Table of Contents
1. Pappas Question of the Day
2. Who Is Floyd Thursby?
3. What Is Floyd Thursby Day?
4. Is Floyd Thursby a Traditionalist?
5. Floyd Thursby and the School Calendar
6. Back to Our Regular Traditionalists
7. A New Commenter: Rob Craigen
8. Conclusion
Pappas Question of the Day
This is my first holiday post of Thanksgiving break. As often happens during vacation periods, the most interesting Pappas question of the week occurs on a day I don't post. Today I will actually discuss
yesterday's Pappas question:
Find
x to the nearest whole #.
[Here is the given info: in Triangle
ABC,
BC = 22,
AC = 7,
AB =
x, Angle
A = 100, Angle
B = 20.]
This isn't strictly a Geometry problem, since it requires using trigonometry on an oblique triangle (although a few Geometry texts actually do mention the Laws of Sines and Cosines.) To make it easier, let me restate the givens as follows:
a = 22,
b = 7,
c =
x,
A = 100,
B = 20.
This uses the traditional notation where a lowercase letter represents the side opposite the angle with the same capital letter. Anyway, let's try using the Law of Sines to find
x. This requires finding the third angle
C = 60, since this is the angle opposite the goal side
x:
b/sin
B =
c/sin
C
7/sin 20 =
x/sin 60
x = 7 sin 60/sin 20
x = 17.72
So the desired side is
x = 17.72. The only problem is that this was yesterday's problem -- and that date was the nineteenth. We can justify rounding 17.72 up to 18, but not all the way up to 19.
Is there an error here? Let's try using the Law of Sines again, but with
a and
A rather than
b and
B:
a/sin
A =
c/sin
C
22/sin 100 =
x/sin 60
x = 22 sin 60/sin 100
x = 19.35
Hmm -- this answer correctly rounds down to 19 now. In other words, we obtained two different answers depending on how we solve the problem. So what gives?
Here's the thing -- most of the time, when we're asked to solve a triangle, we're only given
three parts of the triangle. We use the Law of Sines if we're given AAS or ASA (or SSA, the ambiguous case) and the Law of Cosines if we're given SAS or SSS.
But in this problem, we're given
four parts of the triangle, which is too many. Whenever we're given too much information (an
overdetermined problem), chances are great that some of the givens will actually contradict each other. Here are two (admittedly silly) examples:
a = 5,
b = 5,
c = 5,
C = 70
a = 4,
b = 5,
c = 6,
C = 90
The first is an equilateral triangle that isn't equiangular, while the second is a right triangle whose sides violate the Pythagorean Theorem. Another less obvious example is:
a = 4,
b = 6,
A = 30,
B = 60
This is a 30-60-90 triangle, yet the longer leg isn't sqrt(3) times the shorter leg. An example of an overdetermined problem in Algebra I is if we were given
three variables in two equations. Most likely, the solution for the first two equations won't fit the third. (Maybe if we're lucky, the three lines will be concurrent, but this is rare.)
Technically speaking, last Thursday's Pappas problem was also overdetermined, but fortunately, the givens didn't contradict each other. In general, if there are two different ways to solve a problem, with each method using some of the givens, then the problem is overdetermined.
There is actually a
third way to solve yesterday's Pappas problem -- the Law of Cosines:
a^2 =
b^2 +
c^2 - 2
bc cos
A
x^2 = 7^2 + 22^2 - 2(7)(22)cos 60
Notice that we can almost solve this without a calculator, since we know that cos 60 = 1/2:
x^2 = 7^2 + 22^2 - (7)(22)
x^2 = 49 + 484 - 154
x^2 = 379
Without a calculator, we at least know that
x is between 19 and 20. A calculator gives the solution to two decimal places as
x = 19.47. This does still round down to 19, but just barely. Still, 19.35 and 19.47 are really two different answers, and along with 17.72 we have three different solutions to the same problem.
