New York State
A nice addition to the links here: f(t) is a new (from July) high school math teacher blog. Kate teaches in Syracuse, New York. (I’ve been there!)
So far she’s posted problems, lesson ideas, and a little bit about her work. Nicely written, easy to read.
Best of luck!
In New York State, each school gets a “report card” each year, full of data about the school. This year’s is late (maybe by two months). But principals have embargoed versions, and this year’s report cards, when issued, will include teacher turnover rates for each school.
How calculated? Total teachers who don’t return, divided by total teachers in the new school year. It’s about as simple as it gets.
What good is it? It tells us which schools teachers leave. Sure there can be blips (a bunch of teachers get pregnant in the same year, for example), but when we look at several years, we can get a sense of what is going on. Turnover rates of 30, 40, 50% are red flags.
How old? Several years behind. Maybe 2003 - 04, 2004 - 05, and 2005 - 06? I wish I knew for sure.
How can we use them? They will help us target schools that are abusing teachers or otherwise providing lousy work environments. They will inform new teachers about places that are bad to apply. The fact that they are being published may give principals pause before U’ing new teachers without trying to improve them first.
What else? Once teacher turnover numbers are out there, we will need to work to update the data. Two or three year old numbers have limited use in a rapidly changing system.
I want to write about the cut score. 30 out of 87 is passing. That’s low.
And I sat on a committee that helped recommend a cut score. But I signed a confidentiality agreement, and neither the State of New York nor the vendor have given a clear response about what is covered and what is not covered by the agreement.
So I will restrict myself to what I know or could have figured out outside of the Measurement Review Committee meetings.
Short version (notes, not sentences):
- State expected higher scores, and was stuck. 30 out of 87 is embarrassingly low, means that a more normal number would have come with a high failure rate (politically unacceptable)
- Integrated Algebra - too many topics. Like a topic each day, every day.
- Integrated Algebra - mediocre/ lousy course. Algebra w/stats and probability? Some set theory? What holds it together? No cohesion.
- Integrated Algebra Standards - for a course? or for graduation? Huge problem. Can’t have the same standards for both, or they fail for both. (exam was way too easy for bright kids - the other side of the coin)
- Performance Standards - should only be content standards in mathematics. Deciding which math to use is hard, real hard. At college, engineering students show up with lots of mathematical skills, and the school teaches them how to decide which equation to use where.
My Recommendations:
- New standards. Algebra? Geometry? Trig? Maybe, maybe, maybe. But definitely a separate and clear list of graduation standards in math. We don’t have those today.
- Performance standards: No. Take them out. Test kids on skills and mathematical content. No more grilling on reading comprehension/vocabulary. That is part of other exams.
- Topics: Reduce the number of “indicators” (individual topics). Fewer, with some depth. Take out probability and statistics.
- In the meantime? Who knows? Keep a low cut score while fixing the mess?
In mathematics, we have traditionally taught skills, and then taught applications or “word problems” that go along with those specific skills and use those skills in specific ways. For example, after learning subtraction, pupils read and answer “take away” problems. Later, after learning subtraction with decimals, students work on change problems. After learning percents, students will answer discount questions, or calculate tax or tips. At the level I teach, algebra, after learning to factor, students might solve area problems. After solving equations with fractions, my students apply the skill to “work” or “mixture” problems. Even knowing the skill, these problems are hard.
But performance standards encourage something else. They give the student an unfamiliar situation, and ask the student to identify and apply the correct mathematical skill. Now, at the “Integrated Algebra” level the range of mathematics is not that great, so this is not impossible. But it is far more difficult than the standards writers understand. It is what colleges do with engineers (come to us with a large mathematics skill set, and we will teach you how to choose the appropriate equations). Using performance standards means the mathematics assessments are littered with science, technology, and artificial and contrived context.
New York State introduced performance standards in mathematics with Math A and B ten years ago. They reduced their role with the switch to Integrated Algebra, Geometry and Algebra 2/Trigonometry, but performance standards must be eliminated.
Later today, if all goes well… Later this morning, if all goes very well, New York State Education Department will be posting a conversion chart for the Integrated Algebra.
The conversion chart will probably be here. Also, please complete the Teacher Evaluation of the Exam.
