Saturday, October 28, 2017

The Parent Conference - A Conversation Without Grades

This past Wednesday was parent-teacher conferences at our school and I was booked solid from 5:00-8:00 with appointments for parents and guardians of primarily students in the Fusion program. At one point before the interviews, I looked at my colleagues in the Fusion program and asked them what they were making available to parents to use as evidence of student progress. I have to admit there was this momentary panic as I thought of those times where I would print out mark summaries for parents during interviews and for the first time ever, I had NOTHING of that sort prior to the interviews. I had not produced a single mark in either my Fusion classes or in my Grade 11 class but I think I had assessed more student work and provided more feedback than any time in the past up to this point in a semester. There was a sense of security that I think that mark printout provided. The blunt numbers were there as a stark summary of what had been learned and what hadn't been learned - at least that's what I thought and so did everyone else in the interview. They were not to questioned. THEY WERE THE MARKS!

So my colleagues and I wondered aloud - what should be in an parent-teacher conference that doesn't focus on the grade up to this point in a semester? Here is a summary of some of that thinking and some of the things that also came up organically during the course of the interviews - persistent patterns that made the conversations meaningful for the parents, students and the teacher!

Start with them!
I like to always start the interview by asking about their own questions or concerns regarding the student's progress. This sets a tone that I think is important. This interview is for them. It is not for me to lay out a laundry list of concerns or plaudits.

Evidence? What evidence? Oh!!! That EVIDENCE!
Your better have something! We use an online platform for the collection of student evidence related to each learning goal. And I do have summaries of the feedback provided to students throughout the semester. On top of that, we scan student work that is done in class using the copier so that we have an archive of those products. Also include evidence of the learning skills which are probably more informative at this early stage in the semester than anything else. I like to review the learning skills evaluation and the rationale behind each with the parent and student. Speaking of the student....

Who is this about?
I noticed this year more than any other that the conversation was continually steered back to the student. But before that can happen a key ingredient must be present - THE STUDENT! I insist that they be present for the conference. They have the most skin in the game and so they need to be present. As the interview progresses - once the parent had a chance to raise any questions or concerns and I had given my quick summary - I want the student to take over and lead the remainder of the interview. Here are some of the questions I asked:

  • What learning goals have you struggled with and what learning goals have you felt you mastered?
  • Give me an example of feedback that you received and how you acted on that feedback?
  • What are you doing to ensure that you master the learning goals you may be struggling with?
  • What learning skills do you think need more attention and what can you do to improve upon those learning skills?
  • What is your overall assessment of your achievement and what evidence supports that overall assessment?
This part of the interview is critical. It reinforces to me the most important part of trying to teach without grades - the responsibility for learning lays squarely with the student. They need to be continually reflecting on where they are in mastering the learning goals set out for each cycle of learning.

The most common parallel I draw with my students is my flailing on the guitar. I take lessons and I practice (admittedly not enough). But having my guitar mentor tell me that my playing is at 42% is about as informative as Donald Trump reminiscing about global warming patterns.  The 42% tells me something - it tells me I stink. But having him tell me, as I try to master "Highway to Hell", that I need to work on my fingering for the transition from D to F# is something that DOES HELP! In much the same way, that 42%, 52%, 65%, or 91% relates something to the student and parent but beyond just comparing your position to what seems like an arbitrary benchmark - very little more.


Some of the features outlined above exist in any interview - grades or no-grades. They reflect the communication that evolves when there is a sense of trust between the student and teacher and the parent and teacher. They reflect the belief that the parent recognizes that the instruction and the assessment of what a student has done up to this point in the semester is grounded upon what is best for that student. We had a parent information night about our Fusion program and that did a lot in the way of helping parents see that the enormous amount of effort we were putting into the program was grounded upon OUR belief that what we were trying to do was best for student learning.

If you have any FEEDBACK for ME on other features of the parent conference that can make it a meaningful meeting for everyone involved, please leave a comment. Thanks!

