We were also asked to send our questions and/or concerns about the NCTM Standards to the workshop mailing list. Below is the compiled list of our comments. Please feel free to respond via e-mail directly to the participants.

- Paul Doyle
- Ruth Carver
- Jo Baranko
- Allison Venables
- Howard McKenzie
- Saundra Handy
- Cindy Schmalzried
- Pat Daley
- Mike Diamond
- Roseanne Ratigan
- Ben Preddy
- Mary Denise Curran

Subject: NCTM Standards

The implementation of the NCTM Standards appears to be spotty. That is to say, one tends to find one or two teachers in a school or in a department who are excited and realize that reform is needed. My experience has been, however, that the majority of teachers remain unmoved.

I would be interested in learning of situations where a school or department has made the philosophical leap and embraced the Standards. -- Regards, Paul

Subject: Success with the Standards!?

Hi All, I'm at Swarthmore for the week-long workshop. I was wondering what kind of success you were experiencing implementing the standards. My biggest problem is that we have not really taken a close enough look at the old curriculum to make room for some of the new things the Standards say we should be teaching.

I've implemented the TI-81/82 into my algebra 2 and precalculus classes. It has made an enormous difference. In the beginning the going was slower, but it was definitely worth it. Student understanding and retention of material increased dramatically and students were always amazing me with the discoveries they'd made while exploring. I guess that's the best part, that they weren't afraid to explore.

I would like to use the Geometer's Sketchpad in my geometry classes this year and am wondering how to incorporate it using a standard text. We use
Houghton/Mifflin's *Geometry*. Any suggestions would be greatly appreciated. -- Ruth

Subject: Alternate Assessment

In implementing the NCTM standards, have you used any alternate assessments that were successful that you would like to share? (I am at the Geometry Forum learning to use E-Mail.)

Subject: NCTM Standards and Geometry

I'm participating in the 1994 Geometry Forum at Swarthmore. Today we are learning to send e-mail messages to individuals and groups. Feel free to send me mail and share your workshop experiences with me. I'll be here 'til July 13. -- Allison

Subject: The Math Standards and the inner city school!

How does one implement *successfully* the Math standards in today's inner city classroom with very limited resources and sometimes less than motivated students? When I look back on the Standards, I sometimes get the feeling that it was written with the view that everyone has access to a room full of the latest technology and highly motivated students. What are your feelings on this topic? Inquiring minds want to know.

Subject: NCTM Standards

Currently, DC Public Schools has a draft copy of its Mathematics, Science & Technology Curriculum Framework document. There is a section devoted to the integration of mathematics and science. The difficulty comes with the integration of these without sacrificing the content. We are forever seeking resources that ensure integration while preserving the strength of the content. Please share any resources that you are aware of. -- Sandi

Subject: Textbooks

My new pet peeve is the overstuffed textbooks our students have to lug around. I use the University of Chicago series, which is especially difficult to deviate from, but all the NCTM standard-influenced books contain too much stuff, I think. I like the stuff, itself, but we find ourselves swamped trying to get through it by the book.

This year I had a Russian foreign-exchange student who brought her textbook from home. It is tiny, yet covers topics from Algebra 2 through introductory calculus. I have fallen in love with this approach. Very little is in the book; the teacher and students create the rest. I have heard that the University of Chicago Project has done translations of Russian and Japanese textbooks. Has anyone seen these? Are they slim volumes?

From: cindy@forum.swarthmore.edu (Cindy Schmalzried)

Subject: group tests

The past few years I have done something I said I would never do, which is to give group tests, with just one grade for the group. This year went the best, I think. I have teacher-assigned groups which are maintained for a trimester at a time. All group classwork is done in these groups. When I give a group test, it is also a take-home and in-class and open-book and open-note test. It usually covers more than one chapter and has "hard" or at least discovery-oriented questions, not a rehash of stuff we have done. I give each student their own copy of the test at the end of class one day; one copy of solutions from the group is due two days later, at the beginning of class. They have two nights and the intervening day in class to work on the test. They are "supposed to" look at the test the first night and write down what they can, being sure to focus on the questions they have for the group.

On the in-class day, I can see what the contributions of each student to the group are. I have reformulated groups on the spot if I see some kids being taken advantage of. I feel comfortable that no one gets away with doing nothing, and that no one in any group would do the test correctly all by themself. The process of discussing with other group members is where the learning occurs, I think, and I am adamant about not letting stupid grading details interfere with this learning. The grades on these are usually very high--all A's and B's almost always (I don't do handsprings for group tests). I do not grade on how well the group functioned, etc., but I use their group interactions as fodder for written comments on the students, which we have to do at our school. We have about 6 group tests during the year; also, half of the final exam is done in this manner. Interspersed with the group tests are frequent individual quizzes and cumulative mid-trimester and end-trimester individual tests. Everything is averaged together for the trimester grade.

