|Volume VI Number 3||November 1997|
Inside This Issue
FANS Is Coming!
As announced in the previous Newsletter, the Coalition is, this spring, launching The FANS Project (Families Achieving the New Standards in Mathematics, Science, and Technology), with the financial support of the National Science Foundation. The FANS Project is a component of New Jersey's Statewide Systemic Initiative. This ambitious project intends to convey the messages of the standards to parents of half the school-age children in the state. The principal vehicle for carrying out this plan is The FANS Workshop, which will be replicated for 10,000 small groups of parents over the next three years.
You can read about The FANS Workshop in the article "Everything You Wanted to Know about FANS ... ", and you can learn about the relationship between The FANS Project and our annual Math, Science, and Technology Month.
You will find a Wanted Poster addressed to you. We need you and your colleagues to volunteer to conduct The FANS Workshop and to solicit sites for the workshop. After examining the Wanted Poster (and sharing it with others as well), please fill out the Response Form and send it back to us.
Your participation will make a difference!
BECOME AN AFFILIATE TODAY!
For $25 You Can Help Us Implement Our Programs
Become an Affiliate of the New Jersey Mathematics Coalition today! With your $25 contribution you will be joining with hundreds of others who are supporting the Coalition's efforts to improve mathematics education in New Jersey. Please join us in these important efforts. Just check off the AFFILIATION box on the Response Form and send us a check today.
New Jersey Mathematics Coalition
Wanted: Workshop Leaders ...
... who volunteer to conduct at least two workshops for parents per year over three years
Wanted: Workshop Sites ...
... in order to reach parents and family members in convenient and comfortable locations throughout New Jersey
Major objective: The FANS Workshop will be presented 10,000 times for 300,000 parents over the next three years, utilizing 1,000 workshop leaders. The workshop will inform parents about the new math, science, and technology standards, and about how they can help their children achieve these standards.
The FANS Workshop - Structure: The FANS Workshop is conceived of as a 90 minute workshop which will include the showing of a 30 minute videotape in three segments. In between the showing of the video segments, parents will be engaged in hands-on activities.
Video/Workshop Committee: This thirteen-member committee has been discussing and developing recommendations about the videotape and The FANS Workshop in which it will be used.
The FANS Workshop - Content: A set of key messages for the workshop has been developed, and has been relatively stable through a number of reviews. The videotape will convey the major messages of the workshop, and the workshop activities will reinforce these messages and will provide parents with the kinds of experiences their children should have in standards-based classrooms. The two workshop activities will include one dealing with counting successive generations of a population, and another dealing with estimating the amount of water wasted through a leaky faucet.
Project Staff: Joseph G. Rosenstein and Warren D. Crown are Co-Prinicipal Investigators. Peter Sobel serves as Project Manager. Jennifer Lomench is Project Coordinator, and Clara Munoz is the FANS Project Secretary.
Management Committee: This twelve-member committee advises the project directors on carrying out the project.
Steering Committee: This committee has over fifty members, most representing organizations which have statewide constituencies. The Steering Committee serves as the hub of the network aspect of The FANS Project.
Videotape Shooting: After receiving recommendations from a variety of sources, about 100 teachers were invited to apply to have their classrooms videotaped. Shooting is scheduled to begin during the third week of November.
Videotape Production: The videotape will be created by the Office of Television and Radio (OTR) at Rutgers University and OTR Program Director, Linda Bassett. The Producer is Varda Steinhardt.
Timeline: A rough-cut of the video will be reviewed during the last week of January by the Steering Committee (of the FANS Project), the Board of Governors of the Coalition, and several parent focus groups. The videotape will be revised and completed by mid-February. Training sessions for The FANS Workshop will take place in February and March, and workshops for parents will begin in late March.
Workshop Leader Training Program: The training program for workshop leaders is currently envisioned as a six-hour program which will be available in one or two segments, and will be offered at different locations throughout the state. The program will provide general training on dealing with adult learners and specific training on conducting The FANS Workshop.