Thursday, October 5, 2017

On the Road Toward Gradeless Teaching/Assessment

On the Road Toward Gradeless Teaching/Assessment

I just read a great piece by Jo Boaler entitled "Math Class Doesn't Work. Here's the Solution" published in Time. Boaler points to the primary culprit in classrooms across the US (and I would contend also in Canada) - an emphasis on a performance culture in school. The article resonated with me because it called to mind conversations I have had with students, parents, administrators and other educators about what we have been trying to do in the math department at Fletcher's Meadow.

During the 2016-17 school year, we piloted a program in Grade 9 called Fusion. We ran Fusion in first semester with three sections of Grade 9. Those three sections took place in the same period and allowed us to expand our collaborative tasks on a larger scale. In addition to this unique feature of the Fusion program, the team decided to also try to spiral through the content in the Grade 9 program and embed gradeless teaching/assessment.

By the end of the semester, we had gathered data from a variety of sources including:

  • an online portfolio for each student
  • formative in-class assessments
  • observations gathered during collaborative tasks
  • traditional summative assessments
Reflecting on the process of assessing and evaluating student achievement, we thought we had gathered more data than we had ever used to consider how well a student had done in achieving the learning goals for the course. And I think that was the revelation for me. The focus had shifted from a pressure to achieve an artificial benchmark to an emphasis on learning the content. Students were continually reminded that the absence of grades was not meant to hide a truth that only their teachers were privy but rather to shift their focus to reflecting on what they knew and how well they knew it. The feedback provided on all of the sources mentioned above was like the diagnostic test that my mechanic performs on my overworked VW Wagon that is pushing 240, 000 km - it gave them an idea of things that needed their attention and things that they had mastered. The only difference is that my VW will eventually succumb to the laws of nature whereas our hope is that the students focus on learning will lead to deep recall and retention of that learning. 

Note that the relationship as well between teacher and student also changed from a hierarchical relationship inherent in a process of awarding grades to a partnership of learning. The teacher is tasked with providing the feedback that will assist the student in their mastery of each learning goal. But critical to this relationship is the acceptance of the responsibility on the part of the student for their learning which is something that needed to be EXPLICITLY told to them since this is so different from their experience in the past.

And this is the point that Boaler makes so well in the Time piece. In particular she points out that "Our grading and testing practices are largely responsible." for the pressure that many students feel to perform rather than to LEARN! We expanded our Fusion pilot to 9 of our 11 sections of Grade 9 math this year and I have been blessed with a risk-taking department that has adopted gradeless teaching/assessment in other courses. And this idea that the focus should be on learning is the point that I stress each and every time I talk about the rationale for our move to gradeless teaching/assessment. We had a packed parent information night this year and the response although initially unsure was overwhelmingly positive once they were given the explanation for the move in our assessment and teaching practices. 

This is a journey and we have a long way to go in our own learning. We are still wrestling with providing feedback in a timely manner and making it manageable as we expand to multiple courses. But as I reflect on where we are and where we have been, the tough part to imagine is retracing our path in the journey and returning to grade based performance feedback. We have seen the benefit to student learning and a reduction in anxiety around performance. I know that there will be bumps and perhaps we will venture down some dead ends in our journey but I'm glad we have ventured down this road. It has made all the difference - so far.

Monday, March 13, 2017

7 4 7 - Teaching Through "EDOC" - The Director's Cut

At the T3 International Conference in Chicago, I was asked to be a part of session titled "Seven for Seven" - seven speakers speaking for seven minutes on a topic that they are passionate about. It was a great experience and I want to thank Kevin Spry (@kspry) for the chance to be a part of an amazing lineup of speakers. For those not able to be at the session or conference, the session was on Facebook Live. Along with my talk on coding in the classroom (Teaching Through "EDOC"), attendees got a chance to listen to:

  • Sherri Abel (@sherriabel1014) - Student-centered Teacher-facilitated Engaging-minds Math-science (aka STEM)
  • Todd Morstein (@tmorstein) - Demo Friday: Challenging Students to Question and Problem Solve
  • Valerie Hudson (@vhudson_math) - Helping Student Conceptual Understanding Soar to New Heights
  • Stephanie Ogden (@SoSogden) - A World Without Teachers
  • T3 Leadership Award Winner Marc Garneau (@314Piman...not the astronaut) - Who's Doing the Math
  • Michelle Rinehart (@HowWeTeach) - Transforming Into Our Teacher Leader Selves
The process of creating one these talks is about as enjoyable as a tax audit but as I reflected afterward I thought about how it forced me to distill into a short time frame what I really wanted to relate on the topic of coding in the classroom. In particular, the process of writing out what I wanted to say really helped me organize it into a coherent narrative. And so I thought I would share the text of what I wanted to say here...all of it including what I FORGOT to say.