Also, we technically used all four givens to use the Law of Cosines, but only because we needed both 20 and 100 degrees to find the 60 degrees that we actually take the cosine of. I suspect that this is how Pappas originally intended us to solve the problem, with the Law of Cosines -- but she decided to get cute and have us calculate the angle via Triangle Sum. She didn't realize that by doing so, she opened the door to using the Law of Sines to find a solution -- and by doing so, we found two solutions different from the intended solution (with one of them dramatically different). When I first saw this problem, I immediately used the Law of Sines and didn't think to use Cosines at all (until I got an answer using Sines that didn't match the date).
As the problem is written, there is actually
no solution because the givens are contradictory -- since there are too many givens. Next time, Pappas should just give the angle opposite
x as 60 and leave both 20 and 100 out.
Who Is Floyd Thursby?
Today's special holiday post is titled "Floyd Thursby Day Post." But who exactly is Floyd Thursby?
Well, Floyd Thursby is a traditionalist. He used to comment regularly at the Edsource website -- and he still does from time to time. His most recent comment was from July:
https://edsource.org/2018/pressure-builds-to-change-how-california-measures-student-progress-on-state-tests/600062
Floyd Thursby:
I have an idea, why don’t we skip the tests and just ask kids to draw a smiley face and tell us if they are happy. We will not rate either, for who are we to judge smiley faces and what really is happiness? Let’s all just feel good and know that people are good and try their best. No borders, no profits, no prisons. Everyone is good. Except Trump. He’s bad.
(In case you can't tell, Thursby is being sarcastic here.)
Thursby used to post regularly around the time I first started my blog, and from time to time I quoted him as much as I did the other traditionalists.
Since Edsource is a Californian website, I assume that Thursby lives here in the Golden State. In fact, he appears to be from the Bay Area.
By the way, I suspect that "Floyd Thursby" is a pseudonym. It refers to a name of a character in the novel
The Maltese Falcon. (I've neither read the novel or watched the film. Indeed, all I know about it is via a parody, "The Case of the Maltese
Pigeon," that appears on
Square One TV/
Mathnet.)
What Is Floyd Thursby Day?
Floyd Thursby Day is the Tuesday before Thanksgiving -- in other words, it's today. An equivalent definition is the Tuesday in the 20's of November (or the first such Tuesday if there's more than one.)
I call today Floyd Thursby Day because that particular traditionalist used to mention that day quite often in his comments. Here is a common reference:
https://edsource.org/2014/vergara-rulings-strong-words-in-the-end-will-make-little-difference/63113
Floyd Thursby:
Let principals decide. Then when a principal calls a teacher into a meeting and says were you really sick the Tuesday before Thanksgiving? What do you think of this parent’s complaint? I observed you and you don’t seem to be focused? Why are your students not improving as much as Ms. so and so’s students on the test? Why are you not doing school loop on time and other teachers are? When this happens, they’ll take it seriously. They’ll improve. They’ll be nervous. They know that a wrong response may cost them their job. It’s like any other job. Principals will have power, and that will cause better work. Now teachers can ignore it.
In Thursby's district, Tuesday is the last day of school before Thanksgiving. As we know, in some district students must attend school tomorrow, while in others (such as the district whose calendar the blog observes), Friday was the last day.
Thursby clearly believes that there are many problems with education, but unlike other traditionalists, his biggest concern isn't standard algorithms, eighth grade Algebra I, or AP Calculus. He believes that many problems with education lie with us -- the teachers. And one of our problems has to do with teacher attendance.
One problem with Thanksgiving is that people wish to spend time with their families, but these day, our families live across the country. The holiday marks one of the biggest travel days of the year, and airline tickets are hard to come by, since demand is high while supply is low. Originally schools were always open until Wednesday, in the decades before airline travel was common. Since so many students, parents, and teachers wanted to travel on Wednesday, schools (including Thursby's) began to close that day, so that Thanksgiving became a five-day weekend. But in many cases this isn't enough, since many had to leave on Tuesday to beat the Wednesday rush. In my districts we avoid this by closing the whole week, but in Thursby's the teachers just take Tuesday off too.
