After thinking about this for several months, two questions regarding our school math program and performance stand out:
1. Are we really preparing our students for success after high school, whether in college or in the work place?
2. Regardless of the answer to question one, can we do a better job?
Both of these questions deal with results: Greenwich student results and Greenwich students compared to other students.
I dealt with the first question already in a prior post:
That post figured we are failing about one-third of our students, by not providing an education that would allow them to take college level math without remediation. And I am being generous regarding “college” level, since many colleges and universities grant credit for “college algebra,” which has much the same content as high school Algebra 2. For example, see the course description below for the University of Connecticut’s first level math course, which satisfies part of the Quantitative course requirement for UConn’s College of Arts and Sciences general studies requirement, and earns credits toward graduation.
“Math 104Q is a course designed to serve as preparation for all the other Q courses offered at UConn. It emphasizes two components, the mastery of each is equally important for success in any course employing mathematics. The first component is made up of the collection of fundamental algebraic concepts and their manipulations. Most of this material is taught in High Schools and Community Colleges under the name Intermediate Algebra or Algebra II. Math 104Q covers this material using a college algebra approach. The second component consists of using these algebraic concepts for solving multi-step problems from other disciplines. This practice is called Mathematical Modeling, and is the part of the course that gives Math 104Q its unique interesting flavor, liveliness and usefulness beyond a usual Intermediate Algebra course.”
Interestingly, this course replaced another course which did not earn credit toward graduation. Can almost hear those standards slipping, can’t you?
So my answer to question one is: NO.
To answer question two, we need to determine if anyone in Connecticut, with access to the same resources (curriculum, teachers, technology, administrators) is doing any better. As part of my review of the Math Monitoring Report, I looked at the comparisons between Greenwich and the group of districts with comparable demographics (called DRG B), and between Greenwich and the group of districts outsiders think Greenwich is in, not realizing our diversity (called DRG A, which includes New Canaan, Darien, Westport, and a few other well-off, but homogeneous, districts).
In our (real estate seller’s) dreams, we should be performing as well as the average DRG A district. Ideally, we should be performing at the top of DRG B, as measured on an absolute basis (i.e., our average performance should be better than most if not all of the other DRG B districts average performance). In addition, we should be improving faster than the average improvement of the DRG B districts. In reality, however, we should be performing in the middle of the DRG B group on both an absolute and relative basis.
This reality, if it lasts a few years, will begin to impact real estate prices (negatively, in case you were wondering about direction).
Performance is measured by two Connecticut standardized tests: CMT (for Elementary and Middle Schools) and CAPT (for High School). These tests group student results into one of five categories: Advanced, Goal, Proficient, Basic, Below Basic.
The results for the Proficient level (i.e., percentage of students testing at or above the Proficient level) are used to judge Adequate Yearly Progress for No Child Left Behind purposes. All (100%) children are supposed to be Proficient by the 2014-15 school year. As previously discussed, Proficient doesn’t mean that a student is on track to be able to do college level math. Connecticut’s version of Proficient is barely better than the bottom of the national test’s (NAEP) Basic level.
However, for comparison to other districts, we will use percentage of students at Proficient, Goal and Advanced levels, and we will group grades 3-5 together, grades 6-8 together (all of these grades take the CMT), and keep grade 10 by itself (CAPT).
Comparison of current results (2010-11 school year) shows that, across all three grade groups (3-5, 6-8, 10) and for all three performance levels (Proficient, Goal and Advanced), Greenwich is substantially below the average of the DRG A districts (see charts below). This is to be expected, given Greenwich’s diversity. When comparing Greenwich current results to the average of the DRG B districts, only at the Advanced level for the Middle School (6-8) students and the High School students does Greenwich surpass DRG B. In most of the other comparisons, Greenwich is more than two percentage points behind.
So on an absolute basis, Greenwich is significantly lagging the well-off, DRG A districts, and in most comparisons is lagging the DRG B districts, including across the board at the Elementary School level.
The administration used five years of data to look at trends in Greenwich performance on an absolute basis and on a relative basis to DRG A and B districts. Note that I calculated the 2006-07 High School, DRG A and DRG B figures from raw data, as they were not included in the draft Math Monitoring Report.
There are several ways of comparing trend data. The simple way is to calculate the change from the first year to the last year. This is what the administration did. This gives a crude indication of the trend, since it uses only two data points.
