Plane thoughts – part 1

I recently participated in a meeting for the EdCan Network, part of the Canadian Education Association, in Mississauga. I knew we’d be talking about some heavy issues regarding education in Ontario, especially K-12 education. I spent my time on the flights down and back writing some thoughts I’d been wrestling with. I’m planning to share those thoughts in small posts for a little while. Here’s the first entry.

Learning is not about acquiring knowledge and skills. You’re learning whenever something is changing you. It can be intentional, accidental, or incidental.

Learning can be good, bad, or neutral. Learning to be accepting of others is usually good. Learning to abuse power is generally bad. Learning to factor quadratic expressions is probably neutral.

Learning doesn’t have to be permanent, although it’s not fleeting (because then it hasn’t changed you). Skills can fade, knowledge can be forgotten, and new understandings can supplant old ideas.

If school education is only about the narrow, curriculum-knowledge-and-skills learning, it’s missing the richest and most valuable kind of learning.

Improving the evaluation of learning in a project-based class

I’ve been struggling for a few years with providing rich, authentic tasks for my computer science students and then having to evaluate their work.

My students learn a lot of skills quickly when solving problems they’re interested in solving. That’s wonderful.

I can’t conceive of a problem they will all be interested in solving. That’s frustrating.

In the past, I have assigned a specific task to my entire CS class. I tried to design a problem that I felt would be compelling, and that my students would readily engage with and overcome. The point has always been to develop broadly-applicable skills, good code hygiene, and deep conceptual understanding of software design. The point is not to write the next great 2D platformer nor the most complete scatterplot-generating utility.

Unfortunately, I could never quite get it right. It’s not because my tasks were inherently weak; rather it’s that my students were inherently different from one another. They don’t all like the same things.

I believe that students sometimes need to do things that are good for them but that they don’t like to do. They sometimes need the Brussels sprouts of learning until they acquire the taste for it. But if they can get the same value from the kohlrabi of learning and enjoy it, why wouldn’t we allow for that instead?

So I’ve tried giving a pretty broad guideline and asking students to decide what they want to write. They choose and they complete a lot of great learning along the way. Their code for some methods is surprisingly intricate, which is wonderful to see. They encounter problems while pursuing a goal that captures them, and they overcome those problems by learning.

Sounds good, eh?

Of course, they don’t perform independently: they learn from each other, from experts on the Internet, and from me. They get all kinds of help to accomplish their goals, as you would expect of anyone learning a new skill. And then I evaluate their learning on a 101-point scale based on a product that is an amalgam of resources, support, and learning.

Seems a bit unfair and inaccurate.

I asked for suggestions from some other teachers about how to make this work better:

  • ask students to help design the evaluation protocols
  • use learning goals and success criteria to develop levels instead of percentage grades
  • determine the goals for the task and then have students explain how they have demonstrated each expectation
  • determine the goals for the task and then have students design the task based on the expectations
  • find out each student’s personal goals for learning and then determine the criteria for the task individually based on each student’s goals

I’m not sure what to do moving forward, and I’d like some more feedback from the community.

Thanks, everyone!

Student research I want to read

My Grade 12 Data Management students complete a research project as part of the course. They create a questionnaire to help answer a question they’re interested in, or to look for relationships that bear further study.

While working with one student today to help develop that question, we talked about how she started to take guitar lessons but didn’t stick with it. She said that she regretted stopping the lessons, but that a part-time job and her own laziness got in the way. She expected that she would have been quite skilled by now had she put in the time over the past year.

I asked if she thought that experience was common, and how the music school offering the lessons might have made it easier for her to stay with it. She figured that a lot of people start lessons but don’t continue, and she had some suggestions for improvement that seemed reasonable as well.

Wouldn’t it be nice to know what the most common reasons are for quitting music lessons (and for sticking with lessons), and if there is a correlation between some other variable and perseverance? For example, do students without jobs stick with music lessons longer? What other factors play into persistence?

She might pursue this area of research for her project. I hope she does. I want to know the conclusions she draws from it, because it might have an impact on the way I teach math and computer science.

Which kind of calculator promotes good algebraic thinking?

I teach high school math. Students bring scientific calculators to class, or they sometimes have to borrow one from me. I have two types available: immediate execution calculators and formula calculators. I’ve been wondering lately whether one type of calculator is better for learning algebra than the other.

Here’s how they work (see Wikipedia for a longer explanation:

Immediate Execution

The TI-36X Solar 2004 version immediate execution calculator.

