First few weeks: Foundations for Culture (Part 1)

What is the most important thing in a mathematics classroom?

If you stumbled across this blog via #MTBoS, you may be no stranger to many people's first day posts about what they do.  Most of them point to the importance of building a classroom culture.

This make sense, especially if your definition of 'the learning of mathematics' is similar to mine:

The learning of mathematics is a process that is constructive, self-regulated, situated, collaborative, cumulative, and individually different; it involves individual cognitive constructions of mathematical meaning through interaction with a social environment that may include group work, discourse, and multiple representations of concepts and ideas; it may also be influenced by prior knowledge, cultural contexts, students' conceptions of mathematics and learning of mathematics, students' self-efficacy beliefs, motivation, identities, interests, and emotions.

This definition of mine is, like all ideas, still developing.  However, I think it captures a lot of what I believe about mathematics teaching and learning.

So building a positive classroom culture where ideas are respected, voices are heard, collaboration is valued, in-depth thinking is encouraged, then, is of utmost importance.  (perhaps more so, now that society's polarizing beliefs and, often, failures to communicate with + listen to each other are ever so prominent)  Speed and precision, while still may be of use somewhere, are no longer primary pillars that support learning and deep understanding of mathematics.

I am not typically a fan of 'top ten' strategy lists in educational writings, since it often carries a sense of priority that the authors do not intend.  Which means it loses a bit of the complexity that is involved in the interactions between the 'top ten,' as well as the idea that implementation of the 'top ten' would heavily influence the perceived success of the listed strategies.

Side note: a focus on 'how we do what we do' was one of the sessions that Alex Overwijk, Bruce McLaurin and I planned for OAME 2017 conference this past may.  We put a lot of thought into how to structure the session so that participants focused on thinking about their implementation and the reasonings behind their implementation - as well as other questions and options.  I hope to write about this at some point.

So before I describe some of my practices in the first few weeks, then, I want to begin by emphasizing that these are not placed in any order of importance.  Rather, these have been opportunities that have complex interactions between them in a classroom - interactions that I am still learning about.  I've broadly put some of them in 2 categories: Learning about the students, and problems + tasks.

Some Practices

Learning about the students

Our school board has a system where students past school photos are stored.  I am actually pretty terrible with names.  So I typically spend a week or so learning the students names based on their old photos.  Of course, these are not always accurate, and some student pictures are not available - but it helps me get started.  Throughout the first day of school, then, I match their old pictures to the people they have become.  I never do roll calls.  Instead, I strike a conversation with students as they come into class, and, perhaps most importantly, confirm with them that I am pronouncing their names right. 

In addition to having a sense of what the students look like, I also spend a long time accessing the students' past records.  This is not so I can judge them, but so I can support them.  Besides the few numbers they have been labelled and reduced to in their math scores, I also take a look at what they have been successful in.  This allows me a glimpse into how they may have experienced school, and how they might continue to experience school.

I have done many different questionnaires, icebreakers, start-up activities, too, that are geared toward better learning about my students.  In the past I have also done many things that others have described in their blogposts (e.g. personality coordinates, four corners, 100 numbers...etc.).  I have also attempted to begin with an 'our numbers' thing, where I share a number.  On the right there would be four multiple choice responses, and one of them is the correct response that says something about me using that number.  This was inspired by what Fawn did with her numbers during her 'teacher woman' keynote at TMC (that I watched from afar).  Students would then create their own, and I would take their 'test'.

As I mentioned, I've also done questionnaires.  These ranged from ones that are more whimsical (e.g. what is something you enjoy so much you'd fight a mutant squirrel for?) to ones that have more potential for depth (e.g. Pick one of the following and share some thoughts with me - a) Ferguson, b) ice bucket challenge, c) Robin Williams, d) something else you choose).  

During my first or second year of teaching, I used to have a fairly open questionnaire that left a lot of room for me to respond to students afterwards - and subsequently continue a conversation with them.  Kind of like passing notes in class - except they're exchanging notes with their teacher.

I wanted to combine some of those elements, and so this year I went with a series of questions.  They come in sets of 4 questions, as well as two quotes each.  I will only share the first two sets, in case some of my students stumble here and I ruin the other questions.

Set 1 (Who you've been) download;  

1. What is a memory/experience that is important to you?  Why is it important?

2. Someone once told you that you were amazing at something.  Who was that someone, and what was that something?

3. What do you believe is something you need to work on?  Why?

4. Ask a question about me that you'd like to know.  Tell me why you asked it.

Quote A: "We do not learn from experience... we learn from reflecting on experience" - John Dewey.

Quote B:  "I am not a product of my circumstances.  I am a product of my decisions."  - Stephen Covey.

Set 2 (What you've done) download

5. What is a meaningful problem in your life that you have solved?  How did you solve it?

6. You are proud of something that you've worked on with someone.  What was that something?  Who was that someone?  Why are you proud of it?

7. You helped someone through some hard times.  What was the issue?  How did you support them?

8. Ask a question about me that you'd like to know.  Tell me why you asked it.

Quote A: "Talent wins games, but teamwork wins championships." - Michael Jordan

Quote B:  "Individually, we are one drop.  Together, we are an ocean."  - Ryūnosuke Satoro

The most important thing about these questionnaires was that I dedicate a lot of time responding to each and every one of their responses.  I type up a page for each student based on what they have written (or said), and I address each one by name.  In a way, this is similar to how I carried on a conversation with students in the past with the notes, except this time it was more targeted at specific questions and prompts.

We then continue to converse back and forth through these 'notes.'  I began with the first set 'who you've been', and then after a few rounds of conversations, I ask them to fill out the second set 'what you've done'.

I also borrowed this quote on the first day:

To let them know that I value their voices, and that I would like them to tell me who they are, and not the images and numbers that I have spent time on.

