One class in which my teacher look isn't effective is third period. That students in one back corner do not notice that I'm giving them the look. They start squirreling around rather than stay focused on their art.
I believe the problem in this class is that it begins with the morning announcements, which these days are played as a live stream on YouTube and projected to the class. Many students simply ignore the announcements and talk through them -- and then they continue to talk throughout attendance. It's much easier to establish control when I tell them to be quiet and take roll from the start, but my hands are tied by the need to give the announcements.
I wonder whether I should skip the announcements -- or play them late rather than live. Then maybe I can get their attention and establish control from the start of class. This isn't the first time that I subbed in a classroom and the most talkative class ends up being the period of announcements.
The best behaved class of the day is once again fourth period, with second period the next best. This third period class is the only one that I haven't placed in the top two best behaved classes for any of the three days thus far.
After my first five days of subbing, I still have a way to go before I can call myself an ideal manager.
Today is the Chapter 1 Test. This is what I wrote about the test last years:
I am now posting my first test. It is actually the Chapter 1 Quiz that I posted in the past, but now I'm considering it to be a "test." This is mainly because in my semester plan at the start of the year, I refer to the first day of school up to Labor Day as the first "unit," and then the month starting with Labor Day as the second "unit." Each test that I post corresponds to one of these "units." Still, I don't want to overburden the students with a hard test at the start of the year, so this still has only 10 questions.
Even though my series "How to Fix Common Core" is over, I will often use these quiz and test days to post links to articles about the Common Core debate, including recent traditionalist arguments. I will start by rewriting what I wrote last year about today's test (including my rationale for including the questions that I did), and then link it back to the Common Core debate.
There is a Progress Self-Test included in the book. But even if I threw out the questions based on sections 1-6 through 1-8, there are some questions that I chose not to include.
For example, the first question on the Self-Test asks the students to find AB using a number line. This is very similar to some of the questions that I gave on the Wednesday and Thursday worksheets. But there is one crucial difference -- this one is the first in which both A and B have negative coefficients.
Now I know what the test writers are thinking here. The test writers want to know whether the students understand a concept. There's not enough room on the test to give both easier and harder questions. If a student gets a harder question correct, we can be sure that the student will probably get a much easier question right as well. But if the student only answers an easier question correctly, we can never be sure whether the student understands the more difficult question. Therefore, the test should contain only harder questions, since anyone who gets these right understands the simpler concepts too.
But now let's think about this from the perspective of the test taker, not the test maker. Let's consider the following sequence of hypothetical conversations:
Wednesday:
Student: The distance between 4 and 5 is 9.
Teacher: Wrong. You're supposed to subtract the coordinates, not add them. The distance is 5 - 4 = 1.
Student: Oh.
Thursday:
Student: The distance between -4 and 2 is 2.
Teacher: Wrong. When subtracting, change the sign. The distance is 2 - (-4) = 6.
Student: Oh.
Friday:
Student: The distance between -8 and -4 is 12.
Teacher: Wrong. You forgot the negative in front of the 4. The distance is -4 - (-8) = 4.
Student: Oh.
And we can see the problem here. The teacher wants the student to be able to find the distance no matter what the sign of the coordinates are -- not just when they're positive. But the problem is that the instant that a student finally understands how to solve the first problem, the teacher suddenly makes the problem slightly harder, and the student becomes confused.
Of course, you might be asking, why only give one problem on Wednesday? Why can't we give more problems to check for student understanding of the all-positive case, then move on to negatives? But you see, I'm imagining the above hypothetical conversations as occurring during, say, a warm-up given during the first few minutes of class -- and warm-ups typically contain no more than one or two questions. The student is never allowed to taste success, because each day a little something is added to the problem (like a negative sign) that's preventing the student's answer from being completely correct. The student never hears the words "You're right." And that's just with negative signs -- the U of Chicago text includes questions with decimals as well. I immediately threw all decimals out of my problems -- since decimals confuse the students even more, most notably when we draw number lines and mark only the integers.
