This year I have been assigned to teach two sections of Algebra II. In one of these sections, I also have 3 Algebra II Honors students. Being fairly new to teaching (this is only my third year) and totally new to having two complete levels within one class, I am mostly at a loss as to what to do. I want to do everything in my power (within reason, of course) to make sure that each student receives a quality education. But I am really struggling as to the actual day-to-day mechanics.
To differentiate between two levels of a math class, a teacher typically has three options:
Teach more difficult material or a larger amount to the Honors level students.
Move at a faster pace with the Honors students.
A combination of 1 and 2.
Since the two levels are combined in my case, options 2 and 3 are seemingly out the window for me. So I’ve come up with a plan as to how to tackle option #1. It’s far from perfect, but a start.
My plan so far is as follows:
Begin each class as if all students are on the same level. Most of the material is similar enough that this will work.
About 20-30 minutes into the 41 minute class, have the Algebra II students work in small groups or independently on problems that practice the day’s lesson. During the remaining class time, meet with the Honors students to continue the lesson by either teaching new material or going deeper into what we’ve already covered.
The Honors students all have study halls that match up with one of my free periods, so they could ask for extra help then, if needed.
As I see it though, my plan has three fatal flaws:
While I am teaching the Honors only students, the remaining students are for the most part left to fend for themselves. It would be very difficult to teach one group something new while helping the other group with their work.
It leaves very little time for the Honors students to have in-class practice.
The integrity of a true Honors course is severely jeopardized without the ability to move at a fast pace and go as in depth with each lesson as I’d like.
I cannot stress enough how committed I am to helping all of my students succeed. However, I am limited by the fact that I have 4 other classes to teach, a young baby at home to tend to, and countless IEP challenges to tackle.
So here is where I turn to you, my fellow dopers. I would greatly appreciate any and all advice, tips, etc. you may have to offer. I’ve faced numerous challenges in my teaching career, but this is by far one of the biggest.
You’re absolutely correct in your differentiation, but that would work for Calc, not Algebra 2! Now if I were having this problem in a calculus class, we’d be in for some interesting terminology.
One of our upper level science teachers had a similar situation last year. He created an independent study program for his honors students, and they met for one-on-one instruction during his prep period. It seemed to work well for him…not sure how well it would transfer to Honors Algebra.
That would certainly work. The independent study would only be needed for the more difficult concepts. They could still work along with the rest of us for the remainder of the material. I have had two of the three students in prior classes, so I know they are capable and mature enough to work on their own.
This was discussed as a possible solution. It would help to solve the dilemma, but only in an artificial sense. It still fails to stay true to the core of an honors program which needs to include a greater depth of material.
Well I’m off to bed. I’ll try to check in before I leave in the morning. Unfortunately the SDMB is blocked at my school, so I can’t check during the day. Thanks so much for all the input so far.
Yes, I figured someone else would have made the obvious joke by the time I got to the thread.
Perhaps there’s a way you could make the mixed class work to your advantage? Like, assign a topic for the honors students to learn about and present to the rest of the class; or have them do some tutoring or group work with the weaker students?
I’m not a teacher, but I was involved in an advocacy group for the parents of GATE students for years, and heard lots of teachers, GATE administrators, and psychologists talk about differentiation.
You are right - the more homework solution is about the worst one, since it just makes the kids feel punished for being in Honors. Acceleration is better, but has the problem that the kids may wind up getting the same material next year. Your preferred solution of teaching in greater depth is best.
From what I heard, testing is a good way of determining what you teach. You might have them do the initial reading and homework, test them, and let them do the advanced stuff if they have gotten it. Is your textbook any good, and if not, is one which goes into a bit more depth available? if so you might start them off, but let them get more of the material from the book than you would expect the regular students to get. (If the book stinks, this won’t work.) Another possibility is for them to teach each other. Honors students teaching the others is a bad idea, but I think kids at more or less the same level I think they’d enjoy working out the techniques together. I don’t know if this would work for you, since they might get loud.
After you try this, give them some relatively low importance quizzes to see how they did. I’d suspect that they’ll want to do well on them not for a grade but just from ambition.
