Friday, April 15, 2016

Chapter 15 Test (Day 141)

Today is April 15th, the day that income tax returns are due -- or are they? Actually, as it turns out, taxes aren't due this year until Monday, April 18th -- and you may be wondering why. Since I often write about calendars, let me discuss the calendar quirk that results in the April 18th tax deadline.

Many states observe a holiday called Emancipation Day to commemorate the end of slavery. It is observed on the day that slavery actually ended in that respective state. The most well-known of these is the Texas Emancipation Day on June 19th -- also known as Juneteenth. As the Lone Star State was the last state to abolish slavery, Juneteenth marks the national end of the peculiar institution, and so it is observed throughout the country, even in non-slave states.

The District of Columbia, though not a state, has its own Emancipation Day. April 16th marks the day when President Lincoln freed the slaves in the capital. It is a holiday that causes some schools and businesses in Washington on the 16th no matter what day of week it falls.

Many federal holidays, such as President's Day, Memorial Day, and Labor Day, always fall on Monday to allow for a three-day weekend. But other holidays are tied to an exact date rather than a day of the week. In the United States there are four such holidays -- Independence Day, Veteran's Day, Christmas, and New Year's Day.

Of these, only Veteran's Day affects school schedules, since the other three holidays occur during long school breaks. We know that Vets Day on Tuesday causes problems, as many students and even teachers want to take Monday off as well. The same is true when Vets Day falls on Thursday, since then people want to take Friday off. But as annoying as a Tuesday or Thursday holiday may be, the real problem is when November 11th falls on a Saturday or Sunday -- since the schools are already closed anyway for the weekend.

The rule in this country is that when a holiday falls on a Saturday, it is observed a day early -- for example, July 4th fell on a Saturday last year, so the observed holiday was on July 3rd. On the other hand, Christmas this year lands on a Sunday, so businesses will be closed on December 26th. This of course refers only to when businesses are closed, not when the holiday is actually celebrated. So fireworks were still lit on the 4th last year, and people will still open presents on the 25th this year. In other countries, this is called in lieu of observances, and these are always observed on the following Monday, even if the holiday falls on a Saturday. So if Christmas is on a Saturday, the British have the in lieu of holiday on the 27th, not the 24th as the Americans would. (Schools, of course, are always closed on December 24th in both nations.)

And so the same is true with Emancipation Day in Washington. The big parade is always on April 16th regardless of the day of the week, so the parade will be tomorrow. But today is the day that schools and offices are closed -- and one of those offices is the IRS.

Here's a link explaining more about Washington Emancipation Day:

Notice that unlike holidays, Tax Day can never be observed before April 15th. Weekends and holidays can only extend the deadline, not shorten it. So the three-day Emancipation Weekend falls from April 15th-17th, and so taxes aren't due until April 18th.

In New England, the third Monday in April is known as Patriot's Day. It is the big spring holiday in that part of the country -- many schools are closed for spring break at Patriot's Day, not Easter. The holiday always falls in the April 15th-21st range. When the holiday falls as late as the 21st, it doesn't affect Tax Day, but in years when it falls in the early-to-mid range, it does. This year Patriot Day means yet another day when taxes can't be filed, so the deadline is April 19th. Notice that unlike Washington Emancipation Day affecting the whole country, Patriot's Day only affects the deadline in Maine and Massachusetts.

Next year April 15th falls on a Saturday, and Washington Emancipation Day falls on a Sunday (in fact Easter Sunday). So the observed holiday is on a Monday, and so taxes won't be due until April 18th again, just like this year. Notice that had Lincoln freed the DC slaves on March 16th or May 16th, no one outside the beltway would even know about the date.

Since today is a test day, it's also a good day for a traditionalist post. This week, there is another article about Common Core and the way it encourages Algebra I in ninth, rather than eighth, grade:

I once lived in Scarsdale, N.Y., one of the most education-obsessed villages on the planet. During a big parents meeting at the public middle school, I amused myself by raising my hand and asking how they were going to decide who would be accelerated into algebra in eighth grade.
It was an unkind and immature thing to do. As I expected, my question unleashed a wave of anxiety that forced administrators to abandon the night’s agenda and deal with nothing else until we went home. In Scarsdale, as well as many parts of the Washington area, few topics grab more parental attention than middle school accelerated math.
As usual, I'm going to skip directly to the comments. And as usual, the comments range all the way from "Algebra I should be taught in eighth grade" to "Algebra I shouldn't be taught at all."

Hard to believe I graduated from a school district where Algebra was a 9th-grade class (and this after half-day play-based Kindergarten AND 3 recesses a day thru 5th grade! LOL) and we still managed to have kids taking calculus by senior year and going on to ivy league colleges (even from "The Castle in the Cornfield" where I went to high school in PA). On the other hand, we still admitted 4YO's to Kindergarten rather than turning it into 1st grade and making kids wait til 5YO, resulting in 12YO 5th-graders, so today's 8th-graders are about the same age as way-back-then's 9th-graders, only with an extra year of schooling to look forward to before college. :P

But then CrunchyMama doesn't explain how students could take Algebra I as freshmen and still make it to Calculus as seniors. Many opponents of Common Core lament that the Core pushes some academic topics in the youngest grades much too soon, to the point that "kindergarten is now the new first grade." She goes on to discuss how this led to the delaying of kindergarten cut-off dates -- I've mentioned before how California's cut-off date changed from December 2nd to September 1st.

