Transmitted via satellite, produced by the New York State Education Department and the New York State Satellite Distance Learning Network; broadcast from Bulmer Telecommunications Center, Hudson Valley Community College.

For additional information, call or write:

John Quinn
Room 668 EBA
Office of Curriculum and Instruction
New York State Education Department
Albany, NY 12234
(518) 474-3954
E-mail: jquinn@mail.nysed.gov

>> Rochelle: Good evening. I'm Rochelle Cassella. Welcome to "New York Learns: Test Review."

This June, students facing the regents exam in mathematics will have a choice. They can take the traditional Regents test in math for Course 1 or they can take the Regents exam from Math A, a new exam that in June, 2002, will replace the Course 1 Regents for all students. Why is Math A taking over? For those students taking it this year, what will they face? And what instructional tips can those teachers who started Math A this year offer those teachers who will teach it come September?

Those are a few of the questions we'll address tonight with the help of Lynn Richbart and Jacqueline Marcano, from the New York State Education Department, and Tom Farrelly, a teacher from the Guilderland School District who assisted State Ed this year serving as a scorer and trainer for the Math A exam.

Welcome, everyone. Good to see everybody tonight.

I'd like to remind those math teachers who are watching this evening that Lynn, Jackie and Tom also are here to answer any questions that you may have about this exam, whether your students will be taking the test this June or you'll be teaching it sometime soon. You can call in your questions to our studios at Hudson Valley Community College. That toll-free number is 1-888-313-4822. Phone lines are open. You can call in at any time. If you prefer to fax in your question or your comment, please do so at 1-518-629-8136.

We begin now with Lynn Richbart. Lynn, why is this exam replacing the Course A?

>> Lynn: Well, there are several reasons, Rochelle. We are now being faced with three different changes at the high school level. The freshmen of 1997 and thereafter are going to be required to pass a Regents examination in order to graduate. Those Regents examinations are going to be new examinations called Mathematics A and Mathematics B because they are the new exams that are going to be based on the new learning standards in math, science and technology that were approved by the Board of Regents a year or two ago.

The graduation requirements are even changing. We have some proposed regulations that are going to probably go into effect for the freshmen of 2001. Namely they're going to have to have three years of mathematics. They're going to have to pass one of these exams, Math A, for a Regents diploma, and they're going to have to pass the second Regents exam, Math B, for an advanced Regents diploma.

Now we phased in the Regents examinations, the new exams with the old, over the next several years. So come this June, June of '99, youngsters do have, as you say, a choice between the Course 1 and the Mathematics A. And that's going to be available this year, next year and even into June of 2001. But as you notice, come June of 2002, as you said, all youngsters are going to have to pass the Mathematics A Regents exam for any type of diploma.

Now, in the interim, we want to talk a little bit about the diploma requirements that are required for the freshmen of '97, '98, '99 and 2000. We're stopping short of 2001 because that's when those new regulations go into effect. But for those freshmen to get a local diploma, they'll have to score a 65 or, if their school district permits, a score no lower than 55 on any Regents exam in order to obtain a local diploma.

In order to obtain a Regents diploma, those same youngsters are going to have to pass with a 65 or above both the Course 1 and 2 exam or this new examination we're going to talk about tonight, Mathematics A.

If the youngsters want to go a little bit further and actually get a Regents sequence in mathematics, they would have to pass with a 65 or above Courses 1, 2 and 3. Or if they go and take the Mathematics A that we're talking about tonight, they will have to follow that up with either the Course 3 that exists now or the new Mathematics B that will be developed for June of 2001.

Now, in terms of how the Math A differs, there are several ways that the Mathematics A differs. First of all, unlike the regular Course 1, 2 and 3, youngsters have to answer all the questions. They cannot omit any questions from the test. They will only have 20 multiple-choice items instead of the normal 30 out of 35 that we normally think of in Course 1, 2 and 3. They're also going to be answering their open-ended responses right in the examination booklet rather than on separate paper. Even if the youngster has to do a graph, it will be as part of the examination booklet.

A couple other things that are important is that 50 to 60% of the test is going to be in context or in an application. Right now the present Regents exam, very few questions are in context or an application.

Another thing that we'll be talking about tonight, and that is the fact that these are going to be scored with what we're referring to as open-ended rubrics, specific rubrics for each question. We'll learn more about how that process works tonight.

So there are many changes afoot. Many of them are based on the fact that we do now have the new learning standards, and to get a Regents diploma, youngsters are going to all have to pass the same examination.

>> Rochelle: Okay. If you have some questions about what Lynn just ran down for us, the phone number right up there on your screen: 888-313-4822. 518-629-8136 is the fax number. Lynn, why are these exams being phased in, and students, if they have a choice this June, how do they go about making that choice?

>> Lynn: Well, I think they're being phased in primarily because there was a worry about how well the youngsters were going to be prepared for the new mathematics that are in our new learning standards and our core curriculum. We have a tradition of doing that in New York State. Many of the teachers out there remember when Course 1, 2 and 3 first went into effect back in the '70s, we had a four- or five-year transition so that the teachers would be up and running; they would get to know what is going to be asked on the test; they would be able to prepare their students for the examination. And it felt a little more comfortable to say that, when we're moving into this all-Regents requirement, we could at least talk about the old exam and get the youngsters ready for the new exam.

