Scaffolding Students’ Learning

Marian Small

In this issue’s feature article, we revisit the issue of scaffolding: when, what kind, and how much. Marian examines the importance of “scaffolding as needed and only when it’s needed.” We often suggest we are scaffolding a student’s learning when we intervene with extra activities, questions, or suggestions to make a problem or learning situation more accessible to a student who we anticipate might struggle with the situation without the intervention.

What Might Scaffolding Look Like?

You might think of scaffolding along a continuum that ranges from explicit to implicit.

Modelling a Similar Problem

Some scaffolding is very explicit. A teacher might directly model the solution to a problem similar to the one they are going to pose so that students can use the model to solve the problem.

For example, Grade 4 or 5 students might be given this problem:

• Abiah and Leo are distributing 144 flyers to neighbourhood homes. Abiah distributes twice as many flyers as Leo. How many flyers do they each distribute?

To prepare students for the problem, the teacher might model how to solve this very similar problem:

• Abiah and Leo are distributing 33 flyers to neighbourhood homes. Abiah distributes twice as many flyers as Leo. How many flyers do they each distribute?

The teacher might use counters to model the situation, giving Leo 1 counter for every 2 counters they give Abiah.

So, when students are given the problem about 144 flyers, they should realize that they can also think of 144 in groups of 3, meaning that since 144 ÷ 3 = 48, Leo would deliver 48 flyers, and Abiah would deliver 144 ÷ 3 × 2 = 96 flyers.

Or Grade 1 students might be given this problem:

• Some children were in a room. Then, 5 of the children left the room, and 2 more came in. Now, there are 25 children. How many children were in the room at the start?

To ready students for the problem, again, the teacher might model solving a similar problem:

• Some children were in a room. Then, 5 of the children left the room, and 2 more came in. Now, there are 10 children. How many children were in the room at the start?

The teacher might model the problem with counters, working backwards. First, they could show 10 counters to represent the 10 children in the room at the end. Then, they could remove 2 counters for the 2 students who entered the room, leaving 8 counters, and add 5 counters for the 5 students who left the room, totalling 13 counters. Finally, the teacher would conclude that there must have been 13 children in the room at the start.

This would help students realize that to solve the original problem, they could also work backwards. They could start with 25 counters to represent the students in the room at the end, remove 2, which would leave 23, and add 5, which would make 28. This would help them realize that there must have been 28 students in the room at the start.

Or Grade 8 students might be given this problem:

• A cylinder has a volume of 85 cm³. How wide and tall might the cylinder be?

To ready students for the problem, the teacher might model this problem first:

• A square prism has a volume of 100 cm³. How wide and tall might the prism be?

The teacher might remind students that calculating the volume of a prism involves multiplying the area of the base by its height. They might then suggest a side length of 5 cm for the base, which would mean an area of 25 cm² for the base. They would then divide 100 by 25 to determine that the height of the square prism would be 4 cm.

Although the teacher used a square prism rather than a cylinder to make the calculations easier, the process for finding the dimensions of a cylinder is identical. Students would choose a radius, determine the area of the base, and then divide 85 by the area to get the height.

Providing Substantial Hints

A teacher might scaffold in a slightly more indirect way by providing a substantial hint rather than modelling a similar problem.

For the earlier problem about the flyers, the teacher might ask a question such as this:

• Why would the answer for the number of flyers that Leo distributes be the same (i.e., 48) if instead there were 3 children distributing 144 flyers and they each hand out the same number of flyers?

For the problem about the number of children in the room, the teacher might ask questions such as these:

• How do you know there are 3 fewer children at the end than at the start?
• What is 3 more than 25?

For the problem about the volume of a cylinder, the teacher might ask questions such as these:

• What measurements do you multiply to determine the volume of a cylinder?
• How would you “undo” that multiplication situation if you know the volume and the area of the base?

Asking Students to Solve One or More Simpler, but Related, Problems First

It might be that instead of direct modelling, the teacher could ask students to first solve some simpler problems that are related to the more complex one that follows. In this case, the teacher might break the problem up into several steps or might help students use a pattern to get the answer to the more complex problem.

For example, a Grade 3 problem might be to figure out the total number of items in 6 baskets if each basket holds 7 items.

Knowing that 6 × 7 can be tricky for some students, the teacher might first ask these questions:

• How many items are there in total if there are 6 baskets and each holds 4 items?
• How about if each basket holds 5 items?
• How about if each basket holds 6 items?

Or a Kindergarten problem might be to count a collection of 12 items. The teacher might start by having a student count a collection of 6 items. Then the teacher could gradually add 1 or 2 items at a time until they get to 12 items.

Or a Grade 6 problem might be to figure out how many $5 bills would have to be lined up side by side to make a line that is 10 m long and what the value of that number of bills would be.

In this case, the teacher might start by having students line up ten $5 bills (in play money) to determine how many bills would fit in 50 cm, then 1 m, and then 2 m, while also determining the value of the bills each time. It turns out that 13 bills lined up side by side create a line that is about 2 m long, which will make the transition to 10 m easier when the teacher asks the original question about the 10 m line.

Ensuring Students Understand the Question

Some scaffolding is designed to ensure students really understand what is being asked, whether in terms of the vocabulary being used in the question or what solution the question is actually asking for. This type of scaffolding is a bit less leading than the types described earlier.