Hi! My name is Paul and I teach math. And I code. And I make my students code. There used to be a time when computers seemed intimidating but we would be hard pressed to go without them for a day now and we probably figured out what the steering wheel is for. My goal in just 420 seconds is to relate to you that coding can and should be as familiar to us as our use of any technology.


To arrive at that end we need to agree on what we are talking about. When we think of coding we thing of computer programming - the set of instructions a machine follows to complete a task. But my hope is to also show you that it is much more than that especially in a math class.


I listen to a podcast called All Songs Considered and I am struck once in awhile by the sheer volume of music released. It seems like so many more people are making music available. And so I wonder is it because the way we perceive and therefore make music has changed. What used to seem like something that could only be created between five lines can now be created with anything...including technology.




And so does coding suffer from the same preconceived notions. When our students think of coding, how many of them think of lines of code or the programmer as geek or nerd? Or just the magic that happens behind the screen? By coding in our classrooms we make it accessible to them and maybe get them to think it's okay to be a geek.

Changing perceptions is just one outcome of coding in the classroom. We want to also create an environment that invites collaboration, encourages perseverance, mandates that students challenge themselves and their peers to make their thinking clear and of course celebrate their triumphs.



These traits of a thinking classroom create the climate for what I think is an even greater payoff for the math teacher. There are two broad benefits that I've reflected on as critical to the math classroom once you are coding.




First, the computational proficiency that is inherently required to code is intrinsic to coding. For the program to work, the math has to be right! Writing a simple code to output the area and perimeter of a rectangle or the hypotenuse of a right triangle can only help reinforce the mathematics we are teaching.


Secondly, and in my opinion, an even larger impact is the insistence that coding should be the way we think in a math classroom. We all have seen or use different problem solving models like Polya's classic and we all break down problem solving in the same way needed to be a good coder.


I know the challenges of fitting all that we are told to do into the already crammed minutes of a period. I don't do this everyday in class but once I've covered a skill....I usually say, "I bet a machine could do that." and once the groans subside (they do die away after a time...remember we are changing perceptions), we code that skill! I don't see it as an add-on but just the right spice to make the dish taste better.





So how to start? Well how about coding something that isn't mathematical - get at the computational thinking by coding something that is familiar to them. I'm not too sure how many students know the chicken dance but here's the code! Or even better, get them to code a skill they are good at like flipping plastic bottles to land upright. That's big at my school for some reason.


And be hard on them when they start writing their code because you know the machine will be..."What do you mean syntax error?!?!?". You can use out of order cartoons as a starting point. I like coming back to this idea by giving them a program with lines of code mixed up and they need to fix it. Or here's another example I use every year in Grade 9. It only works once. If you want to try it, follow along. Here's my code: Draw a square. Draw a trapezoid. Draw a circle. Draw a triangle. Alright...everyone done?

Does your picture look like mine? No? That's because my code stunk! There was an error that I'll say was planned especially to my students but repeat to you because I missed it when I made the slide! But also my code needed so much more to make my thinking evident. This is going to speed up now.





Ken Ken. The size of the puzzle tells you the numbers you will use. This is a 3 by 3 Ken Ken so I will use the number 1, 2, and 3. Number 2 will go in the top left because I need to obey the rules of the bold boxes called cages. For the 6x, the numbers are 2 and 3 but like Sudoku I can't repeat a number in a row or column so 3 goes in the top left and 2 right below it. I only have one number left in that column which is 1. What divides to 2 and involves 1? It must be 2 to the right of the 1 which leaves 3 as the last number in the bottom row. Then 1 goes above that since that is the only number left and 3 goes right in the middle for the same reason. The last number is 1 to complete the puzzle. I love the deductive logic needed to solve these puzzles and as the puzzles get bigger and involve all 4 operations they reinforce basic number sense.