So the phase-in has been approved. It allows the schools a little more flexibility, and I think most people are grateful that they have it.

>> Rochelle: I would imagine I would be if I were in school right now.

Once again, how do they go about making the selection? Is it the school has made the decision for them in what is being taught in the classrooms this year? Or is it really basically up to the students, that I can take this test this day or I can take this test this day?

>> Lynn: Well, since I tried to mention a little bit about how it differs, you can see not only does it differ by many of those things that I mentioned in the opening; it also is different in terms of the amount of content that is being covered. The Mathematics A covers what is equivalent to a little less than perhaps one and a half years of our traditional Course 1 and 2 material. Therefore, we would expect that it wouldn't be the youngster who would make the choice. The school has made the choice of when they want to move into this new examination. They are preparing their youngsters either for the Course 1 or the Math A. And as you say, they have that flexibility up until come June of 2002, when everyone will be in that new mode.

>> Rochelle: So do we know how many students are actually going to be taking the Math A Regents this June?

>> Lynn: We don't think the number is going to be large. I don't have the specific numbers. The schools are just in the process of ordering the Regents exams. We're going to be looking, quite interested, to find out exactly how many are taken this year.

The big change or the big number of schools that are going to be involved with it, in the past we've had some variances that schools have been doing something other than our traditional Course 1, 2 and 3. Those schools no longer have that choice of a variance exam for Course 1. They either have to go back into the Course 1 mode or do what many of them are doing, move into the new Mathematics A examination. So we have those schools that were doing something different than Course 1, 2 and 3. We do have a few schools that felt that they wanted to move away from Course 1 and 2, and this was the opportunity to do it. And since it's a standards-based exam, we're really giving the flexibility to the school in terms of the curriculum that they want to choose.

>> Rochelle: Okay. Let's talk a little bit more about the standards-based exam, exactly what's going to be on that exam? And for that, I'm going to ask Jackie Marcano to talk a little about the exam, its format, what kind of student skills and knowledge is going to be assessed, when everything is being given, that kind of information.

>> Jacqueline: Okay, Rochelle. As Lynn mentioned, the first administration of the Math A is this June, June 22nd, in the morning, and the test format for Math A is going to be 20 multiple-choice items. They will also have five two-point open-ended responses, five three-point open-ended responses and five four-point open-ended responses. And in the booklet, they will have the space to show their work right in the booklet. The exam itself will not have a formula page. The students are allowed to have a straight edge, and they are also allowed to use a scientific calculator.

>> Rochelle: Okay. And this is the scientific calculator.

>> Jacqueline: Right, the scientific calculator. It's required for the test for June and August and January 2000. In June of 2000, they will be allowed to use a graphing calculator without symbolic manipulation.

So that's a little bit about the format of the exam. The exam is based on the core curriculum, which is an up addendum to the learning standards. The core curriculum gives the students and the teachers the information that will be tested on the Math A exam.

>> Rochelle: Okay.

>> Jacqueline: That's where the questions will come from. And the percentage of questions in the Math A exam are known by the teachers. They are part of the test map for the exam. So we have a range of questions, a percentage of questions in each of the specific key ideas.

>> Rochelle: Okay. And those key ideas are up on the screen right now. So these would be the kinds of things, the skills and things, that are basically being tested and the percentages -- the breakdown of the questions on the exam in those areas.

>> Jacqueline: Correct.

>> Rochelle: Okay. All right. Sounds good. But we know that you probably have some questions out there, and we want you to know that you can call us at any point in time or fax us if you'd like. The phone number and the fax number are on the screen. So be sure to let us know what's on your mind.

As with other new assessments being introduced by the Education Department this year, scoring of the Math A exam is a bit different than Course 1 exams. Lynn, you mentioned that the scoring is based on some different kinds of rubrics and things. When is scoring going to take place? What's so different about it?

>> Lynn: Well, the scoring is going to be taking place at the normal, typical time. The Regents exams are going to be given, as Jackie said. The Math A is going to be given on June 22nd. As soon as that exam is done, the youngsters will hand in their papers. The teachers will have a scoring booklet. Many of our math teachers are used to a one-sheet, yellow piece of paper that was the complete scoring guide for the Regents examinations. On one side it gave you the answers to the Part 1 questions and on the back it just gave you the answers to Part 2. This year, the Math A will have a booklet of about 10 or 12 pages because it will have, obviously, the correct answers for the multiple-choice part, and then it will have specific rubrics for each of the open-ended questions, of which, as Jackie mentioned, there are 15 of them, 5 two's, 5 three's and 5 four-pointers.

We want the teachers -- and they're going to have to correct them like normal Regents exams, within a day or two, I'm sure, to get the results in to the school before school ends. The one thing we're requiring this year that many schools have already done is we're requiring to have a committee of at least three teachers correct each student's paper.

One of the ways that that can be done is to divide the questions, especially the open-ended questions, divide them up amongst the three teachers so that each teacher becomes an expert on a few number of questions and they correct those questions for all their students. The other thing is we hope that most schools will have maybe two committees so that in fact, if there's any disagreement about some questions, there will be other people, other teachers, to talk about what do you suggest? If it's not quite in the rubric, should it be a two? Should it be a three? And we'll learn more about that tonight.

