I've decided to write this series of posts in terms of the classroom rules that I plan on having. As a sub, I've seldom had to come up with classroom rules -- my job was to enforce the rules established by the regular teacher. In the rare situations where I needed my own rules, my first rule would be something like, "Follow all adult directions." The emphasis here was that if the students wouldn't respect me as a teacher (the attitude of many students toward subs), perhaps they would at least respect me as an adult, hence the rule "Follow all adult directions."
But now I'm going to be a regular teacher myself, so I need my first rule to have a higher purpose than simply to treat me as an adult. The thing is, before the students can respect me, I must learn to respect them.
This post is quite long, so I've divided it into sections.
1. Suggestions from Traditionalists: Math Curmudgeon
2. Strive to earn an A in this class and every class!
3. Suggestions from Traditionalists: Bill
4. Suggestions from Traditionalists: Wurman and Garelick
5. Grade School to Grad School (or From C to Shining C)
6. The Consequences of my C's
7. My Departure from the Traditionalists: Real World Math
8. Let's Break Down My Grades
9. Don't Be a Dren!
10. Heroes and Fraction Fever
11. On Gender
12. Rule #1: The Teacher Respects You
Suggestions from Traditionalists: Math Curmudgeon
Recall that I'm using traditionalist links to guide me through my first year of teaching. The first link I'll give today is a post mentioned by the traditionalist Math Curmudgeon, whose blog I mentioned back in my Father's Day post:
In this post from two months ago, Curmudgeon quotes another person's tweet:
"I just took the 2016 SATs test. I failed. 25% in Maths, 40% in English. Kids, you don't need to know what a modal verb is or a subordinating conjunctive is to get where you want to go in life. You need ideas & passion -- so go on adventures, dream BIG and don't worry about your SATs scores."
Curmudgeon then laments that the original tweet drew comments like "You're my hero!"
There are several things going on here. This is a math blog, so we won't worry about modal verbs and go directly to the math score. At first Curmudgeon assumes that the tweeter is referring to the SAT test, but it's awkward to give SAT scores as a percentage, as this tweeter does. And if the tweeter intends to say 25% of the top score of 800, then this is 200 -- the lowest possible score.
Then a commenter on Curmudgeon's post points out that the tweeter is British (the spelling "Maths" should give it away), and she's actually referring to SATs that are taken by students completing a U.K. elementary school. Then again, this makes the tweet even worse. The tweeter is bragging that she only knows 25% of elementary school arithmetic -- in other words, she's a "dren"!
But again, Curmudgeon's biggest complaint is about the "You're my hero" responses to the tweet. We can easily see why the blog author is upset -- suppose the original tweet said, "I got 85% in Maths and 100% in English," and guess how many "You're my hero" responses this tweet now receives. A good estimate to this question is zero. Instead of "You're my hero," we expect "You're a nerd" responses to be more common.
Many traditionalists like to compare those who excel in academics to those who excel in sports. The NBA season recently concluded. Throughout the regular season, there had been much excitement about Steph Curry, the first unanimous MVP. Then in the playoffs, the accolades were now directed towards LeBron James, the Finals MVP, as he won his third championship. Traditionalists lament that Curry and James are treated as heroes, yet the mathematical equivalents of Curry and James are treated as nerds.
We know that math is near easy nor fun, but neither is training to be a world-class athlete on the level of Curry or James. But I've said many times on the blog that hard work is respected in "high status" fields, which includes basketball, but not mathematics. Yet this leads to yet another question -- why exactly is basketball considered higher status than mathematics?
After all, it is possible to have mathematics without entertainment (which is why many students don't like math classes), but it's impossible to have entertainment without mathematics (especially not modern forms of entertainment). We enjoy watching sports on a variety of media thanks to the inventions of people who earned A's in their math and science classes -- without them, we wouldn't be able to watch the games unless we bought tickets. In fact, what would students rather be doing instead of studying math and science? The answer is almost certainly to use something that was invented by people who earned A's in their math and science classes -- without them, the inventions that they enjoy wouldn't exist. Therefore the real heroes are the students who get lots of A's -- especially in math and science classes. These students should be treated as heroes, not nerds.
Here's another way to think about this problem. Someone who calls Curry and James heroes is thinking, "Curry and James are people just like me, except better at basketball." But if a student excels in math, the thought is, "That student isn't just like me -- he/she is a nerd." It doesn't matter that students are more likely to ace math than they are to beat Curry or James one-on-one -- more people identify with basketball stars than mathematicians.
So my goal as a math teacher is to get my students thinking, "That great math person is just like me, except better at math," and eventually, "That great math person is my hero." Keeping this in mind, I was considering the following as the first rule in my classroom:
Strive to earn an A in this class and in every class!
It's not enough merely to try to earn an A in my class (Yoda: "There is no try.") -- instead, students must work hard and strive to earn an A. This rule is an umbrella rule -- it covers other common classroom rules such as "Bring all books and materials to class." Students who don't bring materials to class aren't really striving to earn an A.
When I was a student, it never even occurred to me not to strive for an A in every class. Of course I was a good math student, but I wasn't great at other subjects, such as history. I will go as far to say that I hated history and didn't find the subject relevant to my future. Yet I never earned any grade less than a B in any history class. It's possible to hate a subject yet still score above 80% on nearly every test in that subject.