I won't lie.  These notes take me forever to write up.  I didn't want to haphazardly respond with useless comments like "oh that's nice" or "I see, that's interesting."  A major part of my wanting to do this, is to not only continue conversations with them, but to provoke thought.  And so I thought a lot about how I would respond, and what I would respond with.  I write these feedback with the utmost sincerity and respect for who they are and what they shared with me.

Problems + Tasks

My kids aren't just writing about themselves all class.  We are also engaging in problem solving. There exists a crazy amount of problems and tasks online.  I sought something very specific.  For most of my classes, I needed to begin with problems that were not 'intimidating.'  Of course, whether or not a problem is intimidating depend on the students, it's a subjective measure based on the students' possible experiences, and how they responded to those experiences.  This is an immensely important part in beginning the foundation for a positive classroom culture.

Another thing is, since I have some repeaters in the class, I also needed to find problems that I had not used before.  This was probably more of a challenge than identifying non-intimidating ones.  I settled on the Pirates and the Diamond problem from Peter Liljedahl, Train problem from Peter Taylor, and many many more.

While the problems themselves are important, what is more important is how I did these.  In alignment with how I have understood the work on thinking classroom (Liljedahl), almost all of these problems were delivered verbally, and the students worked on vertical non-permanent surfaces, with random groups visibly generated daily.

While they are solving the problem, it was important that I am not just sitting around checking my e-mails (I don't even do my electronic attendance until class ends).  I am engaged with them in learning about their thinking, listening to their ideas, prompting and supporting them as necessary while promoting autonomous behaviour.

When we 'finish,' we visit some of the students work together and talk about general strategies and skills they've employed.  By 'finish' I definitely don't mean that the problems are completely solved.  Different groups of students work at different pace.  And with these kinds of problems, almost everyone is on the same-level playing field.  We focus on debriefing the 7 mathematical processes outlined in our Ontario mathematics curriculum, which include Problem Solving, Reasoning and Proving, Reflecting, Selecting Tools and Computational Strategies, Connecting, Representing, Communicating.

We typically focus on one at a time, depending on what the student work best lend itself to discussing.  For example, we discussed multiple representations when students used numbers, dots, and tables of values to make sense of their discoveries with the pirates and the diamond problem.  We defined 'representing' in the context of what the students did, as well as reflected together on why they are important.

More than the first few weeks

What does it mean to 'create' a positive classroom culture?  How do we know for sure that it has been created?  Is there a final form we're reaching for?  It is my belief that a positive classroom culture needs to be maintained and continued throughout the year.  However, I may shift the kinds of actions that I emphasize.  For example, I used to do a lot of quotes of the week (which Andrew Stadel also described here).  I also used to do Ninja Boards (one of many posts here) that celebrate and highlight supportive interactions.  I also continue to be mindful of my own words (e.g. with respect to growth mindset), like these bulletin boards, except I explicitly talk about these in class.

I plan on continuing the conversations (through questionnaires) at least for a few more weeks.  I also have began to shift the problems to ones that are more immediately related to content (depending on the class culture and what they are ready for).  I also plan on having them them explicitly discuss and co-construct criteria for  what 'good questions' are and what 'collaboration' means, as well as using notice-wonder to spiral topics based on their questions.  These are for another blog post, though.

Assessment; process/product; In/after the moment. A response to Ann

This is post is a response to Ann Arden's excellent first post "Beyond Test in HS Math (Part 1)" where she breaks down the following diagram that she drew after conversations with Peter Liljedahl and I during #CAfLNchat back in January 2017.

As usual, @pgliljedahl makes me think. Many Ts seem to spend most of time on "product/after moment". #caflnchat pic.twitter.com/k0HDGV3iet

— Ann Arden (@annarden) January 11, 2017

Go read it if you haven't yet!  Otherwise this post probably won't make much sense.

What a great first post!  I also love how this is only part 1 – looking forward to more!
Lots to talk about here, I think.

I think you’ve provided some very good examples of each aspect of the quadrant – and most align with my practices + thinking, too.  But I think I'd like to dig deeper - and I know you wouldn't mind!  I am just going to haphazardly put down some thoughts and wonderings.

Some thoughts:

1. Presently I am thinking that the grid is helpful for framing temporal aspects of assessment.  In other words, I think both the references to process/product and in/after the moment address when an assessment might occur.  I think there’s another dimension of ‘purpose’ that might also need to be considered (although perhaps that complicates things a bit more and would be harder to illustrate).  In other words, what are we assessing about the process/product or in/after the moment?  Mathematical processes?  Precision/accuracy? Collaboration? Intention is important here, I think, because it not only influence how we respond to students, but how we listen, as well.
2. I think framing assessment in this way helps emphasize that a large part of assessment is about what we do in-the-moment.  I think this is an emphasis that definitely needs to be made more often.  Especially since 'assessment' is one of those hated words - mainly because many have restricted its definition to 'grading' or 'evaluation.'  I think we both agree that it's a shame.  Perceptions of assessment definitely impact what teachers do and what they value about what they do.  Hopefully this diagram of yours (credit to Peter for the idea) helps alleviate some of that.
3. I think there’s also room to think about ‘how’ the assessment is done as well.  You made the point that students have a hard time interpreting low-quality feedback (you referenced Weimer 2013 here), which is a great point. Further, though, even when students receive ‘quality feedback’ (descriptive), it may still be difficult for the feedback to actually serve learning.  I think the ‘how,’ here, then, necessarily involve activities that reflect assessment as learning in some way here.
4. You quoted my tweet where I asked “why separate product and process? To distinguish intention? Do the two not relate and influence?”  I think I still think about those questions.  I think often we separate the two out of convenience, but I think there are many opportunities that we can provide in the classroom where the two are interrelated.  For example, living documents like portfolios would be both a process and a product as students are working through them.  I think perhaps there is a dynamic relationship here where we can go between the two without a clear separation.
5. My question about “what is ‘in’ & what is ‘after’?” refer to how if learning is continuing, then a moment might stretch across time.  Schön (1982) defined ‘action-present’ as “the zone of time in which the action can still make a difference to the situation…, and may stretch over minutes, hours, days, or even weeks or months, depending on the pace of activity and the situation boundaries that are characteristic of the practice” (p.62).  That was super impactful for me when I read it, and I think play a role here.
6. I mentioned pre-moment (noticing) in the threads of conversations there too.  Here, I am thinking of Mason's (2002) work on noticing.  Particularly about how, as we accumulate lived experiences and reflect upon them, we can use these to think about how we might act differently in an uncertain future -- to break out of habitual reactions.

