Please, the more problems you give them, the better off they’ll be. If you can arrange your classtime so that they can do a large portion of them in class, you’ll know that they can do them, they’ll have you to answer questions, and they can’t complain that they’re getting too many, because they’ll be finished or nearly so. My kids get home, do the 3 or 4 assigned problems for each concept, and don’t have a good grasp of it before they move on to the next concept, so that at the end of the homework they are lost again. They really need to just focus on one concept per session, until they “own” the method.
Yet, I’ve heard from many different kids (from several different elementary schools) in the Seattle School district that this is the only method they were taught to do multiplication of multi-digit numbers, if they were taught any method at all. I’ve talked to a few who were taught the tradional method, but the fact that it’s considered optional makes me want to scream. I’ve had a teacher here actually try to justify this method it to me. (If I believed in using smilies, I’d used the one of the guy hitting his forehead right about now.)
I was a long term college prof in Computer Science (which requires using a lot of Math).
I noticed the steep drop-off of retention ability in the 90s. It was astonishing how all the students lost completely the ability to remember anything, Math or otherwise. I would state clearly a factoid at the end of a lecture and state that it will be crucial to recall this factoid for the next lecture. Two days later I ask the class what the factoid was. Not a single one could even remember that I had told them to remember something let alone what it was.
This is a big reason I gave up on teaching.
It’s most noticable regarding Math, but it is not just about Math.
Students are no longer taught how to learn in grade school and high school. They have no concept of the idea of remembering something.
Preach it. A friend is a 2/3 teacher and is afraid to show me the books they use. Lots of pretty pictures and barely any math. Perhaps it does help some kids but I thrived on problem-solving and cold hard logic. It’s beautiful in its own way.
Of course, I am tempted to think that what I grew up with was best. Well, it worked for me. When I took math in HS, it was the practice for the math teachers to give us 15 minutes at the end of class to start on the homework (while the teacher marked the previous day’s work) and that 15 minutes was usually enough for me. The kids I see today have way more homework than I ever did. The only homework I usually took home were for language courses. In all the others, what I learned, I mostly learned in class.
Now in teaching math at the college level, I found a lot of what you describe. Students coming in having forgotten (if they ever knew) their HS math. And even getting them to ask questions was like pulling teeth. Some did come to my office for help. but most wouldn’t.
I’ve heard of the discovery method. On paper it sounds good, but… it is putting 2500 years of development of math out the window. And yet, memorization of formulas that will be forgotten when the course final is over cannot be the right answer. The point of drilling is not to memorize the rules, but to internalize them.
Incidentally, one very good method of getting the students to study is to allow them to take a “cheat sheet” to their exams. A few will do it anyway, surreptitiously, and this will prevent them from having an unfair avantage, but the main thing is that in order to prepare the sheet, they will have to closely review the course. Collect them and make it clear that just copying someone else’s is pointless. First you will see it and second they won’t get the benefit.
I don’t have any other advice. You seem extraordinarily conscientious and what can you do beyond that?
It sounds like your biggest obstacle is the students’ lack of motivation. If they don’t want to learn, don’t care if they learn, and won’t put forth any effort toward learning, they won’t learn, no matter how good an opportunity you give them or how many resources are available to them.
I don’t know the answer to this, but I’ve seen a couple of books on Amazon that look like they might be helpful, though I haven’t gotten around to getting and reading them yet:
One of the things I’ve found helpful with students is making them take step-by-step notes on large index cards for each type of problem (aka. flashcards). Each will have one side that says something like “solving for 2 variables using substitution”, then the other side will have explicit step-by step instructions for doing it.
I find this works for a few reasons:
You can’t fake doing the cards
They can easily be checked by requiring them to bring them to class.
You give them a concrete way of solving problems
They learn by having to take notes, and describe how to solve problems in their own words using plain English. This forces them to develop an understanding of how it’s done.
If need be, you can give them added incentives like bonus points for clear flashcards, or you can allow them to use them on tests or quizzes.
“who the hell ever thought the lattice method is anything other than a parlor trick?”
THANK YOU! My kids go to an IB school and when we went to the parent teacher conference, my husband asked the teacher “what’s up with this stupid lattice method?” Yeah they got the answer but it was sold just like you said, as a parlour trick. Sometimes there’s nothing wrong with the way us old farts did it.
I must have looked a lot like your students - lost and giving up. In fact, for math, it was from 4th grade on - and became a problem in Chemistry, Organic Chem, and then Genetics. Have you asked the kids, in private or anonymously, why they won’t come see you for help?
I had a massive math phobia - afraid to look stupid, embarrassed to have my friends see me struggling and failing, and totally frozen when anything involving multiplication or division came up. I couldn’t get algebra - the first time I saw “2x3” I’d lose my brain. I never did figure it out in high school, and I left college for a few semesters when I had failed math and chemistry a few times.
Finally, I got a class that wasn’t a teacher just standing up there reciting the lectures - I got a brand new TA in organic chem who admitted that she knew nothing about teaching and wanted to learn from us - she would explain things from a couple of different angles, and then ask us which one helped us more. She tailored her explainations to how we learned, and chemistry made sense for the first time.
Another thing that helped me - I was always afraid of the teachers. I couldn’t have spoken up in class if my life depended on it. It wasn’t anything they did, it was my past. When given time to work in class with a classmate to figure out how to do the work, I often could get it - but it was by sharing ideas and trying to figure it out ourselves, not by watching someone do the problems. Have you tried asking the students to try to rephrase what you are saying?
