This view of the city through this rectangular netting puts me in mind of projecting three-dimensional space onto a two-dimensional coordinate system. The rectangular grid seems a bit oblique, relative to the buildings, which makes me wonder what angle I’d have to look through in order for make everything to line up straight.
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
The following question appeared on the June, 2014 Algebra 2 / Trig exam.
Graphs without scales are common on Regents exams (I’ve written about this before). Personally, it’s not a huge deal to me–I’m a lazy grapher, myself. However, a colleague of mine regularly complains about this, and she made an excellent point regarding the grading of this particular problem.
The solution to this problem involves translating the graph one-unit to the left and two units up. But since no scale is given on the graph, it’s not clear what one unit to the left would be. If we assume the box on the graph indicates one unit, then the red graph below would be appropriate. But if we assume a box to represent half-a-unit, the purple graph would be correct.
If no scale is explicitly given, it seems like both graphs should be considered correct and receive full credit. But the rubric doesn’t address this possibility, and it’s unlikely students were given the benefit of the doubt.
I really like the shape of this midtown-Manhattan sculpture. Whenever attempts are made to define or quantify beauty, symmetry is one of the first considerations. But this obtuse,scalene triangle is decidedly unsymmetric.
Maybe its lack of symmetry makes it more noticeable as a piece of public art.
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
Elementary statistics plays an increasing role in high school math curricula, but the ways these concepts are often tested raises some concerns. After all, the manner in which ideas are tested can reflect how the ideas are being taught.
Here’s a question from the 2014 Integrated Algebra exam: which of the following is not a causal relationship?
Causality is notoriously difficult to establish, but I’ll set aside my philosophical objections for the time being. My primary concern here is with (2) being the correct answer.
First, correlation is a relationship between two quantities. What quantity is population correlated with in answer choice (2)? “The taking of the census” is an event, not a quantity. This may seem like nitpicking, but what quantity are we supposed to assume in its place? It seems natural to assume “the census taken” to mean “the number of people recorded on the census”, but then how could there be no causal relationship? What causes a number to be written down for “population”, if not the actual population?
Here’s another question from the 2014 Integrated Algebra exam.
It’s important to talk about bias in surveys, but no substantial thought is required to answer this question: three of the answer choices have absolutely nothing to do with campsites. And for the record, the question should really be phrased like “which group is most likely to be biased against the increase?”.
And this is a problem typical of the Algebra 2 / Trig exam.
I know it’s pretty much standard usage, but no finite data set can be normally distributed. The correct terminology here would be something like “the heights can be approximated by the normal distribution”.
I’m aware that some may see these complaints as minor, but as I’ve argued before, I think it is extremely important to model precision and rigor in mathematical language for students. We expect this from our teachers and our textbooks; we should expect it, too, from our tests.
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
I have written extensively about the unfaithful graphs presented on Regents exams: non-trigonometric trig functions, non-exponential exponential functions, “functions” that intersect their vertical asymptotes multiple times. I really don’t understand what is so hard about putting accurate graphs on tests.
Here is this year’s example. These are some of the ugliest “parabolas” I have ever seen. I can’t look at these without being mathematically offended.
Not one of these graphs are parabolas. Take a closer look at (3), by far the ugliest purported parabola. Look at how unparabolic this is. It lacks symmetry, and appears to turn into a line at one point!
If this were truly a parabola, we would be able to fit an isosceles triangle inside with vertex on vertex.
Not even close!
It’s a fun exercise to show that the others can’t possibly be parabolas either, which I will leave as to the reader.
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