Recruitment: We have been actively recruiting both workshop leaders and workshop sites. Please see the Wanted Poster and complete the Response Form.
Math, Science, and Technology Month: The FANS Project and MSTM '98 are viewed as independent but overlapping projects. The Coalition will encourage the development of MSTM events in April, and will maintain and distribute a calendar of these events. It will also encourage the use of FANS Workshops during April as part of MSTM. However, FANS Workshops will be taking place throughout the year.
Evaluation: Susan Danin of RBS will conduct the evaluation component of The FANS Project. The Eagleton Institute quarterly poll of adults statewide will be used three times (early 1998, mid-1999, late 2000) to measure the impact of The FANS Project.
Should I do a FANS Workshop for Math, Science and Technology Month this year? Is MSTM now a relic of the past?
If you are asking these questions, you are in good company. The purpose of this note is to describe how these two important projects are related to one other.
The Venn diagram below will help us see their relationship. Each pair of bulleted items represents a difference between the two programs. First of all, The FANS Project is very focused on informing parents about the new math, science, and technology standards and how they can help their children achieve those standards; MSTM activities need not have a particular purpose -other than to involve parents and children in hands-on math, science, and technology activities.
|VENN diagram not available|
Because of the focus of The FANS Project, the workshop leader is provided with training so that he or she can follow the prescribed format of The FANS Workshop. Event coordinators for MSTM can select their own format for their activities.
The FANS Project is timely - after three years, it will have accomplished its goal of reaching parents of half of New Jersey's school age children. MSTM is ongoing - we anticipate that more and more teachers, schools, and districts will build MSTM into their annual schedule and sponsor activities for many years to come.
The FANS Workshop will be exclusively for parents, whereas MSTM activities usually involve both parents and children. The FANS Workshop will be offered year-round, while MSTM activities will continue to be held at a designated time of the year, the month of April.
Can FANS Workshops be held during MSTM? Of course they can. Can activities other than FANS Workshops be held during MSTM? Of course they can. As you can see in the Venn diagram, the two circles do overlap.
If you have a well-established activity that you conduct for MSTM, we encourage you to continue to conduct that activity during MSTM. However, we also encourage you to consider leading FANS Workshops, either during April or at other times of the year. If you
are planning to conduct FANS Workshops, we encourage you to do so in April so that they can also be counted and publicized as MSTM events.
For the next three years FANS and MSTM will complement each other, and we anticipate that MSTM will be much better established througout New Jersey after its three year association with FANS.
by Peter Sobel
From July 7 through July 18, 1997, twenty of the most talented 5-8 mathematics teachers and supervisors in the state met and worked hard with a very dedicated staff to try to create ways to share their knowledge and expertise with others who teach at the same level. The second summer of the Standards Dissemination Project was once again funded by Johnson & Johnson and resulted in the development of eight powerful workshops that will help
5-8 teachers implement the new New Jersey Mathematics Standards in their classrooms.