Once you've tilled the soil and planted the seeds with puzzles and coding skills, the ground is fertile for coding. This is what one of my coding challenges looks like. A simple program that requires the output to be the savings on a sale item. I want to give a shout out to fellow crazy person doing one of these talks, Michelle Rinehart for showing me this model called pseudo-code. It is the thinking needed before jumping into the programming. The parallel to Polya's problem solving model is obvious. And the reflect step is when they test their program.

And so they code. Once they feel comfortable with their pseudo-code, the journey begin and they have to bring along passengers. But it doesn't take long before they hit a pothole - syntax errors, logic errors, structural problems like nothing is being displayed. This is not the house I had pictured in my mind! But I am here to tell you...celebrate the bug. Embrace it!



I didn't anticipate it but coding perfectly aligned with some of the work my department had done around growth mindset and the work of Carol Dweck and Jo Boaler. I'm going to break one of the rules of presenting and read this quote because it was exactly what I needed to reinforce why coding was important and it will eat up some time!

Once coding became a part of my classroom it helped with my vision for what I wanted my classroom to be a thinking space. A place where they could think and wonder and make mistakes. Once of the physical changes I made to also help with that was using vertical spaces rather than horizontal desks as the place for collaborative thinking. A shout out to my colleague (and roommate) Tom Steinke for introducing me to the work of Peter Liljedahl and his research around vertical non-permanent spaces.



Here's an example from my class in Vectors. Students asked, "Is it possible to just input two algebraic vectors and have the calculator determine the resultant geometrically?". And of course I said, "I wonder." There was coding as we defined the inputs, figured out what to do with those inputs and generate the output. And you know along the way, it helped them remember the math as well!





So to close, I was trying to think of a flashy last slide that would leave you remembering something like "Everyone can code"...but this just didn't seem right. It felt like, implied in that was "Why aren't you?"








And so I changed it. But this still didn't capture it. You can code...yes but meh. And so I settled on this.

Thank you!

Monday, December 19, 2016

Oh the places you'll go...

Maybe its boredom or maybe inspiration but today I walked into my Grade 9 class and shared the screen below from my phone.

In particular I highlighted the number of steps: 2 408 434!!! 

I was curious to hear what they thought of this screen. It didn't take long to get the response I was hoping to hear...how far is that?!?!? I really didn't want an abstract answer of so many kilometres but preferred to know something we could all relate to. Could I have walked to downtown Toronto? How about Montreal?

Here is what one group determined.

I was curious to see what strategy the students would use to determine the number of steps per kilometre. I had brought in tape measures thinking they may want to measure a typical walking gate but no one ended up using them. This group was typical of the approach that each group used - they searched the number of steps online.

I spent some time after class mapping the different locations that each group derived. Here is the map. 

My personal favourite appealed to my love of the Red Sox - I can walk to and from Boston. They were even kind enough to tell me how long it would take me - 7 days 9 hours....one way. 

I'm not sure where this activity goes from here. I recorded the solutions for all of the groups and was thinking to share them with the class so we can discuss the strategies and whether all of the locations seem reasonable for the distance calculated. Maybe the experience of seeing so much math in a simple number that led to an engaging exploration that addressed the key expectations in 9 Applied of rate of change and proportional reasoning is good enough.


Monday, December 5, 2016

2016 Fields Medal Symposium Lecture

2016 Fields Medal Symposium

I finally had a chance to sit down and watch the Fields Medal Symposium opening lecture. The main speaker for the evening was 2014 Fields Medallist - Manjul Bhargava. Bhargava (born in Hamilton!) is an accomplished number theorist and professor at Princeton University. Initially I thought the lecture was going to be an exploration of obscure number theory (maybe this is why I delayed the viewing) and chuckles at inside jokes about rings and the Farnsworth Parabox. I was so pleasantly surprised by the accessibility of the content (even I could follow it!) and the wonderful connections that Professor Bhargava made to art and the natural world.




After viewing it I decided it would be a great item to share with my students in class and those who show a particular love for number theory. What I thought I would do with this post is breakdown the talk for those who haven't viewed it just in case you want to jump to the bits of particular interest in the event that you want share with your students. The lecture starts at about the 32 minute mark.