Now, since it is a new examination, we do have one little safety built in, and that is, in addition to the scoring, once by this committee of three or more teachers, we are going to have some sort of a -- what we'll call a double-scoring cut point. If the youngster's score after the first committee is just below whatever the passing is, either for a Regents diploma or a local diploma, we will say in the scoring guide, if your youngster just fails by one, two or three raw points, and those will be determined by each test, that in fact the test is going to have to be double-scored. It will be given to another committee of teachers. Or if we only have one committee in the building, at the end they'll switch which questions that they're actually scoring, so that they'll have a chance to actually score that paper with fresh eyes.

Hopefully the two committees of teachers will agree on what will be the final score and, of course, like all things, if in fact there is a disagreement, and Tom will tell you after his work there will be no disagreements, but if there are some disagreements, it will probably be up to the principal or his or her designee as to which scoring takes place.

And like all examinations we've had in the past, including our Course 1, 2 and 3 and even our old Regents competency test, 10% of the papers will randomly be brought back to Albany for a scoring in the Education Department. And this year it will be very important to see how well the teachers are scoring based on these new rubrics.

>> Rochelle: Okay. The idea of the committee of three people is not the idea that each individual scores the entire student paper so that each student paper is read three times; it's that they divide the questions up into sections.

>> Lynn: Yes, indeed. I think that's going to find -- you'll take a pretty good time as it is.

>> Rochelle: I can imagine.

>> Lynn: These questions that are based on the rubrics, we have tried to predict what the youngsters will say. We've looked at field test information, so our rubrics do indicate the most common responses. But we know that youngsters are unique. They'll come up with some solutions that hopefully Tom has done a good job and they'll be able to say, "Hey, okay, this will meet this particular criteria." That's why I'm hoping that there will be another committee in most schools for a little double reaction, if you will, for those tricky ones.

>> Rochelle: Okay. Before we move on, I do want to remind everyone that you can call or fax in a question if you would like, and we do have a caller on the line from Brooklyn. Hi, caller. Are you there?

>> Caller: Yes, I am here.

>> Rochelle: Hi. What's your question, please?

>> Caller: I have a feeling that the ideas that formed the basis for the Math A Regents examination have been tried elsewhere. I'd like to know with what kind of success, because I have a feeling that I -- in California, for example, they tried a similar kind of strategy and it wasn't terribly successful.

>> Rochelle: Okay. The question deals with similar kinds of things being done elsewhere in the country?

>> Caller: Yes.

>> Rochelle: Okay. And how successful, okay? Lynn?

>> Lynn: Well, no place has tried it the way New York State is trying it. We're pretty unique. We have a history of 135 years of state testing. California has no history of state testing at all. California did get a lot of bad press because they perhaps tried some of their more unique type of mathematical programs without perhaps as much teacher input, as much business input. We made sure that our curriculum and our learning standards were based on a very, very balanced program. It's not overly modern or new. It has a lot of the old as well as the new. It does follow some of the national movements to try to make the youngsters explain a little bit more of their work.

We've had a criticism for many, many years, over 40 years as a matter of fact, that some of our curriculum was very theoretical, that we didn't have enough context and application. And that's one of the things the new learning standards did. It made a point that our youngsters should be able to explain what they're doing, and it should be as much real world as possible. But I think, as people see our new Math A exam and they compare it to the content that's in the traditional programs, they won't find the content is much different.

>> Rochelle: Okay. And as a result of teacher requests to change the learning standards and then having to change the assessments, that's how a lot of this change came about.

>> Lynn: Yes. When -- over the last five or six years, schools were given the opportunity to create their own programs and write their own exams, which we call a variance process. We wound up with 50 or 60 schools that had moved into different types of programs. And some of those were not necessarily programs that were more of the theoretical or more of the outlandish type of programs that some people have heard about. Some of them became much more traditional programs. And our feeling was always, that's fine, as long as the learning standards are covered, as long as the core curriculum delineates what a youngster should know and be able to do. We're going to give the schools the flexibility but, at the state level, we're still going to have the accountability that they are where they belong.

>> Rochelle: Okay. Very good. We do want to remind you that you can call in your question or fax in your question. We do have a couple of faxed questions in, a couple of different questions from a couple of different people at Orchard Park High School. Orchard Park wants to know when we can expect to see some sample Math B exams.

>> Lynn: Well, they're getting ahead of the game.
(Laughter)

We're here talking about Math A, but very briefly what I'll say is this: We finally did have our committee in to write the first pilot test for Math B. Math B, we didn't explain too much of it in the opening. Math B is going to be equivalent to somewhere around Course 3, give or take a few topics, primarily being taken by youngsters at the third year of high school unless they're accelerated, and then they could take it a little bit earlier.

But the Math B will be piloted in about 25 school districts. We just brought those 25 pilots into Albany last week, last week Friday, as a matter of fact. They will be piloting eight one-period tests. We will use those eight one-period tests during the summer, once we correct them, to build a Math B test sampler, which will be very equivalent to the Math A test sampler that we produced a year ago, with the hopes that, come June of 2001, we'll have our first administration.