The twenty teachers were selected for participation from over sixty applications submitted in the spring. The participants represent diversity geographically and in terms of gradelevel and responsibility. They are:
|Betsy Blume||Mt Hebron Middle School||Montclair|
|Neil Bress||Morgan Village Middle School||Camden|
|Christine Burton||Hillsborough Middle School||Hillsborough|
|Suzanne Caldwalader||Mt Arlington School||Mt. Arlington|
|Mary Ellen Cignarella||Newark Public Schools||Newark|
|Diane Cobb||Westbrook School||West Milford|
|Patty Cotoia||Herbert Hoover Middle School||Edison|
|Paula Hartman||Hackettstown Middle School||Hackettstown|
|Lee Kornhauser||South Orange/Maplewood Schools||South Orange|
|Wendy Luyber||Northern Burlington County M.S||N. Burlington Cty.|
|Rosemarie Maltese||South Brunswick Upper Elementary||South Brunswick|
|Cyndy Montes||Christa McAuliffe Middle School||Jackson|
|Ruth Mooney||Hamilton Twp. Schools||Hamilton Twp.|
|Marcia Prill||Madison Junior School||Madison|
|Alice Scott||East Amwell Township School||East Amwell Twp.|
|Deb Stolow||Liberty Twp School||Great Meadows Reg.|
|John Veninger||John Adams Middle School||Edison|
|Lanette Waddell||Crossroads School||South Brunswick|
|Teddy Wieland||Friends School of Mullica Hill||Mullica Hill|
|Cathy Yorke||Monmouth Junction School||South Brunswick|
The staff of the institute consisted of: Warren D. Crown - Project Director, Paul Lawrence - Program Director, and Debra Ives, Kinnelon Schools; Richard Moss, South Orange/Maplewood Schools; Mary Oates, Parsippany Schools; and Nadine Williams, Newark Schools
The titles of the workshops created by the twenty particpants are:
|Number Sense (5th - 8th grade)||Measurement and Geometry (5th - 8th grade)|
|Data Analysis (5th - 8th grade)||Patterns and Relationships (5th - 8th grade)|
|Estimation and Mental Math (5th - 8th grade)||Discrete Mathematics (5th - 8th grade)|
|Algebraic Thinking (5th - 6th grade)||Algebraic Thinking (7th - 8th grade)|
Each participant helped to produce and is now prepared to deliver two of the workshops that were developed during the summer. Each of the eight workshops actively involves the teacher participants, elaborates upon and explains the standards that are its focus, are aligned with the Cross Content Workplace Readiness Standards, incorporate concrete manipulative materials, involve technology, and specifically address the four process standards.
For K-4 and 5-8 Teachers
sponsored by New Jersey Mathematics Coalition
January 5th - 9th and March 16th - 19th
January 26th - 29th and March 16th - 19th
workshop presenters are K-4 and 5-8 teachers and supervisors who developed the workshops as part of the Standards Dissemination Project sponsored by the Coalition and funded by Johnson & Johnson
For further information about specific workshops, please check the appropriate box on the Response Form.
LET YOUR SCHOOL AND DISTRICT ADMINISTRATORS KNOW ABOUT THESE WORKSHOPS
Standards Dissemination Project
For 9-12 Grade Teachers
We are seeking 20 teachers of grades 9-12 to collaborate for two weeks next summer (July 13-21, 1998) to develop eight workshops based on New Jersey's mathematics standards, and to deliver those workshops to other New Jersey teachers in the following years. Similar programs in 1996 and 1997 to develop workshops by and for K-4 grade teachers and 5-8 grade teachers have been very successful.
The Standards Dissemination Project is funded by Johnson & Johnson.
To receive an application form in January, please check off the SDP 9-12 box on the Response Form.
YOU ARE INVITED TO APPLY
by Joseph G. Rosenstein
(This article was submitted to the New York Times in August)
The day after "mathematics education" was featured on the New York Times Op Ed page, I was scheduled to speak to a group of high school mathematics teachers and mathematics and computer science researchers about "The Standards Approach to Education". This took place at the DIMACS Research and Education Institute (DREI) at Rutgers University. The program and its sponsoring organization - the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) - are funded by the National Science Foundation.
My choice of topic reflected my background as professor of mathematics at Rutgers University and as Director of the New Jersey Mathematics Coalition, as a result of which I played a major role in developing and promoting New Jersey's recently adopted mathematics standards and accompanying curriculum framework.
The headline "Creative Math, or Just Fuzzy Math?", the picture, entitled "Your New Math Book" whose blank pages suggested a lack of content, and the side-bar, a box filled with apparent jargon on "Answers and Solution Techniques", all created a negative impression of the goals of the reform movement. I would like to address those in this article, and to comment on the relationship of the standards approach to constructivism.