Some wonderings:

1. I continue to wonder about the many implications of framing the temporal aspects of assessment in this way.  How might this diagram help teachers think about assessment? does it actually help?
2. If I were to take the grid as is, I wonder about the frequency of actions within each quadrant.  Even in an ideal environment - would the 'best' frequency be equivalent across all 4?  I recognize that it necessarily depend on the context/student/task, but I wonder about priority/effectiveness.
3. I also continue to wonder about the same questions I posed (which I also somewhat expanded on in #4, 5, 6 above)

Thanks for hitting publish, Ann!  Now there's no turning back!

I belong. Thoughts about #MTBoS & #iTeachMath

(Warning: long-ish post ahead)

Belonging is hard.

If you follow #MTBoS, then you have probably felt the shockwaves sent across #MTBoS over the past little while.  It may seem like it began with this post from Dan Meyer (who maintains that the name #MTBoS is alienating, citing many who echo this sentiment), but if we want to really talk about members wondering about their identities within #MTBoS, or initiatives to help change the perceived exclusivity of #MTBoS, then it's pretty much something that has been happening since the first year (e.g. I recall a virtual meeting about the state of MTBoS back in 2013 that I attended but didn't say much at) of #MTBoS.  Not really claiming to be a historian here, but just noting that this isn't a 'new' issue.

I wrote this as an initial response

#iteachmath, beyond just a shift from the #mtbos hashtag, is about building an inviting community. Let's continue the conversations. https://t.co/osLqT9POXN

— Jimmy Pai (@PaiMath) July 27, 2017

Followed by this string of tweets a few days later.

Besides noting the complexity of the issue as beyond simply a hashtag (and more about our community), I believed (and still do) that conversations about -- who 'we' are and how 'we' can be more -- are important.  Of course, this comes within other complex issues as timing, existing efforts of many from #MTBoS and much more.

In any case though, let me get back to this:

Belonging is hard.

To be honest, I went through most of my life never feeling like I belonged (until probably when I met my now-wife Lucy).  Born in Taiwan, up until I was about 12, parents were never around.  After 12, my mom, my younger brother and I landed in Canada.  A year or so later, just when I felt like I was getting the handle of speaking, writing, and understanding English, my mom left and so it was just my younger brother and I living on our own (beginning from Grade 9).  We lived in a house but it did not feel like a home.

It was not a home.  At least not mine.

Besides taking care of finances, meals, chores, and my younger brother, I did fine at school (I suppose 'great' by some measures).  But I didn't belong at school either.  Not that people didn't like me, more like I would disappear when the school bell sounded (and by grade 12, I only attended classes when there were evaluations).  Belonging is hard and I don't think it was simply the circumstances beyond my control.  By the middle of high school, certain events landed me into some evaluations that concluded I was manic depressive (which I continue to struggle with).  I had a therapist and social worker who had worked discreetly to help me breathe.  I am unsure if the pills helped, but the conversations certainly did (of course I went on to disappoint them with attempts at my life which I am still ashamed of).  I did not belong and felt that I could not belong.  Like I was adrift at sea where noone would hear me drown.

Broad brush strokes.  These were some of my past, in order to help illustrate that, at least for me:

Belonging is hard.

Flash forward years later to #MTBoS.  2011 (or was it 2010), I met Alex Overwijk.  He spoke about spiraling which I gravitated toward immediately (and subsequently incorporated into my teaching).  In passing, he mentioned this online existence of math teachers.

I was intrigued.

I followed a few blogs on and off before deciding to start my own in 2012.  I participated in the blogging initiative, and even blogged through my honeymoon (thank you to the many who organized/participated/commented as part of that year's blogger initiative).  I also jumped into twitter.  Not really a social media user, I strictly used twitter for math ed purposes.  To this day, I rarely tweet about personal events (with a few exceptions that I will mention later), not because I did not see it to be appropriate - it just isn't me.  Instead, I sought conversations.  Often dragging people to other platforms to have conversations in a bit more detail (thanks to those that did this with me: Bryan, Chris, Jonathan, Nik, Jon, Kyle, Anna B, Anna W, Peter, Fawn, Judy, and many many more).  I didn't care very much about number of followers, and strictly followed those that I have had conversations or debates with (with a few exceptions).  I read around for conversations and hopped into them.  Sometimes with success.  Sometimes not.

Then in 2013 #MTBoS started.  I admit that I hesitated using the #MTBoS hashtag myself.  In my mind, I flashed through some of the similar concerns that we currently have about the hashtag.  Even back then, I saw that there were different groups of people having good conversations, and an appearance of a hierarchy.  Despite these concerns, I worked to let others know about the existence of this great online.  In fact, it was during one of these sessions that one of the participants alerted me to the fact that I co-existed with others on what Dan called his 'Blogulty lounge'.  I wasn't alone, there were many others who were (and are) continuing to do great things to invite others into #MTBoS.  After participating in, and leading, a few virtual and face-to-face discussions about #MTBoS and how others could join this community, I realized that I really didn't suit a 'promoter' kind of role.  It just isn't my cup of tea to only rave about the positives (and boy there are lots of positives that others have already mentioned in their tweets and blogposts -- all definitely true) -- as soon as I say something, I almost always think about other view points. Nonetheless, I became okay with simply participating and supporting others through commenting, conversations, and offering wonderings and ideas.

