Curriculum Project I: A basal textbook

This project is designed to help you get a feeling for at least one elementary mathematics textbook and where new material is introduced in the curriculum.

Background Reading

Before beginning the project you must read the article "How Much of the Content in Mathematics Textbooks is New?" by J.R. Flanders (to be distributed in class) and pages 497-499 of Van de Walle.

Project

Go to the curriculum center and look at the third, fourth or fifth grade text you have been assigned. Based on that book, do the following:
  1. Page through the book a bit, read a couple pages here and there. Describe your initial reaction to the book. (Does it look good? Would you like to teach from it? Are there any features you find especially good, bad, surprising, unexpected, etc?)
  2. Summarize Flanders' article in a paragraph or two.
  3. Make a list of the new topics in your text and determine what percentage of the contents is "new". (You will need to look at previous books in the series to do this.) Be sure to explain how you came up with your percentage. How do your results compare with those of Flanders?
  4. On pages 48-50, Van de Walle lists 9 types of problems that he claims "occur across most grade levels and content strands". Find examples of five of them in your book. For each one write down the problem, its location (series, grade level, page), identify its type and explain why you have categorized it the way you have. (Note: some problems fall into more than one category.)
Your report should be type-written (although you may supplement with hand-drawn pictures, etc, if needed). Be sure to include the information regarding which textbook you used for the project.

Curriculum Project II: Arithmetic Operations

For this project you must use the same textbook series that you used for Curriculum Project I, but you will need to look at several grade levels. The goal is to find out when and how the arithmetic operations (addition, subtraction, multiplication and division) and algorithms are introduced in your text.

Project

In each of the following, when asked to locate something, report the page, chapter and grade level. When giving the pages and chapters, include also the total number. For example, page 152 of 356 in chapter 5 of 12. The textbook series should be the same throughout the project, so you don't need to include it each time, but do make sure it appears prominently in the title or header of your report.
  1. Addition. Find out where in your series the addition algorithm for the sum of two 2-digit numbers is introduced. Do problems that involve regrouping occur along with those that do not? If not, locate where problems requiring regrouping first appear. What conceptual rationale is provided for the algorithm in each case?
  2. Subtraction. Repeat part 1 for subtraction.
  3. Multiplication. Where is the multiplication algorithm first introduced? (This will probably involve the product of a 1-digit number with a 2-digit number.) What conceptual rationale is given for the algorithm (repeated addition, array, something else, none at all)? Where does the product of two 2-digit numbers first appear? Does your textbook make use of an "intermediate algorithm" before moving to the "standard algorithm"? Support your answers with relevant examples and citations.
  4. Division.

Curriculum Project III: Everyday Mathematics

Everyday Mathematics is a textbook series produced at the University of Chicago. In this project you will get a chance to to look at this series and compare it to the series you used in curriculum projects I and II. Everyday Mathematics (also known as "Chicago Math") was developed "from scratch" in response to the NCTM standards; it is not merely a revision of the previous version of a textbook series. Your assignment is to see whether the result is really a different kind of textbook or not. For this project you should use the same grade level that you used in Curriculum Project I. Comparing the book of that series with its counterpart in the Chicago math series answer the following questions:
  1. Are there any differences in what material is covered? Make a list of topics that occur in one book but not the other. Do any patterns emerge?
  2. Find a lesson in each book that covers the same topic (perhaps the introduction of one of the arithmetic operations or algorithms). Compare the two lessons with respect to what the students do, what the teacher does, the emphasis of the lesson, etc.
  3. How does Everyday Mathematics stack up against the Standards and the philosophy and methodology laid out in Van de Walle's book? What are its strengths and weaknesses (from the perspective of the Standards? Is it significantly better than the other series you looked at?

Position Project: Calculators in the Classroom

Write a 2-3 page paper outlining your position on the role calculators should play in the elementary classroom. You must decide if they should be used, and if so, how often, for what purposes and at what grade levels. Make your final product polished, concise, and persuasive. Pretend that you will be presenting it at a job interview.

All statements you make must be supported. You should read the relevant portions of Van de Walle and Long and DeTemple, any handouts from class regarding calculators, and articles in journals like The Arithmetic Teacher (now Teaching Children Mathematics). You may also contact K-8 teachers that you know, and you should reflect on ways we have used calculators in this class.

This is supposed to be your personal statement, but it must be substantiated by outside evidence. Be sure to include a bibliography listing any sources you quote or refer to. This should include articles that oppose your view.

Reading Project I: Research and Teaching

This project is intended to introduce you to some research into mathematics teaching or learning.

Project

Find an article reporting on some research into mathematics teaching or learning. Summarize the research project that was done, the main conclusions drawn from it and any unanswered questions raised by it (the author's or your own, but distinguish between the two). Also list two of the items in the bibliography that sound like they would be interesting to read to learn more about the topic in your article. Why do these look interesting?

Reading Project II: Manipulatives

Read "Research within Reach", an article on manipulatives (to be handed out in class). Then find and read two articles discussing the use of particular manipulatives (not general arguments for or against their use generally). Good places to look for such articles include Teaching Children Mathematics (formerly The Arithmetic Teacher), and Mathematics Teaching in the Middle School. Based on this reading:
  1. Give a summary of the two additional articles you read and your reaction to them. For each article, give a summary and your reaction to it. Be sure to give complete bibliography information for each article.
  2. Discuss the importance of using manipulatives at various grade levels. How do research and classroom practice support the idea that manipulatives are an important factor in children's mathematical development?

Reading Project III: Special Needs in the Classroom

This project should introduce you to the needs of some category of "special students" (slow learners, learning disabled, "gifted and talented", girls, minorities, etc).

Project

Find two journal articles pertaining to the same group of students and write a brief summary of each. Be sure to include a full reference for each article (journal, author, date, pages, etc.). 

Page Created: 31 August 98
Last Modified: 
Thu Jul 29 19:58:58 1999
Maintained by: Randall Pruim