For example, before asking students in Grades 4 to 6 for the dimensions of a hexagon with a particular perimeter, a teacher might ask questions to make sure students understand the vocabulary being used:

• What makes a shape a hexagon?
• What part of the shape is the perimeter?

Or the scaffolding might be ensuring that students comprehend the problem by talking about the problem’s critical features.

For example, a Grade 4 or 5 problem might be about Marika buying 3 items that satisfy these criteria:

1. The total cost of the 3 items is less than $40.
2. None of the prices is a whole number of dollars.
3. One item costs exactly $4.35 more than another.
4. One item can be paid for with 1 bill and 4 coins.

To ensure students understand the problem, the teacher might ask these questions:

• Could the total cost be $37.25? Could it be $47.25? (to ensure students pay attention to the first criterion)
• Do you think there are choices in what the total cost could be? (again, to ensure students pay attention to the first criterion, which does not specify a particular amount)
• Could one of the prices be $8? (to ensure students pay attention to the second criterion)
• What is an example of two prices where one is $4.35 more than the other? (to ensure students understand the third criterion)
• What is an example of something you can pay for with 1 bill and 4 coins? (to ensure students understand the fourth criterion)

For an open question such as the one about Marika above, you might want to ensure that students understand what they have a choice about and what they don’t get to choose, which is covered in the first three questions above.

Or Grade 2 students might be given this problem:

• Ming sold 64 cups of lemonade. Jack sold 42 cups of lemonade. How many more cups did Ming sell than Jack?

To ensure students understand the problem, the teacher might ask these questions:

• Who sold more: Ming or Jack?
• How many cups did Ming sell?
• How many cups did Jack sell?
• What would you find out if you added 64 and 42?
• What would you find out if you subtracted 42 from 64?

Or Grade 6 students might be given this problem:

• Each month when Serena gets paid, her company deposits $5280 into her bank account. How much money will they put in her account over a 2-year period?

• How many times will Serena get $5280 in 1 year?
• How many times will she get $5280 in 2 years?
• Could the total for 2 years be close to $10,000? Why or why not? (to ensure students are not confusing 2 months with 2 years)

Providing Learning Tools

Teachers could provide manipulatives or other visual tools for students to help support their work on a problem.

For example, consider this problem that might be used with Grade 2 or 3 students:

• A class of 32 students joins a class of 25 students for an activity. How many students are there altogether?

Or if a teacher were to give their Grade 6 or 7 class the equation 3 × ▲ + 4 = 2 × ▲ + 10, they might encourage students to visualize a balanced mobile.

For example, if students are being asked to think about different representations of a number, the teacher might suggest they use a graphic organizer that has different sections for representations that are symbolic, concrete, in word form, and pictorial:

Encouraging Collaboration

Teachers could scaffold learning more indirectly by ensuring students have one or more partners to work with on a problem.

The partner might end up using one of the suggestions mentioned above by playing the role of the teacher and ensuring the partner understands the question or by asking a simpler but related question. Or the partner or partners might simply be there to bounce ideas off one another.

Asking Probing Questions

Rather than modelling the problem, simplifying the problem, or checking that students understand what is being asked, teachers might use probing questions that are designed to get students thinking about the features of the situation rather than leading them to particular approaches. The idea is that students still have to do the “heavy lifting.”

For example, Grade 3 students might be given this problem:

• Students from Ali’s school and Liane’s school got together for a field day. There were only a few more than 600 students in total. There were almost 200 more students from Ali’s school than from Liane’s. How many students might have come from each school?

Instead of modelling or simplifying the problem, a teacher might provide support by asking one or two probing questions that encourage students to do more of the thinking. For example:

• Could the numbers of students in the two schools be 300 and 500? Why or why not?
• Could they be 200 and 420? Why or why not?

Grade 7 students might be given this problem:

• Selima earned 45% of her yearly income by June. That was $36,000. How much will she earn the entire year?

Again, instead of modelling or simplifying the problem, a teacher might ask these probing questions:

• Will she earn more or less in the second part of the year?
• Will her total income be more or less than double $36,000? Why?

A Grade 1 problem might be this:

• There are 3 batches of toys. Liam puts the 3 batches together to make 1 batch of 11 toys. How many toys might have been in each of the 3 batches Liam started with?

Although the teacher might provide manipulatives, they might still use probing questions such as these:

• Could most of the toys have been in 1 batch?
• Could the batches have been more evenly split?

Teachers might worry that they don’t have enough time to scaffold their students’ learning since the curriculum is so packed and the extra questions would be time-consuming. However, research shows that scaffolding can actually decrease the amount of time students spend on the main problem.

On the other hand, some teachers assume that students will struggle, or at least that some will, so they always scaffold their students’ learning. My concern with this is if we’re always scaffolding their learning, students might come to expect it and will not try on their own; they’ll just wait for help. This lack of independence is not ideal, especially as students get older.

It is for that reason that I tend to use the latter forms of scaffolding described above, that is, providing visual or concrete tools, ensuring that collaboration is possible, and using probing questions, rather than more explicit, or direct, modelling.

I believe in scaffolding as needed and only when it’s needed. Ideally, I’d like students to work on a problem for a while before I intervene, unless I intervene by providing manipulatives or ensuring collaboration, which I believe are always good strategies. I think that if we scaffold students only as needed, we can create independent learners who will flourish in our educational system and beyond.