Those, I can do.

I became a bit clearer about who I was, why I blogged, and why I tweeted.  I was never concerned about popularity, because that wasn't why I blog or tweeted.

At some point I even landed on a list of people that someone had created about teachers who they'd like to see a particular lesson from.  The idea was that people would contribute a clip describing how they'd teaching something.  I forget who started that one (sorry).  It was an honour.

Belonging is hard, but I felt like I belonged in the #MTBoS.  I still had questions and doubts (as I do with everything), but I will get to that later. (Edit: I am not getting to that in this post after all.  But it has to do with my worries about the echo chamber effect and bumper sticker surface statements being perpetuated).

Fast forward a few more years and my attendance to twitter and blogging was significantly less than before.  A few events in life pulled me away from blogging, and eventually from twitter altogether.  It wasn't anything sudden - more of a build-up over time.  Most notably some family deaths, falling behind in grad school/academic pursuits, and the arrival of a baby (and, I think, a deep desire to do better than my parents -- to actually be a parent).

I felt my belonging in #MTBoS slowly fade away.  No one tore it away from me.  It wasn't something someone said to me either.  I just felt it.  It's saddening, but at the same time understandable.

"It's okay," I'd tell myself, "the dust will settle and I will get back in no time."

More time passed.  More conversations went by that I wish I had the time to participate in.  There were many twitter users and bloggers that emerged that I wanted to have more conversations with.  Their thoughts intrigued me, and those conversations interested me.  But I held back.  I was chest deep in many obligations that I had somehow gotten myself into and have failed to shake off (thanks to many who have offered me advice about pulling out of some of those responsibilities: Chris, Mary, Bruce, and many others).  I wanted to talk to them, but I held back.

"It's okay." I repeated to myself in my mind.  As topics came and went, I took solace in the fact that there were many who were offering pushback and debates and wonderings in a similar way that I would have done so (albeit in a different way, with different ideas, and with different conclusions).  I also took solace to know that I was able to successfully push Alex Overwijk to really blog about his work.  Since his work is similar to mine, I felt okay not really being around.

"Conversations were happening still.  Just without me.  For now.  I will be back."  I assured myself.

But I don't know what 'back' means.  Do I still belong?

What does 'belonging' mean anyway?

I had good conversations with Judy about this last year during CMESG.  We spoke about #MTBoS, which she's working on for her dissertation, as well as individuals in #MTBoS and #TMC (which I actually never attended for a variety of reasons).  Inevitably we also spoke about belonging.  I think I described that even since the beginning there were groups of people who worked together and connected with each other in different capacities.  Similar to her comments recently about pockets:

Maybe it's not about getting outsiders to access the mythical 'inside' but to get more pockets going. E.g. #thinkingclassroom is one I'm in.

— Judy Larsen (@JudyLarsen3) August 3, 2017

Which I think pretty much hits the nail on the head.

How do I know if I 'belong?'

Maybe it's when my blog popped up on Dan's blogulty lounge (which I am no longer on - for good reason since I haven't been around)?

Maybe it's when I felt support through moments of vulnerability?  Like here in not enough where I struggle with my desire to always do more for students.  Or the subsequent post about those same emotions.

Maybe it's during the series of blogposts about ninja boards (e.g. here) where many sought to converse more with me about it (thank you John, Jessica, Malyn, and more)

Maybe it's when I was part of long twitter conversations with others about mathematics education.

Maybe it's when I spoke about #MTBoS so fondly to others?

Maybe it's when I contributed, and was subsequently included in the Nix The Tricks book (Thanks for continuing with that initiative, Tina!)

Maybe it's when I saw my own profile picture pop up in other people's ignite slide that mentioned #MTBoS (thanks Kyle)

Maybe it's when my parents only contacted me when they wanted money, and Fawn kindly gave me words of strength (thank you Fawn, I don't even know if you remember that).

Or maybe, it's all of these and more.

Belonging is hard.  It's more than being invited to initiatives or conversations (although those help provide opportunities).  It's more than being able to chat and banter with others who have more perceived popularity.  It's more than any particular moments in time, because it's threaded together by all these moments.

What 'belonging' means is necessarily different for everyone.  We come with our own contexts, our own loves/hates, our own histories, our own stories.  We start to belong when we build moments with others in this space we call #MTBoS.  I am unsure if we belong to 'a pocket', because I think it's a bit more complex than that.  We simultaneously exist in several pockets, and exist in these moments shared and experiences lived.

And so, I am still unsure what belonging means and whether I still belong, but I do believe that a sense of belonging begins with our doing.  We build belonging when we act.

Many have recommended similar ideas moving forward.  From people's personal stories about their #MTBoS starts, or Carl's recent TMC keynote about #pushsend (Carl, incidentally, is one of those people I hope to chat with soon).

Belonging is hard.

My thoughts during the beginning of this recent wave about identities and #MTBoS was that having conversations is good.  I've seen many tweets noting that this debate has changed how they thought about #MTBoS, and I can only think of that as a good thing.  (of course, there were many bad bloods that could have been avoided I think).