This procedure is my way of getting everyone through the course, grade-wise. The group test grades generally raise kids' averages. It means my grades are high, relative to my colleagues', and I'm in trouble for that. It means I may be misleading some students, giving them higher grades than they "deserve." I worry about this some, but I still feel adamant about protecting the learning that is going on.

I am considering adding an individual oral component to the group tests; this would be a nightmare in terms of time consumption, I know. But some kids are much better verbally than on written tests and I feel they should get some credit for it. Other kids, of course, get through the group tests on the strength of their peers.

Any comments? -- Cindy Schmalzried, cindy@forum.swarthmore.edu

Subject: NCTM Standards

I am participating in the summer Geometry Forum at Swarthmore this week (7/6 - 7/13). This morning we are learning how to use e-mail; our assignment is to contact previous participants with a question on the Standards.

I have been trying to implement the NCTM Standards since they first appeared. One area that I still have trouble with is alternative assessment and using portfolios as part of a student's assessment. What kinds of assignments can be included in a portfolio and how do you grade these? I would appreciate any help in this area. -- Pat Daley

Subject: NCTM Standards

Implementing the standards in my school did not even get looked at until I questioned the Headmaster about any standards. My school has had a long string of math teachers who never completed the year. Simple continuity from one year to the next has been very incomplete. I found a lot of cracks many students have fallen through. My Administration is now aware of the problems and has made efforts to ensure that I am the resource to begin NCTM implementation. My attending the Forum is to help give me resources to begin implementing the standards in the coming year. Some funding and budgeting has been set up, but the big question is "What are we budgeting this for?" I must get more information on what is available, where it is available, and how I can get more experienced teachers to implement a technology that they don't want to take the time to learn themselves.

I'd appreciate any and all responses, either personally or on the list. -- Mike Diamond, INTERNET: DiamondM@Citadel.edu

Subject: NCTM Implementation

There are several standards which I struggle to implement. Having spent 25 years consulting and designing computer systems, I feel my students must (begin) to learn to use "the personal productivity tool of the planet" (my characterization). So I experiment with graphing calculators and computers in my classes.

One of the conclusions consultants arrive at in industry relates to communication. Once the analyst has completed an investigation, it is writing and graphs, and illustrations (incl. color) that facilitate the acceptance and understanding of analysis, conclusions, and recommendations. In general, this skill is lacking. I have also come to believe that the process of writing and communicating ideas forces clarity and structure-- eliminating many errors in the thinking.

So, the standards relating to technology and communication are near and dear to my heart. My concern relates to research--are there ways to work on implementing these standards which have been shown to enhance student learning? Are there specific types of activities which inhibit learning? As a teacher and researcher, how can I assess the utility of these activities when I implement them? If it didn't work as well as I would like, is it the activity, or me?

As you could guess I frequently have more questions than answers. Have fun...

Ben Preddy: ben@forum.swarthmore.edu, 9 Rampart East, Media, PA. 19063, (610) 656-6115

Subject: NCTM standards

NCTM standards could be introduced to the majority of the math teachers at department meetings if the teachers were interested. Most teachers have never read any of the standards, nor have they attended any talks on the standards. Many teachers see the standards as a threat and not as a challenge. If they would attempt some of the changes that the standards recommend they would find the classroom more exciting.

It would be helpful if there were some workshops to demonstrate how to interest teachers in the standards. Most classes do not have graphing calculators and/or computers. Teachers need more workshops to help them develop approaches to implement the standards.

Subject: Algebra One Curriculum Guide

As a member of the mathematics curriculum committee of the Archdiocese of Philadelphia, I volunteered to oversee the revision of the Algebra One curriculum guide. My desire was to create a document that would provide a comprehensive framework for Algebra One teachers using the NCTM standards as the basis.

There are 24 secondary schools (gr. 9-12) located in the Archdiocese of Philadelphia as well as the surrounding five-county area. Students from all backgrounds are represented: urban, suburban, inner-city, rural, economically deprived, affluent. Teachers vary in their familiarity and therefore comfort and implementation of the standards.

I was somewhat nonplused as to the approach. My goal was twofold:(1) to develop an algebra one curriculum guide incorporating the NCTM standards and (2) to make teachers more familiar with the standards.

I paraphrased and edited the standards as an introduction and then proceeded to organize the algebra topics and place them in the appropriate place. I was quite happy with the final draft and I believe I accomplished what I wanted.

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Heather Mateyak / Geometry Forum / heather@forum.swarthmore.edu