Teaching the Big Ideas

This summer, as part of my professional development, I am taking an online Stanford course entitled "Mathematical Mindsets". This is a course developed by Jo Boaler, Cathy Williams, and others at YouCubed.org, a part of the Graduate School of Education at Stanford.

As part of this course, the question just posed to me was, "Do you think you could teach to big ideas, instead of all the isolated content standards? Why or why not?" For some reason, I have been working on this course through the lens of my 10th grade integrated math course. But, this question resonated with me in regards to AP Statistics.

One of my great difficulties in my first two years of teaching the course was getting through all of the content in time for the AP exam in May. I have been relying a lot on our textbook. So, my goal has largely been to cover as much of the text as possible. The book is broken up into 12 chapters and each chapter has two or three sections.

Each chapter has its own main idea. But, each section within a chapter has its own ideas. So, I feel like I have been teaching AP Statistics by focusing a lot on the isolated content standards.

I know there are big ideas in this course. Without looking it up, I think there are four. So, I wonder now if I could teach AP Statistics better focusing less on the nitty gritty and more on the big ideas and then study problems and ideas in each. I may not get to every individual smaller idea, which might cause some problems on the multiple choice problems. But, I think this approach might help students do a lot better on the free response questions.

Teaching this way certainly seems possible. I wonder if anybody reading this understands what I am writing and has any experiences that they would be willing to share. Have you tried teaching AP Statistics by focusing on the big ideas? Was it successful? Did you try this multiple times? Has anyone tried this approach but thrown it out because they felt it didn't work?

Improving student learning

It is the middle of summer. Temperatures are in the 90s and 100s. And here I am writing about my AP Statistics course.

This fall, I will embark on my third year teaching AP Statistics. I have not been generally pleased with the learning of my students in the first two years. A very low percentage of my students have passed the AP exam. I do not blame myself too much for these scores. My students thus far have not been terribly dedicated to this course. Senioritis interferes significantly.

But, there were some students that I think worked hard enough to get a three on the exam and fell short. I do think I provided ample opportunity for these students to succeed. I believe they had meaningful learning experiences that could have prepared them well for the exam.

I want better for them. I want to improve my course. Not just to improve AP scores. But to up the interest in the material and the course. I believe if students find the course more interesting, their learning will improve. I also want to make the material easier to access.

My first move is to start the year off with data gathering unit that will culminate in a questionnaire project. Working in pairs, students will design a questionnaire to gather data on an issue of their choice (such as abortion, immigration controls, the legalization of marijuana, etc.). The questionnaires will be distributed to the students and teachers at our school and the data we collect will be used throughout the year.

My second move is to increase the number of projects. Last year, there were four projects. The other main assessment I used was free response questions. So, this year, I am hoping to do six projects and reduce the number of free response questions.

I have been teaching a non-AP statistics course for many years now. That course has always been project-based. So, I have plenty of experience from which to draw. I am hopeful that project work will lead to deeper understanding.

Of course, today, one of our administrators wrote in an email to me that she hopes AP classes will be gone from our school in one or two years. That was a bit demotivating, but I owe it to my students to make the course better. Hopefully, that will be motivation enough.

Homework? To what end?

Is homework necessary to deliver the AP Statistics curriculum?

This week, my class will meet four times and the students have four homework assignments (see below) that they should work on prior to each class. I expect that they should spend 30 to 45 minutes on each assignment. So, I am asking my students to spend around six hours this week on AP Statistics. And this is a fairly typical week. We have about 31 weeks total from August until May for the students to prepare for the exam (vacation weeks excluded). So, that works out to about 186 hours of preparation for a 3 hour exam.

The AP courses are supposed to be college courses. Yet, we have far more class meetings than any college course I ever took. And the course is spread out over a year rather than a semester. My college courses met for 50 minutes, three times a week, over about fourteen weeks (though it may have been fewer than that). If we assume that a one-hour assignment accompanies each class meeting, then that would work out to around 77 hours of study in a semester. We should probably round that up as that does not account for projects or papers. So, let’s say 90 hours.

How is it that a college course expects a student to learn the same material in roughly half the time as a high school student?

Is homework necessary?

I would like to perform an experiment to investigate this question further. That just does not seem practical, or maybe ethical is a better choice of words.