These calculators work by performing calculations along the way as you type in values and operations. For example, you can evaluate the expression

\sin(3 \times 45)

by typing 3, multiply, 45, then the sine key. As you press operations and operands the calculator will evaluate what it can according to the rules of order of operations, or BEDMAS. For binary operands (those taking two values to produce a result, like multiplication), you put the values in order. For unary operations (those taking just one value, like squaring or taking a sine), the value must be present on the calculator screen when you press the operator key. These calculators usually have a bracketing feature to allow the user to work through complex expressions without using memory storage.


The Sharp EL-510R formula calculator.

These calculators work by waiting until the user has typed in a complete expression to evaluate, then evaluating the entire expression. The order of button-pushing is pretty much as the symbols are written in the expression, making them easier to use for a lot of folks. Once a value is calculated, it’s stored in an “answer” variable in case it’s needed for the next evaluation.

Algebraic Expressions and BEDMAS

When we write out algebraic expressions, we have a number of conventions to follow. The most important convention is order of operations, which people usually learn to remember with the mnemonic BEDMAS or PEDMAS:

  • Brackets (Parentheses)
  • Exponents
  • Division and Multiplication
  • Addition and Subtraction

When evaluating (simplifying) an expression, you first simplify the smaller expressions inside brackets. Then you evaluate exponents, then division and multiplication in the order they appear, and finally addition and subtraction in the order they appear. It’s useful to think of brackets as isolating sub-expressions, which then follow the same rules. It’s also useful to think of this order as the “strength” of the operation: multiplication is a stronger operation than addition, so it holds its operands more tightly together, and it gets evaluated first.

When a student is learning order of operations, it often feels like a set of arcane rules. There is no reason, from the student perspective, that it has to be this way. In fact, it didn’t really need to be this way, but the convention was established and now it’s important to abide by it (if you want to be understood, that is).

How a calculator helps (and hinders) learning arithmetic

People often lament that today’s youth can’t perform basic arithmetic in their head. It’s unfortunately true; I often see students reach for their calculator to evaluate 35 \div 5 or even 4 \times 6 . These are facts which prior generations had drilled relentlessly and now have available as “instant” knowledge. Younger people typically haven’t spent enough time practising these computations to develop facility with them. This is partly because the calculator is so readily available.

(Aside for parents: If you have kids, please do make them practise their age-appropriate facts. It’ll help them in the same way practising reading makes things easier)

This will draw a lot of heat, I’m sure, but I think calculators do have a strong place in even K-6 learning. They let students explore quickly without the burden of computation getting in the way of non-computational learning. It’s the same effect that web-based, dynamic geometry software can have on learning relationships between figures, lines, etc. (if you’re looking for awesome dynamic geometry software, try GeoGebra – free and wonderful).

But calculators are a hindrance when students are learning to compute fluently. They allow a student to bypass some of the thinking part of the exercise. Don’t let students (or your kids) use a calculator when they don’t have to. Only use them when students need the speed for the task they’re completing.

How a calculator helps (and hinders) learning algebra (?)

Here’s the part I don’t know about, but I’m speculating about.

I think immediate execution calculators require students to understand the algebraic expressions we write, where formula calculators bypass the thinking part of evaluating expressions.

As with arithmetic, if practising evaluating expressions is not part of the learning, and might be getting in the way of the goals for learning, then either type of calculator is fine.

But as students are developing their understanding of algebra and the order of operations, the immediate execution calculator displays the results of operations as they are evaluated, while the formula calculator obscures the evaluations in favour of a single result.

When a student types 5, add, 6, square, equals into an immediate execution calculator, they see the value 36 as soon as they press the square button. There is a reminder that the square operation is immediate. Similarly when a student wants to evaluate \sin(30+45) they must type 30, add, 45, equals*, then sine, emphasizing that the bracketed portion has to be evaluated first (i.e. before the sine function is applied).

*A student can use brackets, which is equivalent to pressing equals before sine. Also, I hope anyone using the sine function knows that 30+45 is 75 and doesn’t need a calculator’s help for the addition.

Is there research?

I perused the InterTubes to find research into this question, but either it’s not out there or I’m not skilled enough to find it.

I want to know whether one calculator is better than the other for a student who is learning to evaluate expressions.

Has no one looked into this? Help?

How To Become An EdTech Leader

by Noël Zia Lee at, CC-BY 2.0 licence.

by Noël Zia Lee at, CC-BY 2.0 licence.

