Hi intrepid readers, so here’s me homeworking again.

First, the classroom action:

My first week of semester 2 classes has been pretty great. Both math classes have had a full 5 days of beginner-Thinking-Classroom stuff: verbally delivered problems that have interesting patterns / solutions, room for extensions, and working in visibly random groups on whiteboards & windows.

There’s been majority buy-in from the students so far, and the rest are pretty firmly in the “I hate math class because math class has always hated me” camp from what I can tell. No one’s had a meltdown over not working with their favorite friends. I have had a few questions along the lines of, “So when are we going to have a normal class?”, but I’ve just kind of shrugged that off. “Maybe never, we’ll see!”

Content-wise, it’s all been a selection of Good Problems taken from either what I’ve worked on in class myself or from Peter’s site. I’ve been using the same ones in both my Foundations 11 and my Math 10 classes … which just backfired today as the afternoon grade 10 class had talked with someone from the morning 11 class and been given “the answer”. (They still didn’t know *why* it was the answer and they kind of spilled the beans in asking me, but it did mean the time spent on the problem was significantly shorter.) Oh well, was going to move to curriculum-specific problems tomorrow anyway!

I have a few coursework-specific questions to answer that I’ll put after the break.

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Playing some honestly-I’m-behind catchup on my course journaling here, I’m going to sum up what I’ve got in mind so far and maybe add more later to actually properly finish the assignment.

It’s 3:09pm after the first day of a new semester. Today went *great* but I feel like my tension levels are running too high. I need to figure out how to make this more manageable for myself without compromising on what matters – student engagement and building a culture of expecting-to-think.

Quick summary of the last couple weeks: four of my five courses wrapped up, with a mix of ‘Thinking Classroom activities coupled with straight-up commonplace review packages. Of those four, one entire class ended the year with exit interviews instead of an exam; one class was a mix of exams, projects, or interviews; the other two were mostly-exam with a couple of exceptions.

Exit interviews were great, but they would NOT scale well, at least not like this. For interviews, I went through each content unit and asked questions; I had intended to ask some high-level, open-ended questions and let the student guide me through what they learned, but quickly found that neither of us were quite sure how to make that work, so I fell back on specifics. My goal was to be able to gauge their understanding in each area on a 4-point scale; not trying to cover every kind of question an exam would have, but hitting on some concrete example of the main ideas.

Foundations 12 interviews took about 20-25 min; the few PreCalc 12 interviews I did ended up 45-60 min each. This would not have worked out well for me if they weren’t such small classes (under 10 each; they were a combined class in my timetable).

I had a couple of summative projects; they were all right, but again my initial criteria were high-level questions, and the students didn’t have enough experience working at that level in a large-scale way. Not a bad idea but needs to be built up towards next time if I want to repeat it, I think.

So, today. Two new math courses, all started off with students at the whiteboards and windows on some good problems (Pirates and split-25). The classes ran well, but at some point I noticed my tension levels rising. I think(?) what’s going on is I’m just nervous watching them all without either sitting down or talking! I don’t want to sit because I need to circulate and hint/extend – I don’t need to talk a lot unless a group is stuck, and they weren’t often (yay!).

Gonna keep at it for now – I’m committing all my powers of stubbornness to see this through properly and not let fear pull me down …

I have a lot of homework to catch up on for this course, and other questions to discuss in this journal entry, but now off to class.

Hi, readers of sporadic blog! I’m starting the second course of a Master’s in Math Education, and this one involves weekly journaling (or, according to the dictionary, journalizing? ha ha Chrome spellcheck redlines both of them, as well as “redlines”). So I’m going to do my journal entries here for y’all to read.

The course is with Peter Liljedahl, who is gaining some well-deserved internet cred for his research and work in promoting ‘Thinking Classrooms’. This is the second time I’ve taken a course with him, and as was expected we spent our in-class time working on some good problems in visibly random groups on some whiteboards. Makes for a lot of on-your-feet time by the end of a long evening class, but it’s awfully fun.

Okay, now for the content that the prof was actually hoping for.

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October 20, 2017.

