Linda Metnetsky

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Mathematics Learning and TeachingPortfolio:
 
 

The Log/Journal	Reaction Paper	Concept Game	Article Analysis I	Article Analysis II
Problem Solving	Child Assessment	Curriculum File	Multi-Media Assignment	Self-Assessment

For credit in this course you are each to prepare a Mathematics Learning and Teaching Portfolio. The portfolio is not to be viewed as a final paper, rather a performance document which you gradually put together over the semester to demonstrate to the reader (me) what you have learned as a result of this course. A high quality Portfolio definitely conveys a reflective stance.

There are twelve (12) assignments to be completed during this course. All required assignments are included in the Portfolio, which can be published either on paper or using electronic/computer tools. All assignments are to be complete by Monday, December 18^th.

In keeping with the Assessment Standards for Mathematics (NCTM, 1996), I am attempting to involve you more in the decisions about how I should assess your knowledge gained from attendance in this course. I am also heeding the need for multiple means of assessment (not focusing narrowly on one paper/test/curriculum project) as a way to look at the production of your work in multiple contexts. In much the same way, you are to assess your own students' knowledge.

A Portfolio serves as a reflection of you and your work this semester in the field of mathematics teaching and learning. For the pre-service teacher, this portfolio can be a collage of your learning in this course plus your efforts to develop skills as a teacher of mathematics for any age. The portfolio can serve as a basis for self-analysis or analysis with peers or staff developer. Every portfolio must have as a connecting link, your reflective journals describing your learning from this course, with my comments and your reflections and actions to teach within the guidelines of the NCTM Standards 2000.

Every portfolio should have:

Assignment #1: Monday, December 18^th

A table of contents
 

Assignment #2: Monday, December 18^th

A "letter to the reader" introducing yourself, your current work situation, and why you chose the particular items you included to demonstrate your math learning this semester.
 

Assignment #3: Final Log/Journal due Monday, December 4^th

The Log/Journal

The 8 reflective log/journal is required as a tool or resource to support internalization of ideas. Keeping a journal is a way to reflect upon your own learning experiences. Starting with week 1, you should reflect on the experiences in our graduate class, readings, films, research, classroom teaching, observations, problem solving, conversations, and even courses outside of TEED 530. Eight (8) journal entries are required to be handed in and returned to you with comments from the instructor. The final journals must be submitted by the 12^th session for inclusion in your portfolio on the 14^th session. Plan to spread your 8 entries out over the 12 weeks. I will not look favorably upon having to read a slump of your entries all at the end of the course. In addition, a reflective entry is not two paragraphs.

Your typed entries should include your thoughts, feelings, and reactions about teaching and learning mathematics. You can use the journal as a way to communicate concerns and explore or continue to explore a problem you wish to pursue. If you have prior teaching experience, I would like you to relate your own experiences in class with issues you have discovered in your classroom or in student teaching.

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Assignment #4: Monday, September 18th

Reaction Paper- Curriculum and Evaluation Standards

(http://standards.nctm.org/document/index.htm),

• You need to read, after opening this web connection, the following: 1. Vision; 2. Principles (all six sections); 3. Standards: Introduction (only); and 4. Under grade level of choice, select one activity from the E-examples.

Please include the following in your reaction paper.

• Describe your understanding of the key issues/questions the NCTM Standards 2000 raises about teaching mathematics today.
• What questions/concerns do you have about the issues you read?
• At this point in your own professional growth, what do you feel you need to study, learn, and practice as a teacher of mathematics? Do these personal goals related to the Standards 2000 and how?
• How similar or different is the Standards 2000 vision presented here to the experience you had in learning mathematics during your early childhood and elementary schooling through the sixth grade?
• In your best judgment, how would you say the school in which you teach is implementing the Standards 2000?

Assignment #5: December 4^th or 11^th

Concept Game - Design a "Concept Teaching Math Game"

Classroom games can be a highly motivational aspect of any mathematics program. "A game, as different from an activity, is a self-contained experience which inherently contains a challenge for a child or a group of children where there is an element of chance or ‘strategy-building opportunity’ and where the outcome is exciting enough to invite children back again and again." That means a game can be played many times and without adult supervision.

Melnick's Definition of a Concept Teaching Game

A concept teaching game, as different from an activity or a teacher directed lesson, is a self-contained experience which inherently contains a challenge for a child or group of children where there is an element of chance or "strategy-building opportunity" and where the outcome is exciting enough to invite children back again and again. It has a format to learn, rules to follow and clearly has an end. It may require either cooperative or competitive play.

Ideally children operating at different levels of sophistication simultaneously may play classroom games.Any materials we use in the course may support your game’s purpose. It is very helpful to test out your game with adults or children first.

Students in the class will play your game on the day you signed up. If the game is for four people to play at a time then you should be prepared for different groups of four to play. Student playing your game will be able to provide some valuable feedback so that you can improve your game.

NOTE: This is not a skill-reinforcement game where the focus is on a child’s memory of facts or formulas.

PP Please include two copies of a one-page, typed description with at least a one-inch margin at the left, please, describing how to play your game. Include the concept focus of your game, directions, materials needed, a small sketch or photograph (visual very important) and state the age your game is for.

The write up will be put in a book placed in the Math Resource Room for future reference. It is therefore important that all directions and visuals be clear without the use of any other materials.

In the Math Resource Room (624) there are other 3 ring binders with games created by previous students which you can preview.

