I mean, really.
Imagine you are watching a debate for the presidential candidates and you go into the debate with certain opinions on how things should be run – say: tax code. Then, after sitting and watching the candidates outline their rationale (right?! I know I’m reaching here) you think to yourself, ‘huh. Well, that guy just changed my mind.’
Does this ever really happen?
Fairly certain this guy has never been persuaded to a different opinion
Can people who believe in a ‘flat tax’ be persuaded that a ‘progressive tax’ structure is more fair and more worthy of their support? (I threw in the ‘and’ there because you can be shown the rationale for something and agree with it without changing your position)
Can proponents of a ‘pathway to citizenship’ be convinced that it’s simply too impractical to actually be enacted?
Can pro-lifers be converted to pro-choice by the right argument?
(as a side note, I wrote the above statements in a completely arbitrary manner, because I recognize that people also seek out ‘echo chambers’ for their own ways of thinking, which may be a part of the problem as a whole. Anyway, I don’t mean to deter a reader because they see words like ‘pro-choice’ or ‘pro-life’.)
Kepler could have applied himself better…
Sometimes I question whether the Greeks were just wasting their time spending all that energy thinking about rhetoric. They didn’t persuade the Romans to stay out of their lands and to not steal their whole pantheon of gods. Maybe if they spent a little more time practicing their phalanx formations and a little less worrying about whether there was really a place filled with Perfect Forms (I’m looking at you, Plato) that we vaguely remember from before the time we were born, they might have effected a more sturdy border guard.
Nevertheless,
I changed my mind today about something. (I’m still working on changing it about some other things that would make my life easier, but I’m off to a good start) I got an email pointing me to the following post by Brett Berry on Medium this morning.
https://static.medium.com/embed.jsWhy 5 x 3 = 5 + 5 + 5 Was Marked Wrong
My first reaction was to be upset with the teacher who gave this kid points off for correct answers. I opened the article in order to satisfy my own desire for hearing an echo chamber of my thoughts only to find that the author took a different stance.
I kept reading because I was determined to write a comment to express my ire – but, you know, wanted to make sure that I could point out the best examples of the author’s flawed thinking first. I first saw that he was making a reasonable argument, but felt like it was still wrong. Then I saw how his examples supported his way of thinking and was starting to lament that he was making it more difficult for me to undercut him. Finally, he added that, depending on the order that things were taught, the answer could be considered correct under some circumstances, but that it was better to teach the meaning of the maths stepwise in order to law the proper framework for future lessons.
I give up. You win, Math Guy.
Not only did you change my mind on this issue, but you also laid the framework for me to re-examine my whole approach to Common Core.
DownHouseSoftware 
ratabago
October 31, 2015 at 9:07 pm
He didn’t convince me, though he did sort of disallow the commutative law by assertion, which is still one of my concerns.
I personally think this was a dishonest marketing exercise (but I think all marketing exercises are dishonest).
— Simply because commutative and associative laws may confuse beginners doesn’t mean they are wrong, or should be treated as if they don’t exist. Unless the students have been explicitly instructed that they must not use the commutative law (an unknown, but I think it unlikely) I don’t accept his assertion.
— He creates a false equivalency when he compares an abstract process to collections of physical objects.
— If he thinks division cannot be treated as multiplication he’s got a problem. If he is teaching that to others, they’ve got a problem. But he has created another false equivalence here. The claim is not that any and all process that leads to the answer of 15 is equivalent. The claim is that 5×3 and 3×5 are valid approaches to solving this multiplication problem.
— Testing for equality of a string and int in javascript is a dishonest example. The == in javascript does an implicit type conversion, which most of his audience will probably not understand. He has compared two equivalent entities, and then two not equivalent entities, not demonstrated a difference between “equal” and “equivalent”. (This type cast is one of the reasons I hate javascript, and haven’t used it in years, it makes debugging a pain.)
I don’t know common core from a bar of soap, we don’t have it over here. (Common core, I mean. We have soap.) But what I see here looks an awful lot like what is wrong with teaching computing in Australia at primary and secondary levels. Lots of rules solving particular problems within a narrow range by applying preset operations in a strictly enforced script for a specific software package at the expense of understanding. Good little script robot. Have a pat on the head and an extra ration of machine oil.
Children are usually fairly flexible. Maybe they will cope. I have heard it asserted that “common core” is supposed to teach “number sense”. But I suspect the emphasis on tightly applied rules and arbitrary restrictions over understanding that I see in Brett Berry’s article will just drive the interested kids away. At least, I know it would have driven me away from maths as fast as I could go. I don’t see how it will reduce the dislike, or increase the engagement, of those that weren’t interested. We don’t need to be creating new resentments for maths in those that might be interested. It has enough consumer resistance already.
I would have to agree that the answer to the 4×6 problem is wrong in that arrays are not commutative in the same way that scalars are. I have no objection to asking a teacher why they made a decision. And I don’t think that internet shaming should be the go to strategy. But, in general, I am highly offended at the suggestion that parents should blindly trust teachers. That is exactly bass ackwards. Some of the teachers I have come across have been excellent. Some of them have been caring, and deeply engaged. But many of them have just been time serving, and a few have been actively vindictive. And many of them, in areas where I have enough background to know, are simply wrong much of the time (particularly evolution, and also chemical energetics).
ratabago
November 1, 2015 at 2:04 am
Rats, somehow I forgot to cover the first point I thought of reading this. In the narrow context of this exercise the child appears to have a systematic misunderstanding, and there was consequently a teaching opportunity here. But simply writing down the correct answer without explanation missed that opportunity. A simple sentence like “we read 5×3 as ‘5 lots of 3′” might have made a world of difference.
downhousesoftware
November 1, 2015 at 10:22 pm
All excellent points –
In fact. they were the points I started with and found a way to be persuaded to abandon in this case, all of which serves to make me wonder if I had actually wanted to have my mind changed rather than allowed it to be. If that’s the case, then my whole premise about the rarity of changing one’s opinion is misleading.
So, I agree with everything you have said. And point to a need for effective and frequent communication between parents, teachers, and learners as to what the lessons are and how they are intended to be taught. By allowing myself to be persuaded, I think I was relying on several unstated elements of the case (that there was effective communication during the lesson and when feedback was given, both of which we are not privy to in this essay). Those are hefty assumptions on my part and not the sort I like to make without evidence for them, but I think this is further evidence of my wanting to change my mind.
In many situations I have been in the position of oversimplifying rules of nature in order to teach them. I was projecting, in this case, a similar situation and assuming the best about the teacher.
ps -I’m glad to hear you guys have soap. I know it can be hot in the Summertime.