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?
Becoming AP Statistics
Monday, July 24, 2017
Wednesday, July 12, 2017
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.
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.
Tuesday, February 28, 2017
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?
Wednesday, February 1, 2017
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.
Wednesday, November 2, 2016
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.
Tuesday, September 20, 2016
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.
Thursday, January 28, 2016
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.
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