Well, I don't want this to happen, especially not on the quiz or test where most of the points are earned. I want the student to taste success -- and this includes the student who's coming off of a tough second semester of Algebra I and is now in Geometry. Sure, if you feel that some students need to be challenged, then challenge them with all the negatives and decimals you want. But I don't want to dangle the carrot of success in front of a student (making them think that they've understood a concept and will get the next test question right), only to jerk it away at the last moment (by adding extra negative signs that will make the student get the next test question wrong), all in the name of challenging the students.
And so my test questions are basically review questions rewritten with different numbers. My rule of thumb is that the test contains exactly the same number of negative signs as the review. Some teachers may see this as spoon-feeding, but I see it as setting the students up for success. Any student who works hard to prepare for the test by studying the review will get the corresponding questions correct on the test.
Of course, some questions about the properties are hard to rewrite. I considered using the question from the U of Chicago text, to get from "3x > 11" to "3x + 6 > 17." But notice that the correct answer -- Addition Property of Inequality -- is difficult to remember and will result in many students getting it wrong. So even here I changed it to the Addition Property of Equality. After all, the whole point of learning the properties is to be able to use them in proofs. The Addition Property of Equality is much more likely to appear than the corresponding Property of Inequality. All including Inequality on the test accomplishes is increasing student frustration over a property that rarely even appears in proofs.
Returning to 2018, yesterday I wrote about Eugenia Cheng and her latest book, The Art of Logic in an Illogical World.
Well, last month Eugenia Cheng actually debated with a traditionalist on Twitter! (Until then, I didn't know of Cheng's opinions regarding the traditionalists debate.) This particular traditionalist should be familiar -- it's Tara Houle, who often comments at Barry Garelick's blog (in order to agree with him).
It's difficult to find or link to month-old tweets. Fortunately, I do see part of the Twitter discussion preserved at the following blog:
https://medium.com/@sunilsingh_42118/back-to-basics-mathematics-movement-re-imagining-the-classroom-as-a-sweatshop-with-victorian-24fc635ba599
The owner of this blog is Sunil Singh -- who is apparently an author just like Cheng. And in this post, Singh defends his fellow math writer. Here are the tweets that he has preserved:
Tara Houle:
You seem unfamiliar w/Cognitive Load Theory & how anxiety can form if Working Memory is overloaded. Considering it's the very foundation of how novice children learn, your assumption re: memorizing TTs [times tables -- dw] is nothing more than an opinion.
So I think we're done here.
Dr. Eugenia Cheng:
What are you referring to in this article? I don't see it mentioning either memorizing or times tables.
So at this point the debate is "done," but I don't see the start of the discussion. It's obvious, though, that Houle, the traditionalist, is defending the memorization of multiplication tables, and so Cheng, the progressive, is saying that memorization isn't important.
Notice that Singh's post is dated October 29th, 2017. Yet not only does it mention the Twitter war between Houle and Cheng (dated August 16th, 2018), but he also mentions the infamous Barbara Oakley article from earlier in August 2018 (which likely launched the war in the first place.) Then again, Singh writes:
Yeah, I wrote this last year. It needs updating — with a little more gas on the pedal and cranking of some loud road tunes.
So apparently Singh wrote this back in October, and then edited it after the major traditionalist debate began in response to the Oakley article. I myself am guilty of editing some of my posts last year (in order to include some quotes from Eugenia Cheng's second book during my Great Post Purge), but I try not to edit in references to articles or books dated later than the post I'm editing.
I read the Houle-Cheng debate on Twitter last month, but I knew that Cheng's third book was coming out this week, and so I intentionally waited until this week to post about it. All I did was make it more difficult on myself to find the tweets so that I can post them here.
Tara Houle:
This is helpful. 30% of our schoolkids have to learn their times tables in tutoring centers because they're being denied this basic tenet in school, and now we have mathematicians suggesting hey this is fine because SHE [Cheng -- dw] didn't need it.
