Stats, Gangnam Style: YouTube, Assessment, Surprises

My school year is  well underway !  I’m teaching three sections of AP Statistics,  two sections of Precalculus, and working on a new  sports research course  “Sports, Stats, and School.” 

With nearly 50 students in AP Statistics,  I’m finding it more challenging to construct meaningful assessments that allow me to give clear, focused feedback to students quickly and effectively.  This year, two of my students have opened up my eyes about different ways of assessing their understanding of AP Stats.

On the first day of AP statistics, students complete a  Day One Survey.  As they acquire facility in exploratory data analysis,  they  begin working on a short  Case Study in AP Statistics.

This year, two  students constructed a You Tube Video  of their work as they were completing the assessment.

Check out the Day One Survey

the ground rules for Case Study discussing important content from Chapters  1 and 2,

and  the You Tube Video    that was inspired by the process.

The learning payoff  for doing such tasks is hard to overlook, even though some people may view such things as “fluffy”  or “fun” tasks.

The students showed their “smartness” in ways that more “accomplished” students may not be able to do.   Math Teachers: I challenge you to invent lyrics to a fast-paced 4 minute song about math class.

The students ended up doing their best work  on a slightly more traditional assessment of the content:  stronger than anything they had done earlier in the year. I think that the freedom to use their best strengths in one area gave them ways to do stronger work in other areas.

The students generated enthusiasm for the course and future assessments. Hey… can we do that too for extra credit?  What is we do this instead?  What if we….”   

The students made me and my colleagues re-think what qualifies as “legitimate assessment of understanding.”  I believe that the process of creating this video and writing the lyrics required more than simply having fun with the assignment:  they had to create a storyline that made the question meaningful.  They had to contextualize z-scores beyond what I asked i, skeptical. After watching it, one replied, “Wow. That was awesome.”

The video also sparked continued dialogue with my colleagues about alternative assessments in math. We talked a lot about what will happen when more students start doing assessments like these:  how do we support their work without over-taxing the times/ resources of the  students/ teachers /colleagues?  What support tools do we need to provide for students?  Which apps / programs / hardware make these tasks doable for a busy student?  What do we need to learn/troubleshoot?

… and yes, they definitely earned some extra credit!

Comments?  Thoughts?   

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“Stats, Sports and School:” A new adventure beyond AP Statistics

I’ve been teaching AP Statistics since the 1996-1997 school year, the first year the exam was offered by the College Board.  If you’ve never seen / experienced the course as a teacher or student, check it out.  I had always enjoyed statistics in college, but this course was designed with a very different set of goals than my year-long mathematical statistics course had.  In particular, the AP Statistics course wants students to become skilled in four main themes:

* Exploring data   (choosing / interpreting appropriate numerical summaries and visual displays to describe patterns in data)

* Sampling/ Experimentation (designing / implementing studies effectively)

* Anticipating Patterns (the mathematics of randomness, probability, sampling distributions)

* Statistical Inference  (making conclusions about populations from samples,  hypothesis tests, confidence intervals)

While College Board’s course description claims it’s equivalent to a one-semester introductory statistics course, many of my returning students reveal that they go much more deeply than what they saw in a university-level course.   As a teacher, the integration of activities, mathematics and writing in the same course has been challenging and exhilarating.

As I’ve grown in my teaching,  I now find myself wishing I could do more with my students than what is done in the course. Furthermore, our school has been embarking on some cool initiatives:  a Department of Independent Studies and Individual Research ,   and  an Institute for Sports Medicine and Science .

Here’s what it means:

  • The school is encouraging (and supporting) teachers to design courses that help students “go beyond the curriculum,” and
  • The school is working  professional-level researchers to  find ways to educate, support, and study our student-athletes.  Some of the work that’s already been done  is found here.

So I’m jumping in the mix.   My course proposal will be entitled “Statistics, Sports, and School.”   My goals:

  • Create and answer a substantive, interesting research question related to sports or sports medicine.
  • Students will study related topics in library research, sports data, sports medicine, statistics, and writing that will support and inform their work throughout the year.
  • Students will develop their understanding of  statistical reasoning by using randomization tests and bootstrap intervals. 

My hope is that the course helps our kids practice some independent research techniques and learn important skills in writing, research and statistics along the way.  Additionally, I see great potential for students to work with professional researchers to produce studies  that help them progress as student-athletes.  Serious symbiosis, folks.

