# Plane thoughts – part 4

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 fourth entry, which is based on some other peoples’ thinking that I had a chance to hear.

Today’s schooling seems to focus on two types of problems.

First, it tries to address the problems of tomorrow. Prepare for your career. Set goals. You may need this someday.

Second, it tries to deal with some problems that are immediate and accessible. There are social injustices, environmental problems, health concerns. These are issues that students can discuss, appreciate, and have an impact upon. I know of some teachers who work with their students on these meaningful todaythings instead of just possible tomorrowthings.

However, we shouldn’t forget that relevant learning does not only include long-term skill development and problems in the community. But we typically value those problems as “significant” when comparing them to other activities, like developing your identity, expressing your feelings, appreciating culture, and exploring history.

We need to be careful not to overvalue social, environmental, and political change in such a way that it diminishes the other kinds of change that can be meaningful to individuals. We can’t judge the importance of one kind of learning for everyone when its value is necessarily individual. We can’t determine the impact these learnings may have on our children and on our future society.

This kind of learning is less specific but more fundamental.

# Plane thoughts – part 3

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 third entry.

School is not the only organization educating a child. The broader community shares that responsibility and provides opportunities that a school can’t. There is sometimes a lack of connection between a school and the surrounding community, though. There are programs to help bridge the divide, but it’s usually not an integral part of the school system in Ontario.

If a school or community wants to nurture a child but lacks some expertise, it must look beyond its borders for an extended family to draw upon. Today there is a global community available to support our local context with opportunities and expertise.

Regardless of the source of the expertise, there is a critical failure if the “expert” is incorrect. The consensus of expert opinion is required to determine which ideas, skills, and understandings are valuable and which are incomplete, flawed, or even dangerously wrong. The internet is not always good at helping us to determine the consensus, and the skills of critical thinking are the most important to ensuring our learning is accurate.

# Plane thoughts – part 2

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 second entry.

Our curriculum is a Least Common Multiple curriculum. Consider all of the different factors that are components of the complete educations for each child. Our exhaustive curriculum tries to include all of those factors in every child’s education. This is unnecessary and inefficient, and frustrating for the students. This is the Just-In-Case curriculum.

We need a Greatest Common Divisor curriculum. We should identify the factors that are in common between every child’s educational needs and include only those in the compulsory curriculum. This minimalist approach would leave room for children to explore and specialize without wasting their time on irrelevancies. This is the Just-In-Time curriculum.

Consider how schools would be different with narrow curricula and expansive opportunities. A small core and room to explore.

# 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!

# Some advice I give my students

I teach high school. I say these things to almost every class.

“Don’t trick yourself into thinking you understand something you don’t.”

“Write it down.”

“Be gentle with each other.”

“You won’t look back in ten years and wish you had been meaner in high school. No matter how nice you think you are now, when you’re older you’ll see it differently. So be kinder than you think you should be now.”

“Let people like what they like. If they’re not hurting anyone it’s fine. I don’t need you to like the music I listen to, but I do need you to let me like it.”

“Everything is fascinating if you’re curious.”

# Sloppy notation doesn’t seem to be reducing understanding of solving linear systems

A couple of weeks ago I wondered here:

Is sloppy notation for solving linear systems reducing understanding?

The TL;DR is “no, not really”. There are other problems besides notation.

Using subscripts to denote a specific point isn’t something Grade 10 students seem super-familiar with, in spite of their supposed experience with the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

More than three quarters of my students simply neglected to use those subscripts when solving systems. They wrote solutions without following the model I presented to them in class.

The ones who did use the notation had a stronger understanding of the concepts/strategy on average. I don’t believe the use of good notation was the cause of that improved understanding; rather, students who understood the concepts were more likely to use the [more complex] notation I presented.

There were two main barriers to understanding in this unit.

First, students do not connect the graphical and algebraic representations of lines. If presented with an equation like

$y=3x+5$

most students can tell me the slope and the y-intercept. But until I ask for those parameters, or until they actually graph the line, they typically don’t visualize that line at all – it’s just a bunch of symbols.

This lack of crossover between representations means that students are not making sense of their own work and judging the reasonableness of their solutions.

Second, students are neither skilled nor fluent with solving linear equations. They do not always remember the inverse operations, and they rely on phrases and tricks to complete these processes. They have trouble because phrases like “move it to the other side and make it negative” doesn’t work well for multiplication and division, and they forget to apply an operation to each term in an equation.

It’s kind of the same problem as the first. There is a feeling of flailing about in the classroom, of trying to apply poorly understood or misunderstood rules to a fairly complex process without even being able to confidently test whether the result is correct.

So notation isn’t the issue. If you have kids in grades 8 or 9, make sure they can solve equations quickly and accurately, including those with fractions. If you have kids in grade 9 make sure they practice graphing lines and determining equations based on graphs. They’ll be in much better shape when learning the more complex techniques in Grade 10.