Scaffolding Work in Mathematics

Scaffolding is a buzz word that gets thrown around a ton in education. It refers to when teachers change parts of an assignment, or the steps in an assignment, to allow students easier access to the material. For instance, teachers may guided notes or guided practice with blanks to guide students where to put the answers. In math teaching one step equations, I sometimes start with a worksheet that provides boxes where inverse operations would appear (Example below).

The idea is that students are able to get assistance in knowing what to do next through guided prompting. Therefore, they are able to start problems easier without having to be continually prompted by the teacher.

I used to believe scaffolding was a crutch. My thought process would go: “If kids have to solve problems without scaffolding, then why would I teach with it?”

In reality, it is very contradictory to believe that as I scaffold a ton of my lessons. Some are scaffolded less explicitly, but are still scaffold down to particular skills and steps before entering the entirety of a specific concept. In this article, I want to dive more into scaffolding and talk about some tips, suggestions, and dismantle some stereotypes about scaffolding in mathematics work.

The what and why of scaffolding

Scaffolding is presenting information in a modified or broken up manner. It is when we present partial or guided information without presenting the entire concept at once. For instance, if I am teaching writing linear equations from a line on a graph, I choose to teach slope one day, intercepts the next, then teach the entirety of writing linear equations last. Why? This allows students to obtain the information in smaller chunks rather than the whole.

If we think back to cognitive load theory and working memory in my previous article, this aligns well. Students can only hold so much information to think about in their working memory. Therefore, by splitting up our learning into smaller chunks we allow time for processing into long term memory and free up more working memory for students to use on more involved concepts.

Scaffolding is for All Students

Scaffolding is not specific to student services. Much like I stated in my differentiation article, scaffolding is for all students. Every student can benefit from some guided instruction or notes on how to solve problems. But some students can take off the scaffolding faster than other students. For instance, our high achievers may not need to use the boxes for one-step equations after a day because they are already keen to solving them. Other students may need to utilize drawing in boxes to solve to one step equations for more days before it begins to become fluent.

You Probably Scaffold Already

When you take a complex skill and break it down into smaller skills, you are scaffolding. Math teachers do this all of the time when we are teaching new grade level topics. For example, I want to teach students in my Algebra class how to solve systems of equations by graphing. To do that, I first need to show students how to graph a line, which requires them me to teach them how to find slope and an intercept. Therefore, I would not teach them all of these topics in a single lesson, rather I would break this up over two or three days so we can eventually teach the goal of graphing to solve a system.

This is a bit less explicit, but it is still scaffolding. We are allowing easier access to the material by providing smaller chunks of information for the student. As they practice the skill each day, they are storing information into long term memory to allow other information to be held in their working memories.

Scaffolding Is Not Less or Easier Work

Scaffolding is not making the work easier, or giving less work; rather it is making work more accessible. Our goal as teachers is to have the student independently complete and master the learning task. Therefore, we need to guide the students and slowly release the grip of learning. At first, this may look like very basic work of practicing specific steps. But as the learner progresses and is able to deal with more information into their working memories, they are able to succeed without so many scaffolds in place. The problems remain the same difficulty and grade level in all cases, but the presentations may be different for students.

At some point, scaffolding needs to end

At some point, students should be able to solve a problem without scaffolding provided. On a test, quiz, or standardized test students will not be provided the same scaffolds that they had during learning the material. Therefore, at some point the scaffolding ends when the student is comfortable with the material. That point really depends on the students level of mastery of the content.

But that does not mean that students cannot draw in their own scaffolds. I encourage students to draw pictures, set up their equations with lines, and draw boxes as they like. For some, it just helps them remember the steps as they solve

Types of Scaffolds

There are a ton of different types of scaffolds, and you can adjust them to your teaching styles. The biggest help, I believe, are guided notes and modified practice. For instance, leaving blank spaces with cues where to put the material. Or setting up problems for students to finish, and slowly having them ease into setting up the problems. The guided aspect gives the student an opportunity of knowing where to start. Many students have anxiety or uncertainty on how to even begin a problem, and the scaffolding allows them to just get started.

I highly suggest keeping spare scaffold assignments around for students. With students in my 8th grade class I keep many scaffolded assignments of finding slopes and solving equations when ever I need to teach or reteach them. Also, teacher pay teachers or google provides a ton of resources to look at them. Once you have a collection going, there is no need to create your own. Just recycle them through year to year as most students have similar misconceptions and struggles each year with the material.

I hope this enhances your students learning in some way. My opinions on scaffolding and differentiation has evolved since college and teaching now. I am currently still reading and trying a lot of different scaffolding techniques that I am excited to share later on.