To prepare for this course, I’m “wearing my student hat”  and  learning deeply about some of the studies that are currently being done with our students by a team of accomplished UCLA researchers.   They are currently working on a study to answer the following question:

How can an extensive  nutrition program on a group of high-school athletes impact athletes’ performance,  injury risk/recovery, and nutrition knowledge? 

I have been very impressed with the degree of preparation, planning, and effort by everybody involved with the study.  Plus,  it includes collecting data with really cool machines like this one over here.   It’s Called a BOD POD.   It’s measures lean body mass and a ton of other cool stuff  without dunking you into a pool of water.

I found a pair of Alexander McQueen boots in here…

Does anybody  have experience / advice with a year-long course in student research?   

Does anybody have advice/  experience with  teaching bootstrap intervals or randomization tests?   I’d love feedback like the kind Tim Erickson gives at his blog.  

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PCMI 2012: Data Group Results

Well,   It’s been a bit  too long since PCMI Ended:   I promised to follow up on the work that the working group at PCMI did in  Reasoning with Data and Chance .

You can find the abstracts of their work here  ,  and  what they took away from the process here. 

I was struck by a number of things during the working group process.

One of the biggest “take ways” I got from working with my colleagues through this process:

People (including our students)  will ask and  work hard on answering their own questions, as long as they are given the encouragement and incentive to do so.  For myself, it’s often easier to worry about what people have to or  should  learn, and lose focus about what people might want to learn  in mathematics or statistics.  Everybody was very excited about sharing  with colleagues during the process and after the process. It reminds me of how important it is for me to allow my own students to create their own discoveries and to share their work with others.  I have enough experience as a teacher to figure out ways to “klll both birds with one stone,”  and simultaneously teach the curriculum while nurturing curiosity and wonder.

which is why I’m  moving  full-bore on developing a new course for my school.  Stay Tuned.   

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PCMI 2012: Experiments with our Data Group

This will be my seventh and final year with the Secondary School Teachers’ Program (SSTP) at the Park City Mathematics Institute. It has been the most transformative and influential professional development experience of my career. I was a participant for three years and have been an SSTP Staff member for four. If you have the chance to spend three weeks in Park City Utah and think deeply about teaching mathematics, then you should apply. If you look at the  PCMI-SSTP Site at the Math Forum,   you’ll see how much goes on during this program.

There are too many things to talk about, but I will focus on the first two days of what may prove to be an very exciting experiment:  The Data and Chance Working Group .   The goal for every teacher in this group is to create some resource that they (and other teachers) can use with students or teachers.  Sometimes we get teachers with little or no experience with data and probability.  Sometimes we get experienced AP Statistics teachers.   It varies every year.  This year, most of our participants were on the “new” end of teaching detain schools.

I and Carol Hattan, the Working group leader, tried something new.  We asked one simple question: “Let’s think about some Field Day events from school…”

Which ones could we replicate here at PCMI?
What research questions might we ask?”   

Who knew that would work!  Within the first two days of class,  the seven participants went deep into a lot of really important fundamental issues in statistics / data:

Important Statistical ideas discussed on the first day

  • The importance of creating a clear, well defined research question
  • The need for specific, repeatable clear protocols to answer your research question
  • Designing protocols and controls on the measurement variables to reduce bias and variation in the results
  • Choosing appropriate, measures of our key variables:   “amount of practice” and  “cup stacking success
  • Choosing appropriate visual displays to see patterns in the data
  • Describing data distributions correctly (identifying centers, spreads, shapes)
  • Defining appropriate variables to measure improvements (First stack time  – Last stack time)
  • Deciding if the slope of a linear model predicting last time from first time
  • Distinguishing between what happened in a sample and whether we can generalize to a larger population
  • Using simulations as a tool to see if sample results are too large to be due to random chance
  • Interpreting the results of a simulation
  • Executing all of these tasks on a variety of different technology platform (Excel, Fathom, “by hand,” R, Maple)

We didn’t simply pose those two questions and let them go.  We listened carefully to their conversations and allowed the participants to work through and answer their own questions.  They were extremely thoughtful, engaged, and successful at arriving at good answers and resolutions to their questions.  Once in a while, we would be there to suggest a good resource, or push them in a more productive direction, but the conversations were deep, interesting and productive.

More about this later….We’re only two days in, and I’m vey very jazzed…. This plan was a bit of a pilot experiment of something I want to try a couple of years from now at my school:  A project based research course using data.  Stay Tuned.