If I were to eliminate homework altogether, my students would still have about 103 hours of preparation time which should exceed that of any college student. Add in another 20 hours maybe for project work and get a total of 123 hours which would be about 33% more than a college student. That seems like a more appropriate balance. Especially when you figure that the course would be delivered over twice the number of weeks allowing for the work to be presented in smaller chunks, and thus more easily digested.

In my mind, this should be feasible. If the AP Statistics course truly is a college course, that is. My class consists of eleven twelfth graders and two juniors. The twelfth graders are six months away from taking college courses. Do we really expect to be preparing them for college if the transition is so sharp?

Using an activity to teach about unbiased estimators

Today in AP Statistics, we had one of our better classes, so I wanted to share it with you. We did an activity to better understand the differences between parameters and statistics and what makes for an unbiased estimator. I based it off of an activity in our textbook and it worked beautifully.

Each of my 12 students wrote their heights in centimeters on a slip of paper and put that paper in a box. Each group then took turns randomly selecting a sample of size three with replacement. The groups recorded the data and calculated the sample mean and the sample range. Each group then wrote up their data and their statistics on the board. I then had each group take another SRS of size three and report their findings. Meanwhile, two students were tasked with finding the population mean and population range, but they were asked to not share these numbers with the class.

So, now we had eight samples, eight sample means, and eight sample ranges. I briefly talked about how statistics were used to estimate parameters.

I then asked the students which sample mean was the best estimate of the population mean and to explain their thinking. Four students were willing to offer their opinions and they gave reasons such as it seemed like the number in the middle. Interestingly, two students selected 172 cm and two others selected 168 cm.

I then asked the same question regarding the sample ranges. This discussion went differently. One student immediately realized that the largest value, 30 cm, was the closest to the population range. The same student continued and argued effectively that the range was at least 33 cm and that no sample would ever have a range greater than the population range.

We observed and discussed how the various sample statistics deviated from each other. We discussed the centers of the sample distributions. And then I asked the class which of the two statistics they thought was unbiased. One student bravely spoke up and said the sample ranges were unbiased and offered up his reasoning. The others listened and then, respectfully, argued against his claim and presented their own reasoning.

The population parameters were then shared. We then drew dotplots of the sampling distributions and added in the population values to the dotplots so the students could visualize how the sample ranges were all less than the population range and how the sample means fell on either side of the population mean. We also discussed how the sample ranges deviated on average more from the population range than the sample means deviated from the population mean.

The dotplots were very effective. We talked about how the population parameter is the target and the sample statistics are our attempts to hit that target. Using this lens, it was easy to see how the sample mean was a better estimator than the sample range.

This was only a 35-minute class, so we did not get into how we could improve the accuracy of our estimates (so how to affect variability), but that would be an easy extension. Again, a dotplot could be used to show various levels of accuracy dependent on sample size.

Free Responses and Projects

Going into this school year, my intention was to resume blogging regularly. I wrote my first post back in September, but now it’s been a month and a half. My hope had been to write biweekly. Anyway, I won’t bore any readers with the reasons.

If you read my last post, my plan was to change my assessments significantly. And, so far, I have followed through on that. I have given three tests all have been made up of only Free Response Questions. The students have completed one project and will do one more before Thanksgiving. My thought right now is to give a multiple choice assessment before the end of the semester. But that will be the only one.

I just finished grading the last test and it appears that the students are getting better at answering the Free Response Questions.

The next project will be on data gathering techniques. The students, working in pairs, will have to choose a topic, create a questionnaire, devise a sampling strategy, and discuss bias. Their population will have to be found within our school so that they can select the sample and distribute their questionnaires. The questionnaires will be made online using Google Forms. The data they collect can be used for future projects or assessments.

The sixth Free Response Question on the AP Statistics exam is always a longer one called an Investigative Task. My plan is to try to set the project up in some ways like an extended investigative task. I will try to make it so that in the process of doing the project, they will have to address the same sorts of issues that might arise on an investigative task.

Anyway, that’s what’s going on for now.

A New Beginning

Last year, I started this blog as a way to journal about my experience as a first-year AP Statistics teacher. I wanted to share my experiences to help me reflect on my practices and to hopefully initiate some discussions with whomever read my blog and dared to comment. I knew that there would be other teachers out there in a similar position as I and that my posts might help them think through their own situations. I also hope experienced statistics teachers might stumble onto my blog and provide insights. In the end, the blog mostly served the first purpose, and that was fine. But, then I lost my drive to blog and I posted less regularly and then stopped altogether.