Based on this measure, Greenwich is closing the gap to both DRG A and DRG B districts only at the Proficient level for High School and the Goal level for Middle School. In all other cases, both DRG A and B districts are pulling away from Greenwich. Again, the Elementary Schools lag behind the comparable districts’ improvement at all three performance levels.
What does this mean in conjunction with the absolute measure discussed above? We are behind, and we are falling farther behind.
And remember those two instances where we were still ahead of the DRG B districts for the current reporting year (Advanced level for Middle Schools and High School)? In both cases, we started significantly ahead in 2006-07, but are only barely ahead now. For the Middle School Advanced results, Greenwich had 47.8% of its students at Advanced in 2006-07, versus 46.3% of DRG B students. In the current year (2010-11), Greenwich is barely ahead (54.0% versus 53.9%). For the High School Advanced results, Greenwich started with 43.2% at Advanced versus 34.5% for DRG B. Now, Greenwich is barely ahead (38.5% versus 38.3%). Not much of an achievement, given that the students percentage at the Advanced level actually dropped 4.7% for Greenwich while jumping 3.8% for DRG B. Makes you wonder why the 2006-07 High School data was omitted from the draft report.
Realizing that the crude method used may hide some improvement actually made by our students, I used two other methods, which I feel give a more accurate indication of progress. The first method I call “Progress Toward Perfect” (PTP), which takes into account the starting point, since it is usually harder to make progress as you get closer to a target. That is, it is easier to improve from 80% Proficient to 85% Proficient, than it is to improve from 90% to 95%. PTP measures the percentage gain from the starting point to the target, based on the current performance level. So if the target for everyone is 100% Proficient, and you started at 80% and made it to 85%, PTP = 25% = (85-80) / (100-80). The district that started at 90% and had the same 5% gain has a PTP = 50%, meaning they have closed half their gap to the target.
The comparative results from this one are easy to present. Greenwich had slower progress, at all school levels and at all performance levels, than the average DRG A or DRG B district. Last place, across the board. So even where we had a higher absolute percentage, or a larger gain from start to finish, we trail in closing the gap to the target level, at Proficient, Goal and Advanced. And guess what. The Elementary Schools were not even close.
The second method is more sophisticated, and presents a more accurate depiction of progress than any of the other methods because it takes all five years of data into account. The method utilizes the slope of the line fitted to the five data points. This Slope gives an overall trend for the data. A positive number is an upward sloping line (meaning progress toward the target) and a negative number means you are moving away from the target. To give a better feel for the meaning of the Slope, I calculated what I call “Years to Target (100%)” which uses the current performance level and the Slope to determine how many years it will take, at the same rate of progress (same slope), to achieve the 100% target (i.e., all students at 100% Proficient, Goal or Advanced).
For this result, a glimmer of good news. The Middle Schools at the Goal level and the High School at Proficient actually beat DRG A and DRG B district improvement rates, and the High School at Goal level beats DRG A district improvement rates. However, it looks like it will take about 12 years until all our students are at the Proficient level (NCLB target is 100% by 2014-15, four years away). And again, the Elementary Schools fare very poorly.
So what is the point of this elaborate analysis? First, if anyone tries to tell you that our schools are doing well relative to other comparable districts, check their math. There are a few dim points (i.e., low key bright points), but overall we are behind and falling farther behind. Second, try is I might, I could not find any good news when it comes to the Elementary Schools overall. You have to dig deep to find that only Riverside (at Advanced, Goal and Proficient) and North Street (at Goal and Proficient) beat the average of the DRG A and B districts. Old Greenwich and North Mianus beat the average of the DRG B districts at all levels, as did North Street at Advanced and Dundee at Proficient.
A lot of districts are doing better than we are. And some of them use Everyday Math. A crude analysis I did of fifth grade scores for 2005-05 to 2010-11 school years indicates that districts using Everyday Math had the lowest average performance compared to districts using all other curricula.
Question two: Can we do a better job? YES
Could it be the fault of the curriculum? Is it time for a change? Yes to both questions.