I don't expect every single student to earn an A in my class, but I want every student to strive to earn the top grade. After all, every single player on the court strives to win the championship, even though only one team can actually win the championship. Likewise, every single student at a school should be striving to be the valedictorian, even though not every student can actually be the valedictorian.
At this point, you may ask, what about tanking? Aren't there players and teams who aren't actually striving to win a ring? But think about it: teams tank because they want to draft great players -- players who will eventually win them a ring. So in reality, every team is trying to win, either in the current year or in a near future year. On the other hand, students who "tank" in math class aren't trying to pass math ever, either now or in the future.
In theory, every single student should be striving for an A, but in reality, some students aren't trying to pass at all. I'm getting ready to teach at a middle school -- and often it's in middle school when students decide to stop working hard in their classes.
Just before Memorial Day, I blogged about the movie Akeelah and the Bee, where the title character is a girl who's trying to win the National Spelling Bee. At the beginning of the movie, Akeelah is encountered by two girls who criticize her for earning so many A's, then beat her up. Of course, these girls are wrong to hit Akeelah, but that doesn't change the fact that they hit her. This is something that I must watch out for as I teach -- even though Akeelah's school in the movie is a fictional middle school in Los Angeles, the charter school where I'll be teaching is, frankly, located not that far from where the movie is set.
The tweet mentioned in Curmudgeon's post earlier is a symptom of a larger problem -- we simply don't want to hear that the most successful people in life are those who earned the top grades. Yes, it's possible to be successful without earning A's, but such people are exceptions to the rule. There have even been books written about how A students aren't the most successful people in life -- just look at the title of Robert Kiyosaki's 2012 bestseller: Why A Students Work for C Students. Meanwhile, a book with a more truthful title such as Why A Students Run the World wouldn't have been a bestseller.
In my class, an A isn't the only acceptable grade, but it is the only acceptable goal. It's okay to earn a B if you were striving to get an A. It's okay to earn a C if you were striving to get an A. It's even okay to earn a D -- but by that point, I'm skeptical that you were really striving to get an A.
I want to tell the story about my own grades, from grade school to grad school. But first, I have several more traditionalists to discuss, as they were particularly active in posting this week.
Suggestions from Traditionalists: Bill
As usual, I'm getting these comments from the Joanne Jacobs site, which in turn links to articles from other websites, but the traditionalists comment only on the Jacobs site. The first link involves my home state of California, except it's Northern California:
The link describes how in San Francisco, all eighth graders take Common Core Math 8 rather than the class that traditionalists prefer them to take, Algebra I. I've discussed this topic so many times on the blog, so let's just skip to the traditionalists' comments.
I was expecting the traditionalist Bill to comment on the Jacobs site, and he didn't disappoint:
It looks like high schools are more interested in diversity rather than actually learning math, the foundations of which start in Elementary School…if they don’t have the basics down by the time they head to 6th grade, they’re gonna struggle in math the rest of their lives…UGH
Another poster, a community college professor, wrote about a student in his class who didn't know how to calculate the average or arithmetic mean. Here is Bill's response:
The student should have never been allowed to be enrolled in this class without a math placement examination (IMO), but I’ve seen students like that myself who couldn’t handle basic stats/probability…it’s painfully evident how math challenged our society has become…
Suggestions from Traditionalists: Wurman and Garelick
But there are other traditionalists in the comment thread as well. I wasn't expecting the traditionalist Ze'ev Wurman to post here, but he does. He basically echoes Bill's comments:
Ze'ev Wurman says:
That’s what happens when your goal is to assure equal outcomes rather than pursuit of excellence.
Another surprise traditionalist posting a comment is Barry Garelick. Jacobs herself wrote that in order to get to senior year AP Calculus in districts that don't offer eighth grade Algebra I, some districts offer a choice between taking a single course that combines Algebra II and Pre-Calculus, and simply doubling up in math one year. Here is Garelick's response:
Barry Garelick says:
That isn’t the case here in San Luis Coast USD. Students have to double up courses one year.
As it turns out, Garelick has a comment on the original article as well:
I've already mentioned the traditionalists' solution to the Algebra I problem. They don't make students take two classes in one year to reach Calculus -- instead, they compress nine years of math (that is, Common Core K-8) into eight years (K-7). To accomplish this, they cut out all Common Core K-8 Standards that they don't like (especially those involving nonstandard algorithms) and drop down a grade those that they do like (especially those involving the standard algorithm). Garelick hints above at what the resulting seventh grade class would look like -- it is basically Common Core 8 without the unit on stats (and probably the unit on transformations as well) and cutting three weeks out of the unit on slope and functions.
Our next thread is a little closer to home -- it involves high schools in LAUSD. Remember that I will be teaching at a middle school (not a high school) and it's a charter school (not LAUSD proper). But it's possible that many of my students will be moving on to LAUSD high schools if they fail to be admitted to a charter high school. The topic is credit recovery.
Credit Recovery programs are a scam designed to boost graduation rates, period…you cannot learn a semester’s worth of information in less than usually 80-100 hours of instruction time (give 5 hours a week for 13-15 weeks), and the issue of taking a 10 question multiple choice exam and getting a pass for 60% is a joke, since the students failed the class in the first place (the cut score should be at least 75% using 20-30 questions of multiple choice, fill in the blank, and true/false)…
Later on Bill responds to a teacher describing a similar situation in South Carolina. I'll leave that part out and stick to California in my post.
