TJanik

Toni Janik February 28, 2008

EDC448 Annotated Diverse Text Set


 * Context for using the text set:** This collection of resources is intended for a 9th-grade Geometry class. The unit of study is the Pythagorean Theorem. The ability level of the students varies for both literacy and mathematics. Texts have been selected to promote content area mastery in conjunction with improving literacy. The diversity of learners was taken into consideration in the selection of texts, specifically the varying degrees of mastery, issues of gender, race and ethnicity, and different learning styles. The texts were also selected to help students connect mathematics to other areas of study and to their own lives. Finally, the texts were selected to promote literacy by providing students with a variety of materials to choose from.


 * A. Print Resources**


 * Text #1:**
 * Citation: Ellis, J. (2004). //What’s Your Angle, Pythagoras?: A Math Adventure//. Watertown, MA: Charlesbridge.
 * Text Summary: Pythagoras is a curious young boy who lives in ancient Greece. When he travels with his father to Alexandria, Egypt, he meets a builder who stirs his interest in right triangles. His observations and experiments help him to understand the special relationship among the sides of those triangles. He then uses this knowledge to solve real-life problems.
 * Rationale: I selected this text because it provides an introduction to the Pythagorean Theorem in a clear, entertaining and informative format. The illustrations provide visual context for the historical period and dialogue. The dialogue helps the reader to understand the math without diverging from the storyline. Puns and wordplay are intricately woven into the dialogue, providing enjoyment to more advanced readers without distracting those who are not as advanced.
 * Use of Text: I would ask students to read this text at the beginning of the unit on the Pythagorean Theorem for several reasons. I think it is important to dispel the prevalent image of mathematicians as old white men who lived ages ago and have nothing in common with the students. I want to provide them with both verbal and visual explanations of the theorem so they can achieve true understanding rather than simple memorization. I hope that the real-life problems in the text help the students identify how they can use the theorem to help them solve problems in their own lives.
 * Attachment: This is a 32-page book, so I did not include it here.


 * Text #2:**
 * Citation: Reimer, L, & Reimer, W. (1990). //Mathematicians are People, Too: Stories from the Lives of Great Mathematicians, Vol. 1.// Palo Alto : Dale Seymour.
 * Text Summary: This non-fiction book is a collection of short biographies of mathematicians that reads like a collection of short stories. The mathematician’s specific contribution to the field is explained, but personal anecdotes are also included.
 * Rationale: I selected this text because of the diversity of the mathematicians who are highlighted. It includes people from different time periods, a variety of cultures, women as well as men, the famous and the relatively unknown. This cross-spectrum provides students with the opportunity to identify with one or more of the mathematicians on many levels including gender, culture, and personal traits.
 * Use of Text: I would provide the biography on Pythagoras as a handout to the students, to be used in conjunction with //What’s Your Angle, Pythagoras?//, so they could use one or both to learn about Pythagoras and his theorem at the beginning of the unit. I would relate interesting information on other mathematicians who are included in the book and with whom I think one or more students can identify to encourage them to read more of the book and perhaps to spark an interest in other areas of mathematics.
 * Attachment: This is a 152-page book, so I did not include it here.


 * Text #3:**
 * Citation: Pythagoras’ Theorem. Pythagorean Triples [chart]. Retrieved February 22, 2008. Ministry of Education, Wellington, New Zealand. http://www.nzmaths.co.nz/measurement/Length/Pythagoras.aspx
 * Text Summary: This is a chart of the primitive Pythagorean Triples for which a, b, and c are all no larger than 100. It includes both primitive and non-primitive triples.
 * Rationale: I selected this text because it provides the context for the portion of the unit that is dedicated to Pythagorean Triples. It allows the students to test the validity by applying the algebraic equation to the specific set of numbers. It also allows them to test the validity by constructing geometric representations either on the computer or in hard copy.
 * Use of Text: This text will be used to assist students in differentiating between primitive and non-primitive triples. Students will also use the chart to grasp the relationship among some of the triples, i.e. they are multiples of other triples. Students will be encouraged to use this text as a resource when working with triples and as they move into a more advanced study of mathematics.
 * Attachment: See Attachment #3 for a copy of this text.


