I just don't get it. Adding and subtracting polynomials is basically adding like terms. How can they get to this point in Algebra 2 and not be able to combine like terms correctly? I have several students who tell me that 3x^2 + 6x^2 is 9x^4. I still have students, in spite of having calculators available, who cannot add or subtract integers properly. I have students who will take an expression in parentheses such as (6x^2 + 10x - 3) and try to combine it into one term such as 13x^3.
I understand there can be confusion keeping straight what to do with the properties of exponents. I'm multiplying (4x^3y)(2x^2y^4) and you want me to add exponents but multiply the numbers? When I divide you want me to subtract the exponents? When I raise something to a power I'm supposed to multiply exponents? It can be a little confusing. But when I explained it one on one to some students the day before and gave them as many hints as I could to help them keep it straight - remember, you are not doing the same operation to the exponents as you do to the numbers; notice that the operation you are doing is one step lower on the order of operations list - they still don't remember it the next day.
And those are just the graded learning targets. On the feedback learning targets, multiplying wasn't horrendous, but there are still some errors that I'm not happy about seeing them. On the factoring problems, most students didn't even attempt them and of those who did, about half (that I've seen) didn't have much of a clue. It's like what we've done for the previous 2 days totally was a waste of time.
This week is the end of the grading period. I can pretty much tell what's going to happen. The students who care about their grades will want to re-assess the learning targets to bring up their grades. From the surveys I gave them after their test (same one as the Advanced Algebra 2 students with many surprisingly similar results as far as the comments went - but that's another post), I can see that they do care - about their grades. That, of course, means between Wednesday and Thursday there will be a bunch of students who want to come in to re-assess so they can get ___ grade. The problem is, they don't have the skill. Some of them do, but for the most part, my students don't have it. The students who really don't have it most likely won't re-assess. They will continue to not get it. Since math builds its knowledge on previously known things, as the year continues, those students will continue to struggle and this issue will compound.
So, I am sitting here on Saturday morning pondering the same question I was yesterday as I drove home from school - now what? I know that if the students don't have the skills I tested them on Friday, there are going to be places they struggle the rest of the year. If they don't understand the properties of exponents and adding and subtracting polynomials, trying to do multiplication of polynomials is difficult. If they don't understand how multiplication of polynomials works, how are they going to factor them? And let's not even get into the implications for later topics (solving quadratics by factoring, other polynomial skills, exponentials, etc.). I thought by doing the stations activities that it would help their understanding but obviously if it did, it didn't stick in their brains.
I have a four day week when we return. Do I go back over these skills and provide the opportunity to re-assess in class for the whole class? How do I go back over these skills? I have already taught, provided in-class activities, put together 2 screencasts (exponent rules and +/- polynomials) for them to be able to view outside of class, plus helped them in class as they asked for it. I'm kind of at my wits end - I'm frustrated that they aren't doing preparation they should be. I'm sure part of it is my fault - I don't check their homework and I don't go around and mark whether they've done it. I had good intentions at the beginning of the year, but it takes time to do that at the beginning of the period and in spite of my best intentions, many students spend the time talking instead of working through the warm ups like they should. I suppose I ought to collect those too.
Add on top of that a fairly busy week this week outside of school. It's not like I have hours and hours of time to prepare a whole lot of things for them. Probably one of the more frustrating things right now is that I spent 6-7 hours putting together those stations activities I blogged about earlier and now that they've had the assessment on it, I feel like it was somewhat wasted time. They still don't have the skill. I'm not really feeling like putting in a ton of effort on something they a) aren't going to "care" about and b) won't really put forth the effort they should to do. But I know as a veteran teacher that I will always put in way more effort than they will. I also know that it doesn't change that I need to do something.
So, I guess I'm doing two things here. First, I'm venting. I'm frustrated and I need to vent (not that any of you have ever been there before....). Second, I'm looking for suggestions. What would you do? Would you give re-assessments in class this week? What would you do to make sure students understood these two concepts? I probably only have 1 or 2 days tops to review with them (again) before the end of the grading period if I'm going to do anything as far as re-assessments. I'm just stumped at the moment. Please comment and help. Thanks in advance!