The math finals are given next Monday. And I’m really curious about how my Algebra II students will do, especially as the year comes to a close.

But I will say this: I predict that the average score on the final exam will be 85%. Why? Because according to my new grading program this year (EasyGradePro), the average EVERY QUARTER was 85%. Crazy. And at least for the first three quarters, there were exactly 4 (of 15) students in the A range. (I’m not done calculating the fourth quarter grades yet.) I bet it’s mostly coincidence, but it also suggests that I’m keeping the course pretty consistent in terms of difficulty level.

Back to final exams.

My biggest concern this year was that we didn’t have a midterm (because of the school tragedy). And I didn’t do much time throughout the year reviewing topics from the first semester [1]. To battle this, I assigned each student a semester 1 topic, and told them to make a study guide of that topic for their classmates.

The other teacher of the course and I thought this was a good idea for a number of reasons.

- We wanted to have one more assignment which focused on student communication. (That’s something we’ve been emphasizing this year, but we need to ramp it up next year.)
- Our students are 10th and 11th graders, and we think that now they are ready to take ownership of their own studying. We didn’t want to provide them with a study guide or packet of problems. We wanted them to figure things out. (I would, to put things in context, probably not do this in 9th grade.)
- We thought that students would desire to do a more thorough job on their study guides if they knew they were for their classmates too.

I taught students how to use Equation Editor in MS Word and I asked them to use either www.graphsketch.com or their virtual TIs for graphing. And then they went at it.

Now I have a confession. I had talked with the other Algebra II teacher about doing this, but we both sat on our hands until the last possible moment. And since I didn’t want laziness to get in the way of our students’ success, I banged out the instructions and rubric in an hour. But I’m so glad I did. The project needs a lot of work for next year, but I think we’ve got ourselves a winner.

My instructions/rubric: Final Exam Review Project (PDF)

I put all the study guides on a website for students to access. Since the guides have the students’ full names, I’ve password protected the site. But you can see what it looks like here (Image of Algebra Two Website). Students can download and print out the individual guides from that site.

The good (what worked well):

- Students seemed to get into this project. One said, after working in class on the study guide, “wow, this is actually pretty fun.” I think part of the fun was using Equation Editor (they liked that), and part was creating something collectively.
- Most students did actually work really hard.
- Most students were actually really good at explaining their concepts clearly. The ones which were more didactic (e.g. “Now let’s make things a little bit harder…”) and sounded like someone speaking/teaching were the best!
- Students seem to be actually using them. During the review days, many were using them. There are 15 students in my class. As of now, the site with the study guides has been accessed 261 times. The site has only been up for four or five days. So students are coming to the site and looking at a guide or two, and then coming back and looking at more guides later.

The problems (what to fix for next year):

- I didn’t get to have a good discussion on what makes an effective study guide and what makes a poor study guide. I should have talked about tone, layout, clarity, etc. Also, I could have students make these guides earlier in the fourth quarter, and have them exchange them with a partner for critical suggestions for improvement.
- I should have shown an excellent study guide, an okay study guide, and a bad study guide. Luckily for me, if I do this next year, I can use examples from this year!
- Many guides were turned in with mistakes. Almost all had mistakes, in fact. I read through each one of them carefully, and noted all the mistakes, and returned them. I hadn’t anticipated this many errors, so I gave students 1 day to fix the errors and turn them in again, to raise their grade by up to 5 points or if they didn’t make any changes, to lower their grade by up to 5 points. Most errors were fixed. But next year, I must insist upon a comprehensive draft.
- I insisted in students typing everything — because some have terrible handwriting and I also wanted them to get familiar with Equation Editor. (I was horrified by the fact that my seniors in Multivariable Calculus didn’t know how to use Equation Editor; I want to make sure all my students know they can write math on a computer!) However sometimes that requirement got in the way of clarity. There were some guides that had parts that would have been much better if there were some things that were handdrawn in. So, for example, if there was a tricky step in a series of algebraic manipulations, putting a handdrawn arrow to that tricky part and saying “CAUTION! Be sure to flip the sign of the inequality when * or / by a negative number!” would be more effective than typing it out after all the equations are worked out.
- I need to come up with a better way to talk about the number of practice problems required in each study guide, and talk about how these questions should be representative of the types of problems that we did in homework or got on assessments.