Based on these traditionalists' posts, my goal is to make sure that the students see the value in actually learning the material. Even if there are high school "credit recovery" classes where students can graduate without actually knowing any math, it's far. far better to know math anyway. As a student, it never even occurred to me to try to graduate without learning anything. I'd like to say that I earned all A's and B's in my classes, but unfortunately, I did get a few C's along the way.
Grade School to Grad School (or, From C to Shining C)
The first C grade that I ever received was in first grade, when I earned a C in handwriting. But when I was in middle school, I earned a few more C grades. Even at the time, I considered each C grade to be a mark of deep shame, and I still am ashamed of my C's to this today. Of course I earned A's in all of my math classes, but in several other classes I earned C's.
Here are all the C's that I earned in middle school. My school divided the year into four quarters, and so I will give each class plus the quarter in which I earned the C:
-- 6th Grade Health/Self Esteem, third quarter
-- 7th Grade Art, first quarter
-- 7th Grade Science, fourth quarter
-- 8th Grade Science, first quarter
-- 8th Grade Science, second quarter
-- 8th Grade English, second quarter
-- 8th Grade English, third quarter
-- 8th Grade Library Aide, fourth quarter
I'm the most ashamed of my eighth grade science C's. This is because 8th grade science has always been a physical science class (as opposed to 6th grade earth science, which wasn't established in California until after I passed the 6th grade). Of all the sciences, physical science is the most allied with mathematics. No student with A's in math -- especially as the only 8th grader in Geometry -- has any business earning C's in physical science, yet that's exactly what happened to me.
Throughout high school, I strove to make sure that I earn all A's and B's in order to erase the shame of my "seven C's" of middle school. Notice that I used the pun "seven seas" = "seven C's" of middle school, yet in reality I earned eight C's in Grades 6-8. This is because at the time, sixth grade was considered elementary, not middle school, so I didn't count my sixth grade C with the seven C's of middle school.
In high school, I sometimes had low grades after the first quaver (half of a quarter) of a class. This often occurred in my English classes, where there were very few graded assignments the first quaver (when the focus was on just reading the material rather than turning in work for a grade). Sometimes I received a low grade on the first major assignment -- and since there was hardly any other assignment to balance out my grade, I'd receive a D grade on the first quaver progress report.
I even once had an F grade as my first quarter grade in my junior-year English class. I don't wish to make excuses here, but that year, my teacher injured herself the second week of school, and so there were a series of subs for over six weeks. One of the subs assigned a major assignment -- I think we had to write a poem. But I forgot about it because none of the other subs had given us longer assignments, and so I'd become accustomed to doing homework for other classes, not for English. At the end of the quarter (by when the regular teacher had returned), this poem made up the largest part of our grade, and so I ended up with something like 55% for the quarter.
Ironically, this was right around the time when I was being considered for the magnet program (as I explained in a previous blog post the second week of June). I was transferred anyway despite the F -- as it turned out, the grade appeared as D on the quarter progress report. This might have been because I was being transferred from Honors English 11 in the old program to English 10 in the magnet (as the magnet is a year ahead of the regular program) -- as honors classes didn't begin until 11th grade, I was graded on the non-honors grading scale, where 55% was a D! (Notice that if I hadn't switched districts and applied to the magnet at the end of 8th grade as was standard, I probably would have been rejected for earning too many C's in the 8th grade!)
My new English teacher told me that she had to include the quarter grade as part of the semester grade, but she would weigh the second quarter more heavily. In the end, I earned a B that semester -- and indeed, I ended up with all A's and B's every semester in high school.
My college career, however, was a different story. The first C grade I earned at UCLA was in a biology class. But I'm most ashamed of my lowest grade I ever earned in any class -- a C- in the third quarter of first-year Physics. I'd passed AP Physics C Electricity and Magnetism with a grade of 4 (and unlike Calculus, Physics AP's never receive equivalence at UCLA), and so I'd probably assumed that I could get a good grade in this Physics class without much effort. Obviously, I was wrong.
Even though my Physics C- was my lowest grade ever, my most destructive grade was actually the C+ that I earned in a Graduate Analysis class. The problem is that this was the first quarter in the grad program at UCLA, and grad students are really supposed to earn only A's and B's. Actually, what matters the most is the overall GPA, which should be at least 3.0. That quarter, my grades in the other two classes were B and B+, which made my overall GPA 2.87 (as plus-grades are worth an additional 0.3 point). Just as with my missing poem in 11th grade English, the problem was that there were no other quarters to balance out my grade, as undergrad quarters aren't included in calculating the grad GPA at all. My 2.87 grad GPA meant that I was officially on academic probation until I raised the GPA to 3.0 or better.
Again, I don't want to make excuses, but I heard that the Analysis prof was a tough grader. Indeed, so many students were failing the class that the prof was encouraging students to drop the class and move down a level to Honors Upper Division Analysis -- again, this was a class that I had already taken and passed with a B. So once again, I'd become jaded and assumed that just because I'd passed the previous class, I could pass the later class without much effort.