The schools I went to were heavily into tracking, so we were segregated by ability. Do you not have enough honors kids in your school for an honors algebra class, or is this against the philosophy of the district?
f(x) goes into a bar. The bartender says “Sorry, we don’t cater for functions.”
f’(x) goes into a bar. The bartender says “Sorry, we don’t cater for functions.”
The same joke twice? No, the second one is derivative humour…
If f(x)=0, then the derivative is 0 since the function is constant (always equal to 0). Plus, it’s not really a function any more. Just an equation where x=-5/3,0.
Have your honors students work the first problem and your regular students work the second pair.
And after looking at the rest of the thread, the consensus seems to be that this is seen as punishing better students. I always liked showing off by doing harder problems, but maybe I’m different. (Actually, I probably am.)
Another possibility is working in math history as solutions. Have a set of problems work out to Pascal’s triangle, perfect squares, something like that.
Please don’t do this one. Just because you are quick to learn algebra, it doesn’t mean you have any skill at teaching. Or, for that matter, any desire to teach. If you are a gifted math student you will probably thrive on tackling harder marth, but being forced to go over the lower stuff, over and over if you are tutoring a kid who just doesn’t get math, is punishment.
Not good for the bright student, not much good for the dull one. I mean, c’mon, if Johnny Dull doesn’t understand when a trained teacher explains, how likely is he to get it from Billy Bright who simply sucked it up like a sponge because it ‘was obvious’ to him, and he has no idea how to explain it?
When I was in school, my district was very against tracking - which was wonderful in some ways and not so great in others. We frequently were to work in groups, teach each other, and learn from each other. And there is some benefit to learning how to explain concepts to other students. There are times where students learn better from their peers than they do from a teacher, and being able to explain a concept helps solidify your own knowledge. That said, if it happens all the time, it feels like a chore and a kind of punishment.
In one of my classes (Algebra I), the teacher handed all of the students a book at the beginning of the year, said that he’d be teaching at one pace, and we were required to go at least that pace. But if we thought we could do it on our own, he had the end of chapter tests. As long as a student got above a certain grade on the test, they could keep going on their own. If they got below the grade on the same test twice, they were required to rejoin the main group that was following his lessons. I loved that class.
But if I couldn’t be left to my own devices, for me, harder problems with more depth would be the better solution. I would feel like it was honors, of course I should be doing harder work. More problems would be punishment. If I understood the concept quickly, more practice at something I already get would be a waste of my time, and logically shouldn’t the people who were struggling really be doing more problems?
So, when the teacher was going over something you had completed already, what did you do? And what happened if you finished the book before the end of the class?
Whatever I was working on. If he was on chapter 4 and I was on chapter 6, I read chapter 6 and did problems from chapter 6 and got ready to take the chapter 6 test so I could move on to chapter 7.
He didn’t complete the book during the year, so for the most part, students who were working at their own pace just got farther in the book than the main class did. For the ones who finished the first book, there were other books.
I have no idea how to do this and not punish the smart kids. Maybe let them read if they have finished the chapter? Let them have the class as a free study period?
How about collecting some fun number theory puzzles, the kind of thing you would see on math team? Don’t grade it, but do let them discuss it.
How about some problems from SAT practice tests? A lot of them should be in range for younger Honors students. There used to be the Underwriters exam, a math contest for high school kids. I never took it, but my roommate in college got the highest score in Texas history. If there are sample exams around, that might be fun. You might look at some of Martin Gardner’s recreational math books also.
Congratulations on your dedication to making this work for your students. I am considered an expert in differentiating the curriculum, in particular for high ability math students - GATE. I was flown to the US to speak at a conference on this very topic last year. Oh dear, now I have to put my ideas up for public scrutiny. I have worked on practical ways of doing this for a range of subject areas and age groups, from upper primary to senior secondary. I do hope some of this may be able to be adapted to your situation.
I think you are absolutely right to start the whole group together and move as fast as you can for the honors and top of the regular class. I would imagine this could be less than 20 minutes. Then the honors students move on to the practice while you work with the regular group. The regular class also needs differentiating, so this will work for them as well. So far, so good.