Belonging may be hard, but in order to say "I belong" I would need to sound out who "I" am, and to recognize that it begins with me.  What does blogging/twitter mean to you? What can they mean to you?  It may sound like a cliche by this point, but #MTBoS truly is what you make it.  (For this reason, I disagree with those that imply #MTBoS can be described with a single label.  E.g. not all #MTBoS'ers are doing group work, or formative assessment, or etc... in ways that we have defined those terms ourselves.  To pretend that everyone in #MTBoS is at the same place would be a mistake, and, in a way, exclusive)

The only thing you can be, is you (re-recorded 5 min clip from my Ignite a few months ago).

And with a tweet, a blogpost, a comment, a read - you're already stepping into this vibrant community of #MTBoS.  It's up to you to then make it yours.

In any case, here I stop rambling about #MTBoS and #iTeachMath and #pushsend before the baby wakes.

Be you - Re-recorded with slides

Shhh.  I'm not actually fully back to blogging and twitter yet.  I am so close to some finish lines, and am looking forward to returning soon.

Thank you all for the overwhelming positive support and love for my Ignite at OAME 2017.  Many have subsequently thanked me or requested a video to be used for various purposes.  I decided to re-record the poem, and put in the slides to go with it.

Here it is:

Here's the link to the previous post that contains the words of the poem.


Update: the official ignite video is out and here

An Ignite: Be You.

So I lifted my pseudo-self-ban from twitter and blogging somewhat over the past few days.

I am seeing an end to the end of most of my writings (not to mention some person life things are resolving) and so I am really really looking forward to coming back to #MTBoS in full force again.  Because I truly enjoy that experience and always get a lot out of interactions there (as well as on people's blogs).

I didn't plan on writing this blog post.  However, I had so many DM's and 'thank you's and requests for a post - that I felt that it was important for me to share this.  After this post I'm diving back into the water to finish off my commitments and then will certainly come back in a few months :)

For OAME Annual conference (Ontario Association of Mathematics Education) in Kingston this year I did an ignite.

A huge thank you to Kyle Pearce (@MathletePearce ), Jon Orr (@MrOrr_geek ) and Al Overwijk (@AlexOverwijk ) for recording my ignite and sharing it with me.

**note
Also check out Kyle Pearce's blogpost about his ignite here: The Beauty of Elementary Mathematics
and Jon Orr's blogpost about his ignite here: Being Picky

I begin with the recording and I will follow up with the poem.  I packed a lot of into this poem and so there are lots to be elaborated on.

I had initially planned on elaborating in this post -e.g. on the struggling with the choice of people's faces in the first slide, or the decision on writing 'vertical non-permanent space' instead of 'surfaces' - but I think I may have to save those discussions for another post.

So I wrote and performed a piece of spoken word poetry called

Be You.

I must say that I stumbled a bit in the beginning and messed up a few phrases but hopefully the message still got through.

I highly recommend scrolling down to the text and images as the video plays - since I think the slides are more important than my face.  A note that there will be an official Ignite video that will come out as well - since we were video recorded.

Huge thank you to @MathletePearce  and @MrOrr_geek for recording this one

Huge thank you to @AlexOverwijk  for recording this one

--------------------------------------
Text (with images)

Be You.

You all have these people.

They are wonderful

teachers or

researchers or

originators of your inspiration and their innovation and passion have often

astounded you, challenged you, supported you,

or led you here.

But let me be clear.

They are not

You.

Your classrooms are not made of

three cups of Mary,

two table spoons of Dan,

one teaspoon of Peter, topped with some basil and sauce,

and baked at four hundred and fifty degrees in Desmos. No

it's not

some puzzle

with pieces that don't belong to you.

And while even with the best intentions

you cannot forcefeed students information

you are still there in your actions

in what

you do and how

you do it.

You matter.

You

are more than whiteboards, patterns, or cups stacked

more than soccer balls, lanterns, pikachus, or videos that start your 3-acts

You 

are 

more

than all of that.

Because these

are merely beginnings,

static pictures on some ignite slides,

on some very restricted timing. Because

Every

Day

you are also a you that you couldn't have been before.

Maybe last year at the end of your spirals and plans

you came across these kinetic sands, and

maybe this year you spiral around your students' wonderings and questions about these sands and

from exploring those questions you tie-in the curriculum strands.

Maybe at the beginning of your semester

you noticed your students didn't work well together

and even with continued visibly random grouping

there's still an undercurrent bullying

based on superficial judgements

of mathematics,

of peers,

of what's important.

And so maybe

you explicitly

discuss and model positivity

that mathematics

is constructive

collaborative

about creativity

and for all students

no matter their race, gender, or beliefs

no matter these -

identity

politics

Maybe with statistics and scenarios you start conversations,

turning their weapon intentionally

into lessons in empathy.

And maybe yesterday,

you heard one student say

"I just can't -- math isn't in my DNA" when she noticed that she made a mistake
and then quickly erased it from her vertical non-permanent space

and

so

today.

when you select,
sequence,
and connect,

besides advancing mathematical thinking
you pay attention

to the multiple representations

including

the one

she made

disappear.

Because you

play

a major part in

building

their sense of agency

and

mathematical identity.

There are countless opportunities

for you to learn and talk

with one another.

To grow and push your thinking

and your doing

further.

To not stop at being good enough

but to 

always

strive

for better

And this means looking through mirrors

which include you, your students, and other educators

and can only ever

be seen through

your-eyes

and moved with

your-hands.

Because reflections

are the only chances we have to discover

our blindness

and to recognize

that the certainties and knowledge of others are,

respectively,

as overwhelming

and tenuous

as our own.

So be you.

There's no point in trading old shackles for some other restrictions.

Be you

because your students 

need you

to be you.

Don't just follow blindly, be --

a you that integrates the resources that you have encountered

and the experiences you have shared with your students

and then channel that into your

own

flow.

because it cannot be anyone's flow

but yours.

so be here --

learn,

be inspired,

but don't 

stop 

here.

Every.

Single.