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Free Response Questions: 2012 AP Stats, possible answers?

Hi All,

The College board recently released the 2012 AP Statistics Free Response questions today.  Possible solutions, 2012 FR questions.

Any corrections, comments, and feedback appreciated.

Note:  I am not a representative of the College Board, nor a member of any committees about the AP exam.  I have been a grader in past years, but cannot represent what are complete /correct answers will look like at the grading.

This is just one teacher posting what might be good answers.   But tear them up if I screwed up.

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My Interview with

About 8 weeks ago, I was interviewed via Skype about my views regarding good teaching.

I was flattered for being asked based on some perceived “expertise,”  but I’m mindful every day about how challenging the act of teaching is.  There are so many dimensions to choosing the right question, activity, reaction, or “move”  to get students to think more deeply, believe in themselves, spark their curiosity, or help them achieve our goals for them.

So take a look.. Would love your feedback.

1. What resonated with you?

2.  What do you wonder/ disagree with?





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Sept 26th: Why I’m not posting

Hey Blogosphere,

I haven’t posted in a while.   The first few weeks are in full swing, and that’s been my top priority.  As much as I love the feedback and sharing that occurs from posting, I haven’t  Why?   I think I have a few reasons.

1.   I’m lucky to have plenty of colleagues to share / reflect with in my own office.  

I’m currently working with a teacher who is new to AP Statistics.  He’s asking lots of excellent, important questions. He’s also a very experienced, dedicated teacher as well.  His questions make me reflect and help me justify why we do what we do in AP stats.  His comments and reactions as a new teacher force me to re-evaluate and remind my self why the “norms” of the class exist.  He’s also made be re-think some things that I have assumed to be “best practices.”  His input and feedback are extremely valuable, specific, and helpful.   This teacher is only one of a dozen of great folks who work in the same office I do.   We’ve all been away from each other for three months, and the renewed dialogue,  feedback, and reactions are electrifying.

2. Starting up new classes is time consuming,  labor intensive, and extremely important.  

My students are concerned for their success,  willing to work,  challenged, and  scared.  They don’t know me.  They want to trust me.  I need to earn and build their trust.  This involves correct, specific and helpful feedback about their progress quickly and effectively.  Many of my students are seniors, and highly anxious about those first- quarter grades.  Some may argue that the imperfect evidence of the first few grades are not appropriate ways for students to decide questions like  “Am I in the right class,”  “am I on track,”  or “What do I need to do to get better grades?”

I agree.  However,  their anxiety is real, and their concerns are real.  Whether we like it or not,  first-quarter grades can impact decisions about college, and the students I work with feel these pressures acutely.  I don’t wish that pressure on anybody. For this reason, I  know that students need a lot of verbal and emotional feedback and support.  This takes lots of e-mails,  talks, preparation, clarity, and reassurance.  The challenge for me is to articulate clearly, “You do X well.  Y can improve.  You can do stronger work on Y, and here’s how.”  They also need to be reassured that early grades are not inappropriately weighed in a way that impacts them disproportionately.  So I’m sending lots of e-mails, having lots of student-teacher conferences, and preparing for the questions and anxieties that inevitably accompany the first quarter of any new course. Do I allow “re-do” situations?  If appropriate, yes.  One might argue that students “need perspective,” and “need to stay focused on the process and not the grade.”   If they weren’t being judged by their grades in the college admissions process, I might agree.

The reality, I believe, is different.  They are judged (unfairly?)  by a disproportionate emphasis on first quarter senior grades.  Do I have absolute proof of this?  No, only anecdotal.  But my kids are savvy.  They read the signs from their college counselors and peers. They know where their payoff is.  They are sophisticated thinkers and not passive about their situation.  Their admissions counselors seem to confirm that their concerns are not merely anxiety but also real.   So I will take the extra time required for them to gain early success,  clearly articulate their areas for growth, and help them improve.

