Syllabus  —  Education 316  —  Math Methods

Text:  Riedesel, Schwartz, Clements,  Teaching Elementary School Mathematics

Education 316:  Math Methods

Text:  Riedesel, Schwartz, Clements,  Teaching Elementary School Mathematics

Supplemental References:

Barody, Arthur J., Fostering Children’s Mathematical Power.  New Jersey: Lawrence Erlbaum, 1998.

This text provides an explanation of using cuisenaire rods to model operations with fractions, and it provides a plot synopsis of useful children’s literature.  You might also find some of its investigations interesting.

Burns, Marilyn, Cuisinaire.  Sausalito, CA: Math Solutions, 1995

This series has lots of good ideas for place value multiplication and division concepts.  An inexpensive set you might like to purchase.

Fendel, Daniel M., Understanding the Structure of Elementary School Mathematics.  Boston: Allyn and Bacon, 1987.

This is an old book, but it gives a lot of mathematical information from a conceptual perspective rather than the more usual organization of topics by the order they are presented in school.  The first seven chapters contain a very useful perspective on mathematics.  The “pedagogical comments” section in each chapter is excellent.  I would recommend that you read at least the portions of the book that apply to topics you will teach during student teaching.

Good, Thomas L., Grouws, Douglas A., and Ebmeier, Howard.  Active Mathematics Teaching.  New York: Longman, 1983.

This is a complete summary of the Missouri Mathematics Effectiveness Project.  It presents the results of several research projects at different grade levels.  While it is dated, the project was based on well established learning principles that still hold and are included in more recent projects.  Although the emphasis may seem to be less constructivist than the NCTM Standards, I think most of the principles apply to all types of lessons, and I do not think it is the author’s intent to discourage constructivism.

Hatfield, M.M., Edwards, N.J. and Bitter, G.G., Mathematics Methods for the Elementary and Middle School.  Boston: Allyn and Bacon, 1993.

The features of this text that I would like to call your attention to is the “common misconceptions” for each topic in math.  I is also a good source of games and activities.

Krulik, S. and Rudnick, J.A., Problem Solving, A Handbook for Teachers (1987) and Problem Solving, A Sourcebook for Teachers (1984).

This is a good source of problems and while I would not suggest you teach problems by type, it can be useful to have a resource that provides them by type.

Labinowicz, Ed, Learning from Children.  Menlo Park, CA: Addison-Wesley, 1985.

Older but good for its ideas about interviewing students and examples of student work and possible student responses.

Leutzinger, Larry, Strategies for Learning the Basic Facts.  Iowa: Iowa Council of Mathematics Teachers, 1981.

This is excellent and will probably cause you to reorganize your teaching if you have a traditional text.  It is well worth the $3.00.

Richardson, Kathy, Developing Number Concepts.  New Jersey: Dale Seymour, 1999.

This three volume series has lots of good lesson ideas for K-4 mathematics.  You might well want to purchase these inexpensive volumes.

Trafton, Paul and Thiessen, Diane, Learning Through Problems.  Portsmouth, NH: Heinemann, 1999.

A wonderful book from a staff development workshop for primary teachers.  Shows student work and teacher reflections.  It is very short and a must read.

Troutman, Andria P. and Lichtenberg, Betty K., Mathematics, A Good Beginning.  Monterey, California: Brooks/Cole Publishing, 1991.

One of the strengths of this text strengths is the excellent activities and resources at the end of each chapter that you might like to include in your resource notebook.  It also has some good masters of things like graph paper in the appendix.

Wiebe, James H.  Teaching Elementary Mathematics in a Technological Age.  Scotsdale, Arizona: Gorsuch Scarisbrick, 1988. 

This text does an excellent job talking about the merits of various concrete models especially for place value.  It also has good criteria for games and a good section on estimation.

Van de Walle, John, Elementary and Middle School Mathematics.  New York: Longman, 2001.

This is in many ways the best mathematics methods text available.  I have chosen to have you read about many of its ideas in the primary research instead of in a text, but I suggest you get in the habit of consulting this text as you prepare lessons.  It is clear, succinct, completely up-to-date and it has excellent examples of how to teach.  When I assign pages in this text, you would often benefit from examining the entire chapter.  He has excellent subheadings and inserts them often, so it is easy to skim and find what you want.  His technology notes are a good source for notebook inclusion and the sections on children’s literature are another useful feature.

Grade:   Your grade in this class will be determined in the following manner:

Resource Notebook

Your notebook should have three major sections:  1) early concepts, addition and subtraction, 2) multiplication and division, 3) decimals and fractions.  You should separate the sections with tabs for each section.  There is no one best way to organize your notebook, but as a minimum I make the following suggestions.

1. Put only one idea on each page.
2. Put a clear category heading (from the list below) on each page so it is easy to skim and find what you want.
3. Include a complete reference for each idea (APA style).
4. Add your own evaluations and opinions about the use of an idea.
5. It may be more efficient to copy an idea than summarize it.  If you glue something in your notebook, use rubber cement.

Each of your sections should include the following items.

1. Summary (with or without copy) of relevant articles (2 or 3) from Teaching Children Mathematics or the older title Arithmetic Teacher (indexes are in the issues)
2. Two games that meet the criteria we have studied for good games.  Note how it meets the criteria.
3. One estimation activity that meets the criteria we have studied.
4. One calculator activity.
5. One computer program review - try one of the programs in the curriculum library and write a one paragraph review about it (file under principle J)
6. Two problem solving ideas - include routine and non-routine problems
7. One project idea
8. Miscellaneous - newspaper articles, career information, stories, cartoons, puzzles (minimum of 4 pieces)
9. Microteaching lesson plans

Your notebook will be graded on completeness, usefulness, quality and quantity.

Due dates:  February 22, March 8, April 26

Microteaching

Prepare a written lesson plan for each microteaching session.  Your plan should be complete enough that I can understand it even if you do not present it.  If your independent practice requires a worksheet, attach a copy to your lesson plans or give the page number and assignment you would make from a text.  Do not write your own worksheet unless you are unable to find anything suitable.  It is more efficient (and realistic) to adapt an existing text worksheet than to design your own.  See p. 51 of Van de Walle.  Please type your lesson plans.

Every lesson should include:

1.  Warm-up - This can be review and/or set the stage for the day’s lesson.  It must, however, get the students’ attention and actively involve all the students.  In this case active involvement means that the activity requires an overt response from every student.  Calling on students one by one is not a way to involve everyone in making an overt response.

2.  Development - This is the body of the lesson.  It may include a brief review of prerequisite skills especially if that was not accomplished in the warm-up.  It should include a statement of the objective - usualy at the beginning of the lesson.  It must include checking for understanding (usually an oral spot check of a few students) and guided practice (check on the entire class).  You should write out the questions you intend to ask during development and possible right and wrong answers.  You should usually progress from predominantly product questions to an increasing number of process questions.  For initial product questions you should provide the explanation that you will later ask in a process question.  These guidelines apply to inductive/constructivist lessons as well as to direct instruction.

3.  Independent Practice - Every lesson must have some independent work in which which students get to practice.  This can be a traditional worksheet, an activity, or a cooperative learning task, but there must be individual accountability.  It isn’t necessary that there be a product for the teacher to collect although most often that will be the case.