Monday, 9 October 2017

Exploding Dots - for Fraction Division (operations)

So... I came across this tweet earlier tonight




While I have typically leaned on this resource from Marian Small, I was curious about using exploding dots for something like this.

If you are not aware, this week is #GlobalMathWeek, lead by Global Math Project's work with exploding dots.  I highly recommend signing up if you have no already.

The idea of exploding dots leverages the deep concept and structure of place value, and use it to basically explode your mind :)

In any case, let me get on to doing what I came here to write about.

Fraction division.  The dreaded topic of many.  Again, there are many great resources out there using area and number line model.  Here, I am mainly playing with the exploding dot ideas.  I dug around for existing work using exploding dots for fraction division, but I came up short.  So I thought I'd play around with it and see what comes out.

Before I begin, I'd like to highlight that I am just playing.  I am unsure if it completely follows the logic that has been previous established by James Tanton, although I certainly tried hard to preserve the concepts/structures there.

I'm going to begin with the idea of representing 3/2 with a box.  Note that for my purposes, I only need two boxes.


As you can see, when the box on the right fills up, it becomes a '1' which goes in the left.  So I can use a similar idea to 'un'explode the dots to make 3/2

Ok so now I move onto something like (3/2) times (2)

Well that's just taking the dots and then duplicating each one.  All at the same time, remaining in the (1/2) box, which means I have 6, as seen below



Which can, in turn, also turn into 3 groups of 2 that 'explodes' into the 1's.  In other words, equals 3.

But wait, I'm not doing multiplication here.  So let me move into playing with division.

So (3/2) divide by (2) is what I want to do next:



So here is where it gets tricky.  In order to 'divide' by two, I am splitting the boxes into two.  Each of my 'sub'boxes now need to be filled before the entire box is filled and I can explode it into the 1 box.

And so since I now require '4' dots to fully explode, I have (3/4)

Ok so that was alright.  Let me do (3/2) divide by (3)

In the same vein, I split the existing box into 3 pieces


Each 'sub'boxes require 2 dots filled in order for the whole box to explode.

And so since I need 6 dots in total to explode, and I only have 3, I end up with 3/6.

Ok so now I need to add a new idea of what happens when I divide a fraction by a fraction....

(3/2) divide (1/2)

In this case, I split each dot into two.  But each half is now counted as a full one (since we're counting by halves).  So I can think of it like mitosis or the fact that I am counting differently now.  This is similar to, but slightly different than, how I multiplied by 2 earlier.



And so once I count by halves, I note that I now have 6 dots in that box, where every 2 can explode into the next one.  And so, once again, I end up with 3.

So putting everything together...

If I have (3/2) divide by (3/2):


So here, I begin by both splitting the dots into 2 (doing the 1/2 aspect), as well as splitting the boxes into 3 (doing the divide by 3 aspect), which then leaves me with 6 dots but in 3 'sub'boxes.  Since now I have each box being full, it fulfills my requirement of the entire box being full, and so I get 1.




As I mentioned in the beginning... this isn't really polished, and as I mentioned here, it isn't as intuitive as I would like it...




And so this is more of an open invitation for others to think about this with me!

Let me know your thoughts.

Let's have lots of fun exploding dots this week!






Posted by at 1 comment:
Labels: , ,

Tuesday, 3 October 2017

Foundations for Culture (Part 2)

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.
The above quote is from the part 1 blogpost where I shared some thoughts and strategies about how I work on a positive learning culture in the classroom.  The two main categories were "learning about students" and "Problems + Tasks"

In this post, I continue to share some thoughts and strategies.

Listening to students

No, like really listen to them.

Davis (1994, 1997) differentiated between 'listening to' and 'listening for' as well as establish the ideas of evaluative, interpretive, and hermeneutic listening.  At the risk of being brief and simplistic, I will offer some definitions of these three ways of listening:  Evaluative listening is where we look for specific things that the student is saying.  Seeking our own opportunities to say "correct" or to check off a box (a good reason to be careful with observation checklists).  Interpretive listening is when we attempt to make sense of what the student is saying, and consider the depth and complexity of their understanding.  Hermeneutic listening is when we listen and participate in the same mathematical exploration that students are involved in.