Secondly, they don’t know what I deem important (as the giver of grades).  My  expectations may differ from previous teachers.  They don’t know what “good work”  may look  like  in this class.  We teachers hope that they can make abstractions from  what they’ve learned before, but this ability is certainly an adult skill, from what I’ve learned. My students are not yet adults.  They are bright, ambitious,  and willing to work,  but they are not yet adults.  In addition, “good work,” at the detail level, truly does differ from teacher to teacher. Is roundoff error at the fourth decimal place important?  Sometimes it is, depending on the course and the situation.  Throw in different teacher expectations, and kids can easily become confused.  I frequently re-asses what are “universal norms”  of clarity, precision, and  specificity for my students. I’m not convinced that we teachers all tow the same line in this respect.  Should we?  I don’t think so.  But this means that our kids need our clarity and help in our class.  This is especially true in my AP Statistics class, where writing is a heavy component of their work. They are not used to allowing some things to slide (like mild computation/ roundoff error),  and  little/no tolerance for incorrect use of language  to justify their reasoning (like mis-using terms like “most,”   “majority,”  “more likely,”  etc…).

The social culture of our math class has, I think, been turned upside-down.  They are used to writing carefully (?)  in classes like English or History, but maybe not in mathematics.  But this is essential in Statistics. I see universal norms  (from looking at English and History teachers’ rubrics for “good work”),  but that doesn’t mean my students know how this is applied in a math class.  I have to think and  prepare class questions/activities  to make these expectations clear, specific, repeatable, and achievable by my students. My best students see this, but not all of my students.

If/when I achieve this clarity for my students, I think my students will feel supported and ready to succeed.    I’m on the way, but much work still needs to be done.

So to summarize,  I have been deeply involved in the kind of feedback,  sharing, and thinking that these blog posts are intended to represent.   But I have found it necessary (and helpful)  to keep them focused on the micro-community of my school and my students.   No offense.   I love your help, feedback, reactions, criticisms, and questions.  But for me, first things first:  my school, classes,  and new students are my baby right now.  

My partner  is  not amused. But he’s used to it.

So what about y’all?   What  issues in your classes require extra attention and care for helping students?   

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Update: Dear Santa. I want great online software

So  I was looking up the population of China and India, and I stumbled upon this:  


It looks like,    but with all of the power / ad-free majesty of Google.   I’m hopeful and intrigued.  I’d love to:

  • Have the ability to “remove a variable”  in the scatter plots, and look at a dot plot / histogram / box plot of the data
  • Make comparative univariate plots vs outcomes of a categorical variable.
  • Easily see the data in tabular form.
Maybe these tools are already in there.  I will start exploring.



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My Goal this year: Making homework work for seniors.

This year, I  will teach two sections of AP Statistics, as I have since 1997.   I feel confident in providing good activities for kids, setting appropriate standards for the students I teach, modeling the kind of writing/ reading/ thinking from my students,  and  closely monitoring their work and providing good feedback.  I always know that more can be done on all of these fronts, but feedback from students suggest that things are “working.”

In the feedback I received from students in AP Statistics last year, one of the least helpful tools for helping them learn were the daily homework assignments.  I  thoughtfully picked good problems, and didn’t overwhelm them with too many.  Assignments were, for sure, time appropriate.  But I want Daily Homework to be a better tool for their learning.   

What I don’t want to do right now:

  • Lament the effort level of students, and say, “none of them see the value homework.”  If that is true, then it’s my job to select better tasks, or make the connection more clear for them.
  • Blame myself for “not being tougher about homework.”  I don’t think that’s the issue.
What I do want to do:
  • More precisely identify the role of daily homework as a tool to help seniors achieve my goals for them in AP Stats. In particular, what’s the evidence that doing these problems helps them be more successful on the things I want them to do at the end of the course?  
  • Find better ways to bring that connection to the surface for my students.  Show (don’t tell) them how it’s important.  
Why it’s different for (my) seniors in AP Stats than other classes:   
  • I notice that in AP Stats,  there are  fewer “typical problems,”  and more problems that require unpacking of concepts in new, different contexts. In other courses like precalculus and algebra, most students more easily see the “problem types” that  are likely to emerge on assessments.  in AP Stats,  the  reinforcements of concepts tends to look more different from problem to problem.
  • In AP Stats, students struggle more to communicate their understanding clearly – especially when using verbal arguments. They “get it”  in their head, but falter in communicating their understanding with correct precise language. What makes these problems “hard” is in providing clearly communicated evidence.
  • I think seniors (by this time) tend  do the business of school very well.  They work for what pays off.  If they don’t get “paid” for it, they are less likely to do it. “Payoff,”  however, isn’t just about grades: it’s also about getting clear feedback about whether they meet expectations.