I have similar problems teaching high school chemistry. I would not have thought of this on my own, but my system allows for retaking tests for a grade’s worth penalty. I’d rather have kids fix the problem by relearning what they missed. This allows me to mollify parents who act concerned “There’s always hope! Just have Millicent come in for tutoring and retakes” even though it almost never happens. It means I get to put the responsibility on the kids. I never get the blame from parents, because they had the opportunity to fix it. There’s almost never a parent who cares enough to make trouble whose kid didn’t fix it, anyway. If the parent really cares, the kid usually performs.
Regarding taking notes: This is something I (and several other people) strongly discourage. If a student is taking notes, they are not paying attention and so the whole lecture is useless. I’ve seen so many students with meticulous notes that are of no help at all to them since they have no clue what they mean.
There are two scientific studies that I know of that have established this. (I’ve mentioned the humorous incident with Katie Couric and the Harvard researcher in previous threads.)
Note taking is one of those crappy anti-learning things that bad grade school teachers. If you are a teacher and think note taking is a good idea, you are decades behind the times.
Even if you are a note-taking fetishist, please, please allow those students who know better to make the right choice for them. Nothing makes students hate school (and do worse) than being forced to do something they know is wrong.
Wow - learning how to take notes properly is one thing that helped save my bacon. Taking the notes in my illegible scrawl and shorthands in class, then transcribing them at night while discussing them with study groups. Turns out I CAN memorize something if I write it out twice, and that explaining my notes to classmates made it make more sense to me.
If you think real note taking is of less-than-no-value, you have I Think not read the real literature.
There is a huge difference between mindlessly copying something and taking notes for study.
I’m not saying that most HS students are willing to read their notes, but the idea of note taking incorporates both concept understanding and restatement. Both are of large value.
Why all the hate for the lattice method? I graduated from grade school in 1964, so I learned the old way, but I was always very good at math. The lattice method is equivalent. In addition, in one way it’s a lot better: you don’t have to remember to carry then add after multiplying the digits in the next position. The carrying all takes place at the end.
However, I think students should learn ONE method well rather than two poorly.
Until I see the actual studies, I do not accept their results. Just because Harvard says it’s so doesn’t mean it really is. And the phrase “note-taking fetishist” is simply personal abuse, not a valid argument. Why use it if your argument is compelling? The usual reason is that it isn’t compelling. My working theory is the studies didn’t identify important variables, i.e., there are other things going on that produced the improved results, NOT the mere elimination of note-taking.
These are probably the same people who say our current ways of teaching reading and math are sound. So I’ll really trust them on note-taking. :rolleyes: As my favorite Orwell quote (in a different context) goes, “One has to belong to the intelligentsia to believe things like that: no ordinary man would be such a fool.”
In my more cynical moments, I’d swear our education system is being deliberately and systematically fucked up precisely to destroy this country. How much worse would things be if this were really true?
A guy in my year 9 maths class once asked the teacher about this. “What the hell is the point? We’re never going to need this!”
The teacher answered “You’re right. Yeah, some of you might go into higher maths or physics, but most of you are never going to need to do algebra after high school. That’s not the point. We’re not doing this to teach you how to solve equations, we’re doing it to teach you how to think. To approach problems rationally. Learning algebra helps you learn to think logically about the world - and you are going to need that.”
It was the best answer I’ve heard to that question.
When I was in school I would not remember a lecture at all the next day if I didn’t take notes on it. I did the worse in subjects where the teacher just gave handouts (and then went through the material too fast for me to take notes as they were talking). I have to write something down to truly learn it. People have different ways of learning and your blanket statement of saying note taking is bad is as dangerous as saying all students should take notes.
The Katie Couric story. This was back when she was on The Today Show. She has this Harvard researcher on and starts off by saying how a new study has shown how helpful note taking is. The reseacher steps in right away to correct her and says it’s the opposite. Katie blanks out. Her eyes wobble. “But, but, but…”. Great TV. I know prepping for a bunch of early morning interviews each day is difficult, but at least know the minimum Katie.
I’ve met a lot of people who claim that note taking helps them alot. But then I start asking them questions. Like, “Have you ever really tried doing without and comparing?” Belief is one thing, facts are another.
I’ve been teaching math for 11 years now, and I’ve certainly experienced the issues you mention. I’ve also seen a major decline in the student’s ability to use and remember algorithms for solving problems of all types. I agree with what many have posted–there isn’t one cure-all for this problem.
I do feel that you are going in the wrong direction, however. Students, especially high school students, are mostly searching for the easiest class they can find. Some of your students may actually be trying to dupe you into making the class easier for them–so they have less work. Even if this is not the case, lowering the standard of the class will only invite them to work less. Raise your expectations, make the class challenging, and see who rises to the occasion.
I do not grade the homework in my math classes. I do not give extra credit, participation points, bonus questions, etc…If a student’s grade should reflect their mathematical knowledge, then giving them points just for showing up (basically) is not going to help anyone (including the student) honestly evaluate what the student knows. Look into Formative Assesment to get an idea of where I’m currently heading with my class.
Why would your students complete their homework if it’s not worth anything? The first approach is you discussing with them their need to practice the skills if they are to do well on your tests. Since they will have fewer grades and no “free” points–the tests will completely determine their grade. Not practicing would be a massive error on their part.
I’m also very strict about getting homework completed. If they don’t bring it in when it’s due, they have to bring it in the next day. If not, I take them out of study hall to do it, or make them do it during lunch. They get the idea pretty quickly that they may as well do it the first time.
Of course I’ve learned all of these lessons through experience. I’ve tried a hundred different strategies. I can’t stress enough that no matter what your approach to teaching is, you have to have high standards.