The following multiple-choice question, explained here in hopes of helping eighth-grade students and their parents in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2016 test for grade eight math:
Laurie entered the mass, in kilograms, of four substances into a spreadsheet. Her spreadsheet automatically converted the masses into scientific notation:
Which list shows the four substances in order from least mass to greatest mass?
A. Substance A, Substance B, Substance C, Substance D
B. Substance B, Substance A, Substance D, Substance C
C. Substance C, Substance A, Substance D, Substance B
D. Substance C, Substance D, Substance A, Substance B
Analysis of this question and online accessibility
Scientific notation is one of 29 topics that are new to eighth graders in the Common Core math standards, according to researcher Jessica K Griffin at the College at Brockport. It is our hope, as well as hers, that students take the information their teachers present about scientific notation to learn not just how to put numbers in order from least to greatest, but also why scientific notation is helpful to scientists and other people who work with very large or small numbers.
When Voxitatis used Microsoft Excel to show 0.0009 in scientific notation with one decimal place, we got 9.0E–04. This differs from the format shown in PARCC’s math problem in that the spreadsheet program omitted the space before the “E” and a zero is shown in between the negative sign and the number 4. The text of the problem makes no reference to the specific spreadsheet program used, though, so maybe PARCC used a different spreadsheet program.
But then, the problem as published shows a different format for most cells. Three of the four differ in terms of the number of decimal places shown. This would require setting the format on each cell individually, which I suppose is possible, but the “automatic conversion” told to the students by the text of the problem does not reflect the operation of any spreadsheet program currently available on the commercial market.
Voxitatis diligently checked six independent references for information about scientific notation:
Only NYU even lists the spreadsheet notation on the same page with “scientific notation.” NYU refers to the spreadsheet notation not as “scientific notation” but by saying that “exponents are often expressed using other notations.” The other math references universally say “scientific notation” refers only to something like this:
Voxitatis concludes, therefore, based on a preponderance of the evidence, as well as typical worksheets used by eighth-grade teachers across the country, that the question is invalid in that it does not measure students’ understanding of the Common Core standard it purports to measure. If you can’t do what the problem says you should do and get what the problem says you should get, the question itself is invalid and does not test students’ ability to “interpret scientific notation that has been generated by technology.”
(The labeling of the second row from the top as “1” is incorrect, given the functionality of commercially available spreadsheet programs. This is considered a minor or even an irrelevant editorial error, however, which affects neither students’ ability to answer the question nor the fitness of the question for the test.)
A mitigating factor in our analysis comes as we acknowledge the likelihood that eighth graders would understand the spreadsheet notation used in the problem and convert it, in their heads, to the scientific notation PARCC pretends to assess with this problem.
If the fault, however, lies with the wording of the Common Core, which constantly refers only to “scientific notation” and not “spreadsheet” or “calculator” notation, then the problems PARCC presents to students should reflect the actual spreadsheet notation a student would see. If, on the other hand, the fault lies with technology companies that coin a new meaning for an existing mathematical term, we as a society shouldn’t compromise our understanding of the underlying mathematics in order to accommodate spreadsheet manufacturers who are either too lazy to program or too uninformed to comprehend “scientific notation.”
Multiple-choice questions like this one can be delivered easily online for any device students may use. Validity, reliability, and fairness measures should not differ significantly from those found when the question is used on a paper-based test from PARCC.
No special accommodation challenges can be identified with this question, so the question is considered fair.