I began my presentation with a quiz, asking my audience the question which appeared in the box: "I just checked out a library book that is 1,344 pages long! The book is due in 3 weeks. How many pages will I need to read a day to finish the book in time?"
I gave them 15 seconds to come up with an answer, and then selected a dozen people at random to provide their solutions; as I anticipated, this generated a variety of solutions. Some gave the exact answer of 64 (1,344 divided by21), but most gave answers like "about 60" or "around 70". From a show of hands, we learned that only about one-third of the audience had obtained an exact answer; the others had estimated the answer, even though they were all research mathematicians and mathematics teachers and they were all familiar with the techniques of division.
The unnamed author of the side-bar noted, perhaps nostalgically, that "The old way to solve the problem would be to use the algorithm for long division: 1,344 divided by 21." The question is: Who would actually solve the problem that way? I would venture a guess that fewer than 10% of your readers aged 40 and older have used long division even once in the past decade. Anyone who needs to solve a problem like that nowadays would use a calculator. So a fundamental issue in mathematics education is whether we should stress a technique which most students will never master and few will ever use. I will return to this question later.
How did the mathematicians in my audience get their answers? Here are three examples of the kind of thinking that took place: 1,344 divided by 21 is about 1,400 divided by 20, and that's 70; 13 divided by 2 is between 6 and 7, so the answer is a number that starts with 6; since 60 times 20 is 1200, the answer is in the 60s. After discussing the different ways we solved the problem, I showed them the next portion of the side-bar: "The MathLand curriculum guide calls for a new approach, explaining that division in MathLand is not a separate operation to master, but rather a combination of successive approximations, multiplication, adding up and subtracting back, all held together with the student's own number sense.'" My audience all identified with "division in MathLand", because that's how we actually do division.
It is important for your readers to understand that what the Mathland curriculum guide calls for is not a "new approach", but an approach which reflects the thinking of successful users of mathematics. The phrase "adding up", for example, describes what actually happens when we apply the standard method to divide 21 into 1,344.
When we put 6 on top of the line, we are saying, in shorthand, that when we divide 21 into 1,344, our initial approximation to an answer is 60. Then when we divide 21 into the remainder of 84 and put a 4 on top of the line next to the 6, we are saying that in addition to the 60 times that 21 goes into 1344, it also goes in 4 times. Altogether, then, 21 goes into 1,344 a total of 60 + 4, or 64 times. Here we see "successive approximations", "multiplication", and "adding up", all used to help understand the process of long division. So what appeared to be "jargon in the box" is actually an accurate (though technical) portrayal of what should be involved in learning division.
64 ______ 21 | 1344 126 --- 84 84 --
The MathLand problem has another interesting feature which should not be overlooked. It is an example of a problem where an approximate answer, indeed an over-approximation, is preferable to an exact answer. You wouldn't expect the child to stop reading after exactly 64 pages, ignoring chapter divisions, and you wouldn't expect the child to read about 60 pages a day, lest she come up short after three weeks; the most sensible answer would be to read about 70 pages each day. Recognizing what kind of an answer is appropriate is an important part of problem solving.
Earlier, I conjectured that fewer than 10% of adults over 40 actually use long division. One reason of course is the ubiquity of calculators. But another reason is that only a few adults can explain why long division works. They may not explain it as I did in the paragraph above; they likely have their own explanation of how it works - through a process of what is disparagingly referred to as "inventing personal methods of long division" in one of the articles. Those who can't explain it most likely can no longer do it. And, that is my understanding of "constructivism". If we have been able to construct our own understanding of a mathematical concept or our own explanation of a mathematical technique, then it is ours; and it we don't, it is gone. Now I am not a professor of mathematics education, so I don't know whether this accurately captures the notion of constructivism, but it is the notion of constructivism that I have constructed for myself.
