Tips for a first-time HS teacher?

[Anarion]

I hated that idea in highschool. What in the bloody hell is the point in making a student show the work? If you can figure out the answer to the problem in your head, then why should the student get marked down for it? Or what if the student did things differently(but still kinda similar) in solving the problem, and always got the right answer, are you really going to penalize the student for thinking differently? Because I did that a lot as well, and I HATED that I'd lose partial credit for solving the problem differently. I mean, I can understand if you are in college, but in highschool? It's just ridiculous ><

The point of having a student show work is to teach them methods that generalize beyond the immediate problem. To take a lower level example, a student who knows addition could solve a problem like 5*7 just by adding 7+7+7+7+7. But that's not going to work for solving 32545*44654. That's why there's a method for doing it. This remains true at higher levels of mathematics, and the point is to teach people general ways of solving problems and then test that they learned it by giving specific examples. Shortcutting the example is only going to hurt the student in the long run.

That said, using different notation systems or different but generally equivalent methods on problems that can be solved in multiple different ways is perfectly fine and a student should not suffer a penalty for them unless a particular method is specified when the problem is given.

I was one of those students who was disruptive AND got excellent grades. As an adult, I feel a little bad now about wasting the time of other students who didn't pick things up as easily as I did. I didn't care about detentions, notes home, in-house, or any of that. But if you started messing with my grades as a result...yeah I could shape up a little for you.

You're in a statistical minority. You're claiming that you were
1) smart enough to get all the stuff right,
2) didn't care enough to behave and,
3) that a grade-based punishment would have worked where all the behavioral stuff failed.

If that's really true (and I hope you can forgive me for being doubtful), it's still not easily generalized. It's much more likely that you're going to take a couple smart people who are having troubles with maturity and are at a different developmental stage than other people in the class and screw them over. Or that you'll take people who are already struggling, in addition to being less mature than their classmates, and make absolutely certain that they have no chance of ever doing well.

If a student is a disruption to the class, the student should be asked to stop, punished as appropriate, or asked to leave the class. A particularly problematic student may be asked to leave the class repeatedly, and there's probably even escalation from there. Doing that will probably screw the student's grade anyway because he/she will miss all the lectures.

But I remain a firm believer that taking behavioral problems and using them as an excuse to reduce a student's score directly is a huge mistake. It's inherently unfair and insensitive to the fact that different young people develop, both mentally and physically, at different rates even through high school. In addition to that, I'm not even sure I like the concept from a societal point of view: people who are smart, quiet, and law-abiding aren't necessarily better than people who are smart, loud, and a bit wild. It's important that the time of every student is respected, but doing it by screwing over the people who have a hard time sitting still is the wrong way to go about it.

I will grade primarily based on completion (though let them know what they messed up). I'll check their stuff in class, and use a grading app on my iPad.

Just going to point something out. Students, no matter what else they're doing, have a keen eye for inequality. If you want the strict cell-phone ban, having your own iPad out during class is going to make that much harder.

It is a good idea. Keep in mind I've taught college math the past 6 years. What I've found is that incoming students are incredibly lacking in their math vocabulary. What's the difference between an expression and an equation? What's the quadratic formula again? Wait, what's the difference between the quadratic formula and a quadratic equation? That sort of stuff.

It'd be like learning Spanish and only knowing how to conjugate verbs.

This, I love.

Also, for the separating points from behavioral stuff, what about participation points?

A few things. One, I do think this is a bit different. Obviously, if you're giving out points for speaking up in class or calling on students in some regular manner, and a student is not present due to being a disruption, they don't get those points.

Two, you should be very careful about how you do participation points. As much as students hate it, I'd actually recommend cold-calling over taking volunteers. There have been a lot of studies about how men volunteer heavily over women, and to a lesser extent Caucasians over minorities.

Three, again due to developmental differences, I'd expect shyness from some students even with participation grades, and even with cold-calling to force them to talk. One big difference between college and high school is that in college, every student is there because they want to be there. In high school, they have to be there. That means in college, you can expect them to participate and be engaged because otherwise they wouldn't be in the class. In high school, you might get some people who totally freak out on the spot and want nothing more than to disappear from the class, but when it comes to their written work, they do just fine.


I guess, more broadly, the theme that I'm pushing on in several of my responses is that when it comes to grades, I think the most important thing is that a student learns the material you're trying to teach. I firmly believe that a grade should reflect that fact and nothing else. You should set up your grading so that introverts and extroverts are both capable of demonstrating to you that they've learned the material, and that students at varying levels of developmental maturity are also capable of demonstrating that they've learned the material.