Many traditionalists would actually agree that some of the Core Standards in the lowest grades are taught too soon (for example, count to 100 in kindergarten), even while arguing that those in the higher grades are taught too late. But traditionalists certainly wouldn't include eighth grade Algebra I as too soon -- instead they consider ninth grade Algebra I as too late.

Excuse me. Common Core has students at third grade doing algebra. Take a look at these standards: 
3.OA. B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
3.OA.D. 8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 
Looks like algebra to me, in third grade.

Of course, this all depends on what we mean by "algebra." This also goes back to whether students should even be forced to learn "algebra" or not. Those who argue that "algebra" is essential for all often use this third-grade definition of "algebra," while those who counter that "algebra" is a waste of time usually mean the second semester of Algebra I into Algebra II.

Nemessis appears to be arguing that this standard is too advanced for third grade and should be "delayed," because it's "algebra." I wonder whether this standard may be more palatable for third graders if, say, an empty box were used for the unknown quantity, rather than a letter.

CrunchyMama responds:
What I am waiting to see is if introducing so much algebra before many kids are ready for it will yield the results that Coleman and his crew thought it would. A HUGE mental shift occurs around 8YO, so *during* 3rd grade for most kids - but not by any means at a particularly "standard" time (meaning there is a range of what is considered "normal" still).

I've mentioned this "mental shift" before in previous posts -- which explains why I often agree with the traditionalists during the years before this shift and the progressives after.

Frank Little:
I always thought the opposition to Common Core came from evangelicals and State's Rights nuts. I'm shocked to see such a stupid limitation for Algebra to be delayed beyond 8th grade. China probably starts Algebra in Grade 2; India in Grade 4. The USA is so behind, we start foreign languages in 9th grade. Most of the world speaks better English than American kids by Grade 8.

Political comments aside, I wonder, what does Little mean by "algebra" when he writes that Chinese second graders start "algebra"? It's probably the same as the "algebra" that appears in the third grade Core Standards quoted by Nemessis. So the Core is only a year behind China at this point.

Here's an example of two dueling comments:

I think if you look at almost any elite college the majority of admitted students will have completed at least a course in Calculus during high school. e.g. 94% of admitted Harvard students have had at least AP Calculus AB regardless of what they're planning to study and fewer that .5% have not completed pre-Calculus. This is why parents are so crazed about 8th grade algebra I bc traditionally students take geometry, algebra II, and pre-calc as pre-requisites which are typically year long courses and get a student to Calculus by senior year which they will need.

Except that many multimillionaires (MLB players, movie stars, fashionistas, etc.) had no regard for algebra, did not excel in it . . . .

Both Harvard grads and celebrity millionaires are extreme cases. I say that we shouldn't require eighth grade Algebra I just because Harvard students need it, nor should we forbid it just because athletes and other celebrities are successful without it.

Why are we so resistant to allowing students to progress and challenge themselves academically? Should we push kids into math (or any other type) of courses they're not ready for? No, of course not. But if a kid is bored in his class, enjoys learning, and can benefit from taking more challenging (not just more work) classes, let him.  
Would anyone say an athletically gifted child shouldn't go to the sports camp / be on varsity as a freshman / do the all state or traveling team?

And here we go again with the comparison of academics to athletics again. Here lazelank is asking why we avoid academic tracking yet encourage athletic tracking. Again, I say that we need to be more careful with academics than with athletics because, again, professional athletes are rare, but inadequate academics can shut people out of having food on the table or a roof over their head. I don't want to go back to the tired old tracking/demographics issue again, but of course it's on my mind on this day before Washington Emancipation Day.

The next poster mentions a specific traditionalist: Ze'ev Wurman:

Dr. Democracy:
One commenter here [and scrolling down, that "one commenter" is another known traditionalist, Barry Garelick -- dw] references a Ze'ev Wurman article from Breitbart. Breitbart? Jay Mathews calls it "very helpful." Sigh. 
The Wurman article whines about a "decline of 2-3 points" in NAEP math scores as if that were something terrible. It's not. And it's highly explainable. 
First, NAEP scores have been increasing for a long time. At some point, scores will - inevitably - plateau, and perhaps even decline a bit. 
Parents will continue to want algebra in 8th grade - or even earlier - because they've been misled by people like Jay Mathews, who has relentlessly pushed the College Board's AP program, despite the voluminous research that undermines what he sells.  
I count Garelick and Wurman as traditionalists. I don't know enough about the author Jay Mathews to determine whether he counts as a traditionalist or not -- but perhaps he is if he agrees with the others.

