Not all uses of data are equal

Gil Press worries that “big data enthusiasts may encourage (probably unintentionally) a new misguided belief, that ‘putting data in front of the teacher’ is in and of itself a solution [to what ails education today].”

As an advocate for the better use of educational data and learning analytics to serve teachers, I worry about careless endorsements and applications of “big data” that overlook these concerns:

1. Available data are not always the most important data.
2. Data should motivate providing support, not merely accountability.
3. Teachers are neither scientists nor laypeople in their use of data. They rely on data constantly, but need representations that they can interpret and turn into action readily.

Assessment specialists have long noted the many uses of assessment data; all educational data should be weighed as carefully, even more so when implemented at a large scale which magnifies the influence of errors.

Standardized tests as market distortions

Some historical context on how standardized tests have affected the elite points out how gatekeepers can magnify the influence of certain factors over others– whether through chance or through bias:

In 1947, the three significant testing organizations, the College Entrance Examination Board, the Carnegie Foundation for the Advancement of Teaching and the American Council on Education, merged their testing divisions into the Educational Testing Service, which was headed by former Harvard Dean Henry Chauncey.

Chauncey was greatly affected by a 1948 Scientific Monthly article, “The Measurement of Mental Systems (Can Intelligence Be Measured?)” by W. Allison Davis and Robert J. Havighurst, which called intelligence tests nothing more than a scientific way to give preference to children from middle- and upper-middle-class families. The article challenged Chauncey’s belief that by expanding standardized tests of mental ability and knowledge America’s colleges would become the vanguard of a new meritocracy of intellect, ability and ambition, and not finishing schools for the privileged.

The authors, and others, challenged that the tests were biased. Challenges aside, the proponents of widespread standardized testing were instrumental in the process of who crossed the American economic divide, as college graduates became the country’s economic winners in the postwar era.

As Nicholas Lemann wrote in his book “The Big Test,” “The machinery that (Harvard President James) Conant and Chauncey and their allies created is today so familiar and all-encompassing that its seems almost like a natural phenomenon, or at least an organism that evolved spontaneously in response to conditions. … It’s not.”

As a New Mexico elementary teacher and blogger explains:

My point is that test scores have a lot of IMPACT because of the graduation requirements, even if they don’t always have a lot of VALUE as a measure of growth.

Instead of grade inflation, we have testing-influence inflation, where the impact of certain tests is magnified beyond that of other assessment metrics. It becomes a kind of market distortion in the economics of test scores, where some measurements are more visible and assume more value than others, inviting cheating and “gaming the system“.

We can restore openness and transparency to the system by collecting continuous assessment data that assign more equal weight across a wider range of testing experiences, removing incentives to cheat or “teach to the test”. Adaptive and personalized assessment go further in alleviating pressures to cheat, by reducing the inflated number of competitors against whom one may be compared. Assessment can then return to fulfilling its intended role of providing useful information on what a student has learned, thereby yielding better measures of growth and becoming more honestly meritocratic.

Beating cheating

Between cheating to learn and learning to cheat, current discourse on academic dishonesty upends the “if you can’t beat ’em, join ’em” approach.

From Peter Nonacs, UCLA professor teaching Behavioral Ecology:

Tests are really just measures of how the Education Game is proceeding. Professors test to measure their success at teaching, and students take tests in order to get a good grade.  Might these goals be maximized simultaneously? What if I let the students write their own rules for the test-taking game?  Allow them to do everything we would normally call cheating?

And in a new MOOC titled “Understanding Cheating in Online Courses,” taught by Bernard Bull at Concordia University Wisconsin:

The start of the course will cover the basic vocabulary and different types of cheating. The course will then move into discussing the differences between online and face-to-face learning, and the philosophy and psychology behind academic integrity. One unit will examine the best practices to minimize cheating.

Cheating crops up whenever there is a mismatch between effort and reward, something which happens often in our current educational system. Assigning unequal rewards to equal efforts biases attention toward the inflated reward, motivating cheating. Assigning equal rewards to unequal efforts favors the lesser effort, enabling cheating. The greater the disparities, the greater the likelihood of cheating.

Thus, one potential avenue for reducing cheating would be to better align the reward to the effort, to link the evaluation of outputs more closely to the actual inputs. High-stakes tests separate them by exaggerating the influence of a single, limited snapshot. In contrast, continuous, passive assessment brings them closer by examining a much broader range of work over time, collected in authentic learning contexts rather than artificial testing situations. Education then becomes a series of honest learning experiences, rather than an arbitrary system to game.