Thirty-seven years and a few months ago, I was three years old and she was a newborn. I remember my parents carrying her into the house for the first time.

 

Seven years ago, she ended her own life. Today’s the anniversary.

 

Yesterday, Dallas Yellowfly of 3 Crows Productions presented “Qwalena: The Wild Woman Who Steals Children”, a modern retelling of an Indigenous story that appears in many west-coast Nations. They did an *amazing* job – the Wild Woman begins life as a girl with a deformity, teased to the point of hatred so deep that she escapes to the forest and learns to hide and steals anyone who comes for her.

After the scary story was over, Dallas told another one. About his dad.

His dad was abused by a priest in a residential school from the age of six. Tried to run away – didn’t work, they found him and brought him back. He buried his pain until it turned to hate. He learned to deal with problems with his fists. When he was sent “home” at 14, he had no real connection with his family and a lot of reasons to be angry at the world.

When Dallas was six months old, he was accidentally hit by his father, who was trying to hit his wife, who was trying to protect Dallas. That was the last day Dallas had his father; his mother took the baby and left for good.

He told us he was here to let everyone know that, “You don’t need a father. If you have one, don’t take them for granted.” How he is proud of where he comes from, but he’s not proud of who his father had become. How his mother walking out had saved him from receiving the full weight of the intergenerational trauma that the Residential Schools had inflicted on his father and his people.

Dallas and his production team do an *AMAZING* job and cut to the heart of the trauma that our country, our people, our government did to our Indigenous brothers and sisters. A few times he seemed incredulous that he was telling this story at all, again.

When Dallas was nearly done telling his story, I realized that my torso was locked tight, tense. My hands, limbs were normal but the core of me was frozen.

When Dallas ended the presentation, students started getting up, and I managed to stop crying about twenty minutes later in the privacy of my classroom.

 

Thirty years ago, I had a little sister. She was visibly different than the rest of our family, but we had grown up knowing that we are all family, the same. Youngest in the family for quite a while, a few years younger than me with a brother in-between. We played together, went to the same small-town school, and other than the occasional nickname of “my little Indian princess” from our loving, safe dad (not to be taken for granted), there was no real attempt to identify her as Cree.

(It’s weird that I feel nervous about posting her name here. I’ve been nervous about sharing her story at all, even though it’s now a part of my story. Maybe I’m just afraid of Google searches, old ex-boyfriends, the past.)

Over a decade ago, I found out that she had been violently, sexually abused by a boyfriend. I heard about it long after the fact; the man in question was no longer in the picture. Mixed thoughts of revenge, sadness, anger, helplessness, failure to protect my little sister fought within me, none of them ever really winning, just fighting over and over inside me with nothing left to say or do on the outside.

I asked her once if it was true, as I had heard it second-hand from someone in the family. She went really quiet, said yes. I don’t remember what I said; maybe a quiet, “I’m sorry,” maybe nothing. I didn’t know how to support her in that moment; I think I apologetically mumbled something about why I’d asked. I believed her, wanted to support her, and didn’t know how, didn’t ask.

 

It’s October 21 now. I can’t write this all down at once.

Seven years ago today, I was trying to get through a few more days of teaching before catching a flight to Manitoba for my sister’s funeral.

A week or so after that, I was speaking with an RCMP officer who had been trying to get a hold of me regarding my sister’s death. She needed to interview me before I flew back home; I had no idea why until I was in the back of her vehicle. The officer told me that my sister had mentioned me in text messages she sent to friends in the hour before she died. Those messages had claimed that I’d told her to kill herself, that I’d been texting her messages telling her to take her life.

The RCMP officer asked me why she would do this. I told her everything I knew; about her having been abused, about her reasons to be angry, about our strained relationship. That her family loved her and the world had been hard anyway. That I really just didn’t know.

Later, I heard that she told my parents I’d said that she deserved to be raped.

I still don’t understand. Did she really believe that? Did my silence or general not-knowing-what-to-do leave too much room for accusing voices in her head to fill in the blanks? She had been angry with me about a family argument the year before she died, but I’d had no clue about this.

My sister hated me when she took her own life.