>> Rochelle: Okay. And we have a caller on the line from Sag Harbor. Hi, caller. What's your question?

>> Caller: My understanding is that the Math A is going to be a combination of all of sequential one and part of sequential two. Would you tell me what topics are going to be covered from sequential two, along with the sequential one to make up the Math A?

>> Rochelle: Okay.

>> Lynn: Sure. Now, of course what I'm saying is very general.

>> Caller: Right.

>> Lynn: What you really need to do is get that math core curriculum and study that to make sure. As a matter of fact, the Math A portion is in the "Testing 1-2-3" booklet that goes along with the teleconference if you don't have it.

>> Caller: I have that booklet.

>> Lynn: Very good. So what I can say is roughly this: The Math A, content-wise, remember about all the differences about no choice, application, et cetera.

>> Caller: Right.

>> Lynn: In terms of content, Math A covers just about everything from Course 1 with the exception of symbolic logic. We still have mathematical reasoning as part of Math A. They still have to know inverse, converse, contrapositive, but it won't be in symbols and there will be no tautologies. From Course 2, we take most of the geometry, the more sophisticated algebra. The youngsters will do algebra up to but not including the quadratic formula. So we'll be doing quadratics, but they'll be factorable. The youngsters will have to know about parabolas and circles and know those equations and how to graph them.

In terms of the geometry, they're going to have to know most of the geometry that we normally think of in Course 2, with one big exception, and that was decided that, for the Math A, which is going to be the test required for all youngsters, we are going to stop short of formal proof.

>> Caller: Any kind of proof?

>> Lynn: No proof in Math A.

>> Caller: Okay.

>> Lynn: We'll have those questions that say "justify your answer," but the old two-column proof that you normally think of in Course 2 will be part of the Math B exam. That's why I think of it as about a year and a half for Math A, and then the second year and a half for Math B.

Those are the major things. The work with combinations and permutations from Courses 1 and 2 are all part of the test as well. It will be a substantial, significant mathematics examination.

>> Caller: Would you say that -- we have, as I'm sure most schools do, have 8th graders take sequential one in 8th grade and then a year advanced. Would you suppose that that would be possible for honor-type students in the 8th grade to do this in one year?

>> Lynn: Well, it may be possible, but there's no pressure on them to do it, because I think we can still keep the same thing going; namely, the real good student can start the Course 1 material in 8th grade, finish the year material that is covered; go into 9th grade and be ready to take the Math A test after one semester, continue on to Math B and get that done. That will give them one year for pre-calculus and the senior year for an A.P. calculus program.

We don't want to stop the bright youngster from getting one year of calculus as a senior, and this program will not inhibit that. But there's no rush to take the Math A exam. It's not an end-of-year course. It's a standards exam. So there's no rush. The youngsters will pass it. They will pass their courses and those accelerated youngsters will do just as well as they've always done.

>> Caller: Okay. Thank you.

>> Rochelle: Thank you very much, caller.

Well, sessions to train teachers on how to score the Math A Regents exam have been taking place in many schools. These lessons provide information that goes beyond scoring day, however. The lessons learned here have implications for what takes place in the classroom next fall or as teachers start to teach Math A. First we have videotape of Guilderland School District math teacher Tom Farrelly conducting a training session using the Math A rubrics and actual student work.

>> Tom: New aspects of the Math A exam which makes it different from the current Regents exams are instead of having three response questions that are only worth three, there are going to be questions worth two, three and four. We're going to take a look at the three-point style questions, simulate some grading and first of all start to take a look at what we call the three-point holistic rubric. The scoring on these exams is going to be much different than in the past. There is not going to be a punitive-style grade. We're going to look to take off points. We're going to look at the entire question and then score it from that point of view.

And with that in mind, the three-point rubric starts out, "A three-point response will be something that is complete and correct, very obvious. Demonstrates a thorough understanding of mathematical concepts or procedures that are embodied in the task," et cetera. "Contains clear and complete explanations or adequate work required."

The two-point rubric would be a response that is only partially correct. This response would have something that only demonstrates partial understanding of the mathematical concepts and/or procedures. And as you can see, all of the other explanations are listed out here.

A one-point response would be something that would be incomplete, exhibits many flaws, but is not completely incorrect. There is something here, the student does understand some part of the mathematical principle that the question is asking for.

And the zero response would be something that is completely incorrect, irrelevant or incoherent. A student can accidentally get a correct answer but still receive no credit. An example of that might be a question which involved a student was asked to find the leg of a right triangle, given that one of the legs is 3 and the hypotenuse was 5. Might take 3 and 5, add them together, take the average and accidentally end up with 4. A response like that is what we refer to as a completely incorrect or irrelevant response.

Now when we take a look at an actual question, it's a traditional question that we look at in Course 1. They're given several scores. The average ends up being a little lower than 80 here and we have to come up with a sixth score, what that would entail in order for the average to be above 80. Now, this score will be on the three response question on the section that is worth three. So keeping in mind with the holistic rubric, this rubric is then created, and obviously basically we're looking at the student does a traditional trial-and-error, guess-and-check or, as I said, the traditional algebraic method, and arrives at a correct answer.