______________________________________________________
Elementary School – DRG Comparison
Advanced | 2006-2007 | 2007-2008 | 2008-2009 | 2009-2010 | Five Year Change | Progress Toward Perfect | Slope | Years to Target (100%) | |
2010-2011 | |||||||||
DRG A | 46.5 | 50.2 | 53.1 | 53.3 | 55.8 | 9.3 | 17.4% | 2.17 | 20.4 |
DRG B | 42.2 | 44.8 | 46.4 | 48.4 | 49.1 | 6.9 | 11.9% | 1.74 | 29.3 |
Greenwich | 42.5 | 42.2 | 45.9 | 45 | 44.9 | 2.4 | 4.2% | 0.76 | 72.5 |
Goal | |||||||||
DRG A | 85.6 | 86.8 | 88.3 | 89.7 | 89.6 | 4 | 27.8% | 1.09 | 9.5 |
DRG B | 81 | 81.6 | 82.9 | 84.4 | 84.8 | 3.8 | 20.0% | 1.04 | 14.6 |
Greenwich | 81.1 | 78.7 | 79.7 | 81.1 | 80.4 | -0.7 | -3.7% | 0.10 | 196.0 |
Proficient | |||||||||
DRG A | 95.2 | 96.6 | 97.6 | 97.4 | 97.5 | 2.3 | 47.9% | 0.54 | 4.6 |
DRG B | 92.9 | 93.7 | 94.7 | 95.4 | 95.5 | 2.6 | 36.6% | 0.69 | 6.5 |
Greenwich | 91.6 | 92 | 92.5 | 93.4 | 93.5 | 1.9 | 22.6% | 0.52 | 12.5 |
Middle School – DRG Comparison
Advanced | 2006-2007 | 2007-2008 | 2008-2009 | 2009-2010 | 2010-2011 | Five Year Change | Progress Toward Perfect | Slope | Years to Target (100%) |
DRG A | 55.7 | 58.2 | 60.8 | 63.6 | 63.3 | 7.6 | 17.2% | 2.06 | 17.8 |
DRG B | 46.3 | 48.1 | 51.4 | 53.8 | 53.9 | 7.6 | 14.2% | 2.09 | 22.1 |
Greenwich | 47.8 | 46.5 | 50 | 52.1 | 54.0 | 6.2 | 11.9% | 1.80 | 25.6 |
Goal | |||||||||
DRG A | 90 | 91.3 | 92.3 | 93 | 92.6 | 2.6 | 26.0% | 0.69 | 10.7 |
DRG B | 82.7 | 84.1 | 86.7 | 87.8 | 87.6 | 4.9 | 28.3% | 1.35 | 9.2 |
Greenwich | 78.4 | 79 | 82.8 | 82.7 | 83.6 | 5.2 | 24.1% | 1.41 | 11.6 |
Proficient | |||||||||
DRG A | 96.8 | 97.4 | 98.1 | 98.6 | 98.7 | 1.9 | 59.4% | 0.50 | 2.6 |
DRG B | 94.3 | 94.6 | 96.5 | 97 | 96.9 | 2.6 | 45.6% | 0.76 | 4.1 |
Greenwich | 92.2 | 92.6 | 93.8 | 93.8 | 94 | 1.8 | 23.1% | 0.48 | 12.5 |
High School – DRG Comparison
Advanced | 2006 -2007# | 2007 -2008 | 2008- 2009 | 2009 - 2010 | 2010-2011 | Five Year Change | Progress Toward Perfect | Slope | Years to Target (100%) |
DRG A | 52.2 | 53.1 | 46 | 47.4 | 53.4 | 1.2 | 2.5% | -0.33 | |
DRG B | 34.5 | 36.9 | 34.6 | 35.1 | 38.3 | 3.8 | 5.8% | 0.58 | 106.4 |
Greenwich | 43.2 | 34.4 | 37.6 | 39.3 | 38.5 | -4.7 | -8.3% | -0.45 | |
Goal | |||||||||
DRG A | 82.1 | 86.8 | 83 | 83.1 | 87 | 4.9 | 27.4% | 0.61 | 21.3 |
DRG B | 66.6 | 72.8 | 70.7 | 72.6 | 73.2 | 6.6 | 19.8% | 1.30 | 20.6 |
Greenwich | 70.8 | 68 | 70.2 | 72.3 | 71.9 | 1.1 | 3.8% | 0.65 | 43.2 |
Proficient | |||||||||
DRG A | 97.0 | 97.2 | 97 | 97.6 | 98.0 | 1.0 | 33.3% | 0.24 | 8.3 |
DRG B | 92.6 | 93.7 | 93.4 | 94.1 | 94.5 | 1.9 | 25.7% | 0.42 | 13.1 |
Greenwich | 89.7 | 89.8 | 92.2 | 91.2 | 92.3 | 2.6 | 25.2% | 0.66 | 11.7 |
# - data calculated by Brian Peldunas, needs to be validated
No comments:
Post a Comment