Constructivism focuses on "understanding" and "explaining", rather than simply on memorizing or doing. Those who advocate constructivism do not insist that one shouldn't "memorize" or "do" until one can "understand" or "explain", or, beyond that, that one shouldn't "memorize" or "do" at all. (There are of course "radical constructionists" who hold those views.) But many teachers and curriculum leaders seem to think that constructivism implies that children should be exempted from learning the multiplication table. In fact, in order to solve the division problem above, you have to know and use many multiplication facts quickly. Should children learn the multiplication table? They certainly should.
Has the use of calculators affected children's learning of the multiplication table? It has if teachers haven't required them to know their multiplication facts and to solve problems regularly using those facts. Children should be using calculators, and they should be learning to multiply without them. That's common sense. When people complain about the damage caused by the use of calculators, I imagine similar complaints when the use of the abacus became widespread thousands of years ago. True, we lose some skills when technology advances; but that's a trade-off that we're willing to accept. I would guess that none of your readers has used in the last decade the method for finding square roots that I learned in school, and that no one has mourned its loss. Will that be the fate of long division?
What should be the goals of mathematics education? The point of the "standards approach" is first, to determine what those goals are, and second, to try to achieve those goals. We cannot achieve our goals until we determine what they are. What do we want all children to know and be able to do? There may be disagreement with the current answer to that question, but presumably we should all agree that an answer to that question would be of importance.
Standards are important because they describe what we value, those elements of education that we believe are critically important to the child's future. Standards are important because they can raise expectations for all students. All students can achieve more than they are now expected to achieve. Teachers and parents get, at best, what they expect. Standards can convey to both teachers and parents the goals that they should set for their children. In New Jersey, the State Board of Education last year adopted standards in seven content areas, and cross-content workplace readiness standards. The mathematics standards provide high achievable standards for all students, and they encourage all students to be continuously challenged and enabled to go as far mathematically as they can.
Although the mathematics standards of the National Council of Teachers of Mathematics are influenced by the constructivist approach - they do emphasize teaching for understanding, and they do encourage children to work together to help build each other's understanding - that is not all they are. They attempt to describe what mathematics children at various ages should know and be able to do. They focus on solving problems, not the one- or two-step problems like the one above, but problems that originate in real world situations. (Example: What size air-conditioner is needed to cool the classroom?) They insist that children learn how to reason mathematically and explain their reasoning. And they have energized teachers to expect more of their students.
My involvement with K-12 education began with the observation that students entering college were not able to do what we expected of them. In the early 80s I was Director of the Undergraduate Program in Mathematics at Rutgers (New Brunswick), at which time we instituted a placement test for all incoming students. To our amazement and dismay, about 20% of those taking the test were placed into non-credit remedial courses and an additional 20% were placed into a high-school level precalculus course; this despite the fact that at that time Rutgers required three years of college preparatory high school mathematics. Changing that statistic was the initial impetus for my getting involved in education. I mention that here because, in her article, Lynn Chaney mentions parents' complaints "about high school graduates who get A's and B's in whole-math classes and have to do remedial work in college." That's nothing new.
[Interestingly, there is no such approach as "whole math". The term was apparently invented by people in the California contingent, who are trying to associate the mathematics reforms with the failed results of implementing an extreme "whole language" approach to reading and writing in California.]
And now back to the question of what goes into "Your New Math Book". As noted earlier, the multiplication facts certainly are still there, although students will also need to know what they mean. They should be able to represent multiplication facts visually; for example, the product of 5 and 7 can be pictured as an array of dots arranged in five rows and seven columns. An elementary school teacher recently told me that she never knew why the "square numbers" - 1, 4, 9, 16, 25, 36, etc. - were referred to in that way. That means that she had never seen the multiplication facts explained visually, since square numbers are those which correspond to square arrays.
Does long division belong in "Your New Math Book"? Here the answer is not so clear. We certainly expect that every child should understand division and be able to use it appropriately. We certainly expect that every child should be able to recognize - mentally and quickly - that dividing 328 into 78,965 results in an answer which is between 200 and 300. (Can you do that?) That requires understanding of the various components of division mentioned earlier, as well as doing long division using single-digit divisors. (It also requires mastery of the powers of ten.)
