Level Up: Using Scaffolding to Help Students Succeed in Math

Recently I bought myself a new desk.  You know, one of those “L” shaped desks that fit nicely in a corner with enough surface space for two monitors and a little shelf on one end for your printer.  Dreamy right?  Of course!  But then it arrived in a large box with what seemed like a billion confusing pieces of all sizes and shapes. To make things worse, the instruction manual (if you can call it that) was only about 3 pages long.  After thoroughly reading said 3 pages multiple times, and several failed attempts, my husband offered to help. I begrudgingly accepted. He looked over the instructions once, referenced them a few more times while working and had the desk assembled in less than an hour.  I was grateful that he put the desk together for me, but I was also infuriated that he was able to do it so easily while my attempts had left me feeling frustrated and well, honestly…. also feeling stupid.

I tell you this story because I feel like to students, math can seem a lot like my desk and the instruction manual that came with it: a lot of complex problems to solve, not enough step by step instructions.  There are those rare students who, like my husband with the desk, can watch a teacher work through a problem one time and then they are able to successfully solve similar problems independently.  However, most students need things broken down more.  I have no doubt that if that instruction manual for my desk had step by step directions with accompanying visuals, I could have put the desk together myself.  Sure, it probably would have taken me a little longer, but that’s okay!  Many times, all a struggling math class or student needs is for a skill to be broken down more.

What is Scaffolding in Math?

In math, the art of breaking lengthy problems and math skills into smaller pieces is a form of scaffolding.  The Iris Center at Vanderbilt University defines scaffolding as, “a process through which a teacher adds supports for students in order to enhance learning and aid in the mastery of tasks.”  

Different Types of Scaffolding in Math Instruction

The majority of math teachers naturally provide basic scaffolding in their instruction.  They first model a new math problem to the class explaining each step as they solve it and checking for understanding. Next, they provide guidance and support as students practice solving similar problems until gradually the responsibility of solving the problem from start to finish can be released to the student.  But what about when you provide instructional scaffolding in this way and students are still striving to master a skill?  Sometimes reteaching and additional practice do the trick and sometimes you need more.  This is where combining material scaffolding along with instructional scaffolding can help. Material scaffolding provides students with those added supports on the work they are expected to complete by breaking it down into smaller chunks or providing written prompts or cues.

Math Scaffolding Strategies

There are several ways you can scaffold your math material to help students solve complex math problems.

1. Step-by-Step Example Problems

Instead of giving students a problem and expecting them to remember each step to solve the problem, provide them with an example problem to reference where the problem is worked out, step by step, and written explanations for each step are given.  Encourage them to reference the example problem while solving the first few practice problems, but then to turn it face down and try to see how much they can remember on their own, only referring to the example problem when needed.

2. Guided Fill-in-the-Blank Problems

Take a complex problem and work it out showing all steps necessary, but leave key parts of each step blank for students to fill in.  This can be helpful for multi-step problems and problems that contain new symbols that students are not confident in using yet.  A good method for using this strategy is to provide these supports only for the first half or third of an assigned set of problems, and students would solve the remaining problems without them.  

3. Practice Prerequisite Skills

Most math concepts build upon each other meaning that in order to master a new skill, there are more than likely one or several prerequisite skills that a student will have to know. In a perfect world, they would know and remember everything they learned in previous grade levels and math lessons, but unfortunately, that is never the case.  Thankfully, many times all they need is a quick refresher, but other times students may need extra practice.  Providing them with material that gives them extra practice and review on the prerequisite skill before expecting them to apply that skill in a new problem is also a form of scaffolding.

4. Structured Fill-in-the-Blank/Box Problems

So many students suffer defeat in math simply due to not lining up numbers correctly when solving a math problem.  They either do not understand the importance of alignment, have messy handwriting, or try, but just line things up incorrectly.  Providing them with a space in the form of blanks or boxes can help them get in the habit of setting problems up and solving them using correct alignment.  

5. Gradually Increasing Problem Difficulty

Math curriculum across each grade level increases in difficulty each grade.  Within a grade level, the math lessons in each unit typically do the same.  However, if a class or student is struggling with a lesson or concept, it can be helpful to break the problem down into different levels of difficulty so that students can build confidence as they practice each stage on their way to mastering the most challenging version of the problem. Scaffolded material/worksheets typically start by taking the problem and breaking it down into its simplest form appropriate for the grade level.  Students practice at this level and if successful, move on to the next and continue in this manner until they reach the most difficult level of the problem for their grade level.  This form of scaffolding can take on several different styles depending on the problem type and needs of the student(s).  It may be taking a multi-step problem and breaking it down into one step at a time.  It could also mean working problems with smaller, or simpler numbers and gradually increasing to larger, more complex numbers.  

Examples of Scaffolding in Math

Implementing these scaffolding strategies in your math instruction can often be accomplished with just a couple of small adjustments to what you are already doing. Let's take a look at scaffolding in action using addition with regrouping as an example. This skill can be tricky for students to learn, and there are many things they need to remember in order to correctly solve these types of problems. So, what would scaffolding look like when teaching this skill?

• Start by providing detailed, step-by-step examples during instruction and make sure students have access to reference this example if needed when they first begin solving problems. A poster or anchor chart can also be a great tool for students to reference when starting out.  
• One common challenge for this particular skill is remembering to line up the numbers correctly, both when writing the problem and when placing the number carried over during regrouping. The use of structured, fill-in-the-box problems supports students by showing them exactly where numbers should be placed. Then, gradually remove those visual supports to help students achieve independence. Here's an example of what that looks like in our Adding Within 1,000 with Regrouping worksheets:

• This skill becomes harder with larger numbers, so scaffolding by gradually increasing the difficulty of the problems can be an effective way to help students develop good habits. Start out easy by having them solve problems adding a 1-digit number to a 2-digit number, then two 2-digit numbers, moving up to 3-digit plus 2-digit numbers, and so forth. As students master each level, their confidence goes up and the fear factor often associated with learning a new skill goes down. 

Scaffolding plays an important role in helping students master math skills. Every student has the potential to succeed in math, much like how I could have assembled my desk with the right instructions. By offering the appropriate scaffolding, we empower students to build their confidence, develop their skills, and ultimately achieve mastery.