Now I begin again. I want to continue my professional development and I think blogging will be a terrific means to do that. Maybe some discussion will ensue.

Last year, I was anxious about getting through all of the material in time for the exam. To my amazement, I succeeded. Not only did my students cover every topic on the AP Statistics syllabus, but we still had two weeks to review before the exam.

However, in reflection, I do not feel my students were served best by zooming through the material. A few of them did tell me that they liked that we covered all the material (and finished the entire book). But depth of understanding was sacrificed for breadth and I hated that.

The students' results on the exam also suggested that some changes needed to be made. The students took a mock AP exam as their spring final exam two weeks before the actual AP exam. Based on their performance on that exam and based on their work all year long, I had expected them to score a bit higher. But, when I think about how hard they worked, and how some of them did not work too hard, I wasn't altogether surprised. Those who did the best had the best work ethic. Those who succumbed to senioritis largely did not pass.

This year, one change I am planning is to not worry about covering every single topic on the syllabus. I teach at an independent school (polite speak for private school) and we have only around 140 teaching days, I think, before the exam. My plan is cover 80-90% of the material, but to go into greater depth. The instructions on the AP exam itself state that they do not expect students to know everything. My class looked at scoring and were surprised to learn that you could get 50% of the multiple choice items wrong and still have a very good chance of scoring a 4 or 5.

Another change is that I am not going to give them very many multiple choice assessments. Last year, I gave the students 10 multiple choice items on every test and they had about 11 tests. And then they had 40 more multiple choice items on the mock exam. But I don't think one needs to practice multiple choice tests. Certainly not to the extent that I did last year. And I detest multiple choice items. So, I plan to give them the 40 problems on the mock exam and then maybe two other multiple choice assessments. That's it.

A third change is that I am going to incorporate more project work this year. When I have taught non-AP Statistics, I have always taught it purely project-based as I feel this is the best way to learn the material and the best way for me to evaluate their understanding. It feels more authentic and it removes test anxiety and the time constraints of tests. I will likely write an entire post on projects later.

But now, I must rest.

Thanks for reading.

Blackjack or Bust

Over three weeks in to the second semester and, unsurprisingly, the seniors in my AP Statistics course are finding it harder and harder to get motivated to do school. That means it’s time for some blackjack.

At Tuesday’s evening class, we dealt some cards, made some bets, and recorded lots of data. I have done a blackjack project several times now and it always grabs the students’ attention and interest. Some students learn the game for the first time while others learn the finer points such as splitting and doubling down. But all enjoy watching their piles of chips go up and down.

While they play, the students record such things as card values, number of hits, wins, losses, pushes, and busts. In groups, the students will then use the data to create their own examples that are meant to illustrate the various probability concepts we have studied thus far. These topics include conditional probability and independence, random variables, the binomial and geometric distributions, and sampling distributions. The groups are tasked with teaching their topics to their classmates. As a part of their presentation, a group will also provide a sample problem for everyone to try to solve.

I have come to strongly value students taking over class and teaching their peers. Explaining the intricacies of challenging mathematical ideas is not easy. And many students have anxiety about speaking in front of the class. But it is so worth it. From my experiences with these student presentations, I have seen my students gain deep understanding of the topics and I think the students appreciate having class led by someone other than their teacher. After reading Jo Boaler’s book, Mathematical Mindsets, I now know that research has shown that explaining work to others creates deep learning.

In addition to the presentation, students have the opportunity to collaborate with others. Group work is another prominent part of my classes. I think my favorite classes are when each group is humming along, discussing ideas, solving problems, checking each other’s answers, and helping one another increase their mathematical knowledge. It provides opportunities for students to explain ideas in a small group setting that might be easier than in front of the whole class. Once again Dr. Boaler notes in her book that the research backs the practice.

The project will give the students the opportunity to review many different ideas. I like the idea of doing review now, even though a little more than three months still remain before the AP exam. I want my students to engage with the material as many times as they can before May. I think it’s a bit silly to think that a student can really learn and understand a concept the first time they see it. The more times they try to reason through a binomial distribution problem, the more familiar they will become with the idea. I have taught random variables ten times now, and I am better this year with them than I was last year.

