<p>Maybe we should get rid of middle and high school all together and condense all 12 years of schooling into 6. Think of the money we will save!</p>
<p>Let’s note it was the charter schools who did the worst of all:</p>
<p>[Gary</a> Rubinstein: Dramatic Collapse of Charter School Test Scores | Diane Ravitch’s blog](<a href=“http://dianeravitch.net/2013/08/09/gary-rubinstein-dramatic-collapse-of-charter-school-test-scores/]Gary”>Gary Rubinstein: Dramatic Collapse of Charter School Test Scores | Diane Ravitch's blog)</p>
<p>If we really wanted to know if the kids learned anything, we should forbid all test prep, and give the tests on a day unannounced in advance.</p>
<p>A lot of the charter schools in the cap district have been shut down. They were an utter failure. Some that were shut reopened a year or so after, but again had to be shut down for poor results.</p>
<p>Warning: long-winded, rather detailed comment ahead. </p>
<p>My main point is this: When a student misses a question on a multiple-choice test, it is often assumed that the student didn’t understand the concept that the question was intended to test. Sometimes this is true. However, other times, it may be illuminating to discuss with the student <em>why</em> the student didn’t get the question–it might not be for any reason that the tester has considered. And (with apologies to mini), it might not mean that the the student is headed for Walmart.</p>
<p>My specific comment refers to question 2 on the 3rd grade math test, which is accessible at:</p>
<p><a href=“EngageNY Resources | New York State Education Department”>EngageNY Resources | New York State Education Department;
<p>This question reads: What number sentence is another way to represent the missing number in the equation 36 (divided by) 4 = (open square box)? </p>
<p>(Sorry about writing out the division and box symbols.)</p>
<p>Based on experience years ago of listening to QMP and QMP’s friends, I think it is possible for a question like this to confuse a third grader, due to a lack of familiarity with the “open square box” notation. Since the question comes so early in the test, it might have had an adverse effect on performance on the rest of the test. (Aside from that, I am not completely convinced that the English in the question is at third-grade reading level.)</p>
<p>For those of us raised on similar questions, it’s obvious: “Open square box” is just the blank that you fill in. However, fill-in-the-blank has been tossed out long since, and the meaning can’t be taken as self-evident. If the students have spent time doing work sheets with open square boxes to fill in, then they will know what’s going on. However, a lot of elementary math programs do not have work sheets like that, although the programs are ok mathematically. </p>
<p>QMP encountered a question like this on an achievement test in 3rd grade. It was actually worse from a mathematician’s standpoint, because it read something like:</p>
<p>Put a number in the box to make the number sentence true:
59 + 12 = (open square box) + 59.</p>
<p>QMP asked the teacher for clarification, but couldn’t be given any according to the test rules. Afterwards, QMP asked me, “What does open square box mean?” </p>
<p>If you think that the meaning of “open square box” is totally obvious in the second question (involving adding 59), let me suggest that the correct answer to the second question is 2 times the square root of three–or at least it is, for any student who guesses that “open square box” is most likely the notation for taking the square of the number inside. Actually, “open square box” <em>does</em> denote the square of the number inside on some of the Math League tests at elementary school level. (In this case, the number that should go inside the box on the NY test is 3–and I will say, at least that works in both the question and the correct answer!) </p>
<p>There is another question that a mathematician might ask: What is the meaning of the addition symbol (multiplication symbol, division symbol) between a number not in a box and a number in a box? Or from a scientist’s perspective, does “box” have units? If so, why do none of the other numbers have units?</p>
<p>Difficulty with the second question that I mentioned is sometimes attributed either to lack of understanding of the commutativity of addition or to “format sensitivity,” but that attribution is erroneous either way, in my opinion. It is a question of the use of undefined symbols. Symbols that are not in universal usage (by the readers/audience) ought to be defined when they are introduced.</p>
<p>Even the replacement of fill-in-the blank by open symbols might need a bit of explanation (based on my experience). The transition to “new math” came between my own elementary school years and my brother’s. In third or fourth grade, my brother brought home a work sheet filled with open circles and open boxes. I had no idea what they meant. My mother helpfully informed me that they didn’t mean anything! There were just the “blanks” of the old fill-in-the-blanks.</p>
<p>Incidentally, these days I use some equations that have “open square box” in them, in my work. There it stands for the d’Alembertian operator, which is a linear combination of second partial derivative operators with respect to time and space.</p>
<p>“If we really wanted to know if the kids learned anything, we should forbid all test prep, and give the tests on a day unannounced in advance.”</p>
<p>Why can’t the teacher just give the students their own tests covering material that the student has actually been taught it class, every few weeks or so - with the occasional pop quiz thrown in? The teacher can grade them, return them to the students and go over material with the class, or individually with those that need it. Then, if the child can remember to bring it home, the child can show it to their parents so the parent can see how their child is doing, too. </p>
<p>Then, every so often - lets say between 5 and 10 weeks - the teacher can fill in a card showing how the student is doing in all their subjects. Then, especially in younger grades, the teachers can write out a detailed report about the child, explaining the kids strengths and weaknesses and what areas the child needs to improve upon and even meet with the parent to discuss in depth the child’s progress. The teacher might suggest extra help the child might need or more in depth material for the child. </p>
