How to Homework

Homework. Work to be done at home. Work done after school is over. Work to do because there was insufficient time to complete it in class. Work done before dinner. Busy work so that students' minds do not get dull. Review of the day's lesson to solidify learning. Work done after dinner. Preview of the next day's lesson to get the students' minds turning in the right direction. Work done after bed time. Work.

Hmmm... shouldn't school be fun? I mean, shouldn't students enjoy learning?

No, I do not believe I am an entertainer. But, am I a slave driver?

Let me say right now that my AP Statistics students have impressed me. A lot. We have been going at it now for almost four weeks and I have been laying the homework on. Thick. Because I have to, right? I mean, it's A dot P dot Statistics. This is a serious class. And we have something like 20,000 hours of material to cover during 110 classes. So, homework is necessary. Lots of it.

Or is it?

If you have read my blog before, you know well that this is my first year teaching AP Statistics. One of my initial stresses was how to plan out the course so that the students get to play around with every topic for an appropriate amount of time. And so rather than linger over the mean and the standard deviation and try to gain a deep understanding of the information they reveal, we rush, give them a high five, and check them off a list. Topic covered. Done.

But topic learned? Skill mastered?

To ensure that my students understand the ideas sufficiently, I had it in my head that they should expect to spend at least an hour on homework before every class. That means 4-5 hours a week spent on AP Statistics outside of class on top of the 3.5 to 4 hours a week spend in class.

My textbook was a godsend, or so I believed. In the Annotated Teacher's Edition, I found a sample syllabus and a suggested pacing guide which completed the book in 109 days. Holy cow, I thought. I actually can cover everything and even have one whole day leftover to do something from a different source! But, seriously, I was relieved to learn that it would be conceivable to get through the course in time and here was an outline to follow.

The catch? Well, not all statistics homework problems are created equal. Problem #68 may take two minutes, while #63 may take thirty. I did the lazy teacher thing (also known as the teacher-trying-to-create-a-good-set-of-assignments-while-still-maintaining-sanity-and-family) and I assigned the suggested problems without even reading through them all. And so I found out last week that a couple students were spending two hours on their AP Statistics homework.

As I said earlier, my students have impressed me. Not only have then done all the work I assigned, but they did so without complaint. Just sucked it up and got 'er done. And they have been learning. A lot. The brute force method of teaching has been effective. Efficient? I doubt that.

I only found out about the two hours of homework after casually asking one student about their homework load. Further investigation found that my students were spending 72.5 minutes each night on the textbook problems with a standard deviation of 25.9 minutes. And every night I assign a suggested reading. Some nights, I assign them a video to watch. There's another 40 minutes.

Silly me. I looked at the assignments and I figured 15 minutes on the video, 15 minutes on the reading, and 30 minutes on the problems.

I have already begun re-thinking my homework assignments. I will keep using the suggested assignments, but I will choose a few of the textbook problems to be required and the rest will be optional. And I will assign fewer problems when I also assign a video. Or maybe eliminate the problems on those nights altogether.

And now this question burns in my mind: Can I teach the AP Statistics course without any homework at all?

If you think homework is necessary, I suggest you read some of Alfie Kohn's work and reflect critically and honestly on the role homework plays in your course.

Free Response to the Rescue

Though I demonize standardized tests in general, the AP Statistics exam has a saving grace: the free response questions. The first section is made up of 40 multiple choice questions and counts for half of the exam grade. The other half is based on six free response questions.

Multiple choice questions (about which I have previously written in this blog) are one of the lowest quality assessment tools available to the teacher. How fair is it to the student that they could do a problem 95% correct and get zero credit? Writing such questions is a bore and a pain. Answering them even more so. And, if you develop good test-taking skills, you can learn how to improve your odds of making a good guess. Since there are no penalty points for incorrect answers on the AP Statistics multiple choice questions, students are free to guess away. So, random guessing will, on average, get you eight correct out of 40.

Fortunately, there are the free response questions. I have long strived to develop authentic assessment tools. I want tasks, projects, activities, and problems that develop students' learning skills such as critical reading, analysis, problem solving, and synthesis. The free response questions do pretty well here. Problems are written to present at least quasi-real-life scenarios and students are asked to use their statistical tools in a meaningful way.