 

Over the last few years I’ve learned about the Sixties Scoop. I now know that it’s very likely that my sister was taken from her original family without their consent, or under coercion. That there were thousands of Indigenous children taken from their families to be fostered or adopted into wealthier, whiter families. Indigenous people were considered to be savages and therefore unfit parents. When the residential schools began closing, efforts to separate children from their families turned to the child welfare system. The poverty Indigenous people were kept in, particularly on the reserves, was often used as a reason to take children into custody. The parents had no say and no recourse.

 

October 22, 2017

A few (four? five?) years ago, my wife and I were visiting Bowen Island and ended up in a long conversation with the owner of an Indigenous art gallery. Somehow, we got to talking about family, and why honoring Indigeneity is so important to me, and I explained about my sister who was now gone. The owner (an Indigenous man whose name and nation I unfortunately forget) suggested that maybe, despite everything, maybe she really was saved from something worse. That growing up on some of the reserves out there could’ve been horrible.

I listened, but didn’t really hear. I didn’t really understand until I heard Dallas share his story, his father’s story, how grateful he was to not have been raised by the man his father had become. Not taught those same ways of solving problems.

Something clicked. That it really was possible that my sister having been taken and put into our family may have been the lesser of two evils, that it could have been worse. That the damage done by residential schools was that bad.

 

But I’ll never actually know what she was removed from, whether there was real cause or just racist assumptions.

All I know is, we could have done so much better.

 

After the performance, after I recovered, one of my students stayed nearby to show me pictures of her cats, talk about her life, make sure I was doing okay. She let me know she’d be away from school a few days coming up because of leadership conferences, and an honoring ceremony, and after the honoring ceremony she might get a chance to make her own drum for the first time. She already knew this was important to who she is; she had songs she’d been given permissions to sing. She knew her role in singing them was as a spiritual healer. Did I know she’d been honored with an elder’s blanket once? Oh and she’d be giving the drum to her mother, who’s been looking forward to receiving a drum in the family for years, but who knew it was something you wait for, not something you purchase or make happen. And I’m listening and I’m so proud and those tears are coming back and dammit why now and I know exactly why and it’s not fair that she never had any of this. No Aboriginal support staff in her schools. No honoring ceremony to say, “You are a Cree woman and you are STRONG and your community is proud of who you are.”

My family loved her and honored her the best we knew how; but what did we know? We were white people living in a white world. We had God and we had morals and some financial stability. We had some truth to share, but we also had the same misconceptions as everyone around us, the same uncertainty about Indigenous spirituality that most Christians had. We had the same mistaken beliefs about the Indian Act, about reserves, about how the system worked. We had a goal of making sure she was treated the same, one of us – but we never knew to uphold and honor how she was different, how she *wasn’t* the same, and how that difference could be something to be proud of, part of her identity as a strong Indigenous woman.

 

Today I do my best to listen. I’m sure I still screw up; I still have another sister, who this story wasn’t about, who is also adopted and has Cree heritage, and we don’t always get along. Age gaps and my anxiety disorder and distance and I’m still a smug guy who thinks he’s got things so figured out, and I mess things up. But she’s an amazing woman and I’m proud of her.

 

I’m not writing this to find a moral, to convince you of anything. I’m not sure who I’m doing this for. I still don’t feel I have the right to tell the story of my sister who’s passed on; she died without trusting me. But hearing Dallas tell the story of his father made me realize that sometimes we have to tell a bit of someone else’s story so as to shine a light into the dark places of our own.

Our draft 10-12 BC math curriculum has a phrase that I’m going to verbally process here, as part of thinking through something for a workshop I’m in today.

What does it mean to assess if students can “Apply flexible strategies to solve problems”?

My initial assumption was to make this about recognizing multiple ways to solve a problem. But is that the best way to read this? Flexibility generally means being able to adapt to challenges or obstacles.

Sometimes, having multiple ways to solve something does enable one to switch to a second approach when the first one fails. But say a student is solving a system of linear equations. Does knowing how to graph a solution and knowing how to use substitution necessarily make their strategies flexible? What if they can use both methods but don’t particularly know why to choose one vs the other?