In this same thread, he writes:
Floyd Thursby:
I think you could legitimately expect most teachers not to miss any days most years because they have so many days naturally off, they can use those for personal chores and most of us need a day off or Saturday for that.
To me, part of the problem is that demand for airline travel and other excursions is highly dependent on school schedules. When schools are closed, students and parents are able to travel. Therefore, the cheapest days are when schools are open. The same is true for Disneyland and other amusement parks -- ticket prices are highest when schools are closed and lowest when schools are open. This isn't a problem for most people, but it is for those who work at the schools -- the teachers.
I'm sure Thursby would make the valid argument that loss of flexibility is a fair price for teachers to pay for having so many days off in the first place. Office workers might get only two weeks off, but they can choose the weeks when airline and amusement park prices are low. Teachers get more than two weeks off, but they are stuck with the weeks when airline and amusement park prices are high.
As a teacher myself -- well, a sub, but I did teach for one year -- I must defend us here. Not all of us are looking to take extra days off. Two years ago, I linked to other teacher blogs as part of Tina Cardone's "Day in the Life" project. That year, I even mentioned Floyd Thursby Day since some teachers worked at schools where the last day of school was Tuesday. One such teacher ended up having a snow day on Monday, and so Tuesday was the only day of school that week! Yet she came in and worked hard, as tempting as it might have been to take the day off. So not all of us are as lazy as Thursby makes us out to be.
Thursby also mentions merit pay in this thread. He wants attendance to be considered in determining which teachers deserve bonuses:
Floyd Thursby:
Yes, we’ll have to pay teachers more. Taking away the benefit of a lifetime job will require higher pay and attract better people. Some of the costs will pay for themselves. Until now, the union has opposed merit bonuses and attendance bonuses, said state law disallows them, they divide teachers, or educators. Imagine if instead of an across the board increases, you give an opportunity to gain extra money. Say you tackle the problem of higher absenteeism with a $2,000 bonus for perfect attendence and $1,000 for 3 or fewer, in a district with an average of 11. Every bonus gives the teacher a chance to earn more and afford expenses, but pays for itself as it cuts sub costs. Until now such creativity was unthinkable. Teachers will have to work harder, but they will end up earning more, afford expensive Cities, so it will be good for teachers overall as working harder and having to fear a boss are good for your character and make you self-improve into a better person. It’s good for the soul.
Is Floyd Thursby a Traditionalist?
So far in this post, I've called Thursby a traditionalist. Perhaps this is not the best word to use, since while Thursby wants students to learn more math, he doesn't share all of the same concerns as our main traditionalists Barry Garelick and SteveH.
Thursby strongly believes in merit pay -- and while he mentions attendance as one factor in earning the bonus, the main determinant should of course be test scores:
https://edsource.org/2018/san-francisco-school-finds-key-to-raising-math-scores-teacher-training/599874
Floyd Thursby:
This is a perfect example of how Union Control (Thank God for the long overdue Janus decision) creates nonmarket solutions to market problems. We should pay math teachers more than others if they majored in math and had a high GPA, and we should give a bonus based on test score improvement, which is most measurable in math and English. This seniority/LIFO/tenure situation doesn’t reward or create best results.
Thursby tells us that it doesn't matter whether it's the current Common Core tests (such as SBAC) or the previous CST's (based on eighth grade Algebra I), as long as
some test scores are used to calculate merit pay.
He tells us that improvement is "most measurable" in math and English. Not everyone agrees that test scores are a valid measurement of achievement in those subjects.
My main problem is that many students, especially older students, don't necessarily make a full effort at succeeding on the tests. They might be very smart, yet they score low on the tests because they have no incentive to succeed. Therefore, I only insist that if test scores are to be a certain percentage of the teacher's evaluation, then they must be an equal percentage of the students' grades. In other words, 10% of teacher evaluations = 10% of student grades, 50% of teacher evaluations = 50% of student grades, and so on. (It's clearly not 100% since Thursby has already declared attendance to be part of teacher evaluations.)