Day.

Be a you

That you couldn't have been

Yesterday.

If you know me,

you know I can't speak

without asking questions

and so I ask you these:

Who are you?

and

Who

Can

You

Be?

Reflecting on a dream

I haven’t posted in a long time.  I’ve been writing so much in other contexts, and have been so behind in those writings that I didn’t feel justified to write here.  I felt compelled to write today because of a dream I had.

I also haven’t slept much in a long time.  Primarily due to our newborn (woot woot 7 weeks old now), but more than that due to myself.  After talking to other fathers with newborns who are able to sleep, I realized that my lack of sleep is more tied to my own personal beliefs and choice, and not purely in the child needing to feed every hour, two hours through the night.  My (our) beliefs in breastfeeding, and prioritizing the infant to feed when she needs instead of sleep training her as soon as possible (where timing, method, structure all seem to be contentious issues, even with the recent release of a study from a university in Australia, which I am not linking due to it not being the point of this post).  My beliefs in what I do to help my family through this process (taking care of all except the feeding part during the night).  And so my struggles are self-inflicted.

But these aren’t my reasons for writing this post.  Not my lack of sleep; not my beliefs in parenting.

A Dream

I felt compelled to write because I had a dream.

It’s an actual dream I had (within the 2 hours of sleep that I rarely got).

I feel compelled to share this dream, as well as reflect on various aspects of this dream.

And so here it is, in all of its randomness, nonsense, and lack of clarity.

My dream spanned two days (coincidentally I slept for 2 hours).  The first day of the dream I was heading to some sort of conference, and the second day seemed to be the conference.

At some point during the first night, I was at some sort of building where I came across two children who were stranded at this building with me.  The boy, was waiting for his mother to pick him up, looked about 13 or 14 years old.  The girl was a bit younger, possibly 5 or 6 years old.  She was unreleated to the boy, and seemed to have down syndrome or something like it.  I stayed with the two kids because I seemed to be the only adult there.  The mother of the boy came to pick him up at around 10 or 11 pm.  At this time she mentioned that the parents of the girl have abandoned her and are not picking her up.  Then she left.  She simply left.

I reached out to the police and child services, and then the scene ended.

In a flash I was in the second day, landing in a middle of a large auditorium.  The talk was something about math education.  There may have been something about accountability.  There may have been something about curriculum.  Somehow I found myself with a microphone and asked to speak.  As I looked out into the crowd I began to tell them about my day yesterday (day one of the dream).  In particular, about conversations I had with a boy that I met.  I told the crowd about how the boy demonstrated a sense of distrust when I told him I was a math teacher.  I told the crowd about how I worked to build trust through talking and listening to him, as well as engaging him on various different topics seemingly unrelated to mathematics.

“Maybe” I said to the crowd “there is no point in beginning with mathematics.  There is no point in bashing them over the head with something that they’ve identified as an enemy.  There is no point in shoving content down their throat.  There is no point because it is degrading to both the child and the teacher, and move neither party forward in their learning.”

At this point my microphone was cut off.  I was unsure whether it was because the powers-that-be did not agree with what I was saying, or whether it was a technical glitch, but I continued shouting.

“Maybe we don’t teach math explicitly.  Maybe we don’t do that for a few days, a week, a month, a year.  Maybe we instead engage them in activities that help build their confidence and their sense of being safe in our classroom, in our world, in our conflicted society.  Maybe there is no point in beginning with mathematics, but that we should be beginning with the child.  With connecting and listening to the child.  How can we move student thinking forward if we cannot recognize where they are?  And if they are at a place where the very mention of mathematics or school abhors them, then we need to sit and be with them instead of pouring gasoline all over that fire.”

There was no applause, no standing ovations.  There was no jeers or heckles, no rotten fruits thrown in my face.  Instead I woke to a crying baby.

Possible source of this dream?

This was not scripted or made up or a metaphorical dream.  It was simply a dream I had.  I had to fill in a few pieces that I had difficulty remembering, but the description was true to my dream (also cut out parts where I was cooking for some reason?)

I felt compelled not only to share the dream somehow, but also reflect on why I had the dream, and whether I agree with what I said.  I am no Freud, nor do I follow his worldview or ideologies.  But I thought my dream must at least in part relate to what I had been thinking about yesterday (real day and not in the dream).

Yesterday (real day and not in the dream) I attended a session on effective PLCs, then afterwards had a conversation with several teachers at a different meeting, and then conversed in a network about shifting teacher practice.  In all three instances there was concern for teachers who don’t change, who refuse to change, who would rather stick with binders they’ve reused for years.  I contributed with various ideas.  Ones that aren’t necessarily ideas I 100% believe in.  But I tend to do that with ideas – I throw them on the table for people to think about without fully believing in them first (because otherwise I debate it many times in my head and don’t end up actually putting it anywhere).  Throughout the three instances, I remember thinking about one thing: instead of thinking about how we can move those teachers, what if we recognize that we can’t move them.  What if we listen to them and support them and encourage them to move themselves.  I also remember relating this to teacher-student relationships (maybe that’s where part of the dream came from).

Reflection on this dream?

Did the dream make sense?  I found it interesting that a mother who left her child for several hours in a strange place with a stranger, was the one that commented on yet other parents who have abandoned their child and are not returning.  I am reminded of an old Chinese idiom I’ve heard from years back called 五十步笑百步 (I think initially from Mencius), where a deserting soldier who ran 50 steps away from battle, ridiculed anotherwho ran 100 steps.  It’s a similar proverb to “the pot calling the kettle black.”  I found that interesting.  Perhaps I can relate this to how we all have our own problems of practice that we are working on, and that a sense of superiority or inferiority is unhelpful.  Perhaps I can relate this to being wary of comparisons of scores and an insistence on measurement instead of pouring my efforts into moving student learning.