Finally, projects are such a refreshing change from the in-class timed tests. I like that my students get a chance to show what they know in a much different setting. They are not sitting, working alone, trying to remember when to use which formula. Rather, they are up, working with others, and they can look up information in their books, in their notes, and even on the internet. They can meet with me to talk about their project. The students can choose to spend many hours in preparation so that they can produce exactly the quality of project they want. I am going to try to see if I can test less next year and still prepare my students well for the AP exam. I believe it can be done. Do you? Anybody out there teach project-based AP Statistics course? I would love to hear about your experiences.

Halfway there... a self-evaluation

My greatest concern going into this school year was to effectively teach AP Statistics. Though I have been teaching statistics for ten years, I had never taught AP before and I was worried about pacing and the quality of the lessons and assignments. I was worried about sacrificing pedagogical beliefs for the sake of getting through the syllabus in time and preparing students for the format of the test.

The course is going better than I had hoped. I greatly value projects in lieu of tests. Whereas a test is completed in a set amount of time, contains closed questions, and is done individually, a project is done over a number of days where students can choose how much time to spend on it, is more open-ended, and is done in a group of 2-4 students. Tests have very little value in helping students improve on their knowledge and are limited in their ability how much information they provide regarding what a student knows. Projects can help a student to better understand material and are provide richer information about what a student can or cannot do. My non-AP Statistics course was always completely project-based. I wanted to carry over as much as I could from the non-AP course into my AP course, but I feared the pace would make this difficult. I was optimistic that I could incorporate two projects this year. Happily, the students were able to complete two projects in the first semester alone. I now expect them to complete two more in the second semester at least.

The pace has been fine. While I am going faster than I ever did in my non-AP course, the pace has not been so fast that students are being left behind. The faster pace requires students to be more self-motivated, but, maybe because it carries the AP designation, students have been up to the challenge. Also, I have been able to adjust the pace at times based on feedback from my students. I had concerns that there would not be enough flexibility to adjust the pace mid-semester. But there proved to be more flexibility than I had anticipated.

Back in August, I started this blog regarding my teaching of AP Statistics. I am happy with how blogging has gone. This makes post number fourteen. Though my audience is quite limited, people have been at least clicking on the blog links I share on Twitter. One Twitter user even added one of my blog posts to the Math Education Daily and that particular post had a lot more page clicks. Blogging has allowed me frequent opportunities to reflect on my teaching and that alone has helped me to design a better course. It has provided little so far in professional discourse. I hope to get back to blogging weekly and I hope that my regularity can increase the chances of future discussions about my posts. I have engaged in a couple Twitter discussions with other math teachers. I would like to do more of that going forward.

[Regarding Twitter, I very much want to participate in Twitter Stats Chat. This is definitely a goal of mine. I have yet to figure out how to do that. I know the hashtag (#statschat) and I know that it starts at 6 pm (Pacific Time) on Tuesdays. I have TweetDeck set up for #statschat. But I never see a bunch of posts starting at the specified time in my feed. Grumble.]

In looking over the various assessments I have designed for my AP Statistics students, I am very pleased with the progress they are making. The projects and tests show that they are learning the material at an acceptable rate. Predictably, the multiple choice items have been the least helpful. I do not like such test questions. I have felt compelled to include ten with each chapter test so as to better prepare the students for the AP exam which will contain forty multiple choice questions. However, I am questioning how much practice students really need with such types of questions. This re-evaluation has partly been fueled by Jo Boaler’s book, Mathematical Mindsets, which I am almost done reading. In the book, Dr. Boaler presents research that affirms my views that students do not need practice for standardized tests. Rather, students can actually perform better on standardized tests if they have learned to be confident mathematical problem solvers. For the next chapter test, I have included ten multiple choice questions. But, I have made one adjustment that was suggested by a Twitter user: students can designate a first-choice answer and a second-choice answer. A correct first-choice answer earns two points while a second-choice answer earns one point. However, I think I will include more short answer questions and fewer multiple choice questions on future tests.

The Weekly Menu

This semester, I have started serving something new in AP Statistics: the Weekly Menu. (Click here to see the Weekly Menu for this week.)