Now, a correct answer could be somewhere in the range of 87 to 92 because all of those values round up or round down to 90.

Now, a two-point rubric would be that the student shows the correct work but does not identify the answer or has some incorrect statement. A two-point rubric would also be that the student shows an appropriate method but calculates the average incorrectly, makes a mechanical mistake. And number two, has a correct answer with only some of the explanation shown, does not have the complete explanation, in other words.

And one, gives the answer but with no explanation. That's going to be traditional: If the student only writes down an answer with no response, they're going to get only one point. Does not show any work on any of the three response sections, either two or three or four. Now -- and begins a proper method, using the 390 points or the 78, but does not arrive at a correct score. In other words, if we see 390 or 70, we're going to feel that the student understands something about the concept but has not come to any kind of a correct answer.

And zero is, of course, as we said before, something that is completely incorrect.

Now, the scoring of these is going to have to be done collaboratively. It's going to be a requirement of the state. So keeping that in mind, we have several questions here with actual student responses, and we thought we would go through the process here with my colleagues on how this might be. We might have one teacher supervising several other teachers and kind of be the tie-breaker.

Now, on this scoring system, the rubric is gospel. Whatever the rubric says, that's the score we have to give. If there is something that -- some response that falls what we might think is in the cracks between this, then we will go to the holistic rubric, take a look at what that says and give the student the correct score. The idea is to give the students, in every part of the state, the same score on the same question.

So, ladies, would you like to take a look at this one?

>> Looking over at this problem, it looks as though the student has shown a considerable amount of work. They've taken into account the five grades, and we see 390. They also took into account the sixth grade of the variable "X" there and found the average and came up with the score of 90.

>> This is how I would approach it, too, in teaching my class. It's probably the most algebraic, advanced method that I could see to do it. They go through a formal check and then the answer is clearly labeled.

>> Tom: Yes, nice job in labeling that.

So we agree? A 3?

>> Definitely.

>> Yes.

>> Tom: Okay. Let's take a look at the next one now.

>> Okay. I don't see any algebra used. They added the numbers correctly. They got 390. Then it looks like they divided the first five numbers to get an average of the first five numbers.

>> Which has been correctly done. What else do we have here? We have work that's crossed out. Crossed-out work cannot actually be considered?

>> Tom: Yeah.

>> It can. Okay.

>> So we should check to make sure that's correct then?

>> Tom: No. But if it is correct, it can be considered.

>> Okay. Then they proceeded to add to the sum of the five numbers the sixth possible value that I guess they guessed at.

>> Right. So they used trial-and-error on this problem. Is that what they have gone to?

>> It's unclear how they got the 90. But they did check to see that it worked and still gave them the average of 80, and then clearly labeled the answer.

>> Okay. So through trial and error, it looks as though they've gotten the correct answer and they showed enough work.

>> Right.

>> So a 3?

>> Tom: Okay, good. I would agree. This looks like the correct answer.

>> It looks as though they took the five scores; they added those up, got the 390 and divided by five. Sixth wasn't accounted for. Was it?

>> No.

>> And they received a grade of 90, which is correct on the rubric; it says between 87 and 92, so they have the correct answer, but let's look back on here.

>> So they show a score of between 87 and 92 as their answer, which will result in an average which rounds to 80, such as 390 equals 87. I don't see that as being clear.

>> No.

>> So I'd go to step two, or grade 2. All work shown identifies an answer that's correct.

>> Right. Everything is correct on here, it's just how did they arrive at the score of 90?

>> Right. So it has a correct answer with only some of the explanation shown.

>> Um-hmm.

>> So I'd give it a 2.

>> Okay.

>> Tom: Good.

>> Sounds good.

>> Tom: Here's an interesting one.

>> Okay. Already I see a mathematical error, which knocks them down out of the 3 category.

>> What exactly are you referring to?

>> To the 78 divided by 2. It's not broken up into --

>> Separate fractions?

>> Yes, for the "X" also. So they have work that's not correct there, so down to the 2 category. Has all correct work shown but does not identify answer or has an incorrect statement. Shows appropriate method but calculates average incorrectly. Their answer is 80, right, and it's circled. So that's incorrect.

>> He definitely doesn't have a correct answer then.

>> Right.

>> Doesn't really show an appropriate method. Seems that the student has an idea of averaging by summing numbers and dividing by the total number.

>> Right, take an average. They have that concept, it appears.

I don't see that it clearly fits into number 2, so I'd go down to 1 and see if that satisfies those conditions. So it gives an answer of any number between 87 and 92, and it doesn't do that. So go to the last step. Begin the proper method using 390.

>> And nothing about 390 is there.

>> Okay.

>> Okay. Or presents an average of 78 but does not arrive at the proper score. They have a 78 accounted for here. It doesn't seem to -- they seem to understand that there's an average of 78 but not have the knowledge of how to go through the rest of the problem. I guess I would probably say -- now on here there's nothing that shows a zero, but I would say it's probably a 1 because of the 78 shown there.

>> Tom: But looking at this as a whole, the student does understand average, did come up with 72, made some serious math errors. But, out of 3 points, I think the intention here would be to give him the 1. It's certainly not a zero under that rubric. It's not incoherent.

>> Right.