 * Text #4:**
 * Citation: Wertheim, M. (2006, October 3) Numbers Are Male, Said Pythagoras, and the Idea Persists. //The New York Times.// http://www.nytimes.com/2006/10/03/science/03/comm.html
 * Text Summary: This text explores the continuing bias against women in the fields of mathematics and science. It provides examples of women who made major contributions to their fields but who received little or no recognition for their work. The text attributes the origin of that bias to Pythagoras, who believed that numbers are inherently male, and explains how that bias became institutionalized over the centuries.
 * Rationale: I selected this text because it provides objective evidence that women are men’s equals in the fields of mathematics and science. I believe it is important to provide females with role models so they can develop confidence in their ability to succeed in math. I also believe it demonstrates how baseless prejudice truly is and that lesson is important for all the students.
 * Use of Text: I will use this text to round out the biographical information on Pythagoras so that the students understand that all people are capable of mistakes in judgment, no matter how brilliant they may be. The text will be used primarily to generate discussion about bias and prejudice and to encourage the students to see mathematicians as real people. By contrasting this information with what is contained in the two books, I hope to raise awareness of the need to analyze and evaluate the information that is gathered through various sources in order to determine its validity and usefulness.
 * Attachment: See Attachment #4 for a copy of this text.


 * Text #5:**
 * Citation: Larson, R., Boswell, L., Kanold, T., & Stiff, L. McDougal Littell Evanston IL 2007 Geometry
 * Text Summary: This is a high school geometry book that provides many student resources including a handbook, extra-practice problems, a glossary of terms, a section of tables, charts and graphs, as well as interactive elements. It is a comprehensive textbook that provides a sequential introduction to geometry.
 * Rationale: I selected this text because it is written in a manner that is relatively easy for students to understand. It provides guided practice as well as enrichment activities. Students are encouraged to experiment. It is an excellent resource for students who are first learning geometry because it provides them with basic formulas, theorems, and measures in an easy-to-locate format.
 * Use of Text: I will use this text for some homework assignments to reinforce what the students have learned in class. I will also use it in class for the students to work in pairs or groups on problems.
 * Attachment: This is a 1003-page book, so I did not attach it here.


 * B. Media Resources**


 * Text #6:**
 * Citation: Apostol, T (Producer), & Blinn, J (Animator). //Project Mathematics-Theorem of Pythagoras//[Videotape]. Pasadena: California Institute of Technology. [|http://www.projectmathematics.com/pythag.html.
 * Text Summary: This text provides a video demonstration of how to solve real-life problems by applying the Pythagorean Theorem. It includes historical background, a geometric interpretation of the algebraic equation, and a variety of animated proofs of the theorem. There are also clips that explore more difficult aspects of the theorem that are available to students with the interest to explore further.
 * Rationale: I selected this text because its use of algebra and geometry to explain the theorem demonstrates the relationship between different branches of mathematics. I also selected it because it introduces proofs into the lesson. The animated proofs will appeal to students who prefer technology to other learning tools. This text benefits students who are visual learners.
 * Use of Text: I would ask students to use the text because the animated proofs provide a sequential representation of the theorem’s components. This visual image, when presented in conjunction with the algebraic equation, allows students to conceptualize the theorem. It also demonstrates that it is possible to inform and explain without having to speak or write. That is important for those students whose literacy level is not as advanced as their peers and for those who are uncomfortable with public speaking. Because the students will be asked to complete a small project on this unit of study, it is important to provide examples of the different ways that material can be presented so that all learners have an equal opportunity to achieve.
 * Attachment: See Attachment #6 for the homepage of this website.