In an era where students learn what gets assessed, the answer may be to assess everything.

Using personalized assessment to change the high-stakes testing culture

Criticisms of high-stakes tests abound as we usher in the start of K-12 testing season. Students worry about being judged on a bad day and note that tests measure only one kind of success, while teachers lament the narrowing of the curriculum. Others object to the lack of transparency in a system entrusted with such great influence.

Yet the problem isn’t tests themselves, but relying on only a few tests. What we actually need is more information, not less. Ongoing assessment collected from multiple opportunities, in varied contexts, and across time can help shield any one datapoint from receiving undue weight.

Personalized assessment goes further in acknowledging the difference between standardization in measurement (valuable) and uniformity in testing (unhelpful). Students with different goals deserve to be assessed by different standards and methods, and not arbitrarily pitted against each other in universal comparisons. Gathering more data from richer contexts that are better matched to students’ learning needs is a fundamental tenet of personalization.

If assessments are diagnoses, what are the prescriptions?

I happen to like statistics. I appreciate qualitative observations, too– data of all sorts can be deeply illuminating. But I also believe that the most important part of interpreting them is understanding what they do and don’t measure. And in terms of policy, it’s important to consider what one will do with the data once collected, organized, analyzed, and interpreted. What do the data tell us that we didn’t know before? Now that we have this knowledge, how will we apply it to achieve the desired change?

In an eloquent, impassioned open letter to President Obama, Education Secretary Arne Duncan, Bill Gates and other billionaires pouring investments into business-driven education reforms (revised version at Washington Post), elementary teacher and literacy coach Peggy Robertson argues that all these standardized tests don’t give her more information than what she already knew from observing her students directly. She also argues that the money that would go toward administering all these tests would be better spent on basic resources such as stocking school libraries with books for the students and reducing poverty.

She doesn’t go so far as to question the current most-talked-about proposals for using those test data: performance-based pay, tenure, and firing decisions. But I will. I can think of a much more immediate and important use for the streams of data many are proposing on educational outcomes and processes: Use them to improve teachers’ professional development, not just to evaluate, reward and punish them.

Simply put, teachers deserve formative assessment too.

Statistical issues with applying VAM

There’s a wonderful statistical discussion of Michael Winerip’s NYT article critiquing the use of value-added modeling in evaluating teachers, which I referenced in a previous post. I wanted to highlight some of the key statistical errors in that discussion, since I think these are important and understandable concepts for the general public to consider.

  • Margin of error: Ms. Isaacson’s 7th percentile score actually ranged from 0 to 52, yet the state is disregarding that uncertainty in making its employment recommendations. This is why I dislike the article’s headline, or more generally the saying, “Numbers don’t lie.” No, they don’t lie, but they do approximate, and can thus mislead, if those approximations aren’t adequately conveyed and recognized.
  • Reversion to the mean: (You may be more familiar with this concept as “regression to the mean,” but since it applies more broadly than linear regression, “reversion” is a more suitable term.) A single measurement can be influenced by many randomly varying factors, so one extreme value could reflect an unusual cluster of chance events. Measuring it again is likely to yield a value closer to the mean, simply because those chance events are unlikely to coincide again to produce another extreme value. Ms. Isaacson’s students could have been lucky in their high scores the previous year, causing their scores in the subsequent year to look low compared to predictions.
  • Using only 4 discrete categories (or ranks) for grades:
    • The first problem with this is the imprecision that results. The model exaggerates the impact of between-grade transitions (e.g., improving from a 3 to a 4) but ignores within-grade changes (e.g., improving from a low 3 to a high 3).
    • The second problem is that this exacerbates the nonlinearity of the assessment (discussed next). When changes that produce grade transitions are more likely than changes that don’t produce grade transitions, having so few possible grade transitions further inflates their impact.
      Another instantiation of this problem is that the imprecision also exaggerates the ceiling effects mentioned below, in that benefits to students already earning the maximum score become invisible (as noted in a comment by journalist Steve Sailer

      Maybe this high IQ 7th grade teacher is doing a lot of good for students who were already 4s, the maximum score. A lot of her students later qualify for admission to Stuyvesant, the most exclusive public high school in New York.
      But, if she is, the formula can’t measure it because 4 is the highest score you can get.