Of course, how we listen also has implications for assessment (which I see, at least in part, as practices and strategies for generating, interpreting, and responding to student thinking).  However, in this post I will focus on the implication for culture.

Vertical Non-Permanent Surfaces (VNPS), along with other thinking classroom elements, are valuable structures and strategies in the classroom for providing me with opportunities to listen to students' mathematical thinking, and to encourage students to listen to each other's ideas.  As students continue to interact with different peers each day (through visibly random grouping [VRG]), they earn valuable lived experiences solving problems with one another.  Over time, this often helps facilitate opportunities for the development of a positive classroom culture.

When I listen and participate with students at each board, I am also mindful of what I say and how I say it.

Because it matters.

It matters whether I stop their thinking with my prompts or suggestions.
It matters whether I choose words that paint mathematics or learning in a particular way (e.g. growth mindset).
It matters whether I follow up on their ideas and suggestions or use them as talking points.
It also matters who I pay attention to in the group when I enter into their world of problem solving.

Listening often also include what students are 'doing' with their gestures, diagrams, and more.  For this reason, I also provide manipulatives for students when it makes sense to use them for the activities.  As I watch what students are doing with the items, it can often be helpful for providing me with ideas as to how to better support their learning.

Value their thinking
Along with listening carefully and responding in a way that isn't dismissive, I am also talking here about valuing their mathematical thinking.  When students don't feel like their work is valued, it works counter to the positive culture that we are attempting to build throughout the semester.

**as I prepared this post, I actually had a conversation with many others over twitter about a particular aspect of what I wrote regarding defronting, student notes, and board work.  As a result, I rewrote this section to incorporate aspects of that conversation instead.

It began with Laura's tweet and my subsequent wondering.  I had my own thoughts on this, but I wanted to know how she dealt with this tension of power:




Throughout the conversation, Anna and Peter also jumped in and shared some of her thoughts.

The concern was about how we leverage technology in a way that does not counter the idea of 'defronting' the classroom.

It seemed that many suggestions aligned with some of my own practices.

Notably I summarize two thoughts

1. Letting students have a role in presenting and summarizing ideas










These were actually going to be my responses to a previous question from Joe Herbert:




I often encourage students to take images of their work from the board because the boards are erased from class to class.  But images are useless when it's swimming among million other pictures of my dog or my daughter.  Using google photos, the images I take of their work on the board is often incorporated into tasks for the next day.  These are synced automatically, which allows me to easily transfer and cut the images to a different document. Similar to Anna's work, I provide them with another activity involving these notes, often involving the mathematical processes that we have in Ontario.  These activities often involve several images being stitched together and then provided for students in the same way that Laura had put up.

2. Having the teacher building a narrative through what students have done




At the same time, if I need to personally debrief activities, I either make use of what they have already worked on their boards, or I make use the images and debrief the concepts that way.

So in general, with the images I take of their work, I may structure another activity that allows them to continue thinking about the problem, engage them in reflecting on what they have learned (as well as the math processes), or utilize their work in a debrief of the concepts.

With respect to tech, perhaps this contribution from Michael was the most telling




Thoughts? Ideas?  How do you build culture?

Posted by at 1 comment:
Labels: , , , ,

Thursday, 14 September 2017

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.

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.

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.
Posted by at No comments:
Labels: , , ,

Monday, 7 August 2017

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.


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!



Posted by at No comments:
Labels: , ,

Friday, 4 August 2017

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




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:




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.







Posted by at 3 comments:
Labels:

Sunday, 28 May 2017

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

Posted by at No comments:
Labels: , , ,

Sunday, 14 May 2017

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?



Posted by at 4 comments:
Labels: , , , ,
Subscribe to: Comments (Atom)