Student performance on California’s achievement tests in almost every subject at almost every grade level by every ethnicity has risen — despite recent cutbacks to education funding, according to 2012 STAR (Standardized Testings and Reporting) results released by the California Department of Education today.

But a substantial achievement gap persists between low-income and higher-income students, and between African American and Latino students and their white and Asian peers.

Overall, 57 percent of the 4.7 million students tested proficient or advanced in English and 51 percent scored at least proficient in math — a substantial improvement since 2003, when the tests were first based on state standards and included in a school’s Academic Performance Index (API). In 2003, 35 percent tested proficient or better in both English and math.

“In less than a decade, California has gone from having only one student in three score proficient to better than one student in two,” said State Superintendent of Public Instruction Tom Torlakson in a statement.

The percentage of students in second grade scoring proficient in mathematics dropped by two points, and overall achievement in the General Mathematics CST and the Summative High School Mathematics test remained the same as last year, with 54 percent scoring proficient or higher in the latter. But in every other subject and grade, there was improvement over 2011 scores.

However, Doug McRae, a retired testing publisher from Monterey who was an adviser when the STAR tests were being developed, cautioned that the results are not quite as dramatic as they seem because some students who were doing poorly on the CSTs are no longer required to take them.

McRae, who analyzes results of the test each year, noted that over the past few years, more students in special education have been taking the California Modified Assessments (CMAs) instead of the California Standards Tests (CSTs), which are the regular STAR exams. To be eligible to take the modified assessments, students must have scored below basic or far below basic on the standards tests the year before, McRae said. Removing almost 210,000 students who did poorly on those exams tends to make the results a little rosier than they actually are, he added. The modified assessments did not exist in 2003.

In his analysis, McRae noted that there has been substantial improvement in the number of students who take Algebra I in 7th or 8th grade, as well as the number of those middle school students who test proficient or advanced. In 2012, 68 percent of students had taken Algebra I by 8th grade, and 53 percent scored proficient or advanced – a large increase since 2003, when 32 percent of middle school students took it and 39% tested at least proficient.

Substantially more African American and Latino students are taking Algebra I and succeeding in the course. But the achievement gap still remains between those students and their white and Asian peers, as does the gap between low-income and higher-income students.

In the most extreme example, 32 percent of economically disadvantaged African American students scored proficient or advanced on the mathematics test in 2012. That was exactly twice as many as in 2003. However, this year, 85 percent of higher-income Asian students scored proficient or advanced — a 53 percentage-point difference between them and their low-income, African American classmates. In 2003, the difference between the two groups was 55 percentage points.

A press release from the California Department of Education includes summaries of the data and charts, including breakdowns by ethnicity and income. The full test results are available on the California Department of Education’s Standardized Testing and Reporting (STAR) website. Under the STAR program, students can attain one of five levels of performance for each subject: advanced, proficient, basic, below basic, and far below basic.

Filed under: Featured, Reporting & Analysis · Tags: Tom Torlakson

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The appraisal of achievement gaps in terms of percentage point differences between proficiency rates in this article is fairly standard. But like other analyses of racial and ethnic differences in proficiency rates, whatever the method, the appraisal fails to recognize the ways measures of difference tend to be affected by the changes in the prevalence of an outcome. Percentage point differences tend to be small where rates are generally low, increase as rates grow larger, and then decrease as rates grow very large.

Consider a situation where the mean scores of an advantaged group (AG) and a disadvantaged group (DG) differ by half a standard deviation on three tests that differ in their difficulty. On Test 1 (the most difficult), the initial pass rates are 20% for AG and 9% for DG, an 11 percentage point difference. If the cutoff is lowered to the point where 50% of AG passes DG’s pass rate would be about 31%. So now the difference would be about 17 percentage points, an 8 point increase.