>> Tom: Okay. I would agree. All right. Leslie?

>> This problem looks similar to a problem we just looked at a little while ago in the sense that they accounted for the average of five numbers divided by five and received 78. Guessing, I guess... guessing at the 87. There's no work shown for that.

So looking at the rubric, it appears that -- I don't think they have enough information shown to get the 3, the score of 3.

>> I mean if they had clearly identified, answered 90, which their answer is 87, so it doesn't fit that criteria. And they don't demonstrate that they show 480 total points. So I go to the next. It shows the score of 87 to 92. I think it's important that this is different from the current Regents in that you could get a rounded answer of 80.

>> Right.

>> In the current Regents it would say round to the nearest -- so that's different. You can still get a reasonable answer that rounds to 80.

>> But it's still not -- it shows a score of 87 to 92, which they did, which will result in an average which rounds to 80. I don't see where they show that the average rounds to 80.

>> Definitely not.

>> So go down to step 2?

>> Um-hmm. Has all correct work shown but does not identify answer or has an incorrect statement. Looking at that, the work is correctly done.

Shows appropriate methods but calculates average incorrectly.

It appears that -- they haven't correctly shown everything, I think. Has correct answer with only some of the explanation shown, which is the case here because the 87, it is a correct answer. It's just a matter of how did they arrive at it? So it's probably on a calculator; they had gone through and punched in a few numbers but didn't show their work, which is very important to do.

>> Tom: I think as teachers we're going to have to be really insistent that the students show every step, even the ones that they can do on the calculator, so we can make the transition from where they got from 390, 78 to 87.

So I think, in that case, that definitely is only worth a 2. Okay.

Well, that concludes our little mini-scoring session.

>> Rochelle: Great job! Thank you very much to Tom's colleagues for giving up some of their time to come in and help with this.

Tom, is this a good representation of what an actual training session looks like, this back-and-forth kind of discussion?

>> Tom: We're certainly hoping that that's the case. I think it's real important that this be a collaborative effort. Also I think it's very important that the rubrics themselves are made up collaboratively. I mean, this is a Herculean task for one person to try to do all of this work themselves. I think this is a major change in the way we approach our test making.

I think, also, just to insist upon what I said at the end, I think that we need to make sure, you know, the old fogies like myself, entering this kind of no-man's-land of dealing with a calculator, you know, what's acceptable, what's not acceptable? Kids are going to have to show all of their work, make the transition. Lynn was saying before that the mental part instruction is no longer on the Math A exam. You know, we want to see how they arrive at their answer. This is a new change in forcing -- making the kids clearly make that transition, where they got their answer.

>> Rochelle: One of the things that we've been talking about is the fact that Lynn said, in terms of scoring, the idea of having math teachers do the majority of the scoring, especially in this part, is so that it does have implications for back in the classroom. What actually can we then take from what we've seen on these papers back into a classroom?

So if one of the suggestions you would have then backs the teachers as they go to instruct in these standards and as we move towards Math A for everybody, along with being able to show the student work, how the students show work, what other kinds of things would you say you learned from this to take back into a classroom?

>> Tom: Well, for example, one of the things we're going to try to do is have our mid-term exams, our quarterly exams and try to mimic -- make some of these changes. We're not into the Math A yet at Guilderland. We're making the transition. We're looking hard at what we want to do, as I mentioned before. It looks like it's going to be about a three-semester transition for us. And what material is going to be taught at what point, that sort of thing. But while we're still doing Course 1, Course 2 and Course 3, we feel we can make some of these transitions and really be insistent that our students start to make this movement forward and help all of us.

>> Rochelle: As you go through this training, as you, you know, are trained yourself and then train other teachers on how to score this exam, do you foresee any changes in your style of classroom instruction to accommodate Math A and what's required on the exam, the skills and the knowledge that students are going to have?

>> Tom: I think that is a very individual question. I don't know if I know exactly the answer to that question perfectly. I would say you would have to. We have so much technology available to us now anyway, and as we've said, this is going to be available to the students in the exam.

So, for example, that simple change is going to have to make that effect -- students don't use a graphing calculator, for example, in their Course 1 exam now, in any of the Course 1, 2 or 3. So, obviously, just that simple change right there is going to impact students. I think the technology that we have available is going to make that kind of difference.

>> Rochelle: As you begin to score student work in your Course 1 exams or Course 1, say homework even, do you begin to use some of the rubrics? Do you begin to do some of the things like require students show how they got to their answers?

>> Tom: Well, I'm kind of an old-fashioned guy. I've always kind of insisted that they do that, too. But, again, I think one of the issues is that it wasn't necessarily clear. There was a little bit of a discrepancy there, and I think that, yes, I think that we're trying to make our students understand. I think we've always been -- always had that as one of our goals. We've had them writing explanations of why things are working.

To give an example, we have a major unit where we don't use the two-column proof. We have our students write paragraph-style proofs, and that's really more of a type of argument that people formulate anyway, and so that -- like I said, we've been moving that way for quite a while now.

>> Rochelle: As you go through your training sessions, what kind of questions do you have teachers asking about the exams and the scoring and what's being taught?

