ED 426a: Learning and Assessment in Elementary Mathematics

Learning and Assessment in Elementary Mathematics				Peter Appelbaum
ED 426a, Spring 2004, Taylor 316				Peter's HomePage & Contact Info

As described in the course catalog, this is a seminar/workshop emphasizing the use of a variety of instructional materials in the teaching of mathematics, grades K through 8, including manipulatives, calculators, and other non-textbook resources. This course replaces the old ED 428. Keep this in mind: Not all materials are "things." Some tools are "ideas," or ways of thinking about what could be happening during an educational encounter.

· notions of how to integrate mathematics with other subjects in the school curriculum

· effective strategies of achieving the first two goals through or in spite of the third

We will spend a lot of time thinking about teaching as ongoing assessment (gathering information that helps you learn about your students, make decisions, and reflect on your own practice). (This is different from "evaluation," by which I mean judging, rating, or grading the quality of student performance.)

Enjoy yourself in this course! The purpose of this semester is to re-think what it means to do mathematics, what it means to think mathematically, what it means to live mathematically ... how to connect with the mathematical in your own and your students' everyday lives ... how to help people to cherish and nourish the mathematics ... how to seek mathematical challenges ... [you get the idea...]

Burns, Marilyn. 2000. About Teaching Mathematics: A K-8 Resource. Pearson Learning. ISBN: 094135525X.

Whitin, David. & Robhin Cox. 2003. A Mathematical Passage: Strategies for promoting inquiry in grades 4-6. Heinemann. ISBN: 0-325-005606-0.

Whitin David and Wilde, Sandra (1992) Read Any Good Math Lately? Children’s Books for Mathematical Learning, K-6. Portsmouth, NH: Heinemann. ISBN: 0435083341.

1. Participation and Contributions. A classroom community is made by people who do more than show up. The nature of this course requires that you get involved and try things. Just being here is not enough. You must throw yourself into the experiences, and share your thoughts. Only by talking to others about what you are thinking about, and by listening to the ways that others are thinking, will you begin to articulate for yourself and others what the complexities are, what the issues are for you, how other people might interpret what you would like to make possible for young people. Now, some people are not comfortable talking in class, and others think it unfair to put someone else "on the spot." So we need to expand our notion of "participation and contributions;" this might entail looking over this week's television guide and coming to class with a printed list of good shows to watch this week; or videotaping a news segment that we can watch together; or clipping an article out of the newspaper; or just making sure to ask the questions you want answered -- as many times as necessary in order to get us to address the important points. Feel free to suggest ways that people can contribute other than just talking a lot, even though talking a lot will be a good thing. We also need to think about not talking and listening: how to help each other to facilitate somebody else's developing idea, as this will be a valuable skill in teaching.

2. Weekly Resources and Final Portfolio. Come to each class meeting with a "resource" for teaching/learning mathematics. This could be a sample page from a book of lesson ideas (visit the curriculum center!), or a menu from MacDonald's, or an idea you have for going to a Dentist's office, or the name of a friend who is willing to come to classrooms and talk about how s/he uses mathematics in her/his work, etc. ... Anything you think of. Anytime you watch TV or go somewhere with friends or family members, think about the potential for mathematics education. Once you use a resource (say, a particular book of lessons, or a good website), you can't use that one again (if you receive a resource in a trade -- see below-- you can't use that one as your resource again either). Write a BRIEF description of (a) why you liked this resource; (b) ways you might extend/change/ improve on the activity/idea; and (c) a suggestion for linking this to everyday life experiences. BRING THREE COPIES to class -- one to turn in to me (for my comments, and then to keep), and two to trade with others. Every week you end up with three resources!

Half-way through the semester, we will decide whether to continue doing this, or to modify this assignment to meet our needs more fully.

Final Portfolio: at the end of the semester, you must put together a portfolio that demonstrates you are prepared to implement each of the teaching/learning and assessment strategies mentioned in the article, "Teaching/Learning Mathematics in School." You will probably want to include resources in some way, perhaps some other materials or written statements. Include a 3-5 page orientation to the portfolio which describes: (a) how the reader can use the portfolio to understand your current beliefs about what is really important for you to think about and apply in teaching mathematics in elementary grades; (b) what you believe are the critical questions that must be pursued in order to grow as a teacher of mathematics; and (c) what personal strengths you believe you bring to teaching mathematics at this point in your emerging career. Also include a final statement that describes: (a) How your views on mathematics and the teaching/learning of mathematics have changed over the course of the semester; (b) Two projects that you want to take on in your classroom or during your student teaching semester, and how you will begin to plan for these projects in order to make sure they happen; and (c) Something else that nobody told you to do that you think would be valuable to include in your portfolio.