[Knaight]

Two, you should be very careful about how you do participation points. As much as students hate it, I'd actually recommend cold-calling over taking volunteers. There have been a lot of studies about how men volunteer heavily over women, and to a lesser extent Caucasians over minorities.

A technique I've seen in a number of places is having a can with Popsicle sticks in it, each of which has a students name on it. A name is then drawn from the can to cold-call.

[FinnLassie]

Heheh, that popsicle stick method, I love using it with wee kids. There's no way they have any legit reason to complain that I constantly pick the same people.

[Archonic Energy]

Heheh, that popsicle stick method, I love using it with wee kids. There's no way they have any legit reason to complain that I constantly pick the same people.

I want to see all the sticks to independently verify that you just haven't wrote my name on them all.

*palms stick with my name on *

[sktarq]

Popsicle stick methods is more useful in larger classes but if the class size is under 15 like the OP described it seems a little overboard.

[Knaight]

Popsicle stick methods is more useful in larger classes but if the class size is under 15 like the OP described it seems a little overboard.

It's good at making sure that questions are evenly distributed, and subconscious bias is a powerful force to the contrary. A smaller class size just means fewer Popsicle sticks.

[Anarion]

If it's only 10 people, you could just call on each person once per class (use a seating chart with checkmarks or something).

[TheThan]

The best math teacher I ever had didn’t just teach math. Sometimes he would just sit and talk to us about life. He knew that we were on the verge of adulthood and were about to step out into the “real world” (high school seniors mind you). So he decided that as long as we learned something, whether that was some life lesson or actual math, he felt he was doing his job and doing good by his students.

[Crow]

If that's really true (and I hope you can forgive me for being doubtful),

We're talking high-school level classes dude. Not rocket science. All you have to do to get good grades is put in the work. I wasn't in any AP classes of course.

[Starwulf]

The point of having a student show work is to teach them methods that generalize beyond the immediate problem. To take a lower level example, a student who knows addition could solve a problem like 5*7 just by adding 7+7+7+7+7. But that's not going to work for solving 32545*44654. That's why there's a method for doing it. This remains true at higher levels of mathematics, and the point is to teach people general ways of solving problems and then test that they learned it by giving specific examples. Shortcutting the example is only going to hurt the student in the long run.

That said, using different notation systems or different but generally equivalent methods on problems that can be solved in multiple different ways is perfectly fine and a student should not suffer a penalty for them unless a particular method is specified when the problem is given.

I have no problem with the teacher teaching the proper way, obviously not everyone is going to be capable of doing complex equations in their head. My issue is when I would fail exam after exam because I solved the problem "Differently", or at first, just inside my head. I didn't connect with the way the teacher solved the problem, my brain attacked the problems in a different manner, and I was penalized for it every single time, and that's what I"m saying on this thread: Don't penalize a student just because he does it differently. I very nearly failed geometry because of this, and it was ridiculous because I was getting the right answer every time, but being penalized for it. Who the hell cares if I get it a different way? I've probably used Geometry less then a handful of times since I left highschool, and yet I nearly had to graduate a year later(or at the least, double up on math classes) because my teacher was a [synonym for female dog] over how I solved the equations.

I mean, this woman literally ruined math for me. I used to love math up until her class. I can remember helping upper class-men do their Alg2 homework, because it just came naturally for me, but after this teacher? I hate math, even to this day. When I see people on this forum and others listing out complex equations my brain literally shuts down and forces me to skip it, I can't even look at it ><

[Crow]

When I see people on this forum and others listing out complex equations my brain literally shuts down and forces me to skip it, I can't even look at it ><

Oh man, I am the same way!

[danzibr]

Just going to point something out. Students, no matter what else they're doing, have a keen eye for inequality. If you want the strict cell-phone ban, having your own iPad out during class is going to make that much harder.

I read and appreciate your post, but I want to comment on this. Why should there be equality in the classroom? Between students yes, but the same rules do not apply to the students and teachers.

I've been doing the cellphone ban thing for a long time, but I keep my cellphone out on the front desk to check the time. Occasionally I'll say something about points being deducted from my homework and get a laugh or two.

[...] and that's what I"m saying on this thread: Don't penalize a student just because he does it differently.

Right, I already don't make that blunder. A shame you had that experience.

