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.

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.

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.

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...

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?

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.