I teach a single semester math class that students choose to take in an effort to avoid taking algebra 2. The class is primarily seniors whose highest level of math is geometry, and they plan to join the military or work and take a few classes at a time from our local community college.
With this in mind, I found out that our community college uses the Accuplacer as a placement test. From there, I looked at the College Boards Accuplacer Program Manual. This document lists math “skills” assessed under 3 categories: Arithmetic, Elementary Algebra & College Level Math. I put all of these skills in a spreadsheet and grouped them by content:
Based on this analysis, I should spend the semester focusing on the following topics:
- Proportional reasoning
- solving & graphing equations
- Systems of equations and inequalities
- Functions (Linear, Quadratic, Exponential)
- Solving, graphing, factoring Quadratic Equations
I am confident that the first 3 are skills my students need and I can support their understanding with great modeling tasks and real world applications (and mullets!).
I am struggling with #4 and #5 on the list above for students who are not planning on attending a four year college. This would mean spending weeks on quadratics just to prepare students for a test. I know I can find some good modeling problems, but in all honesty, in my 5 years working a professional civil engineer I did not need to factor any quadratic equations.
My gut instincts and knowledge of these students say to focus on application of exponential functions (credit, interest, population growth, etc) . I also believe that probability and statistics is missing from this list. I want to make curricular decisions based on research, data and experience, not just my “gut instincts”. I also don’t want the class to be a haphazard collection of unrelated tasks.
What would you do for the last six weeks of this class?
Update:
Based on Sandy’s comment below, I looked up our community college score requirements. Here is what I found. Why hadn’t I thought of doing this?!
They are only looking at the Elementary Algebra portion of the Accuplacer! I can filter the spreadsheet above to only show the Elematry Algebra skills and I end up with a much more manageable list. Looking back that the Accuplacer Program Manual (linked above) yeilds this information about the Elementary algebra scores:
Why are system of equations considered to be such an advanced skill?
Whelp, It looks like we will be considering some quadratics. Thank goodness for Algebra Tiles, the Math Assessment Project and Mathalicious!
Crazy Math Teacher Lady 
I was at a conference over the summer where there was someone from a community college in NYC who had a creative way of addressing those students who needed to take a remedial math course at their college. They created a prob/stat course where they built in a lot of the algebra skills the students were lacking. My high school is looking at creating a course for 9th/10th graders who struggle on state testing and I am looking into doing something similar to that community college. You can do so many different activities in a prob/stat course and review many algebra skills without making it all feel like a review class. For example, you could build in linear/quadratic/exponential functions using regressions on sets of data. Plus, prob/stats is so much more useful than a lot of other topics that we teach.
I would think your main goal would be to get these students to get a high enough score on the accuplacer to test out of the remedial (no credit given) math course at the community college. Do you have any idea where that bar is set? For example, I can’t imagine that a student who didn’t know trig would have to take a remedial math course because of it.
Thank you for this comment! I looked at “where the bar is set” above, which really helped my planning. I also submitted a proposal to develop and teach a probability and statistics class next school year.
Great analysis! It’s interesting to see that the only quadratics they need to factor are when a = 1. Did you find the college score requirements on their website? I can’t find anything online for the community colleges in my area but I would imagine that they are similar. We have a similar course at our school for seniors so I’ll have to share your analysis with the teachers who teach that course. I think they go much further beyond what is listed above.
One of the tough issues you raise with this conversation is balancing what you think is most important for a student to understand for her or his life with what she or he needs to know for the high stakes test. Things are of course the best when these two are not in conflict with each other. We know how important understanding and analyzing data will be for students who may not get any more formal math education – even if spending time on this takes away from spending time on “factoring quadratics where a>1.”
While we can see right away what is important about the first – we want our students to be empowered adults who can take care of themselves financially, understand their student loan or mortgage, understand the graphs when they watch the news – and know when someone with a bias is using data to make a point, etc. But we also want to make sure that we are helping students to keep all of the doors open for themselves. They need to reach the minimum Acuplacer score so that math doesn’t hold them back from taking the next step.
It seems like you have a great plan to reconcile these two forces with your class. Looking forward to checking in at the end of your course to see how things went.
Thank you for your comment. In reality, they need both for their futures – the ability to take college level classes upon entering a community college and the real world applicable skills.
I normally don’t chime in on topics, however this time I will. Many students that are seniors that don’t plan on going on to higher education but when they get out into the real world and realize that they want to do more; they find themselves back in someone’s college. I teach a high school level math class called Bridge for seniors that scored less than 19 on their ACT and also at the community college; with that being said they will need to know how to work with quadratics in all of its forms. I teach factoring in about 1 class period using Factoring Fanatic at the high school level and 10 minutes in my Pre-Cal 1 class at the community college: copy the link http://alex.state.al.us/lesson_view.php?id=4152 . It is a great resource, for the students who can’t factor. If they can’t use the process then they will need to use the quadratic formula. This process works with a=1 or a>1. Although you did not use factoring in your job as an engineer, you used it in college to get your engineering degree. We have to give our students every advantage possible so that they can be successful and I have meet you and I know you want what is best for each and everyone of your students. So if they need those skills to be successful on the Test or later, as a teacher find the most effective method of doing it. Hopefully this is not to pushy.
Not too pushy at all! I wrote this post to gain the input of others! After reading your comment, it occurred to me that I should discuss this with the students in the class. To my surprise, they agreed that I should prepare them for success on the Accuplacer.
Since I am not the first person to teach these students quadratics and factoring, I assume they primarily memorized steps, formulas and tricks. I plan to rely heavily on supporting students to develop their own understanding of these skills using algebra tiles. I won’t give them the quadratic equation because I want them to understand and develop their own methods for finding roots of a quadratic, which is more logically established through completing the square (and is also how to derive the quadratic equation).