Or a different perspective: can’t a single strategy be flexible, if it encompasses ways to adapt to unusual challenges?

One example might be solving equations overall. Perhaps simply being able to solve an equation with a variety of algebraic “moves”, selecting them based on the particular situation, is a successful example of applying a flexible strategy.

Thoughts? Would love to hear both BC and non-BC teachers contribute what they think about this phrase.

So one of my major challenges this year is attempting to overhaul my Big Picture on assessment to include our “curricular competencies”. For those outside of this province, the cc’s are a sort of orthogonal set of skills we want students to demonstrate that are, for the most part, content-independent.

Here’s my summary version of what that might look like for PreCalc 11:

precalc11 mega learning chart

The phrases across the top row are my SBG-like summary of the course content. The phrases down the left side are my summarized take on the cc’s as they’re listed in our curriculum doc.

So what does this mean? Do we have to fill this entire grid? How am I going to have students demonstrate Reflection, Indigenous Experience or Multi-modal Representation on every single learning target??!?!?

Well, no. The grid is here for a few reasons:

  • To remind me that simply handing students a quiz might show algebra skill, but does it show conceptual understanding? Can they estimate reasonably with these concepts? Can they represent their ideas visually? etc.
  • To emphasize to students that those things on the left are REAL and they MATTER. That if students show they can be flexible with how they solve something, that’s a strength worth noting.
  • Because I stole the grid idea from Peter Liljedahl and it seemed like a good idea.

My current goal is to have every column get “checked off” at least twice to count as complete, and for every row to be hit at least once during the course. Nothing left out, and by showing more than one connection to the content, students are demonstrating some kind of mastery over it.

BIG FREAKING OPEN QUESTIONS:

  1. When students DO write a normal-looking SBG quiz (eg. focused on an algebraic skill), where would that even fall under this grid? “Reasoning and Logic”?
  2. Can some of the competencies on the left be demonstrated entirely without connecting to the course content? What if I have students work on a ‘numeracy’ task that uses earlier known content but in a way that stretches their communication and reasoning skills?
  3. How the heck do I store data for this? Right now I have a half-started Access database app that could store the info, and a spreadsheet that I’m just old-school-gradebook dropping checkmarks into for the time being. Do I need to store this entire grid? What if I just store the per-column and per-row summaries somehow?

Time to play blog-post catchup now that my summer server migration woes are finally mostly resolved!

This year I’m teaching full-time at an ‘Integrated Arts’ high school, covering Math classes from grades 10-12 as well as a Science 9 (later) and Photography 11 / 12.

I GET TO MAKE MATH ARTSY ANY TIME I WANT

*insert happy dance gif*

I’m going to try to make this semester a more frequently-blogging one. I’m diving headlong into the new BC math curriculum drafts, which means an increased focus on what the docs refer to as “competencies”. I’m restructuring my SBG approach around this, adding in ranked SBG goals as borrowed from Frank Noschese, teaching Foundations of Math 12 for the first time as a combined class with PreCalc 12 … uh yeah writing this all down reminds me *why* I’ve been a bit overwhelmed!

Fortunately, the students are great, the staff and admin are great, the view out my classroom window is great … yep things are pretty great.

Now, back to whatever else I need to get prepped next! Check back later for more!

Those of us who care about math education and making it more engaging generally have strong opinions about “math drills” and the over-emphasis on standard algorithms (ie. doing pencil-and-paper arithmetic the way that one’s parents were taught to.) The progressive view is generally that while students *do* need to learn basic facts, they should also build understanding of what those facts mean so that they can tell where and when to apply them. They should be able to work with the ideas of arithmetic and algebra through multiple representations, and alternate algorithms are great.

(If you want to debate that view, that’s fine, but maybe not here right now. There’s a bigger point coming.)

So in that context, here’s the thought I had that struck an odd chord with me:

Drilling standard algorithms used to be the right answer.

I don’t know if the weight of that statement really hits by just reading it here, so let me unpack a bit.

When something new comes out, it changes how we perceive the previous tools. A classic example is how photography forever changed the role and perception of painting. Before photography, a painting or drawing was the only way to create an accurate, persistent image of someone or something. Post-photography, the role of the traditional visual arts in society had to be re-examined and a new form of art emerged.