<p>At the end of the year this same teacher can then decide whether or not it is appropriate for the student to advance to the next grade. </p>
<p>Does anyone really believe that a teacher does not have the capability of assessing how their students are doing? </p>
<p>This assessment testing is nonsense and was started by some politician’s businessman brother in Texas because he saw what a cash cow it could be. Then everyone jumped on the bandwagon but conveniently ignored when the evidence came out evidence, that the so called, 'Texas Miracle," was a myth.</p>
<p>QM–Okay, I don’t even know what your original questioning is asking with that “write a number sentence” format. My guess would be the “The answer is nine.” But I’m guessing that’s not what they’re asking for.</p>
<p>Let me just note that a couple years ago I got a 750 on the quantitative GRE section, so it’s not like I can’t do math. (and 740 on math SAT back in the dark ages–wish I could remember anything more useful than that these days!.)</p>
<p>I guess I’d need to have been taught to that test to understand the wording of that sentence, nevermind the open square box.</p>
<p>I thought this would be common sense.</p>
<p>Georgia keeps messing around with the Math Standards here…so there was a huge curve…and huge fail rate this year (63% failing algebra)</p>
<p>Hi garland! The choices for the answers are:</p>
<p>box times 4 = 36
36 times 4 = box
36 + 4 = box
box divided by 4 = 36.</p>
<p>So, actually, 9 is not an option. I suspect that the majority of students who got this question right filled in 9 (either in pencil or mentally) and then looked for the choice where if you plugged in 9 for “box” you got a valid equation. Alternatively, they might have been coached, "When you see a question like this . . . " In future years, they almost certainly will be coached that way, now that people know what will be on the exam. And scores will rise! Without understanding shifting at all! Just as happened in the past, with other tests! (Sorry for the cynicism.)</p>
<p>I actually doubt that everyone who got it right has a deep understanding of the relation between multiplication and division that this question is supposedly testing.</p>
<p>There are plenty more where that came from!</p>
<p><a href=“EngageNY Resources | New York State Education Department”>EngageNY Resources | New York State Education Department;
<p>I am having a hard time figuring out whether a mathematician or logician would accept
box = 9
as “a number sentence that is another way to represent the missing number” in the equation given. Maybe Lewis Carroll could be of help! (Lewis Carroll, he dead.)</p>
<p>I really understand your point of view in the last sentence in post #26, garland–and furthermore, based on your posts over the years, I suspect that your verbal scores were even higher than your math scores. Now throw in the fact that the students are 8 or maybe 9.</p>
<p>Hmmm, I don’t see how those sentences “represent the missing number” rather than just restate the original sentence (equation?)</p>
<p>I didn’t say the answer was nine, btw. I said the answer should be “the answer is nine” because it’s a sentence stating what the missing number should be. :)</p>
<p>Ah, Lewis Carroll reincarnated! And just in time! :)</p>
<p>Weirdly (and dismayingly) my verbal on the GRE was actually lower (after 800ing it on all the practice tests!). But by percentile, it was higher. :)</p>
<p>Well, I have no doubt of your ability to handle complexity!</p>
<p>Another issue with the test, in my opinion, is that some of the math questions are very difficult for a child who needs glasses, but hasn’t realized that yet, as often happens right around third grade. Two of the number-line questions fall in that category. With reading, a bright student who can see the general shape of the word can often read it, despite not having fine visual resolution. With the number line with the skinny cross hatches, that is not going to work. I say this because I had to pull off my blended bifocals and squint at the screen to read a couple of the number line questions.</p>
<p>We don’t live in New York and QMP has graduated from college, so I am not complaining about the test out of self interest.</p>
<p>Third question for third graders: The distributive law of multiplication over addition. I think most third graders need to be explicitly taught this, and even then, it doesn’t generally “take” for algebra, and needs to be taught again.</p>
<p>Fourth question for third graders: This one is ok, if the student recalls that > is the symbol for “is greater than.” (Someone had to teach them that, of course.) Dyslexics or students who have forgotten whether > or < means “is greater than” should give up now.</p>
<p>I think the fifth question, about tiling the kitchen floor, is ok, although it does carry some cultural baggage. It’s helpful if a student knows what a “tile” is.</p>
<p>The next one (area of a shaded figure) is maybe ok.</p>
<p>Then the one after that is . . . well, amusing:</p>
<p>The number of objects described in which situation can be represented
by 24 ÷ 4?</p>
<p>A) There are 24 boxes with 4 pencils in each box.
B) There are 24 people on a bus, and 4 people get off the bus.
C) There are 24 marbles that need to be sorted into 4 equal groups.
D) There are 24 books on a shelf, and 4 more books are put on the shelf.</p>
<p>This one can be worked out, but who talks/thinks like that?</p>
<p>If you are following along, in the question about the rectangles on p. 22 of the test, the student is supposed to “join three of the rectangles” (from the previous part of this question) together, without overlapping, to form one figure that has an area of 22 square units. </p>
<p>In the previous question, the rectangles are shown separated from each other, on a grid.</p>
<p>The right answer involves moving the rectangles together without adding any squares, to make a figure.</p>
<p>I have to admit that I misunderstood this question. When the question asked for the rectangles to be “joined,” I thought that one was supposed to fill in some of the squares that separated one or more rectangles, thus “joining” the rectangles.</p>