Other things I noticed about how we deal with homework:  

  • I and the students tended to not discuss these questions in class in a  meaningful way. We devoted more time to “higher stakes” tasks. We both are complicit in treating homework as “practice you should do at home.” But then what’s its value?   I think that nearly all work requires good feedback. It’s hard for kids to do this alone.
  • I relied on students consulting solutions manuals as a tool for self-assessment and checking their own understanding.  If you teach seniors, you know the mantra:  “You’re all mature enough now to know use homework as a learning tool.  Here are the tools. Now be mature folks and do it!” This might work for some students, but I get it when they don’t buy into this approach.
  • Some students  who completed the daily assignments did one of two things:  they tended to do the assignment “halfway,”  or  practically transcribed their solutions from the student solutions provided in the back as a means of “getting the points for homework.” Later assessments reveals that they did not understand what they wrote.
  • Many of my best learners in AP Stats would do what I hoped for:  they used the problems as a gauge to assess their understanding by doing them, checking their work, and then raising  / asking questions  about their work and the online solutions. But these conversations tended to happen in office visits with me, and involved students who tended to take longer getting the  important ideas.
  • My senior students in AP (nearly all seniors)  tended to “rally”  for things that were graded, and not spend as much time on  things that didn’t result in a grade book grade.  Indeed, daily homework was worth, at the very  most, only 5% or 10% of their grade. Because many of them were very quick studies (and truly could get the important stuff without more time /effort on problems),  this approach worked for them on more high-stakes assessments. But I think some opportunities are being missed by not  making all students “check in” on their understanding more frequently.
What I plan to do:  more homework  ‘quizzie poos’
In my precalculus classes, I use short 5-10 minute  “quizzie poos,”   or  “diet quizze poos”  if they are not put in the grade book.   They are short quizzes that give me (and them a gauge of how well they understand the material.  I don’t do this in Stats because I  am very focused on gearing them up for the deeper  “turn in”  problems.  But I think I’ll change that.  I’m writing 1-3  multiple choice questions based on each homework assignment, or finding ones from a set of AP Statistics Flash Cards.   Quick checks,  individual accountability,  generates possible discussion, 7 minutes maximum,  instant feedback.   Will I “grade” them?  Maybe.  I will certainly  want to see how they are doing on them.  Plus, I want them to see how they are doing.   It’s nothing flashy or terribly innovative, but I hope it’s effective.  Let’s see how it goes.
What do you all think?   Am I making too much of this?  What should I be looking/ watching for in my students?
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Response to a NYT editorial (via Patterns in Practice)

I’m so pleased that Al Cuoco crafted a cogent response to a recent NY Times editorial regarding “what needs to happen in math education.” Here’s his post.

A recent editorial in the New York Times: puts forth a plan to “fix math education.'' I'm disappointed. The arguments presented are variations on themes that have surfaced (and been debunked) several times over the past century.  The ones in this NYT piece are especially weak examples of this genre. First of all, the authors set up a straw man in their characterization … Read More

via Patterns in Practice

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Responses to the Plinko Applet “From Cool to Useful #1:”

Thanks for the responses to my previous blog post, where responses can be read.   I was  surprised at the diversity  of responses and ideas with the Plinko applet.  I also appreciated the feedback from others who suggested ways that this applet can be improved and  made more capable of generating discussions (with, of course, our careful questions and  monitoring to help).     Here’s what I am thinking about the most:

1.   The important of “toggling off and on”   different features in the applet –   the more options, the better.  Many folks observed that the answer to possible questions were “given away”  by things that were presented by default.

2.  The inevitable divergence of questions that will  emerge from us teachers and from  our students  the more open-ended we get with the questions.

3. I thought about the importance of having students ask / wrestle with questions  at both the “micro”  and “macro”  level of this applet.  I liked thinking about questions where students wonder about the result of individual  outcomes of the “ball fall:”

  • Where will the ball fall?  Where will it not fall?
  • Will it always fall there?
  • How far from  the “most likely place?”
  • Do you expect any “streaks” in the path of a single ball?
  • If so, how long?
At the “macro level,”  questions emerged about the relationships between different parameters
  • What’s the most likely bin if we change  p?  What’s the expected outcome  Is there a relationship between p, n, and the expected  outcome?
  • How far from the “most likely” bin should we expect in the long run?
  • How does the shape of the overall distribution change as we adjust n and p?
  • How long will it take before we see a streak of all left or all right pathways?
These questions are by no means a lesson plan, but  each one is a legitimate mathematical question, in my view.
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From Cool to Helpful, #1: The Plinko Applet

So I have been reading some of  Dan Meyer‘s  series of “What can you do with this”   posts.  Cool Stuff, to be sure.