But should teachers spend the time required to assure that all students have mastered the traditional method of dividing 328 into 78,965 using long division? On the one hand, that will be a skill that they are unlikely to use, since they will certainly use a calculator. (Calculations is what calculators are designed to do!) And we know that a substantial percentage of students never achieve and retain mastery of the technique. Should we not rather focus our energies on teaching them to checkwhether they have accurately entered the data into the calculator by first making an estimate of the answer? This way, if they divide 328 into 78,965 and get an answer that is not between 200 and 300, they will know that an error has been made, and that they will have to repeat the procedure. On the other hand, the method of long division is a neat way of encapsulating a lot of thinking about division into a shorthand procedure. As such, it merits our attention and admiration. It is part of our culture. Does that mean that it belongs in the book? Yes, but it will not be treated the same way as it was a generation ago.
December 11, 8:30 am - 3:30 pm.
AMTNJ Conference, All about ESPA - The Grade 4 Test - Math, Science, and Language Arts Literacy.
Registration fee of $85 includes breakfast and lunch, Jamesburg Holiday Inn. For registration form, call 973/790-6184.
January 28, 3:00 pm - 6:00 pm.
New Jersey Mathematics Coalition Board of Governors meeting, Educational Testing Service (ETS), Princeton.
Call 732/445-2894 for information.
March 20, 8:30 am - 3:00 pm.
Precalculus Conference. The eleventh annual "Good Ideas in Precalculus and... Conference." Busch Campus, Rutgers University.
Registration is $60 and includes lunch. Open to all high school and college instructors, the conference will include presentations, idea exchanges and software sessions on precalculus, probability and statistics, and discrete mathematics. For further information contact Bonnie Katz at 732/445-4065 or e-mail firstname.lastname@example.org .
Sponsored by the Rutgers Center for Mathematics, Science, and Computer Education.
Math, Science, and Technology Month.
For more information see the article. For information about events in your area call 1-800-44-APRIL.
May 1, 2.
Graphing Calculator Conference
sponsored by the New Jersey Mathematics Coalition, Middlesex County College, and the Rutgers Center for Math, Science, and Computer Education. Friday 5/1 from 1 to 4pm and Saturday 5/2 from 9am to 4pm. Registration fee is $50 for Friday and $70 for Saturday or $110 for both. Call Lisa Estler at 732-445-4065 for more information.
AMTNJ Regional Conferences - Rowan (May 11), The College of New Jersey (May 12), and Montclair (TBA).
For further information call Nancy Schultz at 973/790-6184.
October 22-23 1998.
AMTNJ Annual Conference New Location, Ocean Place Hilton - LongBranch; Supervisors; Conference - October 21.
For further information call Nancy Schultz at 973/790-6184.
The Merck Institute of Science Education was created in 1993 by Merck & Co., Inc. to direct the company's efforts in pre-college science and mathematics education reform. The Institute, based in Rahway, New Jersey, has established a long-term education partnership with four school districts in New Jersey and Pennsylvania. This partnership focuses on the professional development of K-8 teachers. In addition, the Institute lends its support to organizations and science centers whose mission is to stimulate students' interest in the study of math and science. The Institute has supported the New Jersey Mathematics Coalition since 1993. The Director of the Institute is Dr. Carlo Parravano, who has served on the Coalition's Board of Governors since 1993.
To accomplish its goals, the Institute works with:
Featured will be introductory and intermediate sessions on graphing calculators and the Calculator Based Laboratory (CBL) system of scientific probes. These scientific calculators can be linked to a variety of probes and sensors to measure motion, sound, pH, temperature, light intensity, voltage and other physical variables, providing an ideal connection between scientific phenomena, data collection and mathematical modelling.
Cost: Friday $50 Saturday $70 Both days $110
For more information call Debby Toti at 732-445-4065