I still remember one test question that I had particular trouble with -- it was about determining whether a certain function was Lebesgue measurable. (I actually mentioned Lebesgue measure and integration earlier on the blog, in the process of discussing David Kung's DVD course.) I remember the prof saying several times that the open intervals generate all the measurable sets, yet I didn't use this when working on the test. And so I ended up failing the test and getting only a C+ in the course.
Why am I posting all of this on the blog? It's because I want to inspire my students to earn as many A's in their classes as possible -- and I want to show that I wasn't perfect myself, so the students should try to avoid my mistakes. I plan on telling my students about my own grades. This also allows me to empathize with my students -- for many of them, working with fractions is as difficult as Grad Analysis was for me.
I never earned a grade as low as C+ again -- even though I did get a few B- grades. I raised my GPA to above 3.0 in my second grad quarter and ultimately earned my Masters degree with a final GPA of around 3.3 or 3.4. But as I'd struggled so much with my Masters, I decided not to seek a Ph.D degree.
The Consequences of My C's
After leaving UCLA, I wasn't sure what I wanted to do with my life. Yes, I did say in earlier posts that as a young kid, I'd wanted to become a math teacher. But by middle school I wasn't so sure -- I'd seen the way that students treated subs, and I knew that I had to become a sub before I could become a regular teacher.
Of course I wanted to apply my STEM degree, so I applied to some local engineering companies. I remember one interview when I was asked about my GPA. My interviewer had noticed that my undergrad GPA was 3.6, but my grad GPA was only 3.3-3.4. I told him that grad classes are more difficult than undergrad classes, and his reply was that yes, but I should have been a stronger, more mature student by then as well. In the end, I was denied the job -- and based on the sequence of questions, I concluded that it was because of my low grad GPA. In other words, I was denied the job because I hadn't earned enough A's in my classes.
Back in the seventh grade, I'd learned that the largest public employer of mathematicians is in fact the Department of Defense -- in particular, the NSA. After grad school, I ended up applying to the NSA, and I was flown across the country to its Maryland headquarters for an interview. One of the questions I was asked was, "Have you ever been on academic probation?" And I was forced to answer "yes" because of my bad first quarter as a grad student. In the end, I was denied the job -- and based on the sequence of questions, I concluded that it was because of my low grad GPA. In other words, I was denied the job because I hadn't earned enough A's in my classes.
Eventually, I gave up on a STEM career and sought out a teaching credential instead. I worked hard to earn my credential -- with A's or B's in all my classes, of course -- and I'll realize the culmination of that work this fall when I begin my first teaching assignment. In other words, I was offered the job because I'd earned enough A's in my classes.
Students who earn A's in their classes are setting themselves up for a bright future -- students who don't earn A's in their classes are setting themselves up for a dismal future. The only ages that truly matter in a person's life are your 20's, 30's, 40's, 50's, and maybe 60's -- the years when you earn money -- and the only people who truly matter in a person's life are your employers -- the ones who give you money. (Well, of course your family matters -- but you can't start a family unless you earn enough money.) The only people who truly matter want to see as many A's as possible, and their opinion trumps anyone who says that A students are "nerds" or worse.
In particular, a student's peers don't matter, since they aren't employers. Not even I, their teacher, matter, since I'm not an employer. The traditionalist Bill isn't an employer either -- but he often writes about what employers are looking for. This is why I plan on reading some of Bill's posts in class.
I don't really want to tell my students my NSA story -- as interesting as it sounds, I don't want to give the impression that teaching them is only my "second choice." Instead, I want to tell the students about the grades I earned when I was their age -- in Grades 6-8, with emphasis on the C's. In a way, those C's, despite being middle school grades, almost cost me admission to UCLA. This is because ordinarily those C's would have cost me admission to the magnet program -- and many Honors and AP courses, the ones that look attractive to UCLA, were offered only to magnet students. It was only because of a loophole (that is, changing districts during freshman year) that I was allowed to enter the magnet program. I'll tell my students that they shouldn't count on loopholes like changing districts (or "credit recovery" classes) and that it's much better just to learn the material, so that they'll actually know the things that employers want them to know.
My Departure From the Traditionalists: Real World Math
Here is the third post from the Jacobs site that I want to mention:
This post is especially relevant to my upcoming class. It cites a study which purportedly shows that it's better to teach pure (i.e., traditionalist) math than applied math. Recall that my classes will be using the Illinois State text, which is heavy on STEM and applications. This is so important that I will link to the original article as well:
Strangely enough, Bill hasn't posted in this thread yet (as of the time I posted this current entry). But Wurman does have something to say here (after the thread went on a tangent with phonics).
Ze'ev Wurman writes:
All the discussion about phonics aside, the report is about math. And there is little argument that Common Core overall is heavily “problem solving” oriented, problem-solving being a stand in for “real-life problems.”
Another poster, Ray (who isn't a traditionalist), responds to Wurman:
There is something about education issues that can get people so upset that they can start to think that facts don’t matter. Sometimes people get so upset that they start to make things up. Mr. Wurman, you lost a lot of credibility when you wrote that the Common Core math standards defer fluency in division until sixth grade. In fact, Common Core standards require students to “Fluently multiply and divide within 100,” in third grade.
In Wurman's defense, I assume in sixth grade he's referring to long (multi-digit) division, for which the standard algorithm doesn't appear until Common Core Math 6 (but of course nonstandard algorithms appear in Grade 5). On the other hand, Ray cites the third grade standard which is mostly about single-digit division (or two-digits, as in 81 divided by 9 is 9).
