How to use Maths — No Problem! workbooks for assessment
Editor’s notes: This is an updated version of a blog post published on January 20, 2021. The transcript has been edited for clarity.
Workbooks give children a chance to reconcile their understanding of maths through intelligent practice. Here’s how you can use Maths — No Problem! workbooks for assessment.
Many schools realise that they are not able to use Maths — No Problem! workbooks for assessment.
These are the following things you are going to see from the workbook — only two things: students getting it wrong, or students getting it right. Why? Because the workbook activities are basic. Do you see anything in between? Maybe.
Here’s an example question from Maths — No Problem!
Let me just pull out a workbook page to talk about that. So the question is: we cannot make use of the data here because it all looks the same. Every child is getting the right answer. So let’s just take a look at what you have in front of you.
Workbook Question 1: ask learners to count on
The children are asked to do addition [in Question 1]. So the intention is to add by counting on. That’s why it includes the provision of the number chart, to facilitate the counting on. It’s really like smaller numbers and then counting on.
Workbook Question 2: add a challenge by removing the chart
And then for the next one [Question 2], it’s a mix and you need to make your own decision about where to start counting on. So the chart is given, not for every question, and you have to decide for: 50 + 8, for 45 + 4, for 60 + 10.
And you’ll notice that for some of them, you’re hoping that the child will say, “I don’t need to count on”.
Like 60 + 10.
“Oh, I know the answer either because I know it,” or, “oh, that’s like six 10s plus one 10. That’s like seven 10s. I don’t need to count on.”
So they will make good decisions like that for themselves.
“I know you asked me to count on, but I don’t need to. I don’t think this task is necessary to count on. I will kind of ignore the instruction and do what I must and write down the answer.”
And actually you wouldn’t find out, because all you’d see is a correct answer. You wouldn’t find out.
Workbook Question 3: find out if learners can model the question
And then finally, the third thing they need to do in this worksheet [Question 3], is to model after our friend.
Our friend is adding 11 and 5 this way. So am I able to add the way he’s adding?
And then that’s the rest of the task, that’s the end of the worksheet.
What assessment data can you gather from this workbook question?
When you give students the workbook, you are going to see two things:
When learners get it wrong (or what not to do)
The first thing you are going to see is that they get it all wrong. That’s really bad news. It shouldn’t happen, really it shouldn’t happen. So that option, I’m just saying it, but it shouldn’t happen.
Because if you know, the child is going to get it all wrong, that child wouldn’t be doing this by himself. You’d probably gather a group of them around you, and you convert or differentiate the independent work into a guided practice.
So technically that first thing should not be seen at all.
When learners get it right
The second thing, they get it all right. Which is good news. What does that mean? They are competent in the calculation. Are they a high attainer? No, I’m not sure.
The workbook cannot tell you if they have exceeded the expectation of the curriculum. It merely tells you they have achieved the learning outcome. So the workbook is not the place you go to, to find evidence that students have exceeded. The workbook will tell you they have not met the learning outcome, or they have.
That’s it, they have, or they have not.
What’s missing from the assessment picture?
The information that they have exceeded the demands of the curriculum would probably come from one of the enrichment activities you give them — which might likely be in the journal.
So the journal is where you go to get evidence that students have exceeded the expectation. For example, students who get all this right [workbook activities on screen] in addition are also able to write a story.
Some students may finish this very fast. But if you ask them to invent another method and they are not able to, you’ll know they have met the demands and that’s it. They have not exceeded it. Students who have exceeded the demand of the curriculum, will be able to complete one of your enrichment tasks.
So you need both the journal and the workbook to get all your assessment data. The workbook will tell you [whether learners are] meeting the demands or not meeting the demands. But exceeding the demands comes from the journal entries.
How to know when you’re assessing for mastery
Some of you also asked the question: “when they were completing [Question 1], they were fine. When they were completing [Question 2], they were also fine. But when they had to complete [Question 3], they would mess up.”
Do you sometimes see that? Probably because in Question 1 and Question 2, I let you do what you want. Because even though I suggest you count on, if you do other methods, I wouldn’t find out. You can actually use other methods, but in Question 3, you are arm-twisted into adding in this way.
Check on learners’ mathematical thinking skills
So what you sometimes see is students do not know what to do with all of this [Question 3’s method]. They have no idea.
“What do I write here? What do I write here?”
But if you say to them, “oh, nevermind this, can you add…” straight away, they know the answer. But the moment you say, “okay, but what about this [Questions 3’s method] again,” they’re lost.
So do you sometimes see that some children get thrown off by this? That’s because these students are perfectly competent in adding, but they are not competent in taking perspective. They can add using their own method, but when asked to understand another person’s way of doing things, and then use that way of looking at things, they get thrown off.
See whether learners understand other problem-solving methods
So all Singapore textbooks have these two kinds of tasks. Because the Singaporean education system requires students to learn to take perspective. Taking perspective is one of the important things that we think students need to have. So when children are able to do this task, the indicator is: on top of being able to do the maths, he or she is able to understand someone else’s thinking. So that’s assessment data for you.
So you know: can they compute? Can they take perspective?
Then on top of that, look at their journal. Have they exceeded the demands of the curriculum?
These are the three pieces of information that you will be able to get from both the workbook and the journal.
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