First, in past years on the blog, I didn't like the fact that some lessons on logic that appear early in most texts don't appear until Chapter 13 of the U of Chicago text. For example, "Reasoning and Proof" is only Chapter 2 of the Glencoe text. And so I broke up Chapter 13 and scattered its lessons among other chapters.
And second, it turns out that the modern Third Edition of the U of Chicago text does the same thing! I see that Chapters 13 and 14 of the new version correspond to Chapters 14 and 15, respectively, of the old version. The content of the old Chapter 13 is now included in other chapters.
On this blog I continue to follow my old Second Edition of the text. Therefore, we will continue to cover the logic of Chapter 13 as a separate chapter.
Before we start Chapter 13 though, the Queen of the MTBoS has spoken. That's right -- Fawn Nguyen posted on Saturday, St. Patrick's Day. And her St. Paddy's Day post deals with an issue that comes up too often these days: cell phones and technology.
http://fawnnguyen.com/maybe-less-tech-in-math-and-school/
I’m sipping hot sake while waiting for my food. I scan the restaurant, about half full already for an early Friday evening. Two kids are on their smartphones at the table with their parents. They don’t even look up as the waiter arrives to take their orders; I guess the parents already know what to order for them. At the next table, I see a young child sitting in his high chair and watching a video on a propped up smartphone. Nearly every kid in the restaurant is doing something on his/her phone. Never mind the adults.
This scene is all too familiar, too common — so common that it would be “odd” if we didn’t see this. And we’ve been seeing it for some time now.
I’m happy and grateful that technology is here to stay. But I hope we seek opportunities to connect more humanly.There are several things going on in this post. First of all, Nguyen is a middle school teacher, so of course she's in a room surrounded by kids on phones all day. The problem, of course, is that she's describing a restaurant, not a classroom.
It's easy to relate the restaurant to the classroom here. The students want to use phones in the class, but it's not because the lesson is particularly boring. It's because phones are the only things that entertains these youngsters, as evidenced by their use at the restaurant. In other words, if the kids had their way, they'd spend almost 100% of their waking hours using the phones.
And, most important, they believe that anyone who gets between them and their 100% waking hour phone use is "mean" or "unfair." Of course, this means that the teachers who tell them that they can't use phones in class are "mean." Nguyen's story takes place late Friday afternoon -- and to the kids, it's the start of 60+ hours of no teachers telling them to put their phones away. That's an entire weekend with no teachers between them and their 100% waking hour phone use.
We expect middle school students to be interested in 100% waking hour phone use. It's a shame that at least elementary school teachers can't be protected from children who desire 100% phone use, as Nguyen's statement tells us here:
At the next table, I see a young child sitting in his high chair and watching a video on a propped up smartphone.
I've heard of two-year-olds using phones before -- and sometimes I wonder how this is even possible, since they wouldn't even know what buttons to press, or how to spell words to text. Well, I guess this answers the question -- the parents play videos for them, so the toddlers only watch them.
The problem is that not only do the kids view teachers who take their phones away as "mean," but so their parents who won't buy them the phones. And presumably, any parent who gets anything less than an unlimited plan is also getting in the way between the children and their 100% phone use goal.
I don't write about family that much on the blog. But I have said in old posts that I have no children (for example, in old Daylight Saving Time posts where I mention that I prefer Year-Round DST since I have no kids, whereas parents tend to prefer Year-Round Standard Time). So the question I ask myself is, what would I do about phones if I had children of my own?
In our society there are some items which have a minimum age requirement. For example, we can't legally purchase alcohol or tobacco until age 21 -- the latter a California law. (One issue mentioned in last week's walkout is whether guns should be added to the list.) Of course, youngsters often become interested in alcohol or tobacco well before the age of 21 -- but it's not usually as early as six. Most six-year-olds are interested in drinking chocolate milk and soda pop, not alcohol.
Likewise, I'd want my children to be "too young even to be interested in using cell phones" -- as long as possible. For starters, this means I wouldn't play them videos such as the one Nguyen's toddler watched in the restaurant. That two-year-old didn't beg his parents to buy him a phone -- the parents just showed them the phone. If I were a parent, I wouldn't do that.
Sooner or later though, the inevitable happens. My children would see another student at school with a phone, and then the begging begins. So the next goal is for my children to know that I won't buy them a phone without them thinking I'm mean -- as long as possible.
Here's what I'd want them to know -- the older generations criticize and make fun of younger generations who are addicted to cell phones. Fawn Nguyen is either a late Boomer or an early Gen X'er, and in this very post she's criticizing young people. Avoiding cell phones and finding other ways to entertain yourself, then, is a way of making older people like you.