[Anarion]

We're talking high-school level classes dude. Not rocket science. All you have to do to get good grades is put in the work. I wasn't in any AP classes of course.

I'm not doubting that the classes were easy. I'm doubting the combination of the three things I posted: you were smart enough to get it all, you didn't care enough about the class to behave, and that you would have responded to a grade threat even though you didn't respond to detentions and stuff. It's all that together that I'm skeptical about.

I read and appreciate your post, but I want to comment on this. Why should there be equality in the classroom? Between students yes, but the same rules do not apply to the students and teachers.

I've been doing the cellphone ban thing for a long time, but I keep my cellphone out on the front desk to check the time. Occasionally I'll say something about points being deducted from my homework and get a laugh or two.

I said it would be harder, it could still work. You're dealing with a younger age though, so where college students might get the humor, someone who's 15 or 16 might think that since the teacher gets to pull out a phone to check the time, he should be able to do it too.

Right, I already don't make that blunder. A shame you had that experience.

Ditto to that. I'm sorry to hear that your education got that messed up Starwulf.

Edit: Although, why the heck is being uncomfortable with math a thing that people are just okay with? If you were like "oh man, I know, I have trouble reading big words sometimes!" You'd go out and study some more English because that would be hugely embarrassing. Math is important guys.

[Flickerdart]

We interrupt this serious and somewhat heated conversation to bring you a thematically related comedic interlude.

[sktarq]

I read and appreciate your post, but I want to comment on this. Why should there be equality in the classroom? Between students yes, but the same rules do not apply to the students and teachers.

Some yes but there a couple very large differences between the college and HS classes that this can have a major effect.

Firstly college students have a buy-in to the system that HS students often do not. Many HS students are actively looking for ways to challenge you. This kind of behavior is something they can latch onto and undercut your authority with the entire class.

Secondly as a grad student you were more like you students than different. You may be in a position of authority but you were more same than different. You are about to become effectively an alien to your students. You will be fundamentally "other" at least at first. It is not an impossible divide to reach across to have a good relationship but it does mean that you will not be given the benefit of the doubt on things such as fairness.

[Crow]

I'm not doubting that the classes were easy. I'm doubting the combination of the three things I posted: you were smart enough to get it all, you didn't care enough about the class to behave, and that you would have responded to a grade threat even though you didn't respond to detentions and stuff. It's all that together that I'm skeptical about.

If I didn't care about the class, I would not have bothered to do the work. I wanted good grades because it kept me eligibile for sports, and my parents off my back.

Several of the teachers in our school did have a "grade threat". It was a citizenship score. You had a pool of points that contributed to your grade. Misbehavior caused points to be deducted from that pool as the semester ticked on. I was pretty well-behaved in those classes.

It worked well until the beginning of junior year. That was when I discovered surfing, and started to truly not care, which is what I am sure you were assuming earlier. From then on, it was A's on the tests and just enough school and classwork to get D's at the end of the semester.

I guess what I am saying is that just because it doesn't apply to you, doesn't mean it doesn't apply to anyone. I knew several through high school. Chances are, if the OP sticks with teaching, he is going to encounter quite a few students who pull good grades because they need them for some reason or another, but don't walk the straight and narrow.

As I suggested earlier. Place it somewhere in your discipline continuum. Not the first step, but maybe around the third, around where you might contact the parents. Make it well-known that this can happen, so there are no surprises, and always administer it uniformly. If a student continues to act out at this point, they have made that choice.

[Anarion]

As I suggested earlier. Place it somewhere in your discipline continuum. Not the first step, but maybe around the third, around where you might contact the parents. Make it well-known that this can happen, so there are no surprises, and always administer it uniformly. If a student continues to act out at this point, they have made that choice.

And I'll continue to push against that and say that students shouldn't be allowed to make that choice. Behavior and mastery of a subject being taught are separate things and using behavior (beyond a limited class participation points system) to negatively impact a student's grade leads, imo, to unfair results. I just don't believe that students in K-12 are all equally mature and capable of making the decision you're talking about in a way that's fair.

Anyway, I think we've laid out the issue pretty clearly at this point. It's up to danzibr to pick how to handle it, and I do hope we've assisted in making an informed decision.