In fact, we notice that in this article, the school that Thursby commends for raising test scores uses lessons that are decidedly
not traditionalist:
On a recent morning, 4th-grade teacher Sara Liebert led a multiplication lesson with almost no lecturing or standing in front of the class. Instead, she wrote “120” on the whiteboard and asked students how many ways they could multiply numbers to reach that product.
While they debated among themselves and penciled equations on scratch paper, Liebert roamed from table to table, checking their progress and writing correct answers on the board.
Then she had them do the same exercise with “360” and “720,” so they could see the links between the numbers. At the end of the 45-minute lesson, most of the students could easily decipher the jumble of 3s, 5s and 12s that combine to make 720.
“Five years ago the way I taught was, ‘Let me show you, let me show you,’” said Liebert, who’s been teaching for 12 years, the past seven at John Muir Elementary. “Now I’m more of a guide while they do the math themselves. You can see how much more independent they are, how much more engaged. They’re thinking like mathematicians.”
Notice that this teacher's scores rose dramatically. Another traditionalist might argue that of course they improved, since she's teaching Common Core methods for the Common Core test -- are these fourth graders bound for eighth grade Algebra I or senior-year AP Calculus? But to Thursby, all he cares is that some sort of test scores are going up.
Floyd Thursby and the School Calendar
As I watch the news tonight, one of the lead stories is the holiday traffic. The anchors stress that travelers should have left hours ago if they wanted to beat that traffic -- which is at odds with having perfect attendance at a school that's in session today. And if you teach at a school that isn't out until 3:00 on Wednesday and not a second earlier, or work at an office that's open until 5:00 Wednesday and not a second earlier, it's impossible to have both perfect attendance and a smooth ride.
Many students believe that they're entitled to several non-academic free days -- and they'll call anyone "mean" if they try to make them do work those days. This includes not just the last day before Thanksgiving, but the last day before other holidays or the last day of school. And it also includes the
first day of school and first day after holidays.
Some students might even extend this to Fridays -- they believe that all Fridays should be easy days (and all Mondays). But if we were to cancel school on Fridays, then students would believe that they're entitled to free days on Thursdays, and so on. In other words, the purpose of having school on Fridays is to keep them working hard on Thursdays. Parents must put pressure on their students to keep them working hard before the holiday.
But some parents encourage their students to slack off by pulling them out of class early to beat the holiday rush. So teachers must put pressure on parents to keep their kids in class before the holiday.
And then some teachers encourage slacking off by leaving school early to beat the holiday rush. Now it's Thursby's turn to put pressure on teachers to stay in school before the holiday.
At Thursby's school, teachers want to take Tuesday off to beat the Thanksgiving traffic. But if the district were to close on Tuesday (and Monday), then more people would travel those days. So then teachers would take Friday off to beat the traffic -- and who knows how many other days. But with a short two-day week, teachers, parents, and students are likely to take only one or two days off.
In order to beat traffic, one must take off days that are still officially work days. It's impossible to beat traffic and still have perfect attendance.
By the way, this reminds of the Labor Day debate. It definitely makes a clean transition from summer to start school after Labor Day. But many students think that they're entitled to free days of no work at the start of the year. By starting a week or two before Labor Day, students slack off until the "real school year" starts after Labor Day -- it marks a natural transition point. But if the first day of school isn't until after Labor Day, they slack off until some random date in September. The same is true at the end of the year and Memorial Day -- except, of course, that the existence of finals week forces the students to work hard until the actual end of the year.
Around the first year of this blog, I tutored for students who attended a local Catholic school. Back then, the first day of school, last day of school, last day before/first day after Christmas, and last day before/first day after Easter were all Wednesdays. (Nowadays, only the last day before Easter and the last day of school are Wednesdays.) These set up short three-day weeks before and after vacations for everyone to slack off, so that they'll work hard during the following/preceding five-day weeks.