Dr. Eugenia Cheng:
That's a straw man i.e. a misrepresentation (and simplification) of my argument to make it easier to refute.
It's impossible to cut and paste directly from a tweet, so I must type in each tweet one character at a time here on the blog. So I think we're done here with copying tweets.
The Barbara Oakley article has produced long traditionalists' debates at several websites. I haven't seen such heated traditionalists' debates since the Atlantic article written by Barry Garelick (and another traditionalist) nearly three years ago. That year, I kept making traditionalists posts nearly everyday it seemed.
This year, I wanted to show more restraint with the traditionalists label. My first traditionalists post wasn't planned until August 28th -- three weeks after the Oakley article -- and the second such post was scheduled for today. But I didn't realize that the New York Times article would generate such a response similar to the 2015 Atlantic article. It suffices to say that I won't wait until September 26th to make my next traditionalists post if the Oakley-inspired debates continue.
So let's see what we've missed in the traditionalists' debate since my August 28th post. Let's start at our usual source, Barry Garelick:
https://traditionalmath.wordpress.com/2018/09/08/zombie-arguments/
This post, dated last Saturday, is Garelick's most recent post. Here he links to another blog whose author is Greg Gashman:
https://gregashman.wordpress.com/2018/09/07/zombie-arguments/
In this post Ashman starts out by mentioning the original Oakley article and then links to one of his opponents -- the former King of the MTBoS, Dan Meyer:
Meyer’s latest blog post drags up ideas about ‘conceptual understanding’ and ‘maths zombies’ that will be familiar to those of us who have been around the block a few times. I have written a lot of posts about conceptual understanding and it’s actually quite difficult to pin down. If you have the time, try reading some of the ‘productive failure’ literature. This often assesses ‘conceptual knowledge’ and yet the questions that are used to assess it will probably surprise you – they often look for all the world like recall of relatively simple declarative knowledge. This is why I am more impressed with evidence of transfer – but that’s a different blog post.
One of the comments at Ashman's blog is from the aforementioned Tara Houle:
Tara Houle:
Many of our detractors suggest we promote rote over understanding in our “back” to basics movement (a term that the media has come up with unfortunately; not us). However what we have ALWAYS been advocating for is *effective* math instruction. The reason we lobby so hard to ensure memorization and mastery of math facts be enshrined in primary maths curricula, is because most of them are devoid of these crucial steps. Do we prefer rote over understanding? I don’t know anyone who has ever suggested that. What I do know, is that there’s been a serious erosion in primary maths curricula over the past 50 years, and this is what is most significant in addressing, if we ever want to improve our student’s math performance.
Meanwhile, SteveH has finally joined the Oakley-inspired debates. Here's Garelick's post:
https://traditionalmath.wordpress.com/2018/09/08/count-the-tropes-dept-5/
Another in one of an infinite series of articles that has appeared at Forbes and other like publications about how the Common Core math standards are being maligned has surfaced. I gave up counting the tropes in this one. The author makes the assumption that because students were unable to apply standard algorithms or “rote” procedures to “advanced math” (left undefined in the article), that teaching procedures is tantamount to “no understanding”. There is no mention of the difference between how novices or experts think–and in fact, going out on a limb here–I would venture to say that the author of this piece probably learned things in the manner that he now derides.
And here's the comment from SteveH:
SteveH:
Whether or not one learns to count up, a general technique still has to be learned and mastered. Instead of multiplying by 5, divide by 2 (which is easy to do left to right) and move the decimal place over one. You still have to learn how to multiply numbers with no short cuts. There are many of these things. Do they teach them all or do they think there is some magic transference? What about in algebra? Some of them go out of their way to find problems that seem to be a solution of N equations in M unknowns, but have a simpler way to eliminate unknowns. The problem is that these things do not eliminate the need to master the general methods. However, the fuzzies are now declaring them as some sort of litmus test of understanding or whatever it is that they want. They want to claim the high ground of understanding, even over AP/IB, but can’t really explain what it is. Go ahead and give tests with both 3239 – 2747 and 2018 – 1999 as problems. Compare students from a traditionally taught math sequence with those using their sequence.