My efforts will be less ambitious, but still helpful, I hope.  If you don’t live under a rock, you know that there are a boatload of Java Applets and interactive tools out there on the web.  I don’t even want to list a small fraction of them, because I’m sure we each have our own folder of go-to applets.

So many of these are “cool.”   But the “cool”  eventually has to become a useful too to help my students learn.  And that’s where I come in.  I know that many folks have learning worksheets around these tools, and some are really great.  Many, however,  barely scratch the surface of what will actually work in a classroom.  I think that the design & sequencing of questions / tasks / set-ups  is some of the harder work I try to do.  Sometimes I have success, sometimes I don’t.

So I want to propose an invitation to “think and play:”
1.  I post an applet that I think is “cool”  for some math reason.
2. We all play with it, and THEN
3.  We put our teacher hat on and start doing some real thinking…  Specifically:

a. What questions  would you design for  your KIDS that motivate the need to use this tool?
b. When playing with this tool, what would you want kids to see , discover, or struggle with?
c. What mathematical / practice goals  would you want your kids to leave with after playing with the activity?

So Here’s the first “cool tool” I like:   It’s a Plinko Probability Applet.   It comes from the PhET project at the Uniersity of Colorado at Boulder.   This one is particularly cool for a number of reasons.  When you change probability of a ball  falling to the right,  the little pegs actually “tilt”  to the right.

Brainstorm of the quick math topics: binomial probabilities,  empirical probability converging to theoretical probability,  impact of  n and p on the  shape, center, and variability of the distribution of pegs,  yada yada yada.  That’s the easy part.

What would we design for kids?   What questions start to emerge when YOU start playing with it?  How can this get leveraged into cool stuff for kids?    What’s the important math in this?

My intentions is to “wring out”  all of the potential in using this tool.   Maybe an effective lesson or few can emerge from this.   Let’s find out.

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Dear Santa: I want great online data software.

As the final days of the summer wind down for me,   I am starting the “prep time”  that all teachers go through before classes start. I get very ambitious and idealistic, and try to stay that way for as long as circumstances and my stamina allow.  This year, I have a couple of ambitious goals.   Here’s the biggest one.

I really want to  see a revolution in online statistics software tools for students and teachers.  Here’s what I want.

1.  I want a “data viewer,”  that could handle tab delimited text data, and create visual displays, summary statistics, and appropriate tests.  It should look as appealing as

2.  I want it to have,  at a minimum,   the flexibility and  functionality of  Fathom:  Easy-to-create  dot plots, histograms, box plots, segmented bar charts, percentile plots, normal probability plots,  etc… I also want it to run appropriate statistical tests.  Gapminder is great but it does only scatter plots, and no tests / summary statistics.

3.  I want teachers and students to be able to create surveys,  invite subjects to respond with a simple URL + password,  and post  the data up there for others to use.  Data could be uploaded as private or public.

4.  I want teachers and students to be able to join / create public surveys,  and generate  databases .   I want public databases to be available on the web for all to use/ see.

5.  I want  “dots”  to be easily replaced with easy to find icons:  guys, girls, men, women,  numbers, colors,  maybe … perish the thought…. Photos/icons  that students could upload of themselves? Each “dot”  in some displays could be a head?

6.  I want security options to range from public to completely private .

7.  I want it to be cost effective and something that people would pay for / use despte the cost.  Heaven forbid…. maybe free?

8.  I want “social network functionality.”

9.  I want pretty, simple, attractive,  and appropriate visuals.

10.  I want  educators in statistics/ data analysis in on the design of this.

11.  I want one-stop shopping.   Facebook, baby.  Google, baby.

I can think of a dozen different places that have little bits and pieces of this.   It doesn’t seem  too “pie-in-the-sky”  to  make this happen.  I am going to ask the computer science students at my school to consider working on something like this.   Bill Finzer at Fathom –  are you listening?    This could be a revolution, I think.   This seems grant-worthy.

So I need your help.   Who knows who would want to develop something like this?  

Is KeyPress still working on  updating Fathom?   It’s been at least 2 years since an update.  These days, that’s  glacial pace.  