>> Tom: Well, probably the biggest one is do we have to do this?
(Laughter)

The answer is yes. But I think one of the advantages that we have here in New York State also is that we had this exam so that we have a uniformity across the state. I think the thing that we want to insist -- when people ask me why we're doing this, I mean this is a graduation requirement. This is an exit exam. And we want to make sure that the kids in Sag Harbor are graded the same way the kids in Orchard Park are, for example. That is a statewide standard and everybody gets treated equally.

We're trying to take the guesswork out of scoring. By guesswork, I mean we're trying to get away from the punitive scoring technique, to look at a student and have a clear and precise system where everybody knows what this question is supposed to get. And I think that, as Lynn mentioned before, we get a double-sided with some answers written on it -- we do have a guide book about how certain questions are being scored, but again a 10-point question, and I've done some of the work where we've looked at answers and sometimes they range four to five points. So we're going to try to really make sure that every student is treated fairly.

>> Rochelle: Do you get a lot of "Am I opening a huge can of worms here?," the idea that we can give partial credit for some of these? You know, when I was in math class, way back when the dinosaurs roamed the earth, you either got the answer right or you got the answer wrong. And, you know, if I struggle with some of the mathematical things, if I had an understanding teacher, he or she would say, "if you can show me that you understand the concept, that's okay." But that was outside the norm. Then it was black and white. It was right or wrong. Is this a difficult concept for math teachers to deal with now?

>> Tom: I think that we have -- particularly those of us who have been doing this a while, yes. We've been doing something for 26 years. But this isn't about that, and I think that we need to make sure that we all do this as a group. A little piece of advice, for those of us who have been doing this a long time, it's our young rookies that are going to have to live with this decision for a long time. We need to make sure that they're very active in this process and they have a role to play and they take a leading role in this. You know, we can play the mentor role possibly, but they're the ones that are going to have to live with our decisions.

>> Rochelle: Okay. I thought it was very interesting, your comment in the videotape is the rubrics are gospel. If you have any question at all about whether you like the concept or not of, you know, partial scoring or, you know, when you run into a question of what is this, to go back to the rubric. And that's very important for teachers to realize.

>> Tom: And I think also a very important issue, too, is to understand and incorporate the holistic rubrics that we have because there are going to be questions; some students come up with some unique solutions, and there are going to be some things that fall in the cracks, and we need to make sure that, as teachers, we guide ourselves by those holistic rubrics. We create our questions and then create our own specific rubrics. And if we start doing that, I think that the transition will be much smoother.

>> Rochelle: Are you finding a lot of math teachers then are collaborating, getting together as they, you know, look at the rubrics and start talking about teaching Math A?

>> Tom: I think that a lot of people are still on the sidelines. It's not a bad place to be necessarily.
(Laughter)

You know, I think that we're all kind of sitting around and, you know, the train's coming down the tracks, folks, and we need to be prepared.

>> Rochelle: Good. And that's an important issue.

Jackie, I want to ask you about safety nets right now and accommodations for students with special needs who are either taking the exam this year or will be doing it as it becomes a requirement. What's being allowed?

>> Jacqueline: Okay. For the freshmen of '97, they can take the R.C.P. before or after the Regents exam, but they must be participating in a Regents-level curriculum.

>> Rochelle: Okay.

>> Jacqueline: So they have to be preparing to take the Regents Math A or Course 1. And they must take that Regents. Once they take the Regents, if they pass the Regents, if their district has the 55 rule, they can get a local diploma. If they do not pass, then they may use their passing score for the Regents competency. And that's for the freshmen of '97.

>> Rochelle: Okay. Anything else we need to think about on that issue?

>> Jacqueline: Well, there are allowable accommodations right in the "Testing 1-2-3" testing manual for Math A. So on page 41, it does give you allowable accommodations for students with special needs or I.E.P. students and 504 students.

>> Rochelle: Okay, great. And if you don't have a copy of that, we'll show you in a second where you can get a copy of it.

Lynn, we've got a couple of faxes I want to get to quickly. There's a question that came in that says, "Will you please clarify mental math?"

(Laughter)

>> Lynn: See what you said, Tom? You opened up the door!

>> Rochelle: Aha.

>> Lynn: What you'll find, those people who take the Math A this June, you're used to the directions that you normally get at the beginning of Part 2 on, let's say a Course 1 or Course 2 exam. If you read those instructions, it tells you that the youngsters must show all formula substitutions. They must really show where the work comes from, and then it ends with a comment that mental math and mathematics done with a calculator need not be shown.

One of the things we found with the field test is that some youngsters take that a little bit too literally. What we mean by that is that you don't have to show me the algorithm for multiplying or dividing, but you do have to show me the formula, the substitution and then the answer. And if it's got to be rounded off properly, then it has to be rounded off. So it was decided after the field test, we would eliminate that phrase that mental math and arithmetic by the calculator need not be shown, only for the sense that youngsters do have to show all their work. But no, of course, they don't have to show the actual long algorithm; they can use the calculator.

>> Rochelle: Okay. And the following question is: "Isn't it a step backwards to have students showing all of their work?"

>> Lynn: Well, I think what Tom has indicated is that maybe it's a step forward, in that we often are finding youngsters coming up with answers that we don't have any idea where they came from.
(Laughter)

And then someone sits around and says, you know, if you hit these buttons incorrectly on the calculator, you come up with this kind of number.