And in some ways, these even applies to time. I once subbed at a school that dismissed at 3:02. A common problem at many schools is for students to start packing up before the bell rings. At this school, the students often start packing at 3:00, as if that's when "the real school day" ends. But if the bell were to ring at 3:00 instead, they'd start packing at 2:50-
something, which might be much more than two minutes before the bell.
I'm not sure whether I fully agree with this sort of school calendar, but it's something to think about in light of Thursby's comments. Students, parents, and teachers all believe that they're entitled to extra "chill time" at the beginning and end of periods, weeks, terms, and school years. So we might set up the school day and calendar that encourage us all to limit that "chill time" to a fixed length.
Back to Our Regular Traditionalists
Since today is Floyd Thursby Day, I devote this post to Floyd Thursby. But this isn't to say that our regular traditionalists have been quiet lately. Over the weekend, Barry Garelick posted on his blog:
https://traditionalmath.wordpress.com/2018/11/18/beliefs-about-understanding-in-math-dept/
Here are some of many beliefs about “understanding” in math. It was hard to choose from so many candidates, but feel free to add some of your own.
We shouldn’t be teaching kids algorithms before they have the conceptual understanding.
Of course, Garelick criticizes this belief. But let's look at what he quotes from another "blogger":
Next year’s teachers that are used to students using an algorithm for multiplication are aghast when students use unsophisticated strategies like counting by ones by drawing pictures or partial product by drawing boxes, or when the students seem to not have any idea what to do. “What do you mean, just multiply!” But to “just multiply” by mimicking an algorithm isn’t part of what students had been doing. These teachers shrug in frustration and teach “the only right way”. Students are left feeling either shafted by the previous teacher or, most likely, that they must just not be “good at math”.
Here Garelick ignores the many students who are taught the standard algorithm for multiplication, struggle to learn it, and then conclude that they aren't "good at math." He appears to assume that the only students who feel they aren't "good at math" are those who are taught nonstandard methods.
By the way, the other two beliefs about "understanding" highlighted in this post are:
“Students who fail to understand a concept are unable to know how to use it or build upon it. They will end up with misconceptions that can go undetected for months or years.”
“In the past, math classes were about teaching facts, skills and procedures with no understanding,and mechanized drills.”
Let's see what frequent commenter SteveH has to say about this post:
SteveH:
Your goal is like shooting fish in a barrel, but will a teacher audience suddenly realize that what they were (ironically) directly taught by rote is fundamentally wrong? Then there are the educators who know exactly what they are doing – defining the learning process to match how they want a classroom to operate. It’s all about them – “the process is the product.” Beyond the very low level of the Common Core, they abdicate all responsibility for skill enforcement, and in the case of eliminating algebra in 8th grade, they ensure that many kids will never live up to their potentials.
At this point SteveH then launches his usual tirade about "Pre-AP" math (which I partly agree with, but not necessarily his solution), which I don't need to repeat. So let's skip to his second comment:
SteveH:
How do they test for this? We have seen many of their silly examples, like the perimeter question. Traditional math is always taught by “connecting those ideas to what they already know.” There is a lot of understanding that comes from mastery of sequentially scaffolded units in a traditional textbook. That scaffolding and building of skills requires a lot of understanding at many levels. This develops proper understanding a level at a time from the bottom up. There is no magic top down understanding that makes doing P-sets simple for each individual. In-class group projects hide individual fuzziness and allows them to ride the coattails of those who most likely are getting help at home or with tutors. We NEVER hear how these educators support individual success on homework. They only care about what goes on in class. They talk about conceptual understanding, but don’t have a clue how to create it for STEM students.
Of course, I can't help but think about last week of subbing, where I met the two girls who already knew how to solve systems by elimination. One of them indeed was tutored by Kumon, while the other was independently studying for SSAT. SteveH would insist that without all that extra tutoring, neither girl might have even been enrolled in eighth grade Algebra I.