PP Games are played in class the first 30 minutes on one of the following days:

Monday, December 4, 2000

Monday, December 11, 2000

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Assignment #6:
Assignment #7:

Article Analysis -

Select at least two articles that relate to mathematics: to mathematical content, to learning mathematics, to issues of equity and diversity in learning, and to meeting the needs of different learning styles and/or learning disabilities.
 

Your analysis for Article II is to be posted on the Bank Street Discussion Forum (the groups are listed at the top of the Course Outline web page found on the Internet at:
(http://www.edc.org/CCT/BSC/work-bin/lmetnetsky/530descrip.html)
You are expected to post your article analysis by Monday, October 30^th.

You will then use the following week to read other students' article analysis and article, and respond to at least one of the article analysis in your group. You may also respond to any article analysis outside of your group. Monday, November 6^th.

Suggested focus for your article analysis:

Discuss the basic premise of the article.

What big ideas of the article affected you in either a positive or negative way?

Describe your interpretation of the article’s meaning and it’s implications for Instruction.

Relate class discussions, handouts, videos, or classroom experiences to article.

• Agree? Disagree? Reasons? Explain?
• Explore how this article helps you to think about your teaching methods from a different point of view.
• Explore how this article presents a different way of thinking about how children learn mathematics.
• Relate class discussions, handouts, videos, or classroom experiences to article.

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Assignment #8: Monday, October 23^rd.

Problem Solving

Source: M. Burns - About Teaching Mathematics

Problem Solving - Select two "challenging" math problems to focus on. It should be one that you feel demonstrates your understandings of the process of "doing" mathematics. I strongly urge you to work on these problems with a math buddy. . It does not have to be people from the class. You can use the M. Burns, About Teaching Mathematics as a resource. If you find another great problem, please feel free to use it.

The write-up for the problem solving should include in the discussion the people that worked on the problem and the role(s) that they played in your exploration of the problem. Please follow the outline below.

• The problem - a copy of the problem
• The mathematics - the "big ideas" found in the problem
• How did you explore the problem?
• How did you solve it?
• Did a person(s) work with you on your exploration? What role(s) did
they play?
• Did you use any strategies such as pattern? Or working backwards, or using simpler situation or numbers? Etc.
• What did you learn?
• Did you have fun doing the problem?

Assignment #9: Monday, November 20^th

Assessment:

Select one or two students to assess. The students can be from your classroom, family members, other classrooms, or next door neighbors.

For your assessment you can use any of the following assessment activities?

• The conservation tasks from The Piaget Primer.
• The assessment handouts on pre-number concepts and number operations.
• The videotapes of assessment techniques modeled by Marilyn Burns and Kathy Richardson. You can use these assessment strategies in your assessment.

In the report, describe the student(s) you have selected. In what capacity do you know the student(s)? Why have you chosen this student(s)? What would you like to know or need to know about the student(s) mathematical knowledge and learning style?

In your written report, you should, in addition to the above:

• How does this student(s) work and participate in math class? Does he/she talk about mathematics? Does exploring mathematical situations excite them?
• Describe your testing situation? How did your student(s) respond? Was he/she confident, consistent, relaxed, open to explaining thinking, etc?
• Quote some of the questions asked and responses received to support your conclusions.
• Recommend some specific activities that could be used with the student(s).

Assignment #10: Monday, November 27^th

The Curriculum File -

With a partner, explore and write about 10 activities (5 each) from at least two curriculum strands that present mathematical concepts of that stand in a manner that excites and challenges your mathematical interests.

Suggested resources:

Principles and Standards for School Mathematics 2000

About TeachingMathematics,M. Burns,

A Collection of Math Lessons,  M. Burns,

Developing Number Concepts Using Unifix Cubes, K. Richardson

Investigations in Number, Data, and Space, by TERC

or any curriculum listed on the BIBLIOGRAPHY, or from any other resource.

These should be activities that you can use with students that you are presently working with, or will work with, or for your own learning and exploration. The emphasis should be on conceptual approaches (K-6^th).

1. Present the problem - solving activity.
2. Write a short introductory statement describing your personal criteria for selection of activities.
3. Then discfromthe "big mathematical idea" of the activity, how the idea is developed? How would you introduce the "big mathematical idea"?
4. What you learned from doing the activity?
5. Why this activity is important for the students you teach?
6. What mathematical concepts, skills, understandings do your student as the learner develop, explore or master?
7. What accommodations do you think will be necessary for a variety of learning differences (including learning differences and second language
     learners)?

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Assignment #11: Monday, November 13^th

Multimedia Assignment: Computer/Web Learning

Resource: Webliography

Write annotations and analysis of two pieces of software (mathematical based) or at least two web sites that would be useful for a mathematics teacher to visit that will enhance teaching and learning mathematics in the classroom.

Software:

(1) Briefly describe the software program.
(2) What is the focus of the software: educational and content?
(3) How is learning organized and presented in this software?
(4) What assumptions does the software make about the nature of learning?
(5) Would you buy this piece of software? Why? Or why not?

WEB:

(1) Address of the site
(2) The major focus of this site:
(3) What kind of information or activities or curriculum suggestions is found at this site?
(4) How can this site enhance either teaching or learning?
(5) How would you use this site in your own classroom?
 

Assignment #12:

Self-Assessment: Due Monday, December 18^th

Write two to three paragraphs assessment of yourself as a learner.
 

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