca/books?id=s2Tdsgf1KTwC&printsec=frontcover&dq=flatland&hl=en&ei=NADfTI_bH5OgsQOlmPnrCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCsQ6AEwAA#v=onepage&q&f=false

2.     On Friday, February 11, we will watch Flatland: The Movie in class.  Following the movie, each pair will be assigned to one of the two discussion groups that map to the two parts of the book: PART I: THIS WORLD and PART II: OTHER WORLDS.

3.     You and your partner will then chose a geometric shape (not restricted to those in the movie) and create a poster that expresses/advertises the shape, including but not limited to the following:

·      Accurately drawn shape

·      Origin of the name of the shape (eg pentagon => penta is 5)

·      Description of how to draw the shape and what tools were used (protractor, compass, ruler, etc)

·      3 mathematical facts about the shape (eg angles, lengths, area calculation)

·      3 places where the shape can be found in natural and/or man-made settings

·      2 thoughts/ideas about where the shape could be used

4.     You and your partner will then present your poster and ideas to the class on February 23.  Presentations should be approximately 5 minutes.

Marking Rubric

Criteria	Marks Allocated	Marks Assigned
Completeness of Assignment	Contains all the required parts: shape, name origin, 3 facts, 3 places and 2 thoughts/ideas where shape can be used.	/5
Mathematical Correctness	Angles, lengths and geometric relationships are depicted correctly and accurately.	/5
Creativity/Originality	Poster and presentation demonstrates unique and innovative ideas.	/5
Presentation	Presentation was well organized. Delivery was clear and effective.  Duties were shared amongst the pair.	/5
Bonus	Poster explains more than one method of drawing the shape.	/1
Total		/20

Other Project Information not included in worksheet above:

Grade Level: 10.

Essentials of Math 10: In the Section on Shape and Space, there is a Geometry Project with the following elements:

·       C3 measure lengths in both SI and Imperial units

·       C4 estimate measurements of objects in SI and Imperial systems, including length, area, volume, mass

·       C5 interpret drawings and use the information to solve problems

·       C6 draw top, front, and side views for both 3-D rod or block objects and their sketches

·       C7 sketch 3-D designs using isometric dot paper

·       C8 enlarge or reduce a dimensioned object according to a specified scale

·       C9 solve problems involving linear dimensions, area, and volume

·       C10 complete a project that includes a 2-D plan and a 3-D model of some physical structure

Applications of Math 10: Under Shape and Space, there is a Measurement Section:

·       C5 calculate the volume and surface area of a sphere, using formulas that are provided

·       C6 determine the relationships among linear scale factors, areas, the surface areas, and the volumes of similar figures and objects

·       C7 solve problems involving length, area, volume, time, mass, and rates derived from these

·       C8 interpret drawings, and use the information to solve problems

Purpose:

The purpose of this project is to raise the curiosity and understanding of geometric shapes.  The Flatland story gets them thinking about all the implications of living in a 0, 1, 2, and 3 dimensional lands.  It also raises their awareness of how to communicate such concepts based on what the audience already knows.

Total Length of Time:

The total time for this project is 3 class periods (1 for movie and discussion, 1 for group work time and 1 for presentations).  Outside the class would be for reading the book or further project time. The actual time students will have to work is 1.5 weeks.

Materials/Resources:

Materials needed for this project include poster board, compass, protractor, pencil crayons and markers.

Thoughts on 'Creativity, Flexibility, Adaptivity, and Strategy Use In Mathematics' Article

Reading this article took me back to my math classes in elementary and secondary school.  I tried to think back and remember if there was ever any emphasis placed on the creativity, flexibility and adaptivity when learning how to solve problems and I realized that there never was any importance placed the these three abilities.  Instead, I can specifically recall instances (right up until senior level high school math classes) where the teacher insisted we solve problems in a particular manner, using a particular method and/or formula, just so that marking the question would be easier for the teacher.  I believe this was an attitude I encountered a lot from my math teachers and as a result, I became one of the students who could learn how to solve a problem really well but in only one specific manner.  I found this was not the case once I came to university hence I struggled to be creative and come up with new and/or modify known strategies of solving problems.  Concepts like flexibility and adaptivity seemed strange to me because that wasn't how I'd been taught how to solve math problems.  I always felt there was one method and/or strategy that had to be more correct than the others because I'd always been taught there can only really be one "right" way to solve a problem.

Reflecting back on this experience and now reading through this article, it illustrates to me how important it is for students to have a good grasp on all three strategies of creativity, flexibility, and adaptivity.  Math shouldn't be about robotic routines to solve problems but should involve thinking and conceptual understanding.

Practicum Stories

One of my favourite experience during this practicum was when I finally had a chance to interact with a class of junior science students as they worked on a class worksheet.  Up until this point, though I had observed many classes and been introduced in many of these classes, I found none of the students really had any interaction with me.  Since I sat in the back of the room, none of them spoke to me as they came in to the class and ignored me throughout the actual lesson.  I was quite worried at first that perhaps these students hadn't taken a liking towards me and did not want me as their student teacher; however, during my observations of one junior science course, I found that much of the class was confused about the material they learning and did not know how to get started on a worksheet they had been given.  Since it was a large class and the teacher was busy trying to help some of these kids with their questions, I tried to help out and see if I could answer the questions of anyone waiting to see the teacher.  Not only were the students openly appreciative of the help I gave them, but soon many of the kids had formed a group around me as they all wanted to hear about the explanations to solve the science questions.  Up until this point I hadn't had any chance to interact with any of the students, I had begun to feel that the students found me unapproacheable; however, I found once students know you are there to help them, they were more than happy to come up and talk to you and ask you for help.

Another part of the practicum that had an influence on me was the first lesson plan I came up with and the first lesson I actually taught.  I was so proud of myself when I finished my first lesson plan and was printing it off at my home computer.  I was surprised at how long it took me to come up with it though, as I'd expected it would have been simple enough to come up with the lesson as it was for a Math 8 class.  It actually ended up taking me hours to decide how to teach the lesson, make up my notes, etc.  The teaching of this lesson was also a big moment for me, as it was the first time I was actually teaching.  It felt somewhat surreal when I was up there in front of the class and whenever the students called me Ms. Sidhu, I felt like smiling.  I was extremely nervous before starting the lesson but ended up quite happy with how the lesson went.  I felt quite comfortable in front of the class and look forward to teaching more classes during my long practicum!