Spiralling

Spiralling is the act of intentionally revisiting topics/concepts multiple times throughout the year. 

Textbooks are quite often organized by topic, with each chapter focused on a specific mathematical concept. So there may be a whole chapter devoted to adding and subtracting fractions, where the concepts get more difficult as the chapter progresses. Many teachers will teach all the sections of a chapter/topic in a time frame (let's say 3 weeks), and then move on to another topic/chapter. The issue is that often knowledge and understanding that students seem to know at the end of the unit does not appear to be retained later on. Meaning students cannot retrieve this information/understanding at the end of the year or the start of the next year. 

This is where spiralling can be beneficial. Instead of teaching one topic front to back in a set amount of time, a teacher will organize the material so that smaller chunks of the topic are introduced initially, Then another concept from the course is introduced and studied for a short period of time, before moving onto another concept. This pattern repeats until all the major topics of the course have been introduced, at which point the teacher circles back to the first topic and goes a bit deeper. The first time a topic is studied, the goal is to give students a surface level understanding of the concepts, and then go a bit deeper with each spiral that occurs.

As a very simple example, let's say that a grade 8 math teacher has only 4 concepts to get through in a year. These topics are:

1. Multiplying and dividing positive fractions

2. Working with linear equations

3. Multiplying and dividing integers

4. Demonstrating the use of the Pythagorean Theorem

For the sake of argument (in our very simplistic example), let's say that each topic included 3 different sections. Meaning, we are going to have 3 sections to go through for multiplying and dividing positive fractions, 3 sections to go through for working with linear equations, 3 sections to work through for multiplying and dividing integers, and 3 sections to work through for demonstrating the use of the Pythagorean Theorem. A typical progression for teaching these 4 concepts would be:

Mult & Div Fractions Section 1

Mult & Div Fractions Section 2

Mult & Div Fractions Section 3

Linear Equations Section 1

Linear Equations Section 2

Linear Equations Section 3

Mult & Div Integers Section 1

Mult & Div Integers Section 2

Mult & Div Integers Section 3

Pythagorean Theorem Section 1

Pythagorean Theorem Section 2

Pythagorean Theorem Section 3

BUT, if we spiralled the curriculum instead, we would reorganize how we taught this and end up with a sequence that could look like this:

Mult & Div Fractions Section 1

Linear Equations Section 1

Mult & Div Integers Section 1

Pythagorean Theorem Section 1

Mult & Div Fractions Section 2

Linear Equations Section 2

Mult & Div Integers Section 2

Pythagorean Theorem Section 2

Mult & Div Fractions Section 3

Linear Equations Section 3

Mult & Div Integers Section 3

Pythagorean Theorem Section 3

Simply by adjusting the order in which we teach these concepts (by mixing them!), we can help students better retain the information. 

Why? 

Because of the practices already described in this section on retention strategies. Each of these strategies help students better retrieve information and improve academic achievement.

• The way we are introducing material when we spiral the curriculum is by interleaving it. 

• By studying a topic and then coming back to it, we are engaging in retrieval practice and spaced practice. 

• Depending on how we assign practice problems, we also have the opportunity to have students engage in delayed practice. 

Research has demonstrated that these practices will all lead to better retention and understanding then the traditional method of instruction where all the material is introduced at one time and not intentionally revisited (a process called block practice). When we mix the concepts and spread them out, we give learners the best chance to understand the topics. 

As an example, a grade 6 math course might be structured in the following way in order to sprial through the curricular outcomes of the course:

Information accessed from: https://makemathmoments.com/spiralling-guide/ 

Back to the Retention Strategies page.