The Art of Questioning on Math Assessments

Last year, I had a great conversation with a colleague around math assessment. We were talking primarily about how to best triangulate products, observations, and conversations to form an overall balanced assessment of student learning, but a side conversation has really stuck with me.

She told me that on her math tests, for any given learning goal, she gives the students four levels of questions to choose from. The students can then decide how to best demonstrate their understanding of that expectation.

I love the idea of student voice and student choice in how learning is demonstrated. But it's taken me about a year to really wrap my head around this idea, and to start working with teachers in my board to try it out.

Traditionally...

Traditionally, on a test, I might ask students three or four questions all on the same expectation. It might look something like this:

Like most teachers, I started with an easy problem, and each subsequent problem gets a little more involved. There's a chance for students of all levels to experience success, you could argue, however here's the catch: a student who can do only part (a) of the above question will score only 2/8, or 25%. Even though they've demonstrated a basic case of the learning goal, they still "fail" the expectation.

Failing is disheartening for any student. Not to mention the frustration at being asked repeatedly to do something they don't know how to do.

A Shift in Thinking

However, what if we tipped the layout of the question, and instead asked it like this:


There are two significant differences to presenting questions this way. First, it is important to recognize that each problem, regardless of level, satisfies the expectation, just with varying degrees of complexity. A student choosing to answer only the Level 1 component of the above question, but answering it correctly, would demonstrate a level 1 understanding (a grade of approximately 55%). Compare this to the student who could only answer the first part of the question in the previous layout, and scored only 25%.

Second, with the introduction of choice, students can now decide how to best demonstrate what they know. The pressure over having to unproductively struggle* for four questions has been removed. If a student can complete the Level 4 question, do they need to do the previous three? If a student can do the Level 2 question, but no higher, is it worth the frustration to force them to do more complex problems on an assessment of their learning?

*I'm not suggesting we remove productive struggle from mathematics. It is my hope that students will have confidence enough in their skills to want to try a challenge, and persevere until it is solved. However, I also wonder if the best place for those challenges is not on a timed test, but rather on tasks given over longer periods of time.

Rationale

I believe there is value in allowing students to choose their level of comfort with solving problems, and I would hope that this would also alleviate some of the pressure that comes with testing without reducing the number of expectations tested.

My hope is that students gain confidence by experiencing success. In doing so, they might start trying the "next question up," and setting goals for themselves. I love the idea of students driving their own learning.

I like the information this gives me on the student - if a student tries the level 3 question and gets it wrong, but can do the level 2 question, is the barrier easier to identify? Can we more closely identify that student's next steps? If a student will only do level 1, what would the next step be to get them to attempt level 2?

There is also value in me as a teacher looking at each expectation/learning goal and being able to identify basic cases (level 1), cases at provincial standard (level 3), and cases that go deeper into the curriculum, but not above and beyond the curriculum (level 4).

What Will the Students Do?

My wonderings around this include how students will choose which level to complete, and I'm fortunate to have some colleagues who are willing to try some of these questions with their students.
  • Will some students always just choose Level 1, because that seems like less work? 
  • Will some students insist on doing ALL the questions?
  • Will some students always go for Level 4? 
  • Will some try Level 1, decide it's not too bad so then actually decide to try Level 2?
I hope to be able to share more as we explore this idea with students!

Comments

  1. Great post Heather! The idea of getting 25% when the student has some understanding seems unreasonable. As well, you have investigated and shown how students will respond to this format... interesting!

    I am wondering if adding rationals into the equation makes it a level 4 question. How about incorporating distributive property for the level 4 question? or simply adding more terms on either side of the equal sign?

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    1. Those are fantastic suggestions! This is one of my biggest wonderings... what is it that takes a question from "provincial standard" to deeper-and-yet-not-beyond the curriculum? How large is a reasonable jump from level 3 to level 4?

      I'm hoping to get lots of feedback from teachers on this as we continue to try it out. I'm noticing already that some teachers "stop" at a level 3 difficulty of question on assessments, but if the student gets those right, they "earn" the equivalent of level 4 (or even 100%). Lots of soul-searching as we explore the meaning of the curriculum expectations!

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    2. I just came back to this post because of some tweaking I've been doing with assessments. Any other advice or learning since then? I loved this when I first read it.

      I have a couple of thoughts to add...some expectations (those that are really knowledge-y) may not have a 'Level 4.' Above and beyond isn't something that extends to everthing in our curricula (unless you are looking for things like consistency over time) I equate this to writing chemical formulas in my courses - it is very procedural and students can either apply the rules or not. There are questions that are easier or more difficult (different ratios, polyatomic ions, multivalent metals, etc) but in essence this is a knowledge-based skill that doesn't have true extensions unless you introduce special cases/topics. Other items clearly allow for natural extensions that would have true 'level 4' options.

      When I looked at our 10D Science courses it seemed that about 1/3 is cut-and-dry knowledge, 1/3 is ripe for extensions (inquiry, labs, analyses, etc) and about 1/3 requires higher-order thinking by its very nature and invites 'L4' thinking (evaluating evidence, forming opinions, proposing solutions, etc.). So I'm thinking that to achieve L4 in a course you need to master the basic skills (could be L3...not inherently L4 work) and then apply that understanding to go above and beyond on the rest of the expectations.

      Thanks again for this post, Heather!!

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  2. I like this idea. For equations, I think it's relatively easy to see a progression from "level 1 questions" to "level 4 questions" but there are some expectations that might not be so clear.

    I've just started this year grading by expectation and with levels. I'm just using the overall expectations so that I can give a few different types of questions related to the expectation and they I assign a level holistically looking at what they've done as a whole for those questions. I'll have to look back when the semester is over and decide if that was the best approach.

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    1. I agree. It was easier to come up with level benchmarks for "skill"-based expectations (solve for the variable, solve this system of equations, determine the slope and the y-intercept, etc.), and I'm still trying to wrap my head around levelling problem solving expectations (what is the difference between a level 2 word problem and a level 3 word problem?). I'm wrestling with that.

      I would love to hear how your semester goes - I love the flexibility you're introducing by looking at many ways to accomplish an overall expectation! Do the students know there is a change in the way things are graded, or does it look the same on their end?

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    2. As I was thinking on this further, I began to wonder what level I would give to a student who only attempted one question (say the L3 or L4), but did it incorrectly? I don't think you could give them the next level down automatically. I think in this situation I would probably give the question back to the student and ask them if they could do one of the lower level questions, but I'm curious about what others have done/would do.

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