On Test 2 (the second most difficult), the initial pass rates are 50% for AG and 31% for DG, a 19 percentage point difference. If the cutoff is lowered to the point where 70% of AG passes, DG’s pass rate would be about 51%. In this case, the difference remains 19 percentage points.

On Test 3 (the least difficult), the initial pass rates are 70% for AG and 51% for DG, a 19 percentage point difference. If the cutoff is lowered to the point where 90% of AG passes, DG’s pass rate would be about 78%. So now, the difference would be about 12 percentage points, a 7 point decrease.

One would observe the same patterns if, without lowering cutoffs, test performance was improved such as to enable everyone initially scoring between the two points to pass a test at the higher cutoff.

The link below shows these patterns across the test score distributions. It also shows the pattern (also evident in the figures above) whereby, regardless of the rate ranges at issue, as the cutoff is lowered, the relative difference in pass rates decreases while the relative difference in failure rates increases.

http://www.jpscanlan.com/images/BSPS_2006_Table_1.pdf

The patterns must be borne in mind not only in appraising changes over time but in appraising achievement gaps as to different tests or in different settings.

Implicit in the examples above is that an appraisal of differences in circumstances of advantaged and disadvantaged group reflected by proficiency rates should be based on deriving from the rates for the groups being compared the difference between means of the underlying distributions. In the case of the comparison of rates of achieving proficiency in mathematics of high-income Asian and low-income African American students in the article – 71% for the former and 16% for the latter in 2003 and 85% for the former and 32% for the latter in 2012, a difference of 55 percentage point differences in 2003 and 53 percentage points in 2012 – the estimated difference between means would be 1.54 standard deviations in 2003 and 1.50 standard deviations in 2012. In this instance, there occurred a slight decline in the disparity, which was consistent with the conclusion one would draw based on the change in the percentage point difference. But that does not mean that the percentage point difference – or any other indicator that tends to change solely as overall rates change – is a useful disparity measure. For society’s principal interest is in identifying and understanding patterns that are not solely functions of overall changes in the frequency of an outcome akin to those effected by the lowering of a test cutoff.

Of course, in the testing context, one does not have to derive the difference between means of the underlying distributions on the basis of outcome rates. One can examine the distributions themselves.

For a number of examples of the varied ways observers appraise educational disparities based on measures of differences in proficiency rates without consideration of the way measures tend to change solely because test scores generally improve, see these three web pages.

http://jpscanlan.com/educationaldisparities.html

http://jpscanlan.com/educationaldisparities/disparitiesbysubject.html

http://jpscanlan.com/educationaldisparities/harvardcrpnclnstudy.html

Is this meant to imply that there may be acceptable gaps? While I think I understand these phenomena, the fact that a gap exists at all seems to transcend what you describe. Even then, do you think the rates have reached a point where much inaccuracy has resulted? if so, in which direction?

Personally, I think the gaps are inaccurate for many other, more mundane reasons (CMA ‘shift’, special education classification rates, income-level concentrations, etc, etc).

Well 2% is not too big of a drop. It just means there are certain areas where we aren’t progressing anymore.

While I agree that CMA can be used to ‘game’ the system, I have seen as many examples of schools who make a point of continuing CST focus for SWD as those who have move more fundamentally to CMA. Statewide, the number of SWD CST takers dropped by 8% last year and the number of CMA takers increased by 16% (ELA only). So clearly, not everyone is sticking to the CST.

Personally, I think given this gaming, and given general lack of disaggregation for SWD data anyway, I would not have a problem simply focusing on non-SWD takers (CST or CMA) as a statewide measure. That admittedly excludes a group of kids we want to be measuring, but until we can get real data that can accurately compare them with their peers, trying to divine–and remove–that ‘inflation’ is a waste of time. imho. I also think its useful to focus on 2nd grade, where taking the CMA is not possible.

Lets not try to humor those who are trying to turn accountability into a game. Its ok to believe accountability is invalid and unnecessarily punitive, but pretending its working isnt the way to get that point across. imho, of course.. :-)