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On geometry student’s side

Benjamin Catalfo, 16, of Setauket, demonstrates an error

Benjamin Catalfo, 16, of Setauket, demonstrates an error in the state's Regents exam. Photo Credit: Newsday / John Paraskevas

I am grateful for Newsday’s highlighting the work done by Ben Catalfo and his proof that a third question on this year’s geometry Regents exam was based on faulty reasoning [“Angling to fix Regents error,” News, July 19].

The student’s work highlights exactly what we want our students to achieve: an ability to think critically and apply disparate portions of their learning to solving challenging and unfamiliar questions. This is the same skill the Common Core Regents has tried to promote, but this question fell just a bit short of doing so, as the student has correctly proven.

What we ought to learn from this experience is not that we should make the tests less challenging; it indeed is good for our students to be pushed an appropriate distance outside of their comfort zones during tests. The tests just need a bit better vetting. Perhaps an offer should be extended to Ben Catalfo!

Ross Lipsky, North Woodmere

Editor’s note: The writer teaches math at Valley Stream South High School.

Ben Catalfo asks our state Education Department to revisit a problem from the June geometry Regents exam. He shares a mathematical argument and asks for public support. I am an experienced secondary mathematics teacher and a mathematician, and I will not sign his petition.

The veracity of mathematical statements is not determined by popular vote.

Neither is it determined by politicians.

According to Newsday, the Education Department asserts that the problem is fair and that it “appropriately measures a geometry standard” [“Calls to lower passing grade,” News, July 17]. The spokeswoman provides no mathematical justification for her assertion.

Students are expected to meet Common Core State standards. Standard three demands that students develop their ability to “construct viable arguments and critique the reasoning of others.” Explicit in this standard is the expectation that “mathematically proficient students . . . justify their conclusions, communicate them to others, and respond to the arguments of others.” They “distinguish correct logic or reasoning from that which is flawed, and — if there is a flaw in an argument — explain what it is.”

Catalfo constructed a viable argument. The veracity of his argument — not politics or popular opinion — must determine whether the state redresses the problem.

Lisa Berger, Queens

Editor’s note: The writer is an associate professor of math at Stony Brook University.

The decision not to adjust grading in light of an erroneous question on the geometry Regents is wrong.

Although Ben Catalfo’s explanation of the error relies on trigonometry (a subsequent course), it can also be explained using only geometry as found in Euclid’s Elements (the most important textbook of all time). Accounting for some archaic language, Proposition 7 in Book VI addresses exactly the error on the exam (when combined with Propositions 19 and 32 in Book I).

A spokeswoman for Education Department says the bogus question “appropriately measures a geometry standard.” What kind of appropriate geometry standard directly contradicts a result proved in Euclid’s Elements?

Brian Conrad, Stanford, California

Editor’s note: The writer is a professor of mathematics at Stanford University and a 1988 graduate of Centereach High School.