They are far from perfect. Students do better if they understand what the AP readers are looking for in answers. Thus, it is possible to teach free response strategies. Therefore, I feel compelled to do just that and have already begun. My first test involved two free response questions from past AP Statistics exams, as I expect will be the case for each chapter test. That means my students should get at least 24 chances to practice answering free response questions this year before their practice exam in April when they will get 6 more.

That seems like a lot and so I am relieved that I find these to generally be quality questions. I am also very thankful for Jason Molesky's StatsMonkey web site and his list of Free Response AP Problems Yay (aka FRAPPYs). On this site, the questions have been sorted by topics making it much easier for me to write my tests. Once again, the MathTeacherBlogoSphere to the rescue.

One my challenges in using these questions in class will be to apply the scoring guidelines appropriately. The College Board has made these available and easy to find, but it will take me some time to learn how to score the questions correctly. I did an AP Institute this past summer, and that helped some. My experience teaching International Baccalaureate (IB) mathematics helps. Becoming an AP reader seems like an obvious move to help me in this area, but I am three years short of the three-years-of-experience-teaching-AP-Statistics requirement. I do not understand why I must wait three years to be able to have one fewer week of summer vacation.

Some questions for my readers: How do you use free response questions in your teaching? Do you always score them exactly as the AP guidelines suggest? Have you been successful in preparing your students for the AP exam without directly teaching test-taking strategies?

Ever improving

I'm only three weeks into this year's AP Statistics course and I am already thinking about how to make next year's course even better.

I'm not sure there exists a high school course better suited to bringing math alive than statistics. It is absurdly easy to connect the math of statistics with the everyday world. One could build an entire course based solely on FiveThirtyEight.com. Or one could teach the book Freakonomics. I have always wanted to teach a Baseball Statistics course. It would be amazing to teach statistics through the lens of baseball. There is endless material. The Ken Burns series. Moneyball. Bill James. Fantasy Baseball. Strat-O-Matic baseball.

That last idea has already got me thinking about how I might teach probability this year. If you've never heard of Strat-O-Matic and you teach statistics, then you seriously need to check it out now. Essentially, two players roll dice to determine the outcomes of a baseball game. Strikeout? Fly ball? Homerun?

Strat-O-Matic is not just baseball. In fact, you could probably create your own Strat-O-Matic game for Congress and then go about simulating votes all sorts of famous bills in history. You could see what would happen if Michael Huffington had become California's US Senator in place of Dianne Feinstein. I think I have just decided how to teach simulations in my AP Statistics course. High five to blogging.

This summer I got to go to a professional development conference at Stanford, the Stanford Summer Teaching Institute (SSTI). I attended the math workshop which was devoted to teaching mathematics using engaging and rich tasks. Chances are, if you are reading this blog, you know who Dan Meyer is. You probably also know who Robert Kaplinsky is. The leaders of our workshop, Zack Miller (@zmill415) and Anna Blinstein (@Borschtwithanna), led us through numerous activities such as how much a 100x100 cheeseburger from In-N-Out would cost and how to inspire by presenting them with interesting videos or photos that have the potential to stimulate rich math discussions and inquiry.

What is blatantly obvious to me is that an AP Statistics course could be taught exclusively with such tasks and activities. There are already courses out there that use Problem-Based Learning, Project-Based Learning, and/or Activity-Based Learning. So this is certainly not a new idea in the mathteacherblogosphere (#MTBoS). I just feel like I am missing out on a wonderful opportunity to implement these ideas in full force in my AP Statistics course.

Hopefully, somebody reads this who knows of a teacher who is already teaching AP Statistics much like the courses outlined on Emergent Math. I have no desire to recreate the wheel here. I certainly expect to create some of my own materials as I have been doing for many years now. But I know that there are teachers out there doing amazing things in their classrooms and online and I love to borrow the work of others to help my students have the best experience possible. So, please, if you have ideas that can help me, by all means share. Post a comment so others can benefit, too.

An overabundance?

One of my primary concerns with teaching AP Statistics is the pressure to cover the material in time for the test. I have often heard colleagues bemoan not having sufficient class meetings to properly cover the material for their AP course.