I hosted a session at On The Rise this year. I’ve posted my slides as a PDF, but I knew from the start that a 60-minute session would be too short for the topic. Here is the previously-mentioned, obscenely long, supplementary blog post.


Being a leader in educational technology does not mean becoming technically skilled. It doesn’t mean you can write code, recover crashed hard drives, or configure a router. You don’t even have to know what those phrases mean.

Being an EdTech leader means that you have relationships with others, and that you share with them using technology.


In order to lead effectively, you need some goals. Here are a few generic examples of goal types:

  • Develop skills and knowledge to improve yourself and your work
  • Develop skills and knowledge in your team
  • Foster collaboration in your team
  • Give to the larger community (beyond your team)
  • Develop personal and professional relationships
  • Share resources

For example, you might have a goal of learning how to use audio recordings for assessment as learning in a language class. You might have a goal of connecting your teachers to teachers in other school boards. You might want to develop closer professional relationships within your department. You might want to collect and curate resources to support newer teachers.

All of these are great goals, but make sure you follow one simple rule:

Have goals for yourself and goals for others

One or the other type isn’t enough if you’re trying to consciously lead. If you only have goals for yourself, you have no reason to share and support others. If you only have goals for others, you’re just trying to “improve” them without being honest about your own needs. Have both.

Kinds of Communities

There are a lot of ways to categorize communities, but the “publicness” of a community is fundamental.

Public vs. Private

This is really a continuum.

At one extreme end of the continuum we have completely public communities, which anyone can observe and in which anyone can participate. For example, Twitter is generally* publicly and globally available. What you say there is readable by anyone, even those who don’t have user accounts with the service.

(*I’m not going to put asterisks all through this post, but be aware most of these statements can be modified by user settings. For example, on Twitter you can protect your tweets so that only approved users can read them.)

At the other extremity we have completely private communities, which are only visible to the “invited” few. For example, you may have a Facebook group that only approved participants can join. The rest of the world isn’t allowed inside.

What’s best depends on who wants to participate, what their level of comfort is, and what everyone’s talking about.

You might have a private community when you need to talk about something sensitive or confidential, or when the participants are worried about making very public mistakes (particularly if this sort of community is new to them). You might protect the conversation when you need to prevent self-censorship in order to have honest dialogue.

You might have a public community when your local community (e.g. the people you work with) is a small one, and you want outside voices. It’s good to be public with universal issues, like assessment or writing.

You might partially protect the conversation by making it “read-only” to the uninvited. For example, perhaps you share the work you’re doing with your department members on a departmental blog/wiki/etc. The rest of the world can view your resources, but only your department members can update the work or comment on it.

Constructed vs. Organic

Some communities are organized and constructed. For example, you might set up a discussion group about instructional strategies, or you might create a sharing folder for rubrics. The purposes of those communities or activities are clear, and so they’re constructed.

Instead you might just set up a space for conversation to happen. Twitter is my favourite place for this. The topic isn’t defined in advance, so we can talk about anything we want to. The connectedness of the participants is what matters, not the quality of the prompt. Organic communities tend to be participant-directed and very welcoming of tangential thinking.

Halfway between these is the ConstrOrganic community (yes, I just made that up. I’m sure it’ll catch on). This is a community of people which doesn’t have a tight restriction on the conversation, but does sometimes provide prompts. For example, you might ask an open-ended or reflective question on Twitter: “How does your experience with technology in your personal life affect your use of technology in the classroom?” The question itself is posed in an otherwise organic community, but you can try to mould the conversation for a while. In my experience we don’t stay “on-topic” for very long, but that’s fine: the talk goes where it needs to, not where I aim it.

Required vs. Optional

This is one of the hardest to deal with, and it very much depends on (a) who you are, (b) what your role is in your organization, (c) who you are leading or hoping to lead, and (d) what your goals are for the people you lead.

If you’re a principal of a school and you want all the teachers you work with to reflect on their assessment practices in an online space, you might be considering requiring a writing activity in a private, online space. When you imagine how that will play out, you might be concerned that some folks might not participate, or that the participation might not be as deep and reflective as you want.

Rule of thumb: don’t require participation (at least at the beginning) if it’s not anonymous (and therefore safe). People need to trust you in order to follow you. If you don’t already have the level of trust that makes an optional task work well, then you don’t have the level of trust that makes a required task work well with names attached. By removing the names, you’ll remove a good portion of the (legitimate) fear associated with putting thoughts out there.

For example, you can create a shared online document (like a Google Doc) and make it editable to anyone who has the link. Participants can modify the document without identifying themselves, which makes it a lot more likely to be honest and complete.