But while most of us have at least a pop-culture awareness of “modern” art’s experimentalism, what we usually don’t think about is how our view of the pre-photography era has shifted as well. For centuries, painting was valued as a way to (re)produce images from life. If a painter had used tools such as lenses, measuring devices, and mirrors to produce the image realistically, this would have been seen as simply part of the trade and a valuable skill. Nowadays because the actual production of realistic images is trivial, we have instead romanticized the ability to produce beautiful images out of paint and hand-skill alone. Most people would assume that using light tables to trace, lenses to project or Photoshop to digitally paint over a photograph is somehow cheating. This can be evidenced even in the larger art world by the reaction of many art historians to David Hockney’s Secret Knowledge, a book detailing his theory that the shift to photo-like realism in the 1400-1500s and beyond was likely because of improvements in optics that artists could use to project images onto a canvas as a guide. Many of the historians view this as slanderous to the great artists of old, rather than a tribute to their ingenuity.

For 20th century math, the calculator and the computer were to pencil-and-paper mathematics what photography was to painting.

It is incredibly hard to look back at the past through the lens of the present without projecting the present backwards.

In my case, I “knew” that pencil-and-paper used to be the only option for doing math before the calculator. But this wasn’t enough for my imagination to really picture how different the workplace would’ve looked for those dealing in numbers.

The first time something went ‘click’ in my head to upgrade this was an old photo someone had shared online (which I wish I could find again!) of a business analyst’s office from I think the early 1970’s. The entire room was covered with hand-drawn charts. COVERED. Every wall. And we’re talking hand-drawn line graphs where sometimes they had to add an extra bit of paper at the bottom when things went out of the original scale.

Something clicked then – this was all they had. You had to learn how to draw graphs by hand because that was the only way you would have a graph. There was no Excel. The enormity of what this meant for the workplace, not just the math classroom, started to sink in. This wasn’t just an exercise, nor was it paperwork filed away. This was vital business analysis required to understand the direction of the company, and it was done in meticulous hand-drawn, possibly hand-calculated ink.

There were other moments like this – a scene from Apollo 13 where NASA engineers confirm a calculation by having three of them quickly scrawl on paper and then give successive thumbs up; teaching Accounting briefly and learning about the history of bookkeeping and how, yes, it was actual books and here’s how they were organized.

Workplaces used to need people who could not only do hand-calculations, but could do them in a recognizable, standardized way. And anyone working with numbers – anyone dealing with money, measurements, analysis – would be significantly slowed down in their day-to-day work if they couldn’t do those calculations quickly. Speed wasn’t the key to understanding, ever, but it may have been the key to getting the job done by a reasonable hour and going home.

In this light, of course students were being taught to do their math quickly! It was a job skill. Knowing your multiplication tables well may have been the difference between opportunities in ‘knowledge work’ industries such as accounting, engineering, and sciences or having those doors closed, not because math streaming closed those doors but because you wouldn’t get the job without it, even if you did understand the concepts.

I don’t really know this. I mean, by the time I was in the workforce I was already working with PCs and doing store inventory in a database. I don’t know first-hand what the everyday experience of pre-digital workplace mathematics was like. I turned forty this year. I’m not the oldest math teacher around, nor am I the youngest. But I feel like there’s a perspective on why things used to be done they way they were done that’s about to be lost as our most senior teachers retire right now. Even someone sixty-five today would’ve seen pocket calculators begin hitting the market at about the same time as they entered the workforce.

I feel like math education is barely settling into how to adjust to calculators, and still awfully wobbly on how to adjust to computers. I don’t mean that as a criticism, just an observation. This entire complex system of society, technology, curriculum, and classroom simply seems to have a slow and messy feedback cycle. But I wonder if it gets even harder once everyone who understood the context for the old decisions are around to help us evaluate whether they’re right anymore.

 

I needed to write up a statement of my teaching philosophy for a job application I’m submitting shortly, and it just seemed like the sort of thing worth sharing. So here you go. Constructive comments welcome.