For ten years, I taught a non-AP statistics course and I purposefully chose to cover far fewer topics to allow my students to gain depth in those topics we did cover. In "regular" statistics, we would spend a year on about half of the AP topics. It was a project-based course with computer labs in which students would learn the Data Desk statistics software and spreadsheets as well as calculator techniques. Students wrote surveys and gathered data from the student body and faculty. They read "How to Lie with Statistics" and gave sales pitches in which they used statistics artfully to better sell their product. We played craps and blackjack to study probability. And I'm not talking just one period, but multiple days so that we had lots of quality data. Students researched data on the internet and learned how to organize it and how difficult it can be to find quality data. They had the time to make both big and small mistakes and then stop and start over and learn from their mistakes. I had them research data from non-Western countries in an attempt to give the course a global feel.

As I plan for AP Statistics, I certainly do not suffer for lack of material. Rather, the problem is too much. I cannot possibly do everything I want to do with my students this year. Today, I assigned them their first free response question. Their first test is Friday and I plan to give them two such problems, so I felt compelled to provide them with a chance to try one out ahead of time. Tomorrow in class we will go over the scoring and look at sample responses and their scores. In order to fit this free response question in, I dropped a couple other questions from their assignment sheet. And I know that going over the free response question will take the entirety of Wednesday's 35-minute period.

As I peruse my materials, I find a plethora of activities and projects that I want to use. And I don't want to just throw the activities at my students. I want to scaffold them properly. I want to give them sufficient time to reflect on the questions they might answer, what possible answers might look like, the processes they might choose, the information they need to answer the question, and where they might find the information. I want them to have enough time to fully address their questions, to feel free enough to try, fail, re-think their strategy, and try again. And then, sufficient time to write up a beautiful, well-crafted solution, one that displays the salient parts of the process and clear support for their answers.

Don't start feeling sorry for me. I know solutions to my problems will present themselves. Forgive my whining. I don't want my blog to merely be a rant and complaint bucket. I do know I can scale the problems back. I know that rather than address all the different parts in each project and activity, I can have my students focus on one or two of the components at a time. I know I can do this. I just don't want to spend time teaching my students how to AP. I want to help them be more creative, inquisitive, tenacious, fearless, and courageous. Here we go.

The "necessary" evil?

For the last five years or so, I have thought a lot about assessment, and even more about evaluation in my classes. When I first taught my non-AP statistics course 10 years ago, I decided to not use tests or quizzes. I have often tried to make use of alternative assessments such as projects, portfolios, and take-home problem sets. My primary goal has been to create assessments for my students that are closer to something that they might actually do outside of academia. Tests and quizzes as far as I can tell are artifices almost exclusively in the domain of academia.

And yet, here I am getting my students ready for a major exam. Granted, they have eight more months to prepare for the AP Statistics exam, but in a couple weeks, I will give an in-class, timed test. What’s more, it will have 10 multiple-choice questions as part of the test.

I have not given a standard multiple-choice test in 15 years. I long ago swore them off. To me, they are assessments that in no way advantage a student and don’t even help a teacher evaluate a student’s mastery of a concept or skill. Did they get the answer right by luck? Did they get it wrong because they mis-read the question? Did they drop a negative sign in solving an equation and end up with one of the incorrect answers?

As I have told my students on numerous occasions, on a multiple-choice question, one can solve a problem and do 95% of the work correctly, but get no credit. It’s all-or-nothing.

Yes, it will make scoring those problems very easy for me. But my job as a teacher is not to make my job easy. My job is to provide my students with the best learning opportunities I can. Tests, in my mind, are very low on the totem pole of learning opportunities. Multiple-choice tests barely even qualify as a learning opportunity. Learning opportunities worth doing are projects, activities, rich tasks, and presentations. Evaluating a student’s work on a project gives so much more insight into what a student knows and what they can do.

I have avoided AP classes because I do not want to teach to a test. I do not want to rush through material because the College Board has decided that the course must contain certain topics. I prefer to dive deep into a problem and to provide my students the time to fully understand the concepts. My regular statistics students may have only learned half the number of statistics topics as an AP student. But on the material that they did cover, I daresay that their learning went deeper and that they understood better how to properly use the statistical tools. And I bet they also enjoyed the class more.