Instant? Persistent?

Your interactions within your community can be synchronous (instant), like a tweet, or asynchronous, like a blog post and a comment. This is often a tradeoff between speed (synchronous) and depth (asynchronous).

Online conversations are usually persistent (they stay there forever), but they may not be easy to return to or make quick sense of later. Sometimes conversations are temporary, like a back-and-forth on or a Google Hangout.

I wonder if having persistent, asynchronous conversations creates a thoughtful-but-cautious environment, possibly erecting a barrier or self-censorship. Is it true that instant, casual, organic conversations are more honest and allow for experimental thinking?

Email is not an effective community

It could be, I suppose, but don’t just do this. Mass email isn’t personal, interactive, or persistent (for most people), which can be good things to have. It’s typically one-way communication, and you can’t really opt-in or opt out. Other types of services will work better for you.

Possible Roles

In your participation in any community in which work is being done, you usually take on one of four roles. You’ll move between them freely and frequently once you’re a solid member of a functional community.


I have a question or problem, and I’m looking for an answer or solution.

For example, I post to Twitter, “Anyone have a good summative task for the quadratics section in MCF3M?” That’s a specific quest, and I’m the Quester. Anyone else in the community can answer, and anyone else can benefit from the answer.


I am trying something new, and I’m going to share my journey.

For example, I decided to try some physical demonstrations in my classroom for quadratic motion. I wrote a blog post explaining what I had come up with, shared some video from class, and reflected on how effective it was. I wasn’t an expert, but I shared what I found out (even if it turned out to be wrong).


I am learning something new from you, and I may ask questions.

This is great when there is a source of wisdom you can tap into. For example, I can read all about how to use Screencast-o-matic to improve an e-Learning course by watching someone’s videos or reading their tutorials. If there is something I don’t understand, I can ask questions. The answers help me, and both the answers and the questions help others (including that expert).


I have some special skills or knowledge, and I’ll demonstrate or share.

For example, I post instructional videos about how to program a computer using the Java programming language. I’m sharing some niche knowledge that I have, and I invite conversation and questions about it. I’m not looking for anything specific, but that knowledge does very little good bottled up in my own skull.

Choosing a Platform

There are three major considerations:

  1. Does the platform have the level of privacy that I want or need? This is a dealbreaker if it doesn’t. Also consider the granularity of privacy settings, because you might want to “reduce” them later (e.g. become somewhat more public).
  2. Does the platform have the functions I want or need? Think about formats, ease of use, technical support, exportability (if I leave, can I bring my stuff with me?), and cost.
  3. Will/does the community use the platform? If a platform is popular, the community might already exist or be easier to create. No one wants another password to remember.

Some possibilities

Lots of platforms serve multiple purposes. YouTube is for video, but it includes commenting. WordPress is for blogging, but it can serve as a fully functional website. Facebook is a social network, but it has private community pages. Here are a few loose categories and some popular services:

  • Blogging (WordPress, Blogger, Medium)
  • Video or Vlogging (YouTube)
  • Social Networking (Twitter, Google Plus, Facebook)
  • Curating (Pinterest,

Some Challenges and Cautions

Here are some other considerations when you’re adventuring online.

Be careful what you say

Think about maintaining loyalty to your employer, respecting copyright and other licences, and protecting student identity and information. There are some things that you simply can’t say in public.

Who’s listening?

You might draw unwanted attention, even if what you say is “allowed” and isn’t “wrong”. For example, what will you do if a parent has a concern about the conversation between two teachers revealing a lack of professional understanding? Also consider students, other schools, and community members.

What is privacy, really?

When you post something in a private or protected space, you’re trusting the other people in that space to maintain the privacy of your thoughts. Before you post something, consider what might happen if it were “leaked”.

Will this be personal, professional, both?

Each has advantages and disadvantages. Your decision will depend on your goals. Here are some of my thoughts on the matter from a while ago:

No takers?

What if your team doesn’t follow you? What if they want to do something else? What if your team is already doing something different? What if your team is afraid?

You’ll have to work through the reasons for your particular situation, and talk with your team. There might be nothing you can do, except for continuing to share and model good practice.

What if my preferred platform is filtered by my organization?

Is there a good reason for the filtering? Are the people who make those decisions aware of what you’re trying to accomplish? Are they supportive? Have you talked with them about it (really talked, not just made a request by email)?

Sometimes the decision makers have parameters that you’re unaware of, and sometimes you have insight they are unaware of. Talk to each other. In the best situations, neither party thinks they have all the answers.