[The Second]

The problem comes when it actively hurts people's ability to do math. I know I have left a year long HS math class with a lower level ability than when I started (And had just aced my math SAT I and II's) than when I wen in. Trying to work it out the way the teacher wanted left me unable to do it his way or my way. I was horrible at math for years after-only a great TA a couple years later gave me extra help to learn how see calculus in a way my mind works. I went from D and F to strait A's for the rest of the semester in a couple hours worth of private teaching. Until then, and still today, my work would have been a certain shade of blue, billy idol's hair point shape, the scent of burnt meat, the answer because that is how my mind works-and for years it work extremely well. Most math teachers I've had don't seem to share an understanding of how that could possibly work (and I've always assumed self selected towards a limited collection of mental styles to produce disproportionate self referencing communities). In college the students taking math classes (depending of on what your definition of Intermediate Algebra is collegiate Algebra being the beast that it is) is going to be more likely one that already shares more traits with the "common" mindsets that a more random group of HS students who are there because it is a requirement to graduate.

I can relate to this, though at the time I had no idea why I couldn't seem to make things work out the way they were supposed to. To me, math textbooks seem to have been written in some alien language that I've never been able to decipher, and back then, sitting in a class with twenty other students who seemed to be doing just fine made me feel like I was some kind of mentally retarded idiot, so I never said anything until I flunked the first semester. When the teacher came to me and asked why I was having trouble, I told him it was because I didn't understand it. "What don't you understand," he asked. "Any of it," I replied. And was then put in the remedial class, which made me feel even worse. It wasn't until I was junior in high school that a student teacher sat down with me and showed me a way to work out the problems that I could understand. Went from D's and F's to B's, much to everyone's surprise, including my own.

I guess what I mean to add to the discussion is, if someone is struggling with your assignments, don't write them off as a lost cause.

[Pie Guy]

I'm gonna step back in here for a sec and say to not require flash cards because I always hated them, and had less respect for a teacher who made me make/use them.

[Jay R]

I hated that idea in highschool. What in the bloody hell is the point in making a student show the work?

I hated it in high school too. But now that I'm teaching, I've learned why it's necessary.

1. It's an anti-cheating tool. It's harder to copy the work from somebody's paper than just the answer.

2. We are usually teaching methods which will be necessary to do more complicated problems later. But we start you on easy problems. Many bright students can see the answer to the early problems, and will skip learning how the tool works, Then, when they reach harder problems for which they cannot instantly see the answer, they don't have the tools. If I make people learn and use the tools at the start of algebra 1, more students are capable of handling the later chapters in algebra 1.

[Winter_Wolf]

Showing work for partial credit is extremely useful when students don't get a correct answer. If a student consistently makes the same mistake, it shows you what part(s) they're not wrapping their minds around. When a lot of student s make the same mistake, it shows the teacher an area which is either very difficult and needs more time, and/or that the teacher is dropping the ball on actually teaching that particular part. Teachers don't make you show work to punish you, it's to help you even though I never liked showing work I still understood the point.

I know it's trendy to never blame precious bundles of BS (school aged kids) but if all the students are screwing up in the same way, the teacher isn't communicating effectively. That is a teacher problem. If its just one or a few students who are consistently screwing up, then it's a kids issue and needs to be figured out. That's not a blame thing, that's a "what's it gonna take to get this student to be able to/willing to absorb what we're trying to teach" thing. From experience, a lot of kids will make an effort and be willing to try up to a certain point but between parents with blinders, admin that don't care just make the test mark, and teachers who just can't or won't make the effort, some students will just stop giving a flying crap.

[sktarq]

Showing work for partial credit is extremely useful when students don't get a correct answer. If a student consistently makes the same mistake, it shows you what part(s) they're not wrapping their minds around. When a lot of student s make the same mistake, it shows the teacher an area which is either very difficult and needs more time, and/or that the teacher is dropping the ball on actually teaching that particular part. Teachers don't make you show work to punish you, it's to help you even though I never liked showing work I still understood the point.

I get why. I've always gotten why. But teachers who insist on it are harming a subset of their students. For some students the all or nothing (no partial credit) works better for them. 8 points of 10 is close enough and who cares if you actually get the answer right. They well not be doing it to punish a student but it is hurting them all the same.

[Anarion]

I get why. I've always gotten why. But teachers who insist on it are harming a subset of their students. For some students the all or nothing (no partial credit) works better for them. 8 points of 10 is close enough and who cares if you actually get the answer right. They well not be doing it to punish a student but it is hurting them all the same.

I don't understand this argument. If the student does the method correctly, they get 100%. If they're not solving problems quick enough to do them all in the time allotted, they can get 80%. If they mess up somewhere, the teacher can ID it and still give 50-60% on that problem or more.

