Ask Marian

Should we teach imperial measurements in earlier grades?

Transcript

I heard from a teacher in Alberta recently, and the reason I mention it is because Alberta has just changed their curriculum, and they’ve decided to introduce what we call “imperial units”—or “US measurement units” or “customary units” (they’re called by a lot of different names)—early. For example, I think in Alberta it’s in Grade 3. So, children in Grade 3 in Alberta are learning about inches and feet and miles and all those kinds of things, as well as the metric units that we teach with metres and centimetres, and so on. And this person just asked me what I thought of that. Is that a good idea that they introduced this early?

You should be aware that in most Canadian provinces, the US units don’t come up until quite late—often it’s high school—and we work simply in metric before that. So, she just wondered what I thought about this. And it was an interesting question. Partly it’s interesting because I’m also working in the US, and those children are introduced to both metric and their own units very early on, kind of like what Alberta is doing. So, obviously, there is no “this is right and this is wrong.” You just have to think about the advantages and disadvantages of each. Each will have both, and it’s a balancing act, where you believe there are more advantages or fewer advantages that help you make a decision, for example, in another province.

So, one of the reasons that we would introduce these other units early is because kids are surrounded by them. So, if you’re in the US, you’re obviously surrounded by inches, so you might wonder, “Why do they teach them about centimetres then?” But maybe they hear about centimetres sometimes or hear about litres sometimes, and they want students to know what’s going on.

The people who choose to wait are probably choosing to wait because they want kids to get really comfortable with one system before they throw another system at them. So, there’s an argument both ways. There’s not a clear answer. I would say, though, that if you are introducing two systems early, the metric system and the US system for measurements, you want to be cautious not to do what I’m going to call “formal conversions” of numbers from this unit to this unit, so, going from inches here to centimetres here or that sort of thing. You just want kids to have a general sense of the size of these units and where you might use them.

So, you could know that a yard and a metre are sort of close, or you could just know a yard is fairly long but still fits in your room. A metre is fairly long, but it still fits in your room. So, you want kids to have those general ideas, but you probably—certainly with the younger kids—don’t want to do what I’m going to call “formal conversions.”

Would you, or how would you, assess the processes or practice standards?

I think it is our obligation to assess the processes or practice standards, both because they are a real part of the curriculum, and, even more so, because they help students. When we assess these processes or practices, we not only signal to students to pay attention to them, but we also gather important information we can use to help students apply them more effectively.

For example, a student might have created an argument to explain why adding two multiples of 5 gives you a multiple of 5.

In terms of formative assessment, you might pose these questions:

What was good about your argument?

What could make it better?

In terms of summative assessment, you might use a rubric to evaluate whether the argument was incorrect or unconvincing, whether it was limited (based on only a few examples), or whether it was broad and general and based on fundamental concepts.

What sort of exit ticket do you prefer?

I feel like there might be different types you use on different days. Often, I will simply ask, “What’s the most important thing you learned in this lesson?”

On other occasions, I will ask a skill-based question. For example, if we had a lesson where students had learned to represent the addition of fractions, I might ask students to show a model for adding \(\frac{2}{3}\) + \(\frac{1}{5}\).

On other occasions, I will ask conceptual or opinion questions. For example, if we had a lesson where we had talked about what happens when you multiply by 10, I might ask questions such as these:

Without just stating a rule, how would you explain why a two-digit number multiplied by 10 ends up as a three-digit number?

If I asked you to multiply a two-digit number by a one-digit number, what numbers might make this particularly easy to solve? Why?

How do you handle it if a student says something like this: “But my father said this is the way you are supposed to do it”?

I would normally agree that this is a way lots of people do it (assuming that’s true), but I would point out that there are other ways that other people use as well. Let students know that you would be delighted if they could explain their father’s way to you and another way too.

Do you believe in acceleration?

This is an interesting question that teachers face from the parents of stronger students. Although I firmly believe that the best practice is to enrich and not accelerate, I can understand that parents might push for this if they don’t feel that enrichment is occurring. Trying to deepen the curriculum for strong students is not necessarily something parents are even aware is possible. It might be valuable to demonstrate how it’s done and how it could be helpful for students in the long run—even more helpful than accelerated learning.

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What should I do if, when a child adds fractions, the two fractions are not part of the same whole but two different wholes?

Transcript

An interesting thing happened to me. I was working with a teacher a couple of weeks ago, and we were working on children adding 3/8 to 2/8. And what we anticipated was that the kids would take a whole that’s 8 pieces and show 3 of them and 2 of them. But that isn’t what happened.

So, there was a child who showed 3 on top of 8 — he had 3 squares on top of 8 squares, then he had 2 squares on top of a different 8 squares — and he said, “(frac{3}{8}) + (frac{2}{8}) is (frac{5}{8}).” So, the teacher turns to me and says “What should we do, because it looks like there’s 16 and not 8. But he did say the right thing, so what should we do?” And so, that was a real situation that happened recently. And it was interesting because I didn’t anticipate that the child would do that either, but he did.

So, if the child had looked at 3 compared to 8, and 2 compared to 8, and said 5 compared to 16, we would have had a problem because the answer isn’t (frac{5}{16}). But that isn’t really what happened. The kid realized that if I have 3 of those and 2 of those, I have 5 of those. And that turned out not to be an issue. He had an unusual representation, but it was not an issue.

So, I think if students do things differently than you think they would or maybe you think they should, you can probably let it go if they can make sense of it. You obviously can’t let it go if they can’t make sense of it.

Would you start the year with a diagnostic test?

I don’t think I would ever start the year with a “test.” I would rather start with fun, engaging activities to set a positive tone for the year. That said, in some jurisdictions, screenings are mandated near the start of the year, and teachers must figure out what to do.

I would worry about overwhelming students with too much at once, but I can see value in a diagnostic that focuses on a small number of essential prerequisites for the first part of the learning plan for the year. It is a way to get to know your students.

In terms of what it looks like, I feel a diagnostic might work better if presented as an activity rather than a test.

But even more important is what we are screening. I believe strongly that any diagnostic you use should look at both skill and concept prerequisites and not just skills so that you have better information about where your students really are.

I believe that we have to be clear with ourselves about what it means to meet an outcome, standard, or expectation and allow for alternative ways for students to show us that they have achieved what is expected. My use of parallel assessments is sort of “in-between” allowing individual students their own unique way to express their learning (which should be our goal but might be hard to manage) and requiring the identical way from all students.

What’s your favourite grade to teach?

I am not sure I have one favourite, but I admit that I am particularly fond of Grades 4 to 7. Students are still “kidlike” but have lots of background to discuss interesting ideas.

How much should I be influenced by the types of questions that are used on provincial or state tests?

I do not think any teacher is comfortable ignoring high-stakes testing, but I think a teacher’s goal really needs to be long-term success for their students and not just a good mark on one particular test. So, it makes sense to ensure, to a certain extent, that students are comfortable with the format of the types of questions they might meet on such a test. There are, however, many important learning experiences that are not directly tested on high-stakes tests, and these cannot be ignored either.

I am supposed to write equations like 4 + 4 = 2 + 7 and ask students if they are true or false, but isn’t it confusing for students to write a false equation?

I am just as nervous as you are about this issue.

Part of me would be more comfortable if we wrote something like this:

Is 4 + 4 equal to 2 + 7?

Or maybe we could ask students to choose a symbol, either = or ≠, to fill in the blank:

4 + 4 2 + 7