After each class meeting, the Chefs du Jour are expected to add one note taken from class. That note can be anything the student thinks is useful or important to remember. Other students in the class can see the notes posted by their classmates and add to them or even edit them. The Topics du Jour and the SMART Board notes for the day are also posted.

One goal of the Weekly Menu is to get students more invested and active in their learning. I am currently reading Jo Boaler’s book, Mathematical Mindsets, and it inspired me to be more intentional in trying to develop student self-awareness and responsibility. Dr. Boaler outlines Assessment for Learning (page 149 of this book) which “teaches students responsibility for their own learning.” I hope that by assigning some responsibility to students to fill in the document, they will take greater ownership of the course. There is also a level of peer accountability since all students will see what the Chefs have or have not added to the document.

Another goal of the Weekly Menu is to provide students the opportunity to reflect more often on what has been covered in class and what they should be learning.

Additionally, I am hopeful the Weekly Menu will serve as a good review tool. They can use it to review for tests and even for the final exam and AP exam. We will also use it to review what we did the previous day and use it to transition to the next topic.

Students can also use the Weekly Menu as another way to see what is coming up that week. And, if they miss class, the Weekly Menu can get an idea of what happened in class that day.

So far, the feedback I have gotten from students has been somewhat positive. We are only on the second week, so it is still in its infancy. Colleagues of mine like the idea, but ultimately it is meant to be a tool to help students, so it is their opinion that I will value most.

The search for a grade

The first semester at my school ends tomorrow. We do not have semester exams. Some AP teachers at my school give an exam in the evening. I chose not to. I think the main reason my colleagues opt to give an exam is to give the students the experience of sitting through an extended test in order to prepare them for the exam in May.

I am confident that all of  my students have sat a 3-hour exam once before. All but one were students at my school last spring, and they sat final exams at that time.  Therefore, I don't feel the need to give them a long test.

I do want them to be frequently reviewing and revisiting previous topics. So, I am giving them three Free Response Questions that cover the first four chapters. But, those three questions will not combine to form some large percentage of their semester average.

After today, my students will have been graded on 13 free response questions. Two of them were of the Investigative Task variety (that is, Free Response Question #6 from past exams). The others were either taken directly from past exams or were in that style. I am dropping their lowest two scores.

My assessments in AP Statistics this semester have mostly been a departure from how I have evolved otherwise. I have another (dormant) blog regarding my thoughts on assessments and evaluation. My tenth grade integrated mathematics course has zero period-long tests. I have given homework quizzes. But, in that class, grades are largely calculated from projects and presentations. I believe these forms of assessment give me the best indication of what a student can do and knows.

My AP Statistics have completed two projects this semester and they account for a large portion of their grade. I think the projects have given the students a worthwhile opportunity to engage meaningfully with the course topics and skills in a way that will prepare them for the exam. But, I think they also help the students see the utility and relevance of the topics beyond the AP exam. And, I think they provide me with a much better insight into what the students really understand and their abilities to apply the methods they have been studying.

I dislike multiple choice items a lot. (I wrote about this dislike in this blog here and here.) I do not think they are fair nor do I think they tell me much about what a student understands. Perhaps, in a 40-item multiple choice exam, they give a better picture. The larger number of items reduces the chance that a score is based largely on lucky guesses and increases its probability of being due to a student's understanding.

The free response questions are better, but still contrived as they must fit into an arbitrary allotted amount of time and they are written in a way that takes much of the decision-making away from the student.

I do wonder if I could teach a project-based AP Statistics class and still prepare my students for the big, bad AP exam. Seems possible. I guess I have my goal for next year's course.

Anybody have experience teaching AP Statistics as a project-based course? I would love to read about your experiences, recommendations, ideas, and thoughts.

Projections and Senioritis

I had hoped to write weekly. I did that for nine weeks. Then, I lost momentum. I'm not sure why, but I expect it's not all that uncommon for new teaching blogs. You start out with a lot of enthusiasm, some good ideas to write about, and you're not too overloaded with work. Then steam runs out, work piles up, and ideas don't seem so fresh.

Tuesday is my blogging day. It says so on my calendar. I even have my calendar send me a nice email to remind me of that. Here it is Wednesday and I have not written a blog post since November 3. A month. And so, even though I am writing this without much of an idea of what I will write, I push the keys on my laptop hoping something worthwhile will end up coming out of this post.