SteveH writes about "P-sets" (problem sets) and admits that they aren't simple. But many students, if they don't find them simple, will refuse even to attempt Question #1. I often like how students who don't want to do P-sets are more willing to participate in projects. But here SteveH implies that the weaker students are just "riding the coattails" of the students who would have succeed on the P-sets in the first place, so activities don't result in any additional students learning.
Again, I beg to differ. The fourth grade activitiy given by Sara Liebert above encouraged students who wouldn't have been engaged by a traditional P-set. And another Sara(h) wrote the same in her most recent post -- of course I mean our favorite Sarah, namely Mrs. Carter:
https://mathequalslove.blogspot.com/2018/11/twelve-basic-functions-challenge-in-pre.html
A few weeks ago, I had my best lesson of the year so far in pre-calculus. My students were engaged like never before, and they became super competitive throughout the activity. They did way more questions than I ever would have been able to get them to do if I had just given them a homework assignment. When they came into class the next day, they begged to do an activity similar to the previous day's activity because it had been so much fun. Yes, students begging to do math. It made my heart smile.
I emphasize that sentence -- "They did way more questions than I ever would have been able to get them to do if I had just given them a homework assignment" or traditional P-set. I can assure you that students wouldn't be "begging to do math" in any class taught by a traditionalist.
A New Commenter: Rob Craigen
There is another commenter here in this thread at the Garelick blog -- Rob Craigen. Strictly speaking he isn't a new commenter as he's posted there before, but this is the first time I quote him here. He wrote an especially lengthy response to Garelick's post.
Rob Craigen:
Referencing the “Student 1 – Part 2” video there are many problems evident in what the teacher does here, so sorry for the long list to follow (and I’ve surely missed some stuff)
By the way, Garelick provides the link to the video, posted by another Rob (Robert Kaplinsky):
https://robertkaplinsky.com/why-depth-of-knowledge-is-critical-to-implement/
Here we discuss the problem: "List the dimensions of a rectangle with a perimeter of 24 units."
Rob Craigen:
1. The ill-posed problem. I’m complaining both about the problem and also about the use of this category leap to try to force a point about formulas not supporting understanding.
Here Craigen uses "ill-posed" to mean "open-ended." It's obvious that this problem has more than one correct answer. Not enough information is given to find a unique solution. It's the exact opposite of yesterday's Pappas problem, where there are too many givens for there to be any solution.
Rob Craigen:
2. “List the”. Huh? There are generally TWO dimensions for a rectangle. “List” a list of two things? This is a misdirection. Not that it’s bad — I’ll ask students for “ALL the solutions in positive numbers x, y to the equation x^2-6x+y^2-8x +25 = 0” and be happy when they provide the single unique solution x=3, y=4. But I don’t ask this of novices who are first trying to grasp what equations in two variables mean and what one means by a “solution” or who lacks the requisite algebra background to crack this one.
And then Craigen continues on about what a "list" is. I point out that in computer science, the number of elements of a list can be 2, 1, or even 0. Speaking of lists, let's skip to #4 on Craigen's list, since #3 is all about the definition of "list" again.
Rob Craigen:
4. I dislike that the teacher “leads” the student throughout, including leading him astray. You can hear the student listening for cues in the teacher’s questions. The teacher’s voice signals approval when the student writes “24 units” along one side: “okay … ” (signalling “correct so far” so the student believes they are on the right track) “…so how long are the other sides?” (Now the student can infer that the teacher believes by putting that number there, the student was indicating that was the length of the labelled side. And the teacher said “okay”. So if he didn’t think so already the student now “knows” that it is correct to understand that this side has length 24).
Many students are turned off by hearing their math teachers tell them that they are "wrong." Indeed, it's fear of being called "wrong" that leads students to leave traditional P-sets blank. The purpose of giving an open-ended (or "ill-posed") question is for there to be more than one correct answer, so that students are less likely to be "wrong."