I also found what I said in the dream interesting.  Do I really believe that?  In the dream I seem to be addressing interactions with students who deeply resent school and school mathematics.  I prioritized the connections and relationships that must be established in the beginning, and continued to require establishing throughout the learning.  I can see myself believing in that.  I also think it does cohere with my view and experiences with how I help students introduce mathematics in the things they do.

I struggle, though, with stating (in my dream) that we could refrain from introducing mathematics for a month, a year. 

I also struggle with how the events in the dream seemed to point against curriculum and against accountability.  I struggle because I didn’t think I saw these as at odds with one another.  I thought of myself with the belief that we could incorporate these elements within my activities and lessons.  Just as for some classes I have made efforts to incorporate issues of social justice within my activities, and prioritized student conversations.  But I don’t know.

Maybe it's a futile effort trying to interpret this.

Maybe it was just a dream.

I do know that I feel better now that I've written about it.

Thoughts inspired by #MTBOS2015

Seeing the #MTBOS2015 hashtag made me think.

The questions from Ilana (@tchmathculture) are definitely interesting in their own right

#MTBOS: what was your favorite blog post this year? Which of your own blog posts do you want to share? Tag with #MTBOS2015

— Ilana Horn (@tchmathculture) December 29, 2015

And there are certainly lots of great posts that I've read this year.  With respect to the "own blog post" thing, I found it fascinating that some people jumped to their most popular posts, and I wondered quickly about whether that holds any meaning for me.

This post isn't about answering the two questions.  At least not directly.

Instead, the questions from Ilana made me wonder about two other things:

1. What kind of blog posts am I most interested by?  Most impacted by?  What conversations have I wanted to engage with the most?  What does this say about how I interpret the world around me?  What does this mean for how I interact with ideas I encounter?

2. Has my central questions about my teaching practice changed?  How does this blog reflect a change?  Did it even do this?  What are the things I find myself writing about, and are they things that I've been wanting to write about?  How do I stay true to the conversations I wish to begin, as opposed to the conversation I find myself in - and does a difference say something about how I question and what I pursue?

I am unsure how I might approach these wonderings.  It would be one thing to simply answer Ilana's questions and start listing things, but I get a feeling that I would be betraying something that I will be aiming to do for the future of this blog: which is to write things that matter to me.  What a weird statement, right?  Does this mean that I have been written things that don't matter to me?  No, I don't think that's the case.  Instead, I think it's more like I have been regretting not entering into certain conversations while I could - and feeling like I missed the boat on a lot of them.

The questions I posed are huge.  I certainly won't be able to tackle them all here.  And so these are the things I want to tackle in this post, in a corresponding way to the two wonderings inspired by the conversation over at #MTBOS2015.

A. Conversations I wish I pursued
B. Reflections on conversations I continue to have with myself

A. Conversations I wish I pursued

At the risk of being brief, I am going share some thoughts on the following posts and conversations that I wished I engaged at the time.  Not because I "missed the boat" on being able to continue the conversation with them.  No, it's more that - even if I continue the conversation now, I would be having a different conversation than the one I would have had if I engaged earlier.  I am referring to the fact that things have necessarily changed since I last considered the conversation. Some examples include context, state of mind, culture (related to the ever changing #mtbos present and what people seem to be interested in pursuing).

1. A conversation about standard based grading, growth mindset, and the outlook on "fads" of education (mainly with @math8_teacher, @mpershan)

Of course, this is not to lump all three of these guys together.  They all certainly come from different places, hold different opinions, and think differently.  But in my mind, they all relate to a similar conversation.  Dylan (@math8_teacher) wrote about his skepticisms concerning standard based grading here, and I recall tweets (and maybe even a blog post I can't find now) from Michael (@mpershan) about not only SBG but also growth mindset. Then Dylan also wrote about growth mindset here and here (gotta love that search function).

I wanted to engage with them in a more meaningful way.  I think my central theme would be around something like this  where I believe that it is more important to focus on what we take away from an idea, rather than how popular an idea is.  I don't think the ideas (growth mindset, SBG) are all perfect, and definitely not conceptualized the same way from one to another.  My conversations with others lead me to believe that most people continue to refine what they think these ideas mean to them, as they continue what they do.  Or, of course, some meet it with disgust and rejection, or attempt to consume them in some sort of pre-packaged form (which inevitably result in failure due to a variety of reasons).

Is SBG useful? it depends - on how you define it, how you implement it, how you contextualize it, and what it means in your classroom to your students.

Is growth mindset useful? it depends - on how you define it, how you implement it, how you contextualize it, and what it means in your classroom to your students.

To me, I think I like to better understand the ideas by first meeting with welcoming arms.  I critique, reflect, and comment after it has become my own - because then I am critiquing, reflecting, and commenting on something I have more control over - my own practice.  This was the way that I tackled something like the Ninja board.  I wholeheartedly embraced in implementing it in my own way as I spun it to focus on culture in the classroom while building functions into the structure (and thus play it out more in a 3-act-esque fashion), then questioned myself (and others) about many aspect behind why, how, when...  And maybe that's a good approach to have - examining something closely once I have made it my own.  But maybe not.

Are there educational fads that rise and fall?  I think the answers depend on who you are and what the fad means to you.  I still believe it's unhelpful to actively promote the idea of a pendulum or that there exists fads that come and go.  But I suppose I can only comment on why it's unhelpful for me:

It is unhelpful for me because it limits my ability to be open to ideas.
It is unhelpful for me because I would worry about trying something "simply because it's a fad."