But in the end, I can't agree with Wurman or the other traditionalists here. As usual, traditionalists forget that many students sitting in math classes often ask questions like "Why do we have to learn this?" or "When will we ever use this in real life?" The applications are provided in order to provide answers to those common questions -- for without such answers, the students will refuse to work hard enough to learn the material.
From the same thread, here is another poster named Michael Hiteshew:
Michael D. Hiteshew writes:
I think the reason that people who are taught pure math do better all around is that abstract math teaches you (forces you) to think logically and to reason from a known set of information to a solution. It also teaches the use of tools (techniques) that you keep in mental toolbox, and teaches you to ask yourself “What tools do I need to solve this problem?”
So after solving equations, they ask questions like, "What tools do I need to solve this problem?" But before solving equations, they ask questions like, "Why do I need to solve equations?" and "When will I need to solve equations in real life?"
Michael D. Hiteshew writes:
In addition, anyone who was taught Euclidean geometry by proofs forever after asks themselves ‘What do I actually know to be true?’ and keep that separate from what you surmise may be true.
So after doing proofs they ask questions like, "What do I actually know to be true?" But before doing proofs, they ask questions like, "Why do I need to do proofs?" and "When will I need to do proofs in real life?"
As usual, traditionalists like Hiteshew just assume that the students will work on the abstract pure math simply because they are told to work on them, even though they won't see the benefits of doing so until afterward. But the students will never reach a point where they're asking themselves those great questions if they're throwing the worksheets full of equations or proofs in the trash -- because they see no relevance of those equations or proofs to real life.
The goal of the Illinois State text is to show students how math is relevant by way of various math and science projects. Even if students working in the Illinois State text don't learn as much math as students working on worksheets full of equations, they definitely learn more math than students throwing away worksheets full of equations. My hope is that I can open a unit with a project, the students will see how math will help them with their project, and then they'll be motivated to learn the math and start earning those A's.
Of course, suppose the students do finally see the importance of earning A's in math class. But some students will feel frustrated as they feel that they were never good in math. Even in kindergarten, they were struggling to learn the concepts, and not even in kindergarten did they get most of the questions right on a worksheet or hear their teacher say "Great job!" after a math worksheet is completed. So by the time they get to my class, they'd been failing math for six, seven, or eight years, and so they certainly won't start to try hard in math now.
But to me, that's a lousy excuse not to strive for an A in my class. Recall that the Cleveland Cavaliers had never won the championship before this year, and teams from the Forest City hadn't won rings in any sport in 52 years. So Clevelanders had been failing in sports seven times as long as my students have been failing in math. Yet LeBron James and the rest of the Cavs squad didn't use that as an excuse not to strive for a championship.
And of course, the ultimate example of failure in sports is in baseball -- the Chicago Cubs haven't won a championship in 108 years. So the Northsiders have been failing thirteen to eighteen times as long as my 6th-8th graders have been failing in math. Yet Jake Arrieta and the rest of the Cubs squad aren't using that as an excuse not to strive for a championship -- and indeed, right now they have the best record in all of baseball.
Let's Break Down My Grades
This post is all about grades. One consideration I must make is the grading breakdown, including what percentage of the grade is devoted to tests, classwork, and so on. I think back to my student teaching days, and that district had the following policy:
40% -- Tests
30% -- Quizzes
20% -- Classwork
10% -- Homework
These percentages are approximate -- for example, I think there was a separate components of the grade for teacher tests and district tests, as well as the final. Of course, finals won't be a consideration this year as I'm teaching at a middle school, not a high school.
All grades were entered into a computer, and then the grades were weighted so that the percentages for each component (tests, quizzes, etc.) are correct. For example, let's say there are ten 5-point homework assignments followed by a 100-point test. So there are 100 test points and 50 homework points, but tests are supposed to be worth four times as much as the homework. Therefore a single test point is worth twice as much as a single homework point. I disagree with this grading method, as it's deceptive -- a 5-point question on a test is worth more than turning in a 5-point HW paper. I know why the computer is programmed this way -- it helps non-math teachers get the correct percentages without having to perform calculations.
But as a math teacher, I hold myself to a higher standard. I'd much rather do the calculations myself so that a point is a point no matter what. To make the calculations easier, I can choose a number such as 1000 points for the whole trimester. Then there will be 400 points for the tests, 300 points for the quizzes, 200 points for classwork, and 100 points for homework.
For the tests, I can hold four tests each trimester, each worth 100 points. The tests can be staggered so that I'm not testing all my students at the same time. The first test can be given the second week of school to my 8th graders, then to my 7th graders the third week, then to my 6th graders the fourth week, and back to the 8th graders again the fifth week.
On these tests, a grade of A isn't the only acceptable grade -- it's OK to get a grade just below A provided that every effort is made to strive for the A. That is, A is the only acceptable goal on most tests and quizzes. But there will be one instance in my class where A really is the only acceptable grade -- the Dren Quizzes.
Don't Be a Dren!
Back in the district where I student taught, there would often be basic skills tests given. Often these would be on integer operations. Students would be given 100 questions, and they had to get 90 of them right -- an A -- in order to pass. In fact, if the student receives any grade other than A, the test doesn't count and students receive a score of 0 (or possibly 1%, so that parents don't wonder why there is a 0% test on their student's grade report). The test must then be repeated until the student gets at least 90 correct.