  • Nonlinearity: Not all grade transitions are equally likely, but the model treats them as such. Here are two major reasons why some transitions are more likely than others.
    • Measurement ceiling effects: Improving at the top range is more difficult and unlikely than improving in the middle range, as discussed in this comment:

      Going from 3.6 to 3.7 is much more difficult than going from 2.0 to 2.1, simply due to the upper-bound scoring of 4.

      However, the commenter then gives an example of a natural ceiling rather than a measurement ceiling. Natural ceilings (e.g., decreasing changes in weight loss, long jump, reaction time, etc. as the values become more extreme) do translate into nonlinearity, but due to physiological limitations rather than measurement ceilings. That said, the above quote still holds true because of the measurement ceiling, which masks the upper-bound variability among students who could have scored higher but inflates the relative lower-bound variability due to missing a question (whether from carelessness, a bad day, or bad luck in the question selection for the test). These students have more opportunities to be hurt by bad luck than helped by good luck because the test imposes a ceiling (doesn’t ask all the harder questions which they perhaps could have answered).

    • Unequal responses to feedback: The students and teachers all know that some grade transitions are more important than others. Just as students invest extra effort to turn an F into a D, so do teachers invest extra resources in moving students from below-basic to basic scores.
      More generally, a fundamental tenet of assessment is to inform the students in advance of the grading expectations. That means that there will always be nonlinearity, since now the students (and teachers) are “boundary-conscious” and behaving in ways to deliberately try to cross (or not cross) certain boundaries.
  • Definition of “value”: The value-added model described compares students’ current scores against predictions based on their prior-year scores. That implies that earning a 3 in 4th grade has no more value than earning a 3 in 3rd grade. As noted in this comment:

    There appears to be a failure to acknowledge that students must make academic progress just to maintain a high score from one year to the next, assuming all of the tests are grade level appropriate.

    Perhaps students can earn the same (high or moderate) score year after year on badly designed tests simply through good test-taking strategies, but presumably the tests being used in these models are believed to measure actual learning. A teacher who helps “proficient” students earn “proficient” scores the next year is still teaching them something worthwhile, even if there’s room for more improvement.

These criticisms can be addressed by several recommendations:

  1. Margin of error. Don’t base high-stakes decisions on highly uncertain metrics.
  2. Reversion to the mean. Use multiple measures. These could be estimates across multiple years (as in multiyear smoothing, as another commenter suggested), or values from multiple different assessments.
  3. Few grading categories. At the very least, use more scoring categories. Better yet, use the raw scores.
  4. Ceiling effect. Use tests with a higher ceiling. This could be an interesting application for using a form of dynamic assessment for measuring learning potential, although that might be tricky from a psychometric or educational measurement perspective.
  5. Nonlinearity of feedback. Draw from a broader pool of assessments that measure learning in a variety of ways, to discourage “gaming the system” on just one test (being overly sensitive to one set of arbitrary scoring boundaries).
  6. Definition of “value.” Change the baseline expectation (either in the model itself or in the interpretation of its results) to reflect the reality that earning the same score on a harder test actually does demonstrate learning.

Those are just the statistical issues. Don’t forget all the other problems we’ve mentioned, especially: the flaws in applying aggregate inferences to the individual; the imperfect link between student performance and teacher effectiveness; the lack of usable information provided to teachers; and the importance of attracting, training, and retaining good teachers.

Some history and context on VAM in teacher evaluation

In the Columbia Journalism Review’s Tested: Covering schools in the age of micro-measurement, LynNell Hancock provides a rich survey of the history and context of the current debate over value-added modeling in teacher evaluation, with a particular focus on LA and NY.

Here are some key points from the critique:

1. In spite of their complexity, value-added models are based on very limited sources of data: who taught the students, without regard to how or under what conditions, and standardized tests, which are a very narrow and imperfect measure of learning,

No allowance is made for many “inside school” factors… Since the number is based on manipulating one-day snapshot tests—the value of which is a matter of debate—what does it really measure?

2. Value-added modeling is an imprecise method whose parameters and outcomes are highly dependent on the assumptions built into the model.

In February, two University of Colorado, Boulder researchers caused a dustup when they called the Times’s data “demonstrably inadequate.” After running the same data through their own methodology, controlling for added factors such as school demographics, the researchers found about half the reading teachers’ scores changed. On the extreme ends, about 8 percent were bumped from ineffective to effective, and 12 percent bumped the other way. To the researchers, the added factors were reasonable, and the fact that they changed the results so dramatically demonstrated the fragility of the value-added method.