For previous posts on Integrated Algebra: General - Procedures - Scoring
For previous posts on the Regents in General: from me - from a retired NY State math guy
Finally, I was on the Integrated Algebra Measurement Review Committee. (In Albany in April, and then again Tuesday). Some of what we did remains confidential until after the score chart comes out. Trust me, I will have more to say, soon.
The June 2008 Math B exam is available as a PDF from JMAP.
I already posted three bad problems, and then three more. There is ongoing math teacher discussion of individual questions at a Math A/B listserve run by the Association of Mathematics Teachers of New York State)
Here’s the last two that really bother me are 33 and 34, the 6 point free response questions, most valuable on the exam:
#33 Solve for x:
So here’s the deal: TeX Embedding failed!
That’s what the State expected (then solve the quadratic, reject the bad root. Talk about failure to anticipate!
Most kids seem to have done this, instead:
(more common answer, and the worst problem, below the fold)
And the state was not prepared for this. The only guideline that comes close calls for a 50% deduction (3 of 6 points) Clearly the illegal cancellation is a mistake, unless the kid restricts x. But just as clearly, deducting 1 of 6 points would be appropriate. So what’s the state do? In panic, clearly, they say to mark it completely right…
Helps my students, but doesn’t make me happy.
#34. This is the worst.
Gerardo and Bennie are pushing a box. Gerardo pushes with a force of 50 pounds in an easterly direction, and Bennie pushes with a force of 39 pounds in a northeasterly direction. The resultant force forms an angle of 32° with the 39-pound force.
Find the angle between the 50-pound force and the 39-pound force, to the nearest tenth of a degree.
Find the magnitude of the resultant force, to the nearest pound.
So, let’s hear it for meaning what they mean and not what they say. “Easterly” means due east… 0 in polar coordinates. “Northeasterly”? Guess what? it doesn’t mean 45° . Any student taking physics resolves the vectors into components, using the regular meanings of the words, and gets lost.
Bravo, SED. Your rubric fails to specify how many points to deduct from the child who does not misread the way you intended.
The June 2008 Math B exam is available as a PDF from JMAP.
I already posted three bad problems. (edit: There is ongoing math teacher discussion of individual questions at a Math A/B listserve run by the Association of Mathematics Teachers of New York State). Here are three more problems that bother me:
#25 (2 point, free response)
The accompanying diagram shows the peak of a roof that is in the shape of an isosceles triangle. A base angle of the triangle is 50° and each side of the roof is 20.4 feet. Determine to the nearest tenth of a square foot the area of this triangular region.
Consult the diagram in the link above. An isosceles triangle is drawn, sides are marked 20.4 and 20.4, and one base angle is marked 50 degrees.
Their intent was for kids to find the missing angles (50, 50, 80) and apply the formula (given in the text booklet): Area = (½)(ab)sinC where C=80 and a=b=20.4
But kids dropped altitudes, working slightly longer around, and ended up with a minor rounding error. New York says: 1 point. They did more work, good work, and only get 1 out of 2 points?
The question design is poor. It could have been anticipated that there were two, equally reasonable, but not equally easy, points of attack. It wasn’t. No way a two point question.
(more beneath the fold)
#27 (4 point, free response)
Students have a table with dewpoint data by temperature, and are asked to perform an exponential regression, rounding all to the nearest thousandth.
There’s only one way for kids to do this: memorize procedure. Plug both lists into the calculator, call for exponential regression, round the base and the constant, and plug in 50. Four points for memorizing a word, and a bunch of TI keystrokes?
#28 (4 point, free response)
A right triangle, FEP, is drawn with altitude FM dropped to the hypotenuse. Legs are labeled “Elm” and “Poplar,” altitude is “Fern” and hypotenuse is “Maple”. ( Consult the diagram in the link above.)
Four streets in a town are illustrated in the accompanying diagram. If the distance on Poplar Street from F to P is 12 miles, and the distance on Maple Street from E to M is 10 miles, find the distance on Maple Street, in miles, from M to P.
What makes this one bad is its history. In the 1980s and 1990s this problem, sans streets, was a typical Course II question. One version or other was on every Course II Regents that I can remember. But this is the first time, I think, it was ever on B (in 20 odd exams), and I am not certain it is in the State’s list of topics.