Currently,   too many people teaching Stats/  Data analysis are using too many different tools. TI’s,  Fathom, Excel, Minitab, JMP, SPSS,  R,  SAS,  not to mention the online stats tools +Geogebra.    It seems reasonable (at least at the high school level) to construct a tool that meets the needs I outlined above. Imagine a classroom where you have easy access to a ton of databases, without a lot of time teaching kids how to use the software.  Imagine kids getting lots in some really cool data bases.  Imagine them “tinkering”  for hours, and bringing up questions in class.  Imagine asking them to find their own examples and constructing written critiques.

Accessing these files can generate important questions and investigations for kids  that are essential to their growth in statistics.

This is a bit idealistic, but it’s doable.  I’m sure of it.  We just need to time, the money, and somebody to do it.

I don’t want to hear that this can’t be done.   Tell what the obstacles are,  I’m convinced there are ways around them.   

Any ideas?


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PCMI: what is it all about?

You may be hearing a lot about PCMI from me and other bloggers.  What is PCMI?  The Secondary School Teachers program at PCMI  is the deepest, most transformative professional development experience I’ve ever seen for math teachers. Seriously.  Imagine 3 weeks of doing math, reflecting on teaching math and becoming a resource for math teachers.  Plus, you get to attend sessions with top-level mathematicians (for real – we’re talking Fields Medalists).

The time I’ve spent at PCMI has changed me as a teacher.  I pursued a Masters degree in Math Ed because of my contacts at PCMI.  I’ve been able to become a better teacher in my classroom, in ways that are improving how students do.  I also  have been able to be a productive influence in my math department without having to fight, push, or irritate colleagues (maybe a bit).  Plus, I read education research as a tool to inform my teaching.  The work I did at PCMI has also allowed me to win a couple of awards for teaching. I feel PCMI was the single greatest influence on my success. It’s a game-changer.

So check out all the notes and stuff we did this year.   Ask me questions.  There are a TON of cool things.  Oh yeah:  There are notes ten years back.  Each year is different.

PCMI Alumni:  Do you agree?  Tell your story.

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August 1: My reflections on Orlando’s NCTM Institute on Reasoning/Sense Making.

Correction:  I referred to Lisa Henry as Lisa Meyer in an earlier version of this post.  My error, and apologies to Lisa!   

This is a long post:  hopefully future ones will be briefer!

I just returned from Orlando FL, where I presented a 75-minute workshop on “Making Rich Tasks Work” in a math class.  This happened at the NCTM Reasoning/Sense Making Institute.  Handouts for my workshop and others can be found here .  I worried about coming off as a bit of an impostor, as I still struggle to find the right times/ place to integrate these into my own classroom practice. I am, by no means an expert, but I am growing.

I tried to keep that in mind when I designed the workshop.  I didn’t want to talk at them. The bulk of the workshop came from the collaborative work of the staff of the Secondary School Teachers Program at PCMI, the Park City Mathematics Institute.  We were guided by the wise  minds of Gail Burril, James King, and Carol Hattan as well.

So here were my goals for participants, after attending the workshop:

  1. An awareness that using rich tasks effectively in a classroom setting requires time and preparation.
  2. A framework that could guide their future preparation:
  • What’s the potential mathematics in the task (both topics and habits of mind)?
  • Goals: What to I want my students to leave with after doing the task?
  • Evidence: How will I know they are (not) there?
  • Questions/Checkpoints: What will I say/ask to check for their understanding, and move them forward?
  • Feedback:   How will the kids know if they are making progress?

Here was the “rich task” that I started with:  It was a problem that was inspired  from Ben Sinwell’s NCTM Illuminations task: 

Wendy has “cars” of length 1 and 2. She will string these together to make “trains.”   How many different trains can Wendy make of length    5?   6?   8?   n?    A   2-1-2 train and a 2-2-1 train are different.   

I will leave it to y’all to discuss the choice of wording / phrasing I used to launch this task.

Here’s what they had to do after doing the math:

If you are going to use the trains problems in your classroom:

  1. Pick one mathematical goal and one ‘habit of mind’ goal for your students.
  2. Describe evidence that your students are (not) making progress towards your goals.
  3. What questions/checkpoints will you prepare ahead of time to move students’ progress forward?
  4. What feedback will students get? Who gives it?

This is easier said than done, I think.   I was worried I gave them too big a challenge.  But the point was not to complete the challenge:  I just wanted them to engage a bit in the framework that seems to help me.