My own generation -- the late X'er/early Millennial cusp -- is caught in the middle. I remember that as a young child, I often played cheap handheld games, such as baseball and Yahtzee. Most often, these games were kept in the car, and so I played them on long car rides. It never occurred to me that I should spend 100% of my waking hours playing these games, or that anyone who stopped me from playing them 24-7 was mean. I often went days without playing these handheld games -- it never occurred to me that I should bring them to school, much less play them during class. But of course, nowadays parents would entertain their kids on long car rides with phones, not handheld games -- and it's the phones that kids want to use during 100% of their waking hours.
I'd like to tell my children that the kids who use phones 100% of waking hours are future dropouts, and that students who earn A's and B's don't own phones. But this is probably false -- even future valedictorians most likely own cell phones.
But I can make a clearer relationship between math and phones. This is the idea behind the phrase I made my own students say -- "Without math, cell phones wouldn't exist." After all, anyone who wants to work for Google or Apple should have a STEM degree, which requires being good at math.
So here's the idea -- I set some appropriate age for my children to have their first phone -- let's say seventh grade. But this doesn't mean that I buy them their phone as soon as they've completed the sixth grade -- it means I get the phone as soon as they complete sixth grade math. If they are below grade level, then they don't get the phone until they earn a passing grade in the final trimester of Math 6 (or a higher class). If they're above grade level, they can get the phone earlier. If I held myself to this standard, I'd get my phone in second grade -- the year I independently studied Pre-Algebra.
What I really want is to show my children that all the STEM disciplines are relevant to cell phone technology, not just math. So once they get their phones, I'd like to implement the second part of my academic incentive -- the grades the students receive in all STEM classes that appear on the report card (math, science, maybe computers) determine how much money I spend on the phone plan. So if the STEM grades are all A's, then I get an unlimited plan. If the STEM grades are B's then I get some sort of limited plan, all the way down to no plan for D's and F's.
The problem, of course, is that the phone company probably wouldn't like it if I kept on switching between different plans every month. Even if I simplified this a little -- the child gets an unlimited plan and I pay the phone bill if all the STEM grades are C or better, and I skip a month if one of the STEM grades is a D or F -- my credit rating might suffer whenever I skip a payment.
Well, at least I should be able to implement the first part of the plan -- purchase the phone as soon as the student completes sixth grade math -- without any troubles with the phone company.
Returning to Nguyen's post, her main topic is whether schools should embrace technology and find ways to incorporate it into the lessons. She quotes her own tweet:
At BTSA mentor training, 1 of the prompts was "How do u incorporate tech into a lesson?" My knee-jerk response, "You don't." It's back to that tech for tech’s sake that irks me. It's like asking, "How do u add aspirin into your diet?" #ButIDoNotHaveAHeadache @ddmeyer
In many ways, the technology debate mirrors the traditionalist/progressive debate. Progressive reformers tell us that students who have a 100% phone use mindset might complete an assignment if it's online, whereas they won't even answer Question #1 on a p-set in a printed textbook. Indeed, last year at my old school, the history teacher painstakingly scanned every page of the text and posted it online for exactly this reason.
But notice that Nguyen is actually on the traditionalist side of the technology debate. She doesn't believe that technology should be incorporated into a lesson for the sake of including it.
Her mention of aspirin is a reference to the former King of the MTBoS, Dan Meyer. Back during the summer of 2015, Meyer wrote several posts about how certain math topics, such as factoring in Algebra I, are like aspirin without a headache. For example, we see the following post:
https://blog.mrmeyer.com/2015/if-math-is-the-aspirin-then-how-do-you-create-the-headache/
But here Meyer was writing about particular math topics from Algebra I and beyond -- and not something more general like technology. Traditionalists might oppose forcing technology in the curriculum, but they have no problem with forcing factoring into the curriculum.
Today, during the last day of subbing for the digital film class, of course the students used Chromebooks as the elective class is all about technology. But I had two encounters with cell phones during class. The first occurred during silent reading time. In fact, I haven't mentioned it yet on the blog, but this middle school has SSR as part of the regular school schedule. (Last Wednesday -- the one day I wrote a "Day in the Life" at this school -- there was no SSR as both homeroom and SSR were dropped to accommodate the walkout.)