In my class, I will strongly state that a "dren" is a reverse-nerd -- someone who isn't proficient at basic math (third grade and below). And so I will give out Dren Quizzes, where students are asked to solve 50 basic multiplication problems. Just as in my former district, there are only two possible grades -- A and Dren. Any grade other than an A is a Dren grade, and students get only 1/50 (or 2%) until the quiz is retaken and 90% (or 45/50) is earned.
I'd like it so that the second Dren Quiz is on the 2's times tables, the third Dren Quiz is on the 3's times tables, and so on. The first Dren Quiz, meanwhile, won't be on 1's but on the 10's instead. In theory, every single student should get 90% -- forget that, every student ought to get 100% on a quiz on the 10's times tables. Yet the traditionalist Bill has often lamented that there really are some students who would fail a 10's times tables quiz -- for example, here's a Bill comment from about five years ago:
Overuse of technology has left most young persons in society unable to handle many tasks considered common knowledge 25-30 years ago. All a calculator, computer, or a e-reader are tools, but if persons do not understand the basics of reading, writing, and math, all the technology in the classroom will do NOTHING to help them later on.
In another topic, a teacher in chemistry class cringes when his students have to rely on a calculator to handle basic basic math or to multiply a number by 10 (add 1 zero to the right hand side of a whole number to multiply by 10), these are facts that students should have MASTERED in elementary school (grades 1 through 5).
The fact that people are experts in email or text messaging isn’t going to help them when they cannot write a business letter, or a resume, or fill out a job application properly. Ever watch a person who is engrossed in using their phone in public, they almost block out the entire world around them (which in some cases can have deadly consequences, or as I call it, the darwin effect).
Lets get back to using what worked more than a quarter century ago, and quit buying into the latest fad craze, generally foisted upon us by individuals who have spent their entire careers in academia, with no knowledge of the real world, per se.
We may ask, why is a question like "What is 2 times 10?" so difficult for students? Here is what too many students are thinking:
-- 2 times 10 is math, and math is hard, therefore 2 times 10 is hard.
And so when they are asked to find 2 times 10, they don't even think about whether this is an easier or a harder question (like 7 times 8) -- they just react to any math problem with "This is hard!" and either ask for a calculator or answer "I don't know!" And of course, it goes without saying that students will not be allowed calculators on Dren Quizzes.
So just before giving my students the Dren Quiz, I'll read this last five-year-old comment from Bill, so that the students understand why I'm giving them a Dren Quiz. The idea is that students will see that a "dren" is something that they don't want to be, so that they'll be motivated to do well on the Dren Quizzes.
My plan is to rotate so that students take a Dren Quiz the first week after a test (when the students haven't learned much new material yet), then an ordinary quiz the second week (which is about halfway through the new material), and finally the test the third week. All quizzes, ordinary and Dren, can be given on Wednesdays when the classes are shorter (as 50 minutes should be more than enough time for these quizzes).
So the plan for the first few weeks of eighth grade will look like this:
First Test: Friday, August 26th
First Dren Quiz (10's): Wednesday, August 31st
First Ordinary Quiz: Wednesday, September 7th
Second Test: Friday, September 16th
Then on Wednesday, September 21st, the eighth graders take their second Dren Quiz. It will be on the 2's times tables except for those who didn't pass their 10's (which hopefully will be no one except for students absent on the 31st). On the 2's Dren Quiz, I'll sneak in a few 10's. After all, the idea isn't just to learn the 10's for the first Dren Quiz and forget them, but to remember them forever. That way, when the science teacher (as in the Bill quote above) asks for 2 times 10, the reaction isn't:
-- 2 times 10 is math, and math is hard, therefore 2 times 10 is hard.
but for "20" to pop into their head even before they get to "2 times 10 is math."
I'll repeat the idea that students are to avoid being drens over and over again. For example, I might tell the students "dren jokes." Dren jokes are basically blonde jokes, except that I change the word "blonde" to "dren" (and make them gender-neutral, of course). The original version of the following blonde joke is inappropriate for the classroom, but as a dren joke it is very appropriate:
Q: How is a dren like a solar-powered calculator?
A: Neither works in the dark.
I must be careful, though. When telling dren jokes, I will make sure that I'm not directly calling any student in the class a "dren." The only time I'll ever call a student a "dren" directly is in a situation like the following:
Me: What is 2 times 10?
(Student reaches for a calculator.)
Me: Don't be such a dren! Only drens need a calculator to multiply 2 times 10.
Will all of my Dren Quizzes be on multiplication? Perhaps if after the 10's test students make it all the way from 2's to 9's, the next Dren Quiz will be subtraction of decimals, as another traditionalist complaint about youngsters is that they can't make change correctly.
I want my students to view being a dren as a mark of shame, not a mark of pride. If a student is a dren, the first thing is for the student not to admit it. If a student is a dren, the best thing is to hide this fact as much as possible, not brag about it on her Twitter page or laugh at how she was able to make it to middle school without knowing math (as one girl did during my last week of subbing). In other words, fake it until you make it.
So far, so much of this post is about shaming the drens. But what should I do with the students on the other side -- the ones who are actually learning math and doing it well?