Now, the bizarre rubric allows for 2 points for good work with one “conceptual” error. I would interpret a bad guess that the altitude bisects the angle to be a conceptual error.
Kids whose teachers refuse to let go of this topic had a good chance of knowing a shortcut. Kids whose teachers showed them this, even once, would likely search for similar triangles and proportions, and get it or come close. But kids whose teachers did not teach this were likely to flounder about. Read some actual kid comments here on Yahoo Answers: 1 - 2 - 3 - 4 - 5 - 6.
The level of difficulty becomes unpredictable when the test-maker does not adequately communicate the possible range of content to the teachers. And before you start jumping up and down about teachers not covering enough, recall that the “content” of this mile-wide exam goes from circle proofs to trig to functions to regression to complex to … Decisions about what to do and what not to do are high stakes decisions. Adding the occasional “extra” to the curriculum can be risky business. What can we afford to omit?
In my school, fewer students than usual left early (almost none before 2 and a half hours had passed). More than usual worked up to the 3 hour mark.
Meanwhile, at Yahoo Answers, I found this student discussion of the difficulty level.
I also found this conversation about the language on the dilation question.
The June 2008 Math B exam is fairly typical - and that includes too many problematic questions.
Format: the exam is made up of 20 2-point multiple choice questions, 6 2-point free response questions, 6 4-point free response questions, and 2 6-point free response questions (yes, 88 points, scaled so that 46 this year is passing)
I chose several questions I think are bad: one multiple choice, 2 2-point free response, 3 4-point free response, and both 6-point free response.
#18 (multiple choice) A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?
Diagram (omitted) is normal. Whole question is normal. Except lawn care companies don’t measure angles in radians. And math-y folks measure angles in multiples of π radians. Look folks, artificial, contrived context is confusing and weighs problems down. Don’t do it.
(more below the fold)
#21 (2 point free response) The entire graph of f(x) is symmetric with respect to the origin. If the accompanying graph represents f(x) for x ≥ 0, sketch, on the same axes, the graph of f(x) for x ≤ 0.
Leave aside the duplicated value of x. The diagram looks like 
#31 (4 point free response) The engineering office in the village of Whitesboro has a map of the village that is laid out on a rectangular coordinate system. A traffic circle located on the map is represented by the equation 
Find the coordinates of the new center of the traffic circle.
Find the length of the radius of the new traffic circle.
Where to begin? The transformation may be a bit confusing. All the regular NYS texts dilate 95% of the time about the origin, and usually do not state as much. Someone caught this, corrected the language, but leaves the students with a clarifying detail they are not used to reading. Further, the dilation is written as
But more. Context? Could you get more artificial? Bizarre? Village laid out in a rectangle, ok. But x-y equation for a street feature? Arbitrary transformation of a traffic circle? And the result, I’m glad they didn’t give the kids a graph to plot this one on, one traffic circle entirely enclosing the other???
3 more problems, coming soon.
This is a transition year for math Regents in New York State. Math A had its last June administration. Integrated Algebra was given for the first time. But our worst exam, Math B, has two more years to go.
This year’s Math B was fairly typical. The Association of Mathematics Teachers of New York State runs a listserve, and you can find discussion of the exam there. Old Math B exams (not the current one yet), are posted by New York State here.
Math B covers a wide variety of topics that might normally fall into a geometry, algebra II, trig, or precalculus course. There are circles, law of cosines, transformations, logs, compound interest, composition, summations, imaginary numbers, regression… And fractions, coordinate geometry, quadratics…
Math B places these topics into bizarre context, in order to claim “application of math” or “real world math.” A sprinkler covering an angle of one radian? Children keeping score with complex numbers?
In other words, hello grab bag. Mile wide, inch deep. Unpredictable. So, you can concentrate on the exam, and teach over one hundred topics, fairly superficially. Or you can take your chances.
In my school, we teach Algebra, Geometry, Trig, and deal with the misfit. We add units to the end of the trig course to cover the missing material. Many other schools use curricula specially devised to strip depth from all topics and to cover exactly the right group of topics over two years.
The irony is, publishers have taken old Algebra, Geometry, and Trig books, made new covers with titles Math A, Math A/B and Math B, and sold them just fine in New York State. With minimal changes - usually a bit of front material. Blecch.