3. Literature Circle Project. Groups will be formed based on your selection from the literature circle list. Groups will decide together how to read their selection, and what to do and talk about. Based on one aspect of your group work, you will design an event for the rest of the class. We can't say too much about the "event" now, except that it should get people involved in grappling with the ideas and issues that were important in your reading group. You should plan for class participation (not a presentation). We will need to discuss this as the semester goes along so that we can plan together. Group time will be provided in class, but be prepared to contact each other or meet outside of class if you need to.

4. Choose two other assignments from the options. At least one of these must be done with at least one other person.

Appelbaum handout: “Teaching/Learning Mathematics in Schools,” Whitin & Cox Intro & Ch 1; Whitin & Wilde Ch 1

Ginsburg Handout; Burns Part I (to page 42); Play Mancala and Set with friends & family, at least until you start to think strategically (come with ideas for good first moves, ideas for strategies that will lead to you winning, etc.); Whitin & Wilde Ch 12

10 Models & Representations Link Conceptual & Procedural Knowledge. Case Study: Fractions

2 “Why 0.999… is and is not equal to 1,” Bill Rosenthal, Assistant Professor of Curriculum and Instruction and Co-director of the Community School District 4, Hunter College Professional Development School Partnership, New York. Meet at the Castle, 7:00 - 9:00

23 Problem Solving Context Examined: Authentic Problems versus Word Problems; Literature Group Planning; Discussion of Portfolios

Burns 112-116 ("Patterns and Functions"); Whitin & Cox, Ch 5; more literature circle reading;

27 Possible Topics: 3-Dimensional Geometry; Probability & Statistics; Algebra Concepts

Burns 59-75 ("Probability and Statistics"); Whitin & Wilde Ch 2; Self-scheduled reading

Stewart, Ian (2002) Flatterland: Like Flatland Only More So. Perseus Press. fantasy

Doxiadis, Apostolos (2000) Uncle Petros and Goldbach's Conjecture. Bloomsbury. historic fiction, fictinal biography

Flannery, Sarah (2000) In Code: A Mathematical Journey. Workman Publishing Company. autobiography

Petsinis, Tom (2000) The French Mathematician. Berkely Publishing Group. historical novel biography

Pappas, Theoni (1997) The Adventures of Penrose the Mathematical Cat. Wide World Publishing/Tetra.

Quartet of children's books: Anno, Mitsumasa (1999) Anno's Magic Seeds. Paper Star. Friedman, Aileen (1995) A Cloak for the Dreamer. Scholastic. Rocklin, Joanne (1995) How Much is that Guinea Pig in the Window? Scholastic. Lowell, Susan (1995) The Boy With Paper Wings. Milkweed. novel

Please select two from the following list. At least one must be done with at least one other person.

Connections Essays A total of EIGHT essays (approximately every other week with one final statement). You write a reflective essay in which you make a CONNECTION that links the readings, what we discuss and do in class, and your own personal life (present or past). Describe the connection, and form an opinion. Write about how the connection impacts on your beliefs and expectations for teaching and education. Discuss how you think your own personal life experience has affected your opinion. Essays should be approximately 2-3 typed pages. This can also be done as a dialogue journal: two people write back and forth responding to each other about the material of the course and addressing the same set of issues as in the connection essays; you turn in your dialogue three times during the semester.

Assessment Project You select one assessment strategy, and use that strategy at least three times with the same student or group of students (e.g., clinical interview or rubric scoring of open-ended questions). I may suggest that you read an article that I provide. Videotape 5-to-15 minute sessions or collect some form of written documentation, and analyze what happened afterward to plan how you can be more successful the next time; make adjustments and try again with that style of assessment. Keep records and documentation of student work. Your written report should include ideas you have for making this strategy more useful and meaningful for teaching during your student teaching internship or in your classroom; carefully discuss an assessment plan that you will implement which incorporates this strategy .