Heroes and Fraction Fever
As I wrote earlier, students who do great in math aren't nerds -- they're heroes, and I want them to know that they are heroes. The first step is for me to admit that they are heroes, and treat those students as heroes. It's far too easy for me to focus only on the drens -- and this is terrible.
Let's think back to Akeelah and the Bee. We know that the other students make fun of the title character because she is so smart. Now suppose that I have a mathematical Akeelah in my class -- a student who is doing great. I can't really stop the other students from making fun of her. But it's one thing to be ridiculed by the students outside of class -- it's another to be ridiculed by the students outside of class and ignored by the teacher inside the classroom. I admit that when I was a student teacher, I sometimes ignored the good students -- and this I must change.
In fact, I want to go out of my way to make the top students feel like heroes even if it means embarrassing myself, for the priority is to make the top students feel good, not myself. For example, if I make a silly error and a student corrects me, I want to make a show of it. I plan on pounding the table in "anger" and yelling at myself for making the mistake. This will cause the other students to laugh at me -- which is exactly what I want. I want the students to congratulate their classmate who "annoyed" the teacher so much -- because that's the student who really understands the math enough to spot my error. Finally, I may even award a bonus point to the student who catches the error. If this is successful, I might even make some errors intentionally in hopes that the students will catch it!
It would be one thing if the other students feel that they simply don't want to be friends with the smart kids and just ignore them. But it's another for them to physically beat up the smart kids, just as the other girls did to Akeelah. And that's a huge problem -- it's hard to get even the smart kids to know that they're preparing for the only years that matter in their lives (their twenties and beyond) if they can't survive their preteen and teenage years without being beat up.
The best I can do is offer up my classroom as a "safe space" on certain days at lunch, so that students who fear being attacked due to their success in math have a place to stay. Perhaps on an especially rainy day (when students would want to eat in the classroom anyway), I can invite the students with the highest grades into my classroom and inform them that they can eat there on certain dry days as well if they are having problems with the other students.
Again, the idea is to reward students who earn A's as much as possible. I may have two types of rewards -- an individual award to each student who earns an A on a test, and a class reward if sufficiently many students in the class earn A's. Perhaps the existence of a class reward will lead to the kids viewing the top students as the heroes they are.
And the idea that I should celebrate bright students extends beyond the classroom. I don't follow anyone like that British dren on Twitter, but I do have online contact with several of my former classmates, who often write about their children's academic accomplishments. Sometimes I congratulate the children for doing well in school, but I'm not consistent at it. I want to put my mouth where my money is, and make sure that I tell my friend's children that they are heroes the next time that their parents brag about them online.
It's often said that you never forget how to ride a bike. Unfortunately, learning math (or science) is very unlike riding a bike -- people forget it all the time (otherwise, I wouldn't have ended up with C's in my college science classes). Let's get back to our first traditionalist link, Math Curmudgeon, who comments on how often certain topics in math are forgotten by the time students take the SAT (the American SAT, not the British SATs):
Even the best ones have forgotten the most basic ideas. √300 = 10√3 - what magic is this? Proportions and fractions - who knew?
Now sqrt(300) = 10sqrt(3) isn't relevant to the classes that I'll be teaching -- but fractions definitely are (after all, middle school math is A Story of Ratios). For some reason, adding fractions is nothing like riding a bike. According to Curmudgeon, even students who get A's in all their math classes can't add 1/2 + 1/3 = 5/6 instantly. I myself, of course, could have taken a fractions test the very first day of school as a junior year and get a perfect score without studying at all, but this is rare among most students -- even most A students. People ought to remember how to add fractions forever, but they simply don't.
When I was a young child, I remember one of my first computer games. (This was one of those old computers from the 1980's.) One of my favorite games was Fraction Fever. Even though this is an old game, I was able to find a link describing the game:
An educational game dealing with fractions. The player must navigate a bridge on a pogo stick with the objective of landing on the space that answers the fraction shown on screen. Wrong answers remove a space. If too many spaces are removed the player falls to a lower level.
Now it might be possible for me to implement a version of this game in the classroom. No, the students wouldn't jump around on pogo sticks, but I would post answers to fractions near the ceiling so that students would still have to jump (in the spirit of the game) to reach the right answer.
Such a game could fit at the beginning of the school year. The Illinois State texts for all three grades begin with "Tools for Learning," which is essentially a Unit 0:
Tools for Learning:
1. The Need for Speed
2. Show Me the Numbers
3. What's the Best Advantage?
4. Learning to Communicate
I'm not sure how long I will spend in this Unit 0, since it all depends on how long it takes to complete all the projects (which begin with constructing a model car and measuring its speed). But in between these projects, the students will need fraction practice, so I can whip out my Fraction Fever game, which will have higher levels ("floors") where students must add, subtract, multiply, and divide fractions -- not just identify them as in the original computer game. The hope is that students will be prepared for the more difficult projects which require the students to know fractions.
But I suspect that even playing a game like Fraction Fever won't be enough. Curmudgeon's complaint was that students don't remember fractions from year to year, so that by the time they take the SAT they will have forgotten everything. Since it appears that I will be teaching the same students for three years, this puts me in a unique position to encourage the students to remember fractions as each of those three years passes.
Here's my plan: on the first day of school of my second year (that is, in 2017), I will give the seventh and eighth graders a fractions test. Students won't be penalized for failing it, but I want to reward them handsomely for passing the test, with an even better reward for those who get A's on it. I will inform the students at the end of the upcoming school year of this Fractions Challenge.