I get that some students are messed up by being forces into a specific method, but nobody is advocating that. What we're advocating is that the student demonstrate whatever method he's using.

Also, I'd much prefer to reward the kid who did the whole problem right but had a DERP somewhere in the middle and wrote 8*5=45, than I would the kid who has the right number but can't tell me how he got it.

[Asta Kask]

Heheh, that popsicle stick method, I love using it with wee kids. There's no way they have any legit reason to complain that I constantly pick the same people.

And if they do, that's when you teach them about Poisson statistics.

[sktarq]

I don't understand this argument. If the student does the method correctly, they get 100%. If they're not solving problems quick enough to do them all in the time allotted, they can get 80%. If they mess up somewhere, the teacher can ID it and still give 50-60% on that problem or more.

I get that some students are messed up by being forces into a specific method, but nobody is advocating that. What we're advocating is that the student demonstrate whatever method he's using.

Also, I'd much prefer to reward the kid who did the whole problem right but had a DERP somewhere in the middle and wrote 8*5=45, than I would the kid who has the right number but can't tell me how he got it.

Except there very often is no demonstrable method. Or at least no way of communicating it in a way the teacher can make sense of. When I figured out problems via a mishmash of colour, sound, and kinesetic sense of a some martial art move there is no way for a teacher to grade that...but it worked reliably for me. It was the insistence on showing work I didn't have that was the problem. I've never said that if a student puts down partial shouldn't be rewarded for it-but know that it incentiveses putting down stuff over the right answer a lot of the time. I knew several students who used their knowledge of partial credit to skate courses. They never cared if they got the answer right just as long as they got enough partial to pass the class. Your preference at the end is exactly what I am advocating against. For some people 8*5=40 because it just is not because they added 8+8+8+8+8 on the scratch paper. You aren't grading ability there you are grading the ability to explain. It's like the modern art museum where everyone has to read the artists monograph next to each piece.

[Knaight]

Your preference at the end is exactly what I am advocating against. For some people 8*5=40 because it just is not because they added 8+8+8+8+8 on the scratch paper. You aren't grading ability there you are grading the ability to explain. It's like the modern art museum where everyone has to read the artists monograph next to each piece.

This gets into how much work needs to be shown. Past a certain point steps start needing to be dropped - the arithmetic steps I wrote out in 2nd grade were hidden when I took Algebra 2 in 6th, most of the algebra done there I didn't show for calculus, and once in higher calculus some of the lower stuff doesn't get shown any more (such as actually writing out the u and du in u-du substitution). As for grading the ability to explain, that can happen if the teacher is really insistent on a particular method and not another that is just as functional and written out - but at the same time, there's a class of methods that actually work and aren't just intuitively knowing it, and understanding functional methods are really important in math.

[sktarq]

As for grading the ability to explain, that can happen if the teacher is really insistent on a particular method and not another that is just as functional and written out - but at the same time, there's a class of methods that actually work and aren't just intuitively knowing it, and understanding functional methods are really important in math.

Actually if a teacher is insisting on the shown work then it is grading on the ability to explain. If you can explain your method you get the points, if you can't you don't.

And if the method is working by producing the correct answer then it actually works too-if it doesn't then a zero on the question is pretty assured.

[Anarion]

Actually if a teacher is insisting on the shown work then it is grading on the ability to explain. If you can explain your method you get the points, if you can't you don't.

And if the method is working by producing the correct answer then it actually works too-if it doesn't then a zero on the question is pretty assured.

All modern intellectual jobs require you to explain your conclusions. Mathematics papers require that you write out a proof, engineering requires that you save and file documentation before starting any kind of construction or assembly of a project, all scientific experiments require reproducible steps, law requires memos explaining the precedent, politicians write out careful policy memos, teachers themselves have to write out course plans step by step, and so forth.

[sktarq]

All modern intellectual jobs require you to explain your conclusions. Mathematics papers require that you write out a proof,...teachers themselves have to write out course plans step by step, and so forth.

True but applied to HS math class I don't think that an appropriate comparison? I think and have seen that backfire as much as help. If a student does better at dealing with such issues in the form of "support you argument" in an English class it shouldn't be penalized in math class.

[Lycunadari]

My teachers often didn't require to show work, but if you did and got the final result wrong, you still could get part credits. So if you just wrote the result, and it was right, you got full points, if it was wrong, you got nothing. But if you wrote down how you got the result, you could get at least points for the part that was still right. So not showing work was only a good idea if you were 100% certain you got the right answer.