 * Text #7:**
 * Citation: Guffee, H. (2002). //Dance of the Pythagoreans(Determining the Hypotenuse)// [Audio Download]. Pine Mountain Music. [|http://www.songsforteaching.com/guffee/pythagoreans.htm
 * Text Summary: These are song lyrics that describe real-life problems and the use of the Pythagorean Theorem to solve them. The lyrics include the algebraic equation that represents the theorem.
 * Rationale: I chose this text because the rhyme and meter of the song will enhance the students’ ability to remember the equation. By bringing music into the classroom, I hope to engage those students who are musically inclined.
 * Use of Text: The students will be provided copies of the lyrics to follow along with the audio tape of the song. By singing the song at the beginning of the class period during this unit of study, they will be reinforcing their memory of the equation. It will also demonstrate that it is possible to incorporate mathematics into music and vice versa. For those students who have an interest in or talent for music, they would recognize the opportunity to incorporate music into their final project.
 * Attachment: See Attachment #7 for a copy of this text.


 * C. Online Interactive Resources**


 * Text #8:**
 * Citation: Roberts, D. (1999-2007). //Working With the Pythagorean Theorem.// Oswego, NY: Oswego City School District. http://regentsprep.org/Regents/math/fpyth/PracPyth.html
 * Text Summary: This text is an online multiple choice quiz that poses problems based on real-world examples. Students must use their knowledge of the Pythagorean Theorem to obtain the correct answer. The quiz also requires some conversion, e.g. feet to inches, so it is a good review of previous units of study. Students are provided with the correct answer and an explanation of the process by which to obtain it.
 * Rationale: I selected this text because it allows the students to do a self-assessment of their grasp of the topic. The format and colorful illustrations lend a sense of informality that should reduce any anxiety related to test-taking. By providing clear explanations of the process by which to obtain the correct answer, the text serves as a refresher as well as a teaching tool.
 * Use of Text: I would use this text to help the students identify if there are any areas of the topic that they do not understand clearly. I would also use it to review the concept of the Pythagorean triples. The explanations that accompany the answers allow students to identify areas of the topic where they may need some additional assistance.
 * Attachment: See Attachment #8 for a copy of this text.


 * Text #9:**
 * Citation: Pythagorean Theorem. [Interactive Proof]. Retrieved February 22, 2008. http://mathematica.ludibunda.ch/pythagoras.htm
 * Text Summary: This text is a website that contains an interactive proof of the Pythagorean Theorem. Students use geometry to obtain the algebraic equation. The site also contains practical problems that can be solved using the theorem. It contains links to trigonometry and more advanced depictions of the Pythagorean Theorem.
 * Rationale: I selected this text because it provides students with the opportunity to work hands-on with the theorem. It is a benefit for visual learners and for those who need concrete examples of abstract concepts. I also selected it because many of today’s learners prefer technology to more traditional methods of learning.
 * Use of Text: Students will use this text to explore the geometric and algebraic aspects of the theorem. They will have the opportunity to link to sites related to more advanced mathematics if they are interested in doing so. They will also be encouraged to work at creating their own interactive website.
 * Attachment: See Attachment #9 for the homepage of this website.


 * D. Instructional Resources**


 * Text #10:**
 * Citation: Schoepp, S. (2000, June 8). Pythagoras: Triangles, Mysticism, and Murder (…maybe). [|http://lessons.ctaponline.org/~sschoepp
 * Text Summary: This text is a lesson plan designed to test students’ pre-and post- knowledge of the Pythagorean Theorem and its practical applications. It includes content standards, instructional objectives, student activities, references, assessment, and outcomes.
 * Rationale: I selected this text because it provided me with some ideas for developing my lesson plan. The scavenger hunt and the obstacle course are interesting ways to present the course work. I also like the idea of students working in teams.
 * Use of Text: Students will not read this particular text; however, they will take part in a scavenger hunt in which they must find the answers to a series of questions related to Pythagoras and also present a final project on the topic.
 * Attachment: See Attachment #10 for a copy of this text.