But yeah, although I haven’t yet had a chance to talk with my students about if they are finding these guides useful, I have to say that it so far **appears **like they are somewhat successful. At the very least, I know each of my kids have mastered at least one topic from first semester and are able to articulate that topic pretty darn well. And I can say that at least in terms of students using other students’ work, this is much more successful than the video project I did last year, that I was too busy to repeat this year. (See the videos here.) [2]

[1] Next year, I have to remember to build review into the course more formally. I planned on doing it this year, and then it got lost by the wayside. But I’ll tell students that a previous topic not from the current unit will be tested each assessment (and I’ll tell them the topic). That way they’ll be forced to periodically review topics so it won’t all be a shock at the end of the year.

[2] Argh! I can’t believe I didn’t show my students some of the good videos from last year! ARGH!

Just had an additional idea I wanted to put down here for when I come back next year to look at this:

Have students write their own final exam. They can be inspired by problems from the textbook and their homework and their assessments, but they have to write their own problems. Even if it is just changing a few numbers. (And they should write what inspired each problem, so students can go to that source for more problems.)

Also students have to come up with a well-written, clear solution key.

It might be too daunting of a task to write a final for the year. So maybe divide up the class into pairs, and each pair is responsible for writing a final exam for one quarter.

And tell students that at least one question per study guide will be on the final exam. So they will be writing part of the exam, while helping their classmates study.

Ooooh, I’m really digging this idea.

I have my students write a final. It works out well. I am using a lot of the verbiage that you have in your directions for the study guide for this year’s directions…thanks for sharing!

You will be doing your kids a big favor if, rather than imposing MS Word and Equation Editor as the tools, leave that point open and let them know that LaTeX exists: if any of them is ever going to write math on a computer again after high school, it’s almost certain that it won’t be Word they will be using…

I agree with that in principle, but there’s a very steep learning curve there. Not to mention getting IT to put on the necessary software (since they’re probably using an MS OS). I think equation editor is a better bet as it can be quickly picked up and does a pretty decent job of basic mathematics. Ideally if children were exposed to some programming and html earlier on, then latex could be introduced. But I think introducing latex would consume too much class time for too little benefit to too few students.

For the LaTex concerns, I theoretically like the Sitmo Equation Editor that Kate used with her class review blog.

Sam, I toyed with the idea of taking student questions for the final. Didn’t do it this year (interruptions meant that our presentations were still happening the day before the final), but want to hear how it goes if you do it next year.

@everyone: We just didn’t have time to do LaTeX, and even if we did, I don’t think I would make them all download a TeX editor. It’s just not worth it to me at this stage, when all considerations are weighed. (But I personally love LaTeX… I typed all the multivariable calculus problem sets in LaTeX: https://samjshah.com/2009/01/26/this-sunda/)

I am probably going to institute a class blog next year, with student scribes. And early on I will teach students to type some basic LaTeX, because WordPress is so friendly with it (plus I will direct students to the Sitmo Equation Editor). So at least by the end of the year, students will be familiar with the existence of LaTeX and some basic commands, and if they wanted to pursue it, they could.

Sam.

That’s a nice idea (class blog with limited intro to latex). Then if the student encounters a need for heavy formatting they know to look up more about latex.

Sam, does your school have 1-to-1 computing?

Does 1-to-1 computing mean that each student has a laptop? If so, then yes, we are a laptop school. However, currently the wireless/bandwidth is limiting, so I can’t plan classes where everyone logs onto the internet and go to some website to do something.

I just stumbled across this and think the fact your kids are engaged is all that matters. Math editors are really irrelevant in my opinion.