I believe that one of the most difficult things for a sub to enforce is SSR. When a student decides not to do a written or online assignment, the regular teacher will eventually discover it when it's time to check the work. But if the student starts whispering or avoids reading, the teacher may never find this out -- and the students know this. At this school, SSR is always after lunch -- and with the rotation, it means that SSR is attached to a different class each day. Fortunately, today SSR is attached to fourth period -- the best-behaved class.
Anyway, here's the connection to technology -- some students don't have a book to read, so insist on reading something on their phone. I must apologize to Fawn Nguyen, who writes:
(I still need a real book to read from, however, like this one that just came in the mail because the Internet said I should read it.)
As it turns out, one girl has her phone, but there are no books uploaded on the phone either. The TA for the class lends her a book to read.
The other phone encounter is in fifth period -- the worst behaved class of the day. And here's a common problem with students who bring phones to school -- they often lose them. One student thinks he left the phone in another class -- and so during today's entire class, he acts out. He speaks loudly and out of turn and continually leaves his seat.
Back in my January 6th post, I wrote about one girl -- the special scholar -- who also loses her phone (in September). It's difficult to know what a teacher should do in this case. The student desperately wants the phone, knowing how angry the parents will be if they discover its missing. But the teacher doesn't want to waste class time on something the students shouldn't have anyway. I consider calling the office (cf. the January 6th post) but I ultimately don't. (Some schools have it built directly into the rules -- no class time can be spent searching for phones, no matter how expensive they are.)
Let's end our discussion of Nguyen's post with the commenter Pamela Baker, who specifically mentions Geometry in her post:
Pam Baker:
Completely agree with you. I teach Geometry and find it completely fascinating that most geometric discoveries can be done without “technology”. I have tried to do a lot of explorations with paper folding, cutting and coloring. It amazes me that many of my 9th & 10th graders have not had the opportunity to “play” with paper.
Last year, some of the STEM projects indeed allowed the students to "play" with paper. But other parts of the Illinois State curriculum required a computer (e.g., the online homework). And in hindsight, I realize that my school saved money by not purchasing printed science texts. I should have followed the history teacher and tried to have the students in all grades learn science online using the online Illinois State text (not Study Island). It's not until I read Nguyen's post and subbed in certain classes did I realize that classes can be completely dependent on online texts. (Saving money is arguably a valid reason to eschew printed books in favor of online texts.)
This is what I wrote last year about today's lesson:
The other is that I've been meaning to move the first two lessons of Chapter 13 -- namely 13-1 on the Logic of Making Conclusions and 13-2 on Negations -- up to Chapter 2. Dropping Lessons 2-3 leaves a hole right in the middle of Chapter 2, and conveniently, 13-1 and 13-2 fit here. Indeed, 13-1 on Making Conclusions makes perfect sense right after Lesson 2-2 on If-then Statements.
[2018 update: Not only does the modern Third Edition of the text include the old Lesson 13-1 in another chapter, namely Chapter 11, but just as I did in past year, the new edition also combines Lessons 13-1 and 13-2 in its new lesson, which is Lesson 11-2.]
This chapter focuses on mathematical logic, which ultimately helps the students write proofs. I mentioned earlier that the Law of Detachment is often known by its Latin name, modus ponens. In fact, I pointed out that on the Metamath website -- a website full of mathematical proofs -- modus ponens is one of the most used justifications:
http://us.metamath.org/mpegif/ax-mp.html
Notice that I only mention the Metamath website for general information. This website is definitely not suitable for use in a high school math classroom. At Metamath, even a simple proof like that of 2+2=4 is very complex:
http://us.metamath.org/mpegif/2p2e4.html
In fact, believe it or not the proof was once even more complicated because it tried to use pure set theory to prove that 2+2=4, and then later on more axioms (postulates) were added to make the proofs easier -- similar to the postulates for real numbers mentioned in Lesson 1-7. To repeat, the basic idea is that one makes a proof simpler by adding more axioms/postulates.
This is when students often ask, "Why do we have to learn proofs?" Of course, they ask because proofs are perhaps the most difficult part of a geometry course. The answer is that even though mathematical proofs may not be important per se -- but proofs are. Many fields, from law to medicine, depend on proving things. We don't want to guess that a certain person is guilty or that taking a certain medicine is effective -- we want to prove it. For centuries, the dominant way to learn how logical arguments work was to read Euclid. Let's learn about how Honest Abe learned about logical arguments from Euclid:
http://the-american-catholic.com/2012/08/16/lincoln-and-euclid/
Unfortunately, the above link is a political and religious website. Well, I suppose it's impossible to avoid politics when discussing Lincoln, but the webpage is also a Catholic site.
END
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