So we think it's a step in the right direction, mainly to ensure that the youngsters are showing what they know because the object of this test and all the new tests is really to show what the kids know and can do. And if they can show the substitutions and then merely go to the final answer, hopefully we'll have a better indication of their competence in mathematics.

>> Rochelle: Terrific. I think it's a great idea.

In the roughly seven and a half weeks that remain before test day, what resources are available to teachers to either help them prepare students to take the exam this year or as they look to next fall's lesson plans? Well, there are a lot of resources available.

First of all we start with the New York State Education Department website. That is a place to get some information: http://www.nysed.gov/. The next stop would be to check with Jackie and Lynn at the math department. Their E-mails are up on the screen right in front of you and also their telephone number: 518-473-9471. I won't read all those long mail-dot-nysed-dot-gov's. But that's where you can reach Jackie and Lynn if you have some specific questions.

Also we want to let you know that the "Testing 1-2-3" Mathematics A Regents exam manual that accompanies tonight's program, if you need some extra copies or if you didn't get a copy, we can tell you where to get one. Jan Christman can help you out with that. We have her address or phone number available to us as well. There we are. "Testing 1-2-3," mathematics, please contact Jan Christman at 518-474-5922. 518-474-5922, and we have alerted Jan that she may be getting some phone calls. It's a wonderful guide. It does have all those accommodations for special-ed students, a lot of information that was in tonight's program, and some additional information. It's really a wonderful resource as you begin to prepare lesson plans.

Okay. And final thoughts on getting ready? Big word of advice? Tom?

>> Tom: I think we need to start now. I think we need to first of all decide what we're going to teach and when and how we're going to do that.

Just a quick note: One of the things we're considering is actually taking it and making it three separate half-year courses. If the child doesn't advance through one, we're going to have them come back and we're going to recycle through. We don't really feel it makes an awful lot of sense to put a kid in the second level, in the second half of a year and have him unsuccessful in the first half of the year. So we're going to attempt to do that. We're not sure we can, but that's something we're trying to do right now and decide which topics go where.

>> Rochelle: Terrific. Don't wait until the last minute, doesn't really help anybody out, including yourselves -- right? -- as teachers in the classroom.

That's all the time we have for tonight's discussion. I'd like to thank Lynn, Jackie and Tom and the teachers that Tom worked with in preparing our video for us for their time. Thanks also to you, our viewers, for your participation tonight. Your questions and your comments have been very interesting and helpful, and we're glad to know that you're out there watching and that you are concerned about the exam even though it's a little bit down the line before it's actually required.

This is the final program in our "New York Learns: Test Review" series for this year. Next Wednesday, May 5th, from 8 to 9:30p.m., we'll bring you the last of this school year's "New York Learns: Teacher to Teacher" teleconference programs. That discussion centers on technology in the classroom. Much more than a computer lab, technology in school today means incorporating technology into classroom instruction, the computer as another tool for the teacher to use every day.

We're going to visit the totally wired Oswego School District. It's really fascinating. They've got a whole system right up from first grade right straight through to high school, including a television program that students do every single day. We'll see how another teacher in the Sauquoit School District near Utica uses technology as she teaches social studies. And we're going to check out a classroom in Queen's where kindergarteners' computer skills may leave you feeling just a little bit inadequate. It's really unbelievable what these kids can do.

That's Wednesday, May 5th, 8 to 9:30 p.m. It's at your satellite downlink sites and the cable companies participating in Access Education New York.

On Monday and Tuesday, June 7th and 8th, we're going to offer 4th and 8th grade math teachers some very important training on how to score the new math assessments that students will be taking for the first time in live programming beginning at 8:30 a.m. and running until 2:30 p.m., a marathon session. Representatives from Measurement Incorporated will conduct live training sessions in scoring these exams. We'll have individuals being trained right here in our studio and at registered satellite downlink sites. We'll be able to take your questions related to the scoring by fax and by phone and by E-mail, and we'll provide you with immediate responses from representatives of the company which worked with New York State and C.T.B. McGraw-Hill to develop the exam. Some of the registered downlink sites are listed on Page 10 and 11 of the facilitator's guide that's being sent out.

If you would like more information about a downlink site in your area, please contact us at the following E-mail address: jquinn@mail.nysed.gov, or call 518-574-5922.

Before I say good night, I do want to give Tom an opportunity to talk about another resource that teachers may have with regard to "This is a Regents Review." When are you going to be conducting a Regents review on -- PBS, right?

>> Tom: Yes. Sunday morning, the 16th of May, and it will run from 11:30 in the morning to 1 o'clock in the afternoon.

>> Rochelle: Do you actually work out problems on --

>> Tom: Well, we're going to have a call-in session on Regents Review Live. But I will talk -- we will score some things if it gets a little slow, for example. But students who have questions or teachers who have questions or parents who have questions can certainly call in at that time.

>> Rochelle: Okay. Terrific. We know by your work tonight that you'll do a great job and it will be really helpful and informative, help you get ready for those exams coming up.

Again our thanks to everyone for joining us. We appreciate your time and we hope that you enjoy the rest of your evening.