 * Using these texts together in the classroom:** The children’s trade book and the short biography will be used to introduce the unit of study to the class. Students will be encouraged to share something they learned about Pythagoras that they did not know previously. I will then share the information in the newspaper article so they can see that they must research thoroughly, utilizing a range of sources in order to obtain a more accurate understanding of a person or issue. Hopefully this will generate conversation about stereotypes and bias in general. Students will be encouraged to take copies of the article or to read the other biographies in the compilation. I will also provide them with a list of other trade books that may interest them, such as the Sir Cumference series. Students will be given copies of the song lyrics and we will begin each class with a sing-along to reinforce the algebraic equation of the theorem. We will use the textbook to review the prior knowledge needed to move forward in this unit of study. The algebraic formula will be reviewed and students will then use the computers to access the interactive websites. As they work on these sites, I will observe and be available for questions and guidance. Because the websites include practical applications of the theorem, we will have a class discussion to identify other real-life problems that we could use the theorem to solve. During this time, we will be using the textbook for homework assignments to reinforce the unit of study and in class for the students to work in pairs or groups to solve problems. Midway in the unit, students will take the online quiz to test their mastery of the subject in an informal way. I will follow up with a quiz that I create in order to have a more formal assessment of their progress. I will utilize this in conjunction with their work in teams, the class discussions, the work on the websites, and the homework assignments to identify students who may be struggling with the material and to provide additional support. As we move further into the topic, I will introduce the concept of the Pythagorean Triples and provide students with the chart to use as a resource. They can return to the websites to link to the more difficult math if they choose. The unit of study will conclude with a test and a final project. The project will require that the students demonstrate at least one thing they have learned about the Pythagorean Theorem or about any area of mathematics as a result of their work in this unit. Students can present their project in any format they choose including writing a song, performing a skit, writing a paper, creating a video or audiotape, creating a website, or designing their own proof. Students must document where they obtained the information to create their project to reinforce the idea of doing quality research.


 * Learning Objectives:**


 * Content Area:** At the conclusion of this unit of study, I hope that all students are able to use geometric models to gain insights into, and answer questions in, other areas of mathematics. I also hope that they are able to use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture. I hope that the texts that I have selected are diverse enough that all students will be able to find a combination of texts that helps them to master the unit of study.

Research by reading multiple sources (including print and non-print texts) to solve a problem, or to make a decision, or to formulate a judgment, or to support a thesis by R–8–15.1 Identifying __and evaluating__ potential sources of information (Local) R–8–15.2 Evaluating information presented, in terms of __completeness__ and relevance (Local) R–8–15.3 Gathering, organizing, analyzing, and interpreting the information (Local)
 * Reading Strategy: R-15 Breadth of Reading - Reading for Research Across Content Areas**

Toni,

I think that you did a great job on your diverse text set, I really like how you were able to incorporate a video as well as a song into a math lesson as many of the math lessons I remember were taught straight from the book. Being able to touch upon different types of intelligence is great in math since many students struggle with the subject, I also like how you incorporated history of phythagoras before teaching the Pythagorean Theorem and the children's book will help with getting the students interested in the subject. If the students know the history of the Pythagorean Theorem, they may have more interest in understanding what it is about and how it was discovered. The piece that I liked the most from your diverse text set was the article about women in science in math because I think it is very important for girls to get involved in sciences and technology and to push past the stereotypes often associated with science fields. Your diverse text set is very well written and I think it would work great in a math classroom. Math lessons that I had were about the textbook and facts but your texts help to explain the history of the math and will gain student interest.

Nicole Pelletier

Comment 2

You have included many different texts that could make learning math more engaging to students. Math should not be a dry subject as it often is portrayed. Music is a very good idea to help students remember formulas and such (because it can be catchy). Your books provide varied perspectives into the concept, ranging from cute narrative to informative textbook to even a little non-fiction. Your video connects your concepts to real life, showing students how they actually would use this formula in their lives. Including the text about the male dominated math realm could even create a link to other classrooms for an integrated lesson or unit about opportunities and women. It may be a good idea to include more texts with opportunities for the students to practice their skills with Pythagorean Theorem. A webquest or game may have helped with this. Otherwise, good job!

Melissa Rounds