Final thoughts

At On The Rise: K-12 in 2014 Catherine Montreuil (then of Bruce-Grey Catholic DSB) said, “Private practice is inconsistent with professional practice.”

Being connected makes someone a leader, and being open and transparent are the best ways to get connected. You don’t need to be expert, articulate, or tech-savvy.

You just need to be willing to share.


What would you do with a day to improve your teaching?

Andrew Campbell asked tonight on Twitter:

I answered a couple of times.

Then I had a related thought:

If I want to improve my teaching, I can work on something myself or I can learn from others (or both).

What would I want to learn?

A full day… 8 hours… no restrictions, no prescriptions, no requirements, no accountability, no strings… just work to improve my teaching….

It was harder than I expected, until I had the defining thought:

What do my students need me to be better at?

So instantly I landed on Assessment. That’s my area for improvement, and that’s what I would spend my day on.

The Plan

  • Before that day, decide on a specific focus (for me, probably assessment as learning, including peer assessment and self-reflection) and gather some short articles from trusted, external sources.
  • Start the day reading those articles, and writing a short, reflective blog post. The post is to share my learning and hopefully get some helpful feedback from my PLN.
  • Apply my prior knowledge and my new learning to a specific task that I’m planning for my class. If there is time, plan multiple learning opportunities using different strategies.
  • Share those tasks with my PLN and solicit more feedback.
  • Reflect, modify, reshare, etc.

Let’s be realistic – I ran out of time already, and I’ll be finishing at night.

This would be good PD

It would be wonderful to spend a day like this, although I don’t want to miss my class or my family, so it would be a really expensive day in that sense. It might be worth it, though.

What would you do?

Check out Andrew’s response (clever fella):

Improving report card comments with a checklist

It’s report card season in Ontario, and I don’t know too many people who are happy about it.

I don’t love evaluating student performance in general, and the persistent and poisonous focus on MARKS by most stakeholders in student learning is infuriating. Marks are a huge loss of information about student performance, in my rarely-humble opinion. Along with those percentage marks we have a much-less-valued-but-more-valuable evaluation of Learning Skills. My students mostly ignored those, I think.

In truth, the hero of the report card is The Mighty Comment. It has the superpowers of Explanation and Recommendation. It’s here that I can talk about what’s going on, why, and how to improve.

After all, assessment is for improving learning. Reporting a mark of 68% doesn’t do that.

So The Mighty Comment is our hope for the future, the only power that can save our students and their parents from receiving an all-but-useless document.

Let’s do it right.

I’m teaching in a high school, and we have both a provided comment bank and the latitude to write our own comments. The only rules are that we need to follow the guidelines in Growing Success and we have to keep it under 458 characters.

I read an interesting article at called The Unreasonable Effectiveness of Checklists.

Fireworks blazed across my brain. I need a checklist to make sure I’m doing what I want to do with every comment.

So I made one

The Report Card Comment Checklist (catchy name, eh?) is now live. I also included The Verbose Report Card Comment Checklist immediately after it to help explain what I mean. Please leave comments here on the blog if you can help me to improve it.

I sat with each of my students this term to review their marks, learning skills, and comments before I submitted them to my school admin team. I wanted them to know that I tried to write what I thought and that I cared about their improvement. I articulated their strengths and what I need them to do next. I asked them each to reflect on their comment (most of them needed to be prompted) and to tell me whether they thought it was fair, accurate, etc. One student found a typo (yay!) and two asked me to clarify what I meant. About five students said their comments sounded exactly like them, which makes me proud.

I have to admit that I made the checklist this evening; I may have to edit my comments a bit next week before they’re published.

You should just click the link for the complete version, but here it is anyway:

The Report Card Comment Checklist

Check each student’s report card comment and ask yourself these questions:


  • does it include at least one strength?
  • are the strengths related to the course?
  • are the strengths worded positively?
  • do the strengths stand alone?

Next Steps

  • does it include at least one next step?
  • are the next steps related to improvement in the course?
  • if a student reads the next steps, will they know what to do to improve?
  • are the next steps worded positively?
  • do the next steps stand alone?

Language and Tone

  • did I check for spelling, grammar, etc.?
  • did I read it out loud?
  • did I listen for sarcasm and negative feeling in my voice?

The Point

  • will the student feel that I care about their success?
  • will the student “see themselves” in the comment?
  • will the student want to continue to improve?
  • will the parent understand how to help their child improve?