For the early going, Professor Bhargava shares his introduction to mathematics as nurtured by his mother and his grandfather, a Sanskrit scholar. In particular he talks about the role that number theory plays in mathematics. He introduces sequences of numbers. Some of these may be familiar to you and to your students. In particular he looks at the visual or geometric proofs for the sums of these sequences. This seems to be  very timely with the current focus on visuo-spatial reasoning. Jump to the 44 minute mark to see a great visual proof of the sum of the first n odd numbers. Here's some more highlights I noted in the talk.

47 min mark - Sum of ascending and descending whole numbers (e.g. 1 + 2 + 3 + 4 + 3 + 2 + 1)

48 min mark - Hex numbers - Connecting them to a visual arrangement. So cool!!!


52 min mark - Exporing the "atoms of our universe of whole numbers" - PRIMES!

57 min mark - Primes in Nature - Why do cicadas have a 17 year gestation period?


1 hour 1 min mark - The role primes play in encryption.

1 hour 6 min mark - What is special about honeycombs?



1 hour 11 min mark - Professor Bhargava shares his favourite problem as a child - Stacking Oranges


1 hour 16 min mark - The Fibonacci Sequence - Professor Bhargava illustrates an amazing connection to Sanskrit poetry and lots of connections to the natural world.

1 hour 40 min mark - What's so special about the number 142 857?

1 hour 44 min mark - Fractals!

As you can see there is so much here to explore and share with your students. Each and every topic is explained in very accessible language and presented with such clarity it is hard not to be excited by the connections that number theory has to the world around us.

Sunday, November 6, 2016

Lessons Learned from Back in the Day

One of the neatest experiences of being a high school teacher is those too infrequent visits from recent graduates. I love catching up with them and finding about what they are up to and how they are adjusting to life post-high school. A bit of honesty here - I tell all of my current Grade 12s that my memory is dreadful and please do not be upset if you return and I don't immediately recall your name. Actually...even after some time I probably won't recall your name. Now bizarrely, after a brief awkward moment where I admit to forgetting their name, I will invariably blurt out their last name! Not sure what that says about my brain but I can dig out an obscure surname as soon as I hear a student tell me their given name.

On Friday, I was graced with a visit from two students who graduated in June of 2014 - Jaydev and Nuan. As is my habit, I didn't recall their names but no need to worry. I was about to walk into my Gr 12 Data Management class and asked if they wouldn't mind speaking to these prospective grads about their experience post-high school. I was able to skirt the name issue by asking them to introduce themselves to my class and to talk a bit about their university experience. Aha - got the names! 

I have told all prospective grads about my experience in university but I have been honest about what translates from the time I was in school to now. Some of my experiences are of course DATED! My first year tuition was a grand total of about $1500! I had to attend lectures or ask a friend who did attend for their notes if I missed one - no podcasts or online modules to access. The only technology you saw in a lecture was maybe a personal tape recorder. 

But there are experiences that have transcended the passage of one century into the next - yes it was that long ago. I worked doggedly to understand what I didn't. I left no resources or stone untouched. I accessed office hours, teaching assistants and any other resource that may help me in my pursuit of understanding what I didn't. I tell the prospective grads that when they are paying for the privilege of education that they should get their money's worth! It was so good to hear the recent grads echo this advice in the time they spent with my class.

A common refrain on the first day of my classes is that the best resource that a learner has is probably sitting right near them. We are all on this journey to learning and understanding and the experiences of classmates is most like our own. They are most close to our level of understanding and can help when there are any misconceptions. Jaydev and Nuan related similar experiences to mine. Often we would be sitting in libraries, cafeterias and even in the pub occasionally as we worked through a linear algebra assignment or discussed the reading from philosophical theology. We laughed together, sometimes cried together but most often LEARNED together.

The structure of the day in college or university can sometimes lead to a lot of down time between classes. When you aren't working on the latest assignment or reading it is critical to find an outlet that engages you in another way. I'm not talking about a pub crawl. I'm talking about being involved in a club, activity or something that can be a distraction from all of the pressures of student life. It is not critical that this be connected to your school community but it is helpful to form a connection to your school that is not purely academic. I was a commuter student which presented its own set of challenges but I still tried to be involved. I wrote for the school paper. Jaydev especially stressed this point. He didn't get involved in first year and he felt that disconnect. So he made a concerted effort to get involved. It gives you chances to connect with students that aren't necessarily in your academic program and year. 