My blogging statistics show that my posts gets anywhere from 12 to 26 views. I am sure that pales in comparison to many blogs, but I am honored that 12 to 26 people were taking their time to read my ramblings each week. I'm guessing my view count for this post will be lower because of my month off.

To be fair, I was out of town for a week in the middle of November, and then there was Thanksgiving. But, ideally, I would have written those weeks, too.

I have eleven more teaching days. AP Statistics will drop two of those days, so I have only nine more class meetings in 2015.

From where I sit, things have gone quite well this semester. Certainly, there is room for improvement, but I am pleased overall. We have covered about 40% of the AP Statistics curriculum. I made some projections based on the tests they have taken thus far and they are all on track for a three or better. Of my nine students, three of them currently project to a five, which certainly feels good to write.

Second semester will present new challenges. Seven of my nine are seniors. I would guess at least two of them will come down with a bad case of senioritis. That doesn't really bother me. I have been teaching seniors long enough to anticipate this and not take it personally. What concerns me is the potential negative impact they could have on the class as a whole.

For my non-AP Statistics class, I designed the second semester with the second semester senior in mind. I kept the workload light and we played blackjack, played craps, read the book "How to Lie with Statistics", and each student sold a product employing the artful use of statistics.

This year I have an AP Statistics class. Particularly since this is my first year teaching this course, I do not feel I can do the same projects. I expect the second semester workload will mirror the first semester, making senioritis a greater concern for me.

I will do what I can to fend it off. I will try to keep my energy up and do my best to incorporate several engaging activities that simultaneously teach the concepts and keep the interest of the students. But, ultimately, it is not me who will be taking an AP exam in May. The students will have to decide for themselves how hard they want to work and how important that three-hour exam is to them.

PS - If anybody can help me learn how to follow a Twitter StatsChat, I would greatly appreciate it. I have not yet figured that out.

Trying to keep things fresh

Once upon a time, when I was a young, inexperienced teacher, the same-old-same-old was perfectly acceptable to me. Each day was much like the day before. The students learned and we moved forward at a reasonable pace and I was content.

Many grey hairs and many incarnations later, I am far from content. The same-old-same-old is boring. For both me and my students. It does not promote deep learning and it makes for less interesting teaching.

But, the world of AP Statistics sure does lend itself to routine. There is a wealth of material to cover and efficiency is necessary to get through all of it in time. So, many days in my classroom, I find one day feeling an awful lot like another and I see that glazed look in the students' eyes. As I wrote previously, the honeymoon is over and the students understand that they must grind.

But, that doesn't mean I have to give up. No, I won't do that. I am too hard-headed to give up and my expectations for myself would never allow it. Now that I have a better way to teach, I am not going to give it up. So, I constantly search for something new, something different.

As we have been going through the material, there do seem to be multiple processes that one ought to follow when answering certain kinds of AP exam free response questions. Want to compare two groups of a single quantitative variable? Don't forget your SOCS (shape, outliers, center, spread). Have a problem involving the Normal Model? There's a four-step process for that. Want to analyze a scatterplot? There are four characteristics to consider. Need to judge the quality of an experiment design? Be sure to consider the Three Principles.

Memorization is not something I like trying to teach. Yet, to be an efficient test-taker, there are advantages to having such processes down pat. To freshen up the class and at the same time help students remember these processes, I had them create posters. We will hang these posters in the class and they will serve as reminders of topics past. The students clearly enjoyed creating the posters. And I know that an enjoyable learning experience is one that is remembered. Memorization? Check.

Pictures of posters to follow...

Choose your own adventure

When I was young, I got hooked on the Choose Your Own Adventure series of books. As the reader, I got to make choices and the plot progressed based on those choices.

As a new AP Statistics teacher, I am trying my best to prepare my students so that they have the chance to reach whatever AP score they find desirable. For the first four weeks, I set a quick pace and assigned a good amount of homework to complement the work done in class. For many, the amount of work proved to be untenable. In response, I started making some of the textbook exercises optional. I explained to the students that by doing the required homework, I believed they were still being sufficiently prepared to earn at least a 3 or even a 4 on the AP exam. The optional exercises would be more important for those who seek the 5.

I have a variety of students in my class. One boy seems in over his head and a 3 will be a great accomplishment. A few students are very ambitious and will likely try for that 5.

