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?

Bill

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?   

It looks like Gapminder.org,    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.

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.

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.

A recent editorial in the New York Times: http://www.nytimes.com/2011/08/25/opinion/how-to-fix-our-math-education.html 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

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?

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.

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  www.gapminder.org

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?

BT

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.

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 17^th 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.