A pop third-grade math quiz — question No. 4 from a PARCC practice test for grade 3, unit 2 math that anyone can access online:

*Which three statements can be represented by the expression 24 [divided by] 4?*

A. Jake makes 24 muffins. He gives away 4 muffins.

B. Collin has 24 toy trucks. He sorts them into groups of 4 trucks each.

C. Amira has 24 trading cards. She puts them into piles containing 4 cards each.

D. Rosemary puts 24 stickers in each book. She uses enough stickers to fill 4 books.

E. Steven fills a new bookshelf with 24 books. He puts the same number of books on each of the 4 shelves.

Perhaps those puzzled by the failing math scores of Maryland students on the PARCC test should examine the questions.

I tried a number of PARCC practice questions while writing a chapter titled “Why Our Kids Don’t Get Math” for my book on pseudoscientific education practices — of which PARCC testing is an example. I found my extensive knowledge of math to be of secondary use in answering PARCC grade-school math test questions. Instead, many questions tested my reading comprehension.

The question above tripped me up because I missed the plural “three statements” and simply checked choice E. I received no credit for the problem because B, C and E, must *all* be checked for the answer to be correct. I do not agree that dividing 24 objects into 6 groups of 4 is the same as dividing them into 4 groups of 6, but that is the test maker’s understanding of division.

Not only is careful reading essential, but so is clear writing, because receiving full credit for some questions requires students to explain the reasoning for their answers. In addition, many questions, like the one above, test abstract algebraic concepts that are developmentally inappropriate. Note that the numeral 6, which immediately comes to mind as the solution to 24 divided by 4, is not in any of the choices. The question asks third graders to think abstractly at a much higher level than in the past, even though their rate of cognitive development has not changed because it is biologically fixed. The PARCC test is also administered online, which means that it requires the ability to interact with computers by pointing and clicking, operating menus and typing.

Given the content and implementation of the PARCC math test, it is not surprising that only one-third of Maryland students in grades three through eight passed. Because of the language and computer skills the test requires, I suspect that male students, students who have a first language different than English, low-income students, and students who are truly gifted at math may be particularly challenged by these math assessments.

Boys are simply less verbal than girls at young ages, and no matter how much reading and writing skills are pushed back to younger and younger ages, that basic fact of biology and brain development isn’t going to change. When it comes to explaining their reasoning strategies, boys generally will be less expressive than girls. Students for whom English is not their first or primary language will have difficulty decoding the sophisticated vocabulary required to comprehend these questions. Low-income students won’t have the same fluency with the computer interface because their families cannot afford to have as many electronic devices in the home.

It might seem surprising that I include students gifted in math as a category of students who would do poorly on these math assessment tests. However, true math expertise is often a visual, rather than a computational or verbal way of thinking. Ask someone who is extremely facile with mathematical thinking to solve a math problem and frequently he or she will “see” the answer and then have to reverse engineer an explanation for why that answer is correct. Usually there are multiple explanations, and some might be very visual and not easy to translate into words.

In fact, what makes math beautiful, and appeals to the aesthetic senses of those gifted in math, is its ineffability. It is a way of thinking that transcends language. Turning math assessments into frustrating exercises in reading comprehension and written explanation will drive away students who may not be particularly adept at expressing themselves in writing but have the potential to excel at math.

The PARCC math tests are premised on a gross misunderstanding of what mathematical expertise actually entails and of the level of abstract thinking that is age-appropriate for grade schoolers. Education officials expressing surprise at the results are being willfully ignorant.

*Joseph Ganem is professor of physics at Loyola University Maryland and author of “The Robot Factory: Pseudoscience in Education and Its Threat to American Democracy” (**www.RobotFactoryBook.com**).*