3. Value-added modeling is inappropriate to use as grounds for firing teachers or calculating merit pay.

Nearly every economist who weighed in agreed that districts should not use these indicators to make high-stakes decisions, like whether to fire teachers or add bonuses to paychecks.

Further, it’s questionable how effective it is as a policy to focus simply on individual teacher quality, when poverty has a greater impact on a child’s learning:

The federal Coleman Report issued [in 1966] found that a child’s family economic status was the most telling predictor of school achievement. That stubborn fact remains discomfiting—but undisputed—among education researchers today.

These should all be familiar concerns by now. What this article adds is a much richer picture of the historical and political context for the many players in the debate. I’m deeply disturbed that NYS Supreme Court Judge Cynthia Kern ruled that “there is no requirement that data be reliable for it to be disclosed.” At least Trontz at the NY Times acknowledges the importance of publishing reliable information as opposed to spurious claims, except he seems to overlook all the arguments against the merits of the data:

If we find the data is so completely botched, or riddled with errors that it would be unfair to release it, then we would have to think very long and hard about releasing it.

That’s the whole point: applying value-added modeling to standardized test scores to fire or reward teachers is unreliable to the point of being unfair. Adding noise and confusion to the conversation isn’t “a net positive,” as Arthur Browne from The Daily News seems to believe; it degrades the discussion, at great harm to the individual teachers, their students, the institutions that house them, and the society that purports to sustain them and benefit from them.

Look for the story behind the numbers, not the numbers alone

This time I’ll let the journalists get away with their fondness for reporting the compelling individual story, since the single counterexample is the whole point here.

High-stakes testing was bad enough. But high-stakes evaluating and hiring? This is a great example of the dangers of applying quantitative metrics inappropriately. While value-added modeling may be able to capture properties of the aggregate, it makes occasional errors at the level of the individual. Just one error (whether it’s a factual or exaggerated case, it still illustrates the point) demonstrates the ethical and managerial problems in firing the wrong person based on aggregated data.

Nor do I understand the political eagerness to fire teachers so readily. I’m not convinced that teachers are such an abundant resource that we can afford to burn through them so callously. With teacher shortages in multiple areas and a national teacher attrition rate of 15-20%, we would do better to keep, train, and support the teachers we already have, rather than toss them out and discourage new recruits from joining an increasingly unfriendly profession.

While I agree that it’s important to judge teaching by its merits rather than just the years spent, we need to formulate those measurements carefully. Test scores alone give a misleading illusion of greater precision than they actually have and

But what do the data say?

Perhaps this is the time for a counter-reformation” summarizes some choice tidbits on charter schools, test-based metrics & value-added modeling, and performance-based pay and firing, from a statistician’s perspective.

On charter schools:

The majority of the 5,000 or so charter schools nationwide appear to be no better, and in many cases worse, than local public schools when measured by achievement on standardized tests.

On value-added modeling:

A study [using VAM] found that students’ fifth grade teachers were good predictors of their fourth grade test scores… [which] can only mean that VAM results are based on factors other than teachers’ actual effectiveness.

On performance-based pay and firing:

There is not strong evidence to indicate either that the departing teachers would actually be the weakest teachers, or that the departing teachers would be replaced by more effective ones.

[A study] conducted by the National Center on Performance Incentives at Vanderbilt… found no significant difference between the test results from classes led by teachers eligible for bonuses and those led by teachers who were ineligible.

In summary:

Just for the record, I believe that charter schools, increased use of metrics, merit pay and a streamlined process for dismissing bad teachers do have a place in education, but all of these things can more harm than good if badly implemented and, given the current state of the reform movement, badly implemented is pretty much the upper bound.

I’m less pessimistic than Mark is about the quality of implementation of these initiatives, but I agree that how effectively well-intentioned reforms are implemented is always a crucial concern.

Concerns about the LA Times teacher ratings

On “L.A. Times analysis rates teachers’ effectiveness“:

A Times analysis, using data largely ignored by LAUSD, looks at which educators help students learn, and which hold them back.

I’m a huge fan of organizing, analyzing, and sharing data, but I have real concerns about figuring out the best means for conveying and acting upon those results. Not just data quality (what gets assessed, how scores are calculated and weighed), but contextualizing results (triangulation with qualitative data) and professional development (social comparison, ongoing support).