I find it interesting that math (Algebra) which is most students' hardest subject (at least the hardest one to comprehend) is the only one that is taught in middle school. No one seems to talk about taking English 8 in 7th grade (or 6th or 5th) or 9th grade History or Science.

Now BillMath1 does have a point here. I've mentioned before that in elementary school, ELA is harder than math, but at the secondary level, math is harder. Indeed, we can determine, to a high degree of accuracy, whether a school is elementary or secondary just by looking at the percentage of students who are proficient at ELA or math! So if this is the case, then we expect there to be more above-grade level middle school students in ELA or other subjects rather than math -- yet the debate is always about eighth grade Algebra I.

Here's a reply by "oldspaper":

Actually, at BASIS, they teach AP World History in 8th grade.

To me, BASIS -- a chain of hyper-accelerated private and charter schools -- shouldn't be mentioned as a typical example of anything. Actually BASIS eighth graders don't take Algebra I -- because that's considered to late by BASIS standards. The latest a BASIS student can take Algebra I (actually a Saxon Integrated Math course) is seventh grade, with some sixth and even fifth graders taking it!

The generation gap rears its ugly head again in these two posts:

The current group of "academics" who are leading the common core agenda and want the US to return to a world leadership position in the math & sciences should get theirs heads out of the sand. As an ex-math teacher, the US has watered down teaching mathematics including Algebra. We had more smarts in the 50s and 60s with less "intellectualizing" education. Quit the pansy approach to teaching... allowing the use a calculator to multiply 5 x 5 is a joke as evidenced by kids who can't make change when working as cashiers.

You're not kidding. I recently went to the grocery store and asked for an 1/8 pound of corned beef. The 50-something woman (NOT a kid) at the counter said, "An eighth it less than a quarter, right?"

Usually, the generation gap is between millennials/"The Dumbest Generation" vs. the older generations, but here we have a gap between "born in the '40's" and "a 50-something woman" (so likely born in the '60's). But the complaint is the same -- someone in the younger generation is labeled as a "dren" -- a reverse-nerd who can't do simple math.

I call anyone who can't do simple math -- defined as third grade (CrunchyMama's mental shift) math and below -- a "dren". Clearly someone who doesn't know 5 x 5 = 25 is a "dren," but how about someone who doesn't know 1/8 < 1/4? Let's see:

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
1 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Clearly 1/8 < 1/4 fits in this third grade standard -- the numerators are the same and the denominators are in the set {2, 3, 4, 6, 8}. Therefore the 50-something woman counts as a "dren."

I could go on forever with these comments, but I feel that the ones I posted here are representative of the entire comment thread. So let me conclude with a comment about Geometry:

Art Bab:
algebra is for solving word problems. 
if word problems is to take a back seat, teaching algebra has little point 
(The same as teaching geometry without proofs.)

The tax deadline may be delayed this year, but not the Chapter 15 Test. So here are the answers to the test, plus rationale for including some of the questions.

1. 3pi.
2. 1350 square units.
3. 50 cm.
4. Yes.
5. No. They can't even form a triangle, much less a right triangle.
6. 36pi square units, 36pi cubic units. Yes, this is the one sphere whose area in square units equals its volume in cubic units.
7. About 145 million square kilometers.
8. About 32 square feet.
9. a. (-2, 9). b. 7. c. Many answers are possible. To find lattice points on the circle, we go right, left, up, and down seven units, to obtain (5, 9), (-9, 9), (-2, 16), and (-2, 2).
10. a. (0, 0). b. sqrt(72). c. This time, sqrt(72) = 6sqrt(2), so we can go diagonally to find lattice points on the circle, to obtain (6, 6), (-6, 6), (6, -6), and (-6, -6).
11. This is the complete the square question -- included because such problems are on PARCC!
x^2 + y^2 - 8y = 9
x^2 + y^2 - 8y + 16 = 25
x^2 + (y - 4)^2 = 25
So this gives us:
11. a. (0, 4). b. 5. c. (5, 4), (-5, 4), (5, 9), and (5, -1).
12. a. A circle with radius 20 feet. b. 40pi feet.
13. Draw any circle.
14. About 1.68%. I set this question in Brazil because the Olympics are about to start!
15. 15.
16. Cavalieri's Principle. Take that, traditionalists!
17. a. When the line and circle intersect in a point. b. When the line is perpendicular to the radius at the point of tangency. PARCC contains a few tangent problems, and all of them appear to involve angle measures, so that right angle is important.
18. a. 36 degrees. b. 18 degrees. PARCC also contains problems on inscribed angle measure -- possibly in the same question as tangents.
19. a. About 2.5 or 2.6 cm. b. The ratio to the circumference to the diameter is -- what else -- pi. We see that we estimate pi as either 3.08 or 3.2 using this measurement. Interestingly enough, 3.14 is almost exactly halfway between these two estimates.
20. a. 24 square units. (The height is 4, using the Pythagorean Theorem) b. About 38.5 square units.

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