I am totally opposed to using any students to teach others. That is not what they come to school for - they come to learn. Having bright students work in groups can work fine, but can also cause resistance. It depends on the individuals. The range in ability can be large, and many think in visual or global ways, which are not easily described in the logical-sequential way we expect in math exams. Working with others who think differently can be stressful and hold them back. I don’t know your three, so I can’t assess whether to work them as a group.
I would have the more difficult tasks available online or printed. I would then ask the honors students to request assistance by email, not in person. I do hope that is possible in your school. If not, you can use written letters. Sounds tedious - it isn’t, as I hope what I say below will clarify. They can use attachments or write in the email, depending on what they are trying to say and show.
Using written communication has the advantage of you being able to respond when you can find time, which gives you a better chance of surviving. But there is a much more important reason. Your honors students should be starting to develop autonomous learning styles. This is our goal for all our students - for them to eventually not need us teachers. By writing to you with their struggles, they have to verbalize them. This is also an invaluable skill for math students - to be able to describe their thinking in natural language. You will also find many will see something new to try when explaining why they are stuck. Again, an invaluable skill. All of this is very much a method which only suits very able students - differentiating.
None of this is set in concrete, of course. Should you get the chance, you should check in on them during class if your others are all working fine.
When you receive their email questions, try to respond with questions or guidance, rather than lengthy explanations of the ‘correct solution’. For example, if Suzy has lost a square in a function, you could ask if she has checked thoroughly, especially indices. Checking is another habit which should be established. If Suzy has no idea how to start, you ask what she has tried. Or suggest a starting point. Your replies should be brief. If you don’t understand the student’s question or response, don’t spend hours puzzling over it. Ask for a clarification of whatever doesn’t make sense - your students will benefit from having to communicate their mathematical thinking clearly. It means they have to fully understand themselves.
While waiting for your reply, they can move onto the next question. Don’t feel pressured to send a rapid reply. You will be amazed how often you will get a later email saying - “don’t worry, I worked it out”. If they do, try to get the student to explain what the hurdle was - reflecting on their hurdles helps identify the alternative methods in their minds.
A HUGE advantage to doing this is the fun you will have. I have found that my advanced students have a quirky sense of humor which is often suppressed in class. As they get to trust you, you will find you get some wonderful asides and anecdotes!
It is also useful to copy and paste from emails to quote in reports. Parents love a very witty quote from their child being raved about in reports. No idea if you report as we do.
If your honors students want to work as a group, they can copy each other in on emails, and reply - with you getting a copy of everything. You may find the problems are solved before you get a chance to answer. This also encourages them to explain in writing - very good for exam practice.
Then we get to the next stage - what is known in the trade as ‘qualitatively different curriculum’ - the sort of stuff you don’t want to teach to a mixed ability class - concepts which only suit the mathematically able brain. I spent most of my teaching career developing material to extend the able students, and develop autonomous learning, as well as getting into all sorts of great stuff which never makes it into the regular classroom. My math material has been used in the US as well as here. Again, I would put it online so anyone in the class/school could get it any time. You may find some of your other students motivated to play with some of the ‘puzzles’. Math tasks in puzzle format - anything from fractal geometry to the number theory type puzzles mentioned by an earlier response. I ended up with over 250 tasks over a 30 year career in math - plus as many again in other disciplines. No student ever got through even the majority of the math ones, although I had some students doing extension work with me for six or seven years.
You can start quite simply - there are plenty of good tasks online. BUT beware - it is not valid just to have them do anything to entertain them - a good, qualitatively different task links to the bigger picture of math thinking. I could write forever on this - it is what I address conferences about! As suggested earlier, Martin Gardner is a great resource. There are other excellent writers for this area. I have a bibliography of resources I used to develop my tasks which I can send you if you like.
The goal of these extension tasks is to have the students thinking mathematically, but also to find what terrific fun it is - not just doing questions with set answers by expected methods.
I do hope there is something in all that you can adapt to your situation. All the very best!
You’re absolutely correct in your differentiation, but that would work for Calc, not Algebra 2! Now if I were having this problem in a calculus class, we’d be in for some interesting terminology.