I know -- I'm supposed to be preparing for my first year of teaching, and here I am already writing about my second year! Still, this gives me an entire year to think up a suitable reward for those students -- those heroes -- who can remember fractions.
Now Bill and the other traditionalists once again mention race/ethnicity in their comments. This is because the idea of placing San Francisco eighth graders in Algebra I is sort of like tracking, and any discussion about tracking ultimately leads to race. But here I wish to discuss the other major demographic -- gender. This is especially important at a school that emphasizes STEM, since females tend to be underrepresented in the STEM fields.
I remember back when I was student teaching, and I noticed that many of the girls were struggling in my Algebra I class. I fear that the reason for this is that I, as a male math teacher, was displaying an unconscious bias towards my male students when teaching. Here is a link from last September to an article that discusses the problems that male STEM teachers have with female students:
Here on the blog I've devoted posts to several prominent female mathematicians, including:
-- Hertha Ayrton
-- Eugenia Cheng
-- Vi Hart
-- Danica McKellar
-- Emmy Noether
-- Theoni Pappas
And speaking of Theoni Pappas, on her Mathematical Calendar 2016 she featured another female mathematician in June. Iranian-American mathematician Maryam Mirzakhani is the first female Fields Medalist (which is very prestigious considering that there is no Nobel Prize in math). She is currently a professor at Stanford, and her work is on topology -- remember how a doughnut is topologically equivalent to a coffee cup?
But again, I must make sure that I treat the girls in my classes who are doing well in math as the heroines they are. And I want to make sure that I encourage them to work hard on the STEM projects so that they'll be successful in my classes.
One of the women mathematicians I listed above is Danica McKellar. Last year, I wrote how I had bought two of the books in her Girls Get Curves series. I, a male, am not in the target demographic of her books -- but then again, I already know math. The girls in my classes are the ones in the target demo of these books. In fact, yesterday I finally purchased the other two books in that series (Kiss My Math and Hot x: Algebra Exposed! which are geared towards Pre-Algebra and Algebra I students, respectively), now that I'm teaching at a middle school. If at any point it appears that my girls are disengaged, I will bring out the McKellar books and read these books to them in hopes that the girls will get back on track.
Indeed -- and this goes for both males and females -- yet another trick to get the top students seen as heroes is for me to start talking about famous mathematicians and scientists as superheroes. I recently read a commenter (not a traditionalist -- indeed this wasn't even at an education website) who was upset that movies promote the idea of superheroes as people with special powers (not just Batman or Superman, but also wizards like Harry Potter) when the real heroes are scientists. Of course, I wrote last year about two scientist movies (featuring Stephen Hawking and Alan Turing), but those movies were not blockbusters (although Eddie Redmayne won an Oscar as Hawking).
And so whenever I have the chance, I can start talking about McKellar, Hawking, Turing, Euclid, and Dido as if they were celebrities. Vi Hart (another female mathematician from the list!) created a video about the life of Pythagoras, and his strange aversion to beans. I admit that I've never thought of scientists or mathematicians as heroes --one day, one of my elementary school teachers asked me to name my hero, expecting me to name someone like Einstein. I don't remember my response, but I was told later on that my reply was a certain game show host. (Perhaps I'd said Bob Barker -- but then again, The Price Is Right is, in fact, a very mathematical game show!)
My first rule will be:
Rule #1: The Teacher Respects You
I can't help but think back to my student teaching. In my Algebra I class, there was a girl who was a sophomore -- so she must have taken the class as a freshman and failed it. Still, I could tell that she was motivated to learn -- probably because she knew she didn't want to fail the class again, and moreover, she still remembered a little bit of Algebra I from the previous year.
Early in the year, this girl often volunteered to answer my questions -- and I often rewarded her with participation points when she answered correctly. She began the year with two participation points and soon ended up with ten a few days before the test. At that time, I told her that she had earned the maximum number of points I'd allow. Whenever she raised her hand, I would ignore her and use my random name generator (explained in a previous post) to choose a student instead.
The girl passed her test with a C, but I could tell she was upset that I wasn't calling on her. Even though the participation points started over again at the next unit, she no longer volunteered to answer any more questions. From that point on, she was frequently absent from class, and she ended up earning a D in class for the semester.
Two years later -- long after my student teaching was completed -- I happened upon the graduation program for the school. I still remember the names of many of the seniors graduating that day but -- and by now you've figured out where this is going -- the girl's name was not listed. Of course, it's possible that she switched schools (just as I once did my freshman year). But my fear is that girl joined the anti-school subculture -- and it's all because she didn't like how I ran her math class. My fear is that the student failed to graduate all because of me.
So what will I do in my new class to make sure that nothing like this ever happens again? My idea is that early in the year, there should be no limit on the number of participation points a student can earn. Recall that in my most successful student teaching class (sixth period Algebra II), the students were highly motivated to volunteer and learn. Perhaps if the other students saw this one girl always volunteering and receiving praise, they'd want to volunteer as well -- and then in subsequent units, there'd be no need to limit the number of points because there would always be several students volunteering on every question! Finally, I should mainly use the random name generator when there is no one volunteering on a question.
In short, I will respect the students in the way that I failed to respect this girl.