Lisa Henry’s response to my session made me feel good.  Given that she had attended sessions by Peg Smith and Dan Meyer as well, I felt like that I had succeeded in putting together a productive session for at least a few people.  Plus, she thought I had only been teaching for 7-10 years.  Perhaps I came off a bit “inexperienced?”  I’d like to think my daily regimen of Neutrogena and vitamins helped. I’ll be starting my 17th year of teaching high school this August.  But if I looked younger,  THANKS  Lisa!  She also mentioned how more experienced teachers (like myself) may tend to use classroom experience as a basis for informing their classroom practice.  I strongly believe that classroom experience is just as important as using current research to inform instruction. You need to learn about and know your students and school deeply.

My own assessment:

Overall, I was pleased that participants were willing to engage in the mathematical task, and do their best on a pretty tough challenge: identify specific learning goals and questions for a problem that they barely understood.  Sometimes they put up some good possible goals, evidence to look for, and questions to ask students as they monitored work.  I was especially pleased that they were willing to give some strong critiques to their colleagues work (anonymously, via post-it notes).   I worried that during the “feedback” stage, I’d only see a bunch of  “god job…. nice poster” comments that lacked specificity. That did not happen for the most part.

Evidence of Participant thinking during the session:

I’m glad I saved the poster papers and took photos.  The anonymity of using the post-its allowed participants to be very clear about what they saw (or didn’t see) in the posters: “It think this question is too leading.”   “Is this really a math goal, or just a topic?”   I was happy that people were seeing the need to get more specific with their comments.  The time crunch made this hard, but taking the time to do this well is, I think, important.

One participant remarked that in a classroom, the negative tone of some comments might cause some distress with kids, and many agreed. I see her point: you don’t want to emotionally derail a kid’s progress.  This brought out the importance of establishing norms about peer-to-peer commentary, which was nice to see emerge.

Eighty cards were passed out at the start of the session:  I think I got about 45 back. For 25-35, maybe there was little / no take-away?  Non-response bias really sucks, don’t you know?

For the others, responses fell into two main categories:

“This is great. I’m going to do what you just did in my class (gallery walk).”  As much as I liked the “niceness” of these,   I wondered if some of these comments missed the point I was hoping for them to get: I don’t want people to imitate what I’m doing and try to retro-fit it for the wrong purpose.  On the other hand, maybe some of these teachers became more aware of one technique for getting students to work together, commit to a set of ideas, write them down, and receive feedback.

“I need to do more preparation before I use a ‘cool’ problem in the classroom.” These responses reflect more of what I was hoping for: a greater awareness of the need to be more intentional and purposeful as a designer of classroom time.

My favorite comment involved an awareness and a specific thing to re-think in future teaching plans: “I may need to re-think how I use rich tasks in the classroom, and maybe use them more  to help kids practice the reasoning that’s important, and not grade their work.”  This is precisely what assessment for learning means to me: using tasks as a tool to help teachers and students learn from each other.


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Hello world!

Hi Blogosphere!

I have finally been persuaded to start a weblog regarding my thoughts and reactions to things I encounter as a teacher and working with other math teachers.  And other stuff too.

I teach statistics and math at a great school in  California which I love.  I have great kids and great colleagues.   I think a lot about what works best in teaching mathematics, and love to learn from others who are exploring the same questions.

I will probably have a lot of other things on this blog besides math / teaching math,  but who knows.   So Bloggers,  I need your help.   I think I have plenty to write about and react to, but I am a bit more worried about potential “land mines”  that I might not anticipate in starting a blog.  I don’t want a cast member  from Real Housewives of New York trashing me for something I accidentally said / did without intention… you know what I mean?  What’s the “web etiquette”  that keeps things classy?  for this reason, I ask a couple of a prompts to start:

1.   Please finish this sentence:    “When you start posting,  for goodness sakes,  make sure that you  ___________________.”  

Since this is a public document to the world,  I would imagine there are MANY things one should “watch out” for when posting.  What rookie mistakes,  and “common errors”  should I be mindful of?   What are the “norms”  for the bloggers who get a good audience

2.  Please finish this sentence:     “I most love to read  posts  that ____________________.” 

I imagine that one purpose of  blogging is to create and engage in exciting,  provocative and stimulating discussions.   What works for you?

3.  Please finish this sentence:   “After I created my blog,  I never expected  ___________________,  but it happened.” 

So what monsters have you all created in your blogs? What fantastic opportunities emerged?  I look at the work of some contemporaries and I’m blown away by their influence and their power. I don’t predict anything dramatic here:  just a place to share and learn from you all.

Cheers, BT

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