Notice that some of the strategies SteveH gives here appear in Ruth Parker's Number Talks. His "multiplying by 5" may be considered a form of Parker's "halving and doubling" (although Parker, oddly enough, doesn't specifically mention examples with five as one of the factors).
As for SteveH's subtraction example, 2018 - 1999 has been tailor-made for Parker's "Round the Subtrahend to a Multiple of Ten and Adjust." Instead of 2018 - 1999, find 2018 - 2000 = 18, and since we subtracted one too many, add one back to get 19, the final difference.
But with 3239 - 2747, another strategy emerges -- "Decompose the Subtrahend." For this one, to subtract 2747, we decompose it as 2739 and 8. The first subtraction gives 3239 - 2739 = 500, and then we must subtract eight more to get 492, the final difference.
Here's one more Garelick post -- and he mentions SteveH right off the bat:
https://traditionalmath.wordpress.com/2018/09/06/comments-gone-missing-dept/
I saw SteveH’s comment this morning, but then this afternoon it was gone.
So Garelick restores SteveH's comment. I'll include parts of it here:
Garelick, quoting SteveH:
Can we ever get past this cherry-picked strawman? You [former king Dan Meyer -- dw] know that’s not the position that many of your critics take. All traditional math textbooks and teaching methods introduce concepts first in a carefully-built scaffold. Then comes the homework to get individuals to better understand the subtle variations that are far more mathematically meaningful than basic concepts. Even basic skills require subtle understandings. Very few things are ever rote. This deeper level of understanding has to be carefully constructed on a unit-by-unit basis over years using individual problem sets. That’s what all STEM-prepared students get with AP and IB math sequences.
This has never been a question about basic concepts. it’s a question about eliminating low expectations and ensuring proper mastery and mathematical understanding on grade-by-grade basis that keeps all math doors open for each individual student for as long as possible. With curricula like Everyday Math, schools trust the spiral and have abdicated all responsibility of mastery beyond the low CCSS slope. Just ask us parents of your best students what we had to do at home. Engagement and curiosity was not my main focus, but that didn’t stop him [SteveH's son -- dw] from playing with GeoGebra for hours at a time – something that was neither necessary or sufficient. Mastery increased his curiosity, not the other way around.
The first commenter to this post was the former king himself:
Dan Meyer:
Wish I knew what happened there. Maybe after seeing a commenter complain about Everyday Math [U of Chicago elementary text -- dw], “trust the spiral,” and confuse his son’s anecdotal success with research for the 100th time, the spam filter decided the commenter was a spambot. In any case, SteveH’s comment is restored.
Later on, SteveH writes:
SteveH:
They claim the dominance of Jo Boaler level research, but show no real curriculum that produces better results than AP/IB. They need to move past their research phase to show success with an opt-in full high school curriculum that shows better AP/IB test results. We now have the College Board pushing Pre-AP Algebra in 9th grade that emphasizes mastery of skills and pushes the false dream of cramming 4 years of STEM-prep math into 3 years for students subjected to low expectations and mastery for the last 8 years. There is research and opinion and hope, and then there is large scale reality. They are claiming victory a wee bit too soon.
And again, Jo Boaler wrote the introduction to Ruth Parker's Number Talks. As soon as I saw the name Boaler in that book, I knew that she was someone whom the traditionalists don't like.Speaking of missing comments, in another post Garelick is upset that another blogger, Emma Gargoetzi, has challenged the Oakley article yet won't post Garelick's comments (or those of any other traditionalist). I believe that Gargoetzi's blog is one of those at which every single comment must be approved by the author one at a time. In this case, I side with Garelick -- it weakens Gargoetzi's argument when she doesn't post her traditionalist opponents' comments (provided, of course, that the traditionalists didn't use profanity or insult her personally).