Personal Project What skills and interests do you have that you can share with children? For this project, you use a hobby, skill, or interest that you have or want to develop. You are to use something that you spend a lot of time with in your everyday life to think about mathematics. Work on the craft or interest throughout the semester, and develop a portfolio of ideas for teaching/learning mathematics. Do not just report on what you have done: use the portfolio to demonstrate how your ideas about mathematics have evolved through your work with this project. Include in your portfolio plans for several extensions of your work -- projects that you will pursue beginning this summer: what questions will you start with, what arrangements will you have to make, what other people will you need to work with? Include a statement about problem solving and problem posing in the context of project-based learning: reflecting on your experience with such an open-ended, personal growth project; what do you imagine you would have to do in order to incorporate similar experiences as part of your curriculum when you are a teacher?

Thematic Unit Project You prepare a 5-week thematic unit using the model we discuss in class. This is not a collection of lesson plans but a way of outlining what needs to be planned for a thematic unit, including, for example, an introductory activity, classroom library materials and equipment, special arrangements to be made, an outline of possible lessons and projects for the middle, and a final collection of mathematics activities for the archaeology. I discuss the model in "Teaching/Learning Mathematics in School." A good reference for this assignment is How Big is the Moon? Whole Maths in Action by Dave Baker, Cheryl Semple, and Tony Stead (Portsmouth, NH: Heinemann, 1990).

Media Project You analyze media presentations of mathematics & society in order to prepare an exhibition for our class to learn from. Possible projects include: watch and videotape kids’ TV and create a montage emphasizing key representations in these programs; listen(watch)/(video)tape contemporary music videos and create a presentation that effectively demonstrates the representations in contemporary music; research a case study of mass media reporting on a current mathematics topic (e.g., newspapers, television documentaries, etc.) and prepare a report or presentation. This asks you to go beyond the regular expectation that you view some suggested educational programs. A good reference for this assignment is my Math in the News webpage. If you need to schedule class time, please do so as far in advance as possible.

Math Tour You carefully research a local ecological location, your home town, or some other appropriate site, through library research and natural observation. Then you create a guide for a mathematical walking or driving tour. The tour should include a map and sites for a person to stop and read about the mathematics of what they can see and do along the walk; either pose a small project or mathematical investigation at each site, or facilitate the tourists' own creation of problems that they can submit for other visitors. Your guide should be good enough to donate copies to your town library or municipal building to promote tourism. The types of activities at each stop should reflect the kinds of ideas about teaching and learning mathematics that we have been learning about in our course. Share initial ideas and progress with me at regular intervals to make sure you are meeting my expectations.

Creative Project You pursue a creative form of expression for representing an area of concern or interest developed during this course. Examples from past semesters: an interpretive dance, a painting, a documentary video, a spoof video, an environmental studies lab in a school, a quilt, a collection of storytelling performances, a mathematical novella; a collection of poems. Along with your work, provide some written program/guide that helps others understand what to look for in the work that you have created. If you need to schedule class time, please do so as far in advance as possible.

Take-Home Essay Midterm Exam You type responses to essay questions that ask you to apply, synthesize, and critique issues of this course. Tentative dates: Exam passed out in class on March 2; exam due at beginning of class on March 16. Expect to type 7-15 pages.

Outside-of-Class Discussion You facilitate an ongoing, outside-of-class discussion on the teaching and learning of mathematics. (a) Internet option: You join a listserv (I have some suggestions) during the first two weeks of the semester. Find a way to become an active contributor, influencing the trends of discussion and introducing new questions. Print out records of your email and the resulting threads of discussion that ensue. (b) Face-to-face option: Facilitate a series of meetings on mathematics education of current teachers and/or administrators whom you recruit to participate. Take notes on the issues and ideas that are discussed, and especially conflicts that arise regarding what is best for children, schools, and families. Multiple meetings should take place with the same people. On March 2, turn in a progress report and portfolio, including a two-page reflection on your work with this project, and a series of goals that you have for this project for the rest of the semester. I will provide a tentative “grade” to help you meet my expectations. On April 26, turn in a final portfolio documenting your work with this project, and the experience of learning by leading. Carefully describe two or three projects that have grown out of your work in this assignment that you will begin to implement in the next year.

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