Lastly (and predictably I think most important), be open to the path of your passion. I went to school enrolled in a business program. Applied to law school and was admitted to attend Western after two years. Declined that offer and found my passion in a history of math course. Jaydev was initially in health sciences but switched to urban planning when someone recognized something in him that told them that he may like the program. He loves it! Always be open to your bliss as Joseph Campbell would insist. The path may be winding but be open to it and be okay with the occasional detour. 

I wonder if I was to travel back in time and ask a student at the University of Padua  in Renaissance Italy (I have no idea if there is or was a university in Padua) and observed the life of a student if many of these same eternal truths would be evident. The life of being a student - actually of being a lifelong learner may change at the periphery but it doesn't change at its core. With a passion for learning and surrounding yourself with like-minded hungry learners - it is a good life. 

Monday, September 26, 2016

A Lamentable Lament

I have been very fortunate to be working with a teacher candidate from a local faculty. She is a very conscientious teacher and we got into a good discussion on the nature of teaching math during her last classroom visit. She made the comment that sometimes what her and her teacher candidate friends see at the faculty sounds very good in theory but when the rubber hits the road and they are standing in front of a room of students that they need to present the content and make sure it sticks. And so the model of teaching that emerges is very much the same method that they may have been exposed to when they were students. Stand and Deliver.

I really appreciated her candor and I know that this isn't unique. I've been fortunate enough to visit faculty candidates in another school over the last few years and I usually hear this comment made by a few of the teacher candidates. I know I felt the same way when I was in the faculty at Mount Allison in New Brunswick. It was survival mode and so with a very limited repertoire of strategies I fell back on what was familiar. Although there was the one moment at Amherst High School in Nova Scotia where I strode into my Grade 11  class with a powdered wig trying to do my best Isaac Newton impression in an attempt to connect Newton's fluxions and Leibniz's development of the calculus. It morphed into an study of the history of math and that was a glimpse into what was possible outside the box. Its a message that I have often repeated to teacher candidates. The placments they get are opportunities to try the strategies they are learning. They shouldn't feel so afraid to make mistakes in their teaching...isn't that how learning (whether its math or teaching math) occurs?

At one point I asked if she had read Paul Lockhart's "A Mathematician's Lament". She promptly pulled it up on the computer and started reading. I recall the impact when I read it. I read it at a critical moment in my own teaching career. It is an indictment of the way math is taught in too many classrooms. I was ready for the message at the moment I read it and it confirmed to me my desire to change the way I taught math. Coincidentally, Lockhart's Lament came up again over the weekend. I have been very lucky to meet some amazing educators and quite honestly thinkers (you know who you are) in my teaching career and I would include Sunil Singh in this group. Sunil was a guest on the ZPC podcast (Zone of Potential Construction) hosted by Chris Brownell. The podcast is Episode 5: Mathematics, Happiness and the Joy of Discovery. Sunil was talking about his soon to be released book "The Pi of Life" (Nice title Sunil...any tigers in this one?). During the podcast, Sunil talked about the inspiration that Lockhart's Lament provided him in his career and the impact it had on the way he views the teaching of mathematics.

And so I wondered what is keeping us from addressing what are systemic issues in the teaching of math. I am not sure I have resolved the issue...not sure anyone ever has or will. But one thing that keeps nagging at me is this perception that the constucts within which we teach math are its greatest enemy. By the constructs I am referring to the insitutionality of our system of education. It may be time to consider that we are to trying so hard to fix something within a system that may make it impossible. There are some amazing educators doing some creative and innovative things in the classroom but, in the end, even they are limited by the parameters within which they work. Our boards and schools do their best to support teachers with grand schemes of support  that usually happen in some banquet hall to little or no affect. It may be time to think bigger. It may be time to significantly shift what we consider to be the way students are taught math.

All this from a single conversation with a very honest teacher candidate. And perhaps that is a reason for optimism. The next generation of teachers will take up the torch and at least raise the questions again and again. But I hope it isn't an infinite number of times.