On the other hand, I do see many people trying the same thing at roughly the same time.  This is the case in our board for ideas like vertical non-permanent surfaces or visibly random groupings.  Or the case where Al (@AlexOverwijk) and Mary (@MaryBourassa)recently spread the seeds in many people's minds about spiralling via #MTBOS and #TMC.  The fact that many more people are trying these ideas are helpful to me.  I am comfortable with the fact that everyone is taking and incorporating them in different ways, or reflecting and criticizing different aspects of them.  These conversations are helpful to me.  They are helpful to me as I continue to consider and reflect my own knowings of what these ideas mean to me - and how it is applied to my classroom.  It is unhelpful to me to insist that they are fads.  Ultimately, I ask myself: does thinking that they are "just another fad" help me?  No.  And so I stay away from that mindset.

2. Struggles with certainty, doubt, and roles of research.

Earlier in the year I attended a talk on the fallacy of certainty (not the right title).  It was about how misleading certainty can be in mathematics, and how it is important to help our students recognize the important role that uncertainty plays in mathematics.  This was presented to us from a speaker who had engaged in research in environmental science before move to educational research.  I missed the chance to reflect on this talk at the time, but this related to several other conversations over twitter - big or small.  Sometimes people talk about better (or best) ways to teach, better (or best) ways to write blog posts, better (or best) ways to do professional development.

Certainty is sexy.  Certainty sells.

It is unfortunate it is that way.

Maybe it's because certainty is often coupled with confidence, and confidence is an helpful ingredient for sharing and spreading ideas.  It is unfortunate because it gives the false impression that ideas (e.g. perhaps shared at a workshop or talk) are perfect.  That the ideas being shared are absolute.  That examples shared are the best examples.  That recommendations are scripts to be followed.  Unfortunate, woefully untrue, and even potentially damaging to the idea itself in the long run.  I can try to make an argument using SBG or Growth mindset as examples, but I think that's a longer post than I had intended.

Certainty is also something that we seek.  @mathcurmudgeon mathcurmudgeon ranted about research here where he argued that "the whole point of research is to answer a question, either to prove it or disprove it."  I read his (self-proclaimed) rant as a further indication of that people (principals in his case) take away ideas in different ways.  But then he called for research to settle debates, to solve problems - or else leave him alone.  This is another conversation that I wish I had time to flesh out - but will likely not be able to.

3. Dissecting spiralling - celebrating and questioning how we implement and what it means to us. (mainly with @AlexOverwijk, @MaryBourassa, and @BDMcLaurin - also many others).

I wrote about this before back in 2012, but have never delved into how I unpack spiralling for my own class - for my own purposes.  The conversations I've often missed out on, though, are opportunities to further explore the differences for how we implement it differently.

This might be a strange turn (though not in my mind), but I see people doing this very differently across the board.  I think that's great.  At the same time I also see people attempting to craft formulaic approaches to "spiralling the curriculum."  This is problematic for me.  Especially since what enticed me the most about the concept of spiralling, was the degree of freedom that we would have as teachers.  We would be able to follow students' intuitions, questions, interests, wonderings.  I couldn't do this before with a unit-by-unit approach.  It seems to me that attempts to standardize implementation would go against the core reason why I supported it in the first place.  Besides that feeling of unease, though, when I have conversations with others about this, I am genuinely interested in how people have shaped the idea into their own practice.

I don't want to make people feel vulnerable or uncomfortable by jumping straight into the problems they have with spiralling - but that's actually what interests me more.  I recognize the importance of celebrating the things that work, but I really want to find out what and why things don't work.  This is in a similar way to how I treated my ninja board.  Now that I've done it for a while, I want to split it open and put it through a gruesome set of interrogations.  I want to know what it still means to me, what it should mean to me, and what it will mean to me.  Furthering a conversation about spiralling is the reason why I began with this post outlining a shell of what I did with one idea.

B. Reflections on conversations I continue to have with myself

Looking back at the blog, I wonder how much of it represented things I've been interested in, thinking about, and reflecting on.  With the exception of a few, I rarely write about lessons.  I had been unsure why.  Maybe it just doesn't interest me as much.  I recognize that lessons may get more traffic, but that's not why I write in the first place.  I went so far as suggesting that maybe we shouldn't share act 2s back in 2013.  I think this was primarily spurred on by seeing people starting to make very detailed step-by-step plans to follow (which coincided with some of my own real life conflicts with others).

At the beginning of this blog, I intended it to be a place where I explore the three themes that fascinate me - mathematics, mathematics education, and philosophy.  Since that time I have found myself moving away from writing about mathematics or philosophy (or even at all).  Mathematics, in particular, had not been very prominent in what I write about.  Not to say that these aren't embedded in the things I write about, but my posts have often been about mathematics education.  It totally makes sense to me.

But I think I want to continue these conversations with myself (blog) in a way that allows me to explore some mathematics and philosophy as well.  I wonder if these might naturally take the forms of more elementary topics over the next couple of years as we expect our first baby soon.

There are many things that I've put on the backburner, though.  At several points in the past year or so, I've had many drafts where I recorded partial thoughts on a few things.  I think I am going to delete all those drafts.

It isn't because the topics aren't interesting anymore.  But more that how I think about them are slightly different, and set on a different background.

There are many conversations (with myself or with others) that I've been wanting to pursue.  Some were listed earlier, many have sunken deep into the sands of time.  But I don't think I will be able to pursue them all.

I have to focus.

I've taken on way to many things this year - despite taking a one year leave from teaching.  I don't even know how that happened.  But I don't want to lose out on using this blog as an opportunity to pursue conversations.  And so I think I will take things one at a time with respect to this blog.  I will begin with continuing to unpack this post that I've set up for further reflection.

In any case.  I went on a bit of a tangent, but these were things I thought about when I saw Ilana's post.  I am grateful for this opportunity to explore the few things that I've left on hold over the past few years - even if it just skimmed over the many thoughts and reflections I've had.