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Last week Jason Stanford of the Texas Observer wrote an article, titled “Mute the Messenger,” about University of Texas – Austin’s Associate Professor Walter Stroup, who publicly and quite visibly claimed that Texas’ standardized tests as supported by Pearson were flawed, as per their purposes to measure teachers’ instructional effects. The article is also about how “the testing company [has since] struck back,” purportedly in a very serious way. This article (linked again here) is well worth a full read for many reasons I will leave you all to infer. This article was also covered recently on Diane Ravitch’s blog here, although readers should also see Pearson’s Senior Vice President’s prior response to, and critique of Stroup’s assertions and claims (from August 2, 2014) here.

The main issue? Whether Pearson’s tests are “instructionally sensitive.” That is, whether (as per testing and measurement expert – Professor Emeritus W. James Popham) a test is able to differentiate between well taught and poorly taught students, versus able to differentiate between high and low achievers regardless of how students were taught (i.e., as per that which happens outside of school that students bring with them to the schoolhouse door).

Testing developers like Pearson seem to focus on the prior, that their tests are indeed sensitive to instruction. While testing/measurement academics and especially practitioners seem to focus on the latter, that tests are sensitive to instruction, but such tests are not nearly as “instructionally sensitive” as testing companies might claim. Rather, tests are (as per testing and measurement expert – Regents Professor David Berliner) sensitive to instruction but more importantly sensitive to everything else students bring with them to school from their homes, parents, siblings, and families, all of which are situated in their neighborhoods and communities and related to their social class. Here seems to be where this, now very heated and polarized argument between Pearson and Associate Professor Stroup now stands.

Pearson is focusing on its advanced psychometric approaches, namely its use of Item Response Theory (IRT) while defending their tests as “instructionally sensitive.” IRT is used to examine things like p-values (or essentially proportions of students who respond to items correctly) and item-discrimination indices (to see if test items discriminate between students who know [or are taught] certain things and students who don’t know [or are not taught] certain things otherwise). This is much more complicated than what I am describing here, but hopefully this gives you all the gist of what now seems to be the crux of this situation.

As per Pearson’s Senior Vice President’s statement, linked again here, “Dr. Stroup claim[ed] that selecting questions based on Item Response Theory produces tests that are not sensitive to measuring what students have learned.” While from what I know about Dr. Stroup’s actual claims, this trivializes his overall arguments. Tests, after undergoing revisions as per IRT methods, are not always “instructionally sensitive.”

When using IRT methods, test companies, for example, remove items that “too many students get right” (e.g, as per items’ aforementioned p-values). This alone makes tests less “instructionally insensitive” in practice. In other words, while the use of IRT methods is sound psychometric practice based on decades of research and development, if using IRT deems an item as “too easy,” even if the item is taught well (i.e., “instructionally senstive”), the item might be removed. This makes the test (1) less “instructionally sensitive” in the eyes of teachers who are to teach the tested content (and who are now more than before held accountable for teaching these items), and this makes the test (2) more “instructionally sensitive” in the eyes of test developers in that when fewer students get test items correct the better the items are when descriminating between those who know (or are taught) certain things and students who don’t know (or are not taught) certain things otherwise.

A paradigm example of what this looks like in practice comes from advanced (e.g., high school) mathematics tests.

Items capturing statistics and/or data displays on such tests should theoretically include items illustrating standard column or bar charts, with questions prompting students to interpret the meanings of the statistics illustrated in the figures. Too often, however, because these items are often taught (and taught well) by teachers (i.e., “instructionally sensitive”) “too many” students answer such items correctly. Sometimes these items yield p-values greater than p=0.80 or 80% correct.

When you need a test and its outcome score data to fit around the bell curve, you cannot have such, or too many of such items, on the final test. In the simplest of terms, for every item with a p-vale of 80% you would need another with a p-value of 20% to balance items out, or keep the overall mean of each test around p=0.50 (the center of the standard normal curve). It’s best if test items, more or less, hang around such a mean, otherwise the test will not function as it needs to, mainly to discriminate between who knows (or is taught) certain things and who doesn’t know (or isn’t taught) certain things otherwise. Such items (i.e., with high p-values) do not always distribute scores well enough because “too many students” answering such items correct reduces the variation (or spread of scores) needed.

The counter-item in this case is another item also meant to capture statistics and/or data display, but that is much more difficult, largely because it’s rarely taught because it rarely matters in the real world. Take, for example, the box and whisker plot. If you don’t know what this is, which is in and of itself telling in this example, see them described and illustrated here. Often, this item IS found on such tests because this item IS DIFFICULT and, accordingly, works wonderfully well to discriminate between those who know (or are taught) certain things and those who don’t know (or aren’t taught) certain things otherwise.

Because this item is not as often taught (unless teachers know it’s coming, which is a whole other issue when we think about “instructional sensitivity” and “teaching-to-the-test“), and because this item doesn’t really matter in the real world, it becomes an item that is more useful for the test, as well as the overall functioning of the test, than it is an item that is useful for the students tested on it.

A side bar on this: A few years ago I had a group of advanced doctoral students studying statistics take Arizona’s (now former) High School Graduation Exam. We then performed an honest analysis of the resulting doctoral students’ scores using some of the above-mentioned IRT methods. Guess which item students struggled with the most, which also happened to be the item that functioned the best as per our IRT analysis? The box and whisker plot. The conversation that followed was most memorable, as the statistics students themselves questioned the utility of this traditional item, for them as advanced doctoral students but also for high school graduates in general.

Anyhow, this item, like many other items similar, had a lower relative p-value, and accordingly helped to increase the difficulty of the test and discriminate results to assert a purported “insructional sensitivity,” regardless of whether the item was actually valued, and more importantly valued in instruction.

Thanks to IRT, the items often left on such tests are not often the items taught by teachers, or perhaps taught by teachers well, BUT they distribute students’ test scores effectively and help others make inferences about who knows what and who doesn’t. This happens even though the items left do not always capture what matters most. Yes – the tests are aligned with the standards as such items are in the standards, but when the most difficult items in the standards trump the others, and many of the others that likely matter more are removed for really no better reason than what IRT dictates, this is where things really go awry.