For that post, I'll only give a link and highlight one comment -- made by another major traditionalist, Ze'ev Wurman:
https://traditionalmath.wordpress.com/2018/08/31/unpublished-comments-on-the-rebuttal-to-barbara-oakleys-nyt-op-ed/
Ze'ev Wurman:
The comment is not about his personal observations how *some* of his students learn, but rather he [Dan Meyers -- dw] generalizes how the whole population learns based on his limited exposure as a teacher. Now, Dan has barely a fresh PhD in education, not in cognitive psychology. So why exactly should we listen to Dan with his shallow scientific record and not to accomplished educational and cognitive psychologists like David Geary, Paul Kirschner, or John Sweller, who have studied this issues for many decades and came to essentially opposite conclusion?
Before we leave this traditionalists' debate, let me point something out important on (progressive) Sunil Singh's blog:
I finally decided to set this blog loose after seeing a recent series of tweets attacking Rochelle Gutierrez — from the usual suspects that are named later in this article. This isn’t the first time Gutierrez has been attacked. It also won’t be the last.
The name "Rochelle Gutierrez" has appeared recently in some traditionalist debates. Unfortunately, it's difficult for me to discuss Gutierrez and her perspective, because both she and her opponents bring up race and politics.
We're already aware, of course, the race often appears in traditionalist debates. I've quoted other progressives and traditionalists, but not Gutierrez or her opponents in order to avoid the racial part of the debate for now. But Singh writes:
Tara [Houle] and her get-along-gang peddle limp mathematical ideas with steroidal disdain for the entire math community that Gutierrez and [Eugenia] Cheng represent — common insults are math gurus, educrats, thought leaders, etc.
Here Singh clearly links Rochelle Gutierrez and Eugenia Cheng. Based on a few reviews of Cheng's third book, it appears that the author will mention race in one of the chapters. And since Cheng's book will be my next side-along reading book in the next few weeks, the topic of race will most likely be unavoidable.
Let's step back and recall what the traditionalists' debate is all about. As I wrote earlier in this post, all I want is for our students to "taste success" in math -- especially near the start of the class. And especially in the higher grades, I believe that students are more likely to taste success via a progressive/reformer curriculum than the traditionalists' preferred curriculum.
But to that end, I still wonder whether this test is easy enough for students to "taste success." A few weeks ago, blog challenge champ Elissa Miller wrote the following post -- the last link in this very link-filled post of mine:
http://misscalculate.blogspot.com/2018/08/odds-and-ends.html
This was the last activity before their quiz. After like 6 DAYS of point, lines, and planes, the grades were still bad. I think the highest was an 86% and the majority of the class was between 50%-75%. Why is this so hard? It's like the more time I spend, the worse it gets. I hate that it's the first lesson of the year because it drags on forever, they get a bad grade, and then they decide that geometry is too hard and they're going to fail.
So like me, Miller is concerned that her students won't taste success at the start of class. But just as she feared, most of her students earned a C or lower with no A's. (That's like the grade distribution of a summer class for failed math students -- except that this surely isn't summer school.)
And her first unit is very similar to Chapter 1 of the U of Chicago text -- perhaps with a little more emphasis on planes (not covered until Lesson 9-1 in U of Chicago) and a little less emphasis on finding distances. I would have thought that Miller's quiz would be easier than mine. On neither test do students need to multiply or divide -- and on hers they didn't need to subtract either. And yet we see the low scores on her quiz. How well, then, would her students fare on the test I'm posting today, where they actually need to subtract to find distances?
So now what are Miller's students learning in Geometry now that they're finally past the points, lines, and planes unit from hell? Believe it or not, it's special right triangles (not covered until Lesson 14-1 in the U of Chicago). And so far the students seem to be doing better here than with points, lines, and planes -- go figure!
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