And so, I give my students the chance to Choose Their Own Adventure. They can choose to go the easier route, maybe not be prepared for a 5, but still have sufficient preparation to pass the exam. Or, they can select the more demanding option and give themselves a greater chance at a 5. I wonder how many will take the second adventure...

Honeymoon's over

Today, there was a palpable difference in the attitudes of my students. The mystery and wonder of just what AP Statistics is has worn off. College application deadlines are no longer small specks off in the distance. Summer is now a long time ago. The senior fall outdoor trip is a fading memory. We are six weeks into the new school year and the word "new" no longer applies as a modifier for "school year".

Here we are. Here we go.

The students by now should fully understand the expectations and demands of this course. As they juggle the many demands on their time, they are likely finding it a bit harder to give as much attention as they might want on certain subjects, such as AP Statistics.

I do not think their dedication has flagged, but I think the flood of work that comes in the first semester of the senior (or, in a few cases, junior) year is wearing them down. So while they still aspire to certain outcomes, their energy is lower.

A few did not have their homework complete today. This even after I made a conscious effort to lighten the load. The spark was not quite as bright today in class, the attention not as sharp.

In reflecting on my use of class time, I know that I have kept it varied. They just completed a group project. This was an assessment that had a very different feel from the tests. They found their own data and used technology (StatKey and Google Spreadsheets in addition to their graphing calculators) to analyze their data. Then they wrote meaningful conclusions based on their statistics and displays. I have already evaluated their work and returned it. And, because I want them to produce the best possible work they can, I have given them the opportunity to improve on their work and re-submit it for a potentially better grade.

So, I am not taking the change in mood personally; I am not taking it as a repudiation of my teaching or of the course. No, I think it's just the normal rhythm of the senior year. At least for the near future, it will be an extra challenge for the students. Can they grind through it until the mood brightens?

Fortunately, for students and teachers alike, our two-day Fall Break is this weekend. Timing is everything.

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.

The Calm before the Storm

Amazingly, we seem to be a school that starts late. Amazing because we are still starting before Labor Day. As a kid, school always started after that holiday. From my new Twitter adventures, I realize that many in the Math Twitter Blogosphere (MTBoS) are already well underway. Meanwhile, we don't start until next Monday.

Anyway, I haven't had a lot of time to devote to AP Statistics since I last wrote. Last week, I renewed my Wilderness First Aid certification and this week we have had our opening of school meetings. I have now taught at four different independent schools and so I am well aware that such meetings are pretty much universal. But maybe there could be fewer and shorter ones? I would much more value focused work time so I could make my courses as rock awesome as possible.

I did have one recent significant AP Statistics moment.

A week or so ago, I contacted my textbook rep about some of the instructor resource materials. I also tweeted for help from the Math Twitter Blogosphere about which of the resources were useful. Naturally, my MTBoS colleagues won the quick reply challenge. In under 12 hours, I had multiple suggestions and recommendations. It took my textbook rep a bit longer to get back to me.

Then, earlier this week, a mysterious box arrived in our package room for me. Since I live at a boarding school, this package could have contained just about anything. Lo and behold it was a back-to-school package full of every resource I had asked the textbook rep about. Solutions, test banks, teacher resource CD. I had not planned on ordering it all and I had expected that I would be limited by my department's budget in what I purchased. Being a math teacher, I can say definitively that FREE fits within our department's budget.

Now, I understand a bit about business, especially the textbook business, so while I was pleasantly surprised, I was exactly flabbergasted at the free goodies. I am quite certain the publishing company will make a lot more money if we order a dozen new textbooks next summer than if we get one or two teacher resources. So, by sending me these materials, it's a good business move because I become more likely to stay with textbook especially if I am more reliant on their resources. It's a move done by salespeople the world over in all sorts of commerce, legal and otherwise.

Part of me is hugely embarrassed at admitting to being so smitten with textbook resources. I also teach an integrated high school math course, and last year we didn't use any textbook at all. I usually avoid having a textbook company design my course. But, this is my first time teaching AP Statistics and I have to start somewhere. And, I admit that the textbook we are using may be the best textbook I have ever used (in my opinion, of course).

Next week, I think I'll write about making my first AP Statistics multiple choice quiz. Yes, multiple choice. I haven't given a multiple choice assessment in 15 years...