But unfortunately, a length of 24 doesn't lead to one of the infinitely many correct answers. (As Craigen writes later on, this would imply that the width is negative.) We seek out a way to inform the student of this without using the word "wrong."
Rob Craigen:
5. Now using good Socratic technique, when the student is now apparently lost, the teacher prompts “so this side is 24 units long?” Student: “Yeah”. The teacher has now effectively reinforced the misconception and signalled the student to use that as a starting point for finishing the problem.
6. The teacher asks how long is the opposite side — the student correctly replies (using obviously formulaic knowledge about the properties of rectangles — what ought to be recognized as “understanding”) “24” But this display of understanding goes unremarked.
Notice Craigen's use of the words "astray" and "misconception." To him, the only intellectually honest thing for the teacher to say after the student writes 24 is "You're wrong."
The problem is that human beings aren't Vulcans -- we're emotional, not logical. If we tell people that they're wrong, they're more likely to quit or defend themselves rather than correct themselves. In order to convince others to change, we should do so without using the five-letter w-word. I admit that this is difficult in math where answers really are incorrect, but again, human beings don't suddenly become logical just because they're in a math class.
I think back to the class I subbed in last week. I'd called one guy to the front of the room and asked him to solve a system of equations by elimination. But then he just added the two equations when he needed to multiply one of them by a constant first. So I said to him, "The name of this method of solving systems is
elimination. Which variable did you eliminate?" He then quickly realized that he needed to multiply first. I suspect that if I had told him "You're wrong," he would have either quit and sat right back down or defended his error.
Is there a way we could have corrected the student who gave the length as 24 -- without either leading him astray or using the five-letter w-word? Perhaps we could have labeled the opposite side as 24 quickly and asked him to add 24 + 24, so that he'd have realized faster that he's wrong.
Garelick responds to Craigen's comment:
Barry Garelick:
“…a rich problem is almost always a classical word problem with some information taken away. In other words it is an ill-posed problem, such as “The difference of two numbers is seven. What are the numbers?” ”
In the meantime, the poor 6 and 7 year olds presented with this so-called “rich problem” feel they are bad at math, which is the opposite of what the purveyors of “rich problems” wanted.
OK then, suppose we have two group of six- and seven-year-olds. To one group we teach them Common Core methods and give them the rich problem mentioned above. To the other group we teach them the standard algorithm for subtraction and ask them to find 20 - 13. Which task is more likely to lead to the students feeling they are bad at math? Garelick would probably say the first task, forgetting that some students will begin by subtracting the units place as 0 - 3 = 3, and then the (traditionalist) teacher would immediately say "You're wrong!" You can't tell me that this won't cause the student to think they're bad at math!
Conclusion
I like to sneak the more controversial comments (especially those relating to politics or race) into the bottom of holiday posts, and this one is no exception.
It's still Floyd Thursby Day, so let's check out the following link:
https://sfpsmom.com/tracking-what-happens-when-your-are-in-the-dumb-class/
This post is about tracking -- and we all know what that means. Floyd Thursby comments:
Floyd Thursby:
You are assuming effort is not at play. Cuban Americans (Latino) and Nigerian Americans (black/AA) outperform whites. In California, Asian students study 13.8 hours a week from 11-18 and whites 5.6, and 60% of Asian American kids are taught to read before starting Kindergarten vs. only 16% of whites In San Francisco the white percentages are higher as many are Russian and immigrants, or Jewish American, or in general highly educated. The average California kid watches over 40 hours a week of TV but those making it to a UC about 10, on average.
The response by the blog author, Alison Collins, speaks for itself:
Alison Collins:
Wow! So let’s see, to restate: “Asians are better parents”, “black parents let their kids watch too much TV” and “whites are lazy”…. Thanks for proving my point that racial bias underpins this whole debate.
Let's end this post right here. My next holiday post will be on Saturday.