 

My teaching philosophy centers on my core values. I highly value practicing compassion and empathy for students; I value digging deep into the joy of learning something new and mind-expanding; and I believe in making learning as fun as possible.

Compassion and empathy can easily be mistaken as running counter to “rigor” or serious learning. However I see them as being central to creating a learning environment where everyone can feel safe enough to dive heavily into seriously challenging skills and ideas. This is pretty easy to do with students who you feel a connection with because of common interests, backgrounds, etc, but to make a classroom safe for all students can often mean deliberate, soul-searching work. I believe this really deeply matters to the lives of students, and to the future of our STEM professions which we want to see diversify.

I really enjoy the challenge of learning, and I love seeing students experience that same sense of mastery when they understand something that used to be incomprehensible. I’m also awfully stubborn about assessing students in ways that demonstrate deep understanding rather than shallow recall. I’ll check for small details here and there, but I would much rather see that students can be handed the sorts of information they could’ve looked up online anyway and see them work out something challenging with it.

I also believe that all of the above can create a fun atmosphere to learn in. Difficult challenges in a safe environment are a foundation for engaging gameplay, and I believe a classroom can be this best kind of game. It’s not easy, but I’ve seen glimpses of it and I want to see more of it in my teaching career. This has to be deeply challenging stuff, and it has to be safe enough that failure isn’t a game-breaker. (For more on this, you can read this blog post of mine from a few years ago.)

Here are some examples of how I’ve worked towards this in practice.

My usual classroom assessment practice has quickly settled on using “standards-based grading”, something that’s been slowly growing in usage in math education circles via blogging and Twitter networking. SBG is based on the idea of tracking ideas/skills assessed, rather than tracking individual assessments. It takes a bit more planning up-front but allows for much easier reassessment along the way and helps move assessment more towards being a measurement of learning rather than a collection of abstract points.

I spent one year developing and running a digital media program for Abbotsford Middle School which I focused mostly on Scratch-based narrative, art and game development. This was an incredibly valuable time for me as I got to see first-hand the value of wide-open, inclusive access to computing education – and it was FUN! Students from diverse backgrounds, ability levels and of both genders regularly surprised me with their accomplishments and enthusiasm. (For more detail on how I approached the program, here’s another blog post.)

Another goal I have strived for in my teaching is to emphasize active learning in the classroom instead of passive listening. I have worked with low-tech “clickers” for in-class polling, random-group standing whiteboard work for exploring new mathematics, and whole-class assessments that drive students to collaboration and discussion. While I am very capable at explaining ideas on a whiteboard, I believe that students who are actively processing new ideas in the classroom are more engaged with the learning itself, are more likely to form a healthy learning community, and will walk away with more self-efficacy than if they simply hear me explain things in a clever way.

For more examples of my thoughts on teaching, as well as a cross-section of some of my other interests, I encourage you to browse around my past and current blogs:

http://joshg.wordpress.com

http://thoughtlost.org/

 

thank you,

– josh giesbrecht

I need to recap earlier chapters, but I’m currently reading the chapter on Advanced Actions and this bit just grabbed me in that “just blog this immediately” sort of way.

12.10. Action variables

And we will want the photographing action to have the player use the best-quality camera which comes to hand. We will give the action a variable called the ‘camera photographed with’, thus:

The photographing action has an object called the camera photographed with.

Every action’s variables must be named differently from those of all other actions, because there are some “before” rules (for instance) which take effect for many different actions, and which might need access to any of their variables. So action variables should be named in a way marking out to which action they belong. The best way to do this is to include the past participle of the action name – just as “camera photographed with” contains the past participle “photographed” of the action “photographing”.

A stuffy OOP programmer could look down his nose at this – why, you’re asking me to simply name global variables with an identifier???!?! What about encapsulation?!!!

And yet, the solution results in totally reasonable, fully comprehensible English. After all, language isn’t encapsulated. Oh, sure, there are some things we understand best within a particular context, or meanings that change depending on context. But nothing’s stopping me from referring to calipers while in a kitchen. The English language has no mechanism for programming’s encapsulation, and yet somehow we get by.