3 Ways Teaching Conceptually Can Save You Time In The Mathematics Classroom

Fun Fact: The principles in this article can be applied to all learning areas.

There has been an increasing demand for Mathematics teachers worldwide to adopt a conceptual approach where fostering active learning in students is the primary aim. However, the shift from a traditional procedurally-based approach to one that is conceptually based is significant for teachers to make. Several misconceptions surrounding conceptually-based teaching have made this shift more difficult.

One of the strongest misconceptions is that teaching conceptually is more time-consuming than teaching procedurally.

This is a misconception because a well-run, highly structured, conceptually-based approach will do the opposite; it will save classroom time.

The Hybrid Conceptually-Based Approach

Many commentators assume that conceptual and procedural approaches are mutually exclusive, that using a conceptual approach means ‘a lack of teaching of procedures’. This is not the case with the approach I refer to as 'Understanding-first, Procedures-second'. The approach acknowledges the need for students to understand the concepts that underpin the procedures they are learning.

Three Ways Teaching Conceptually Can be a Time Saver for Teachers

Below are three reasons why a well-run, Understanding-first approach can be a time saver for teachers.

1. Better understanding = Less time working with confusion = Time saved

A majority of students struggle with mathematics, clearly due to an insufficient understanding of the concepts involved. When students lack a genuine understanding of the mathematical concepts underpinning a procedure, the task of remembering that procedure becomes more exponentially difficult.

Any 'lay person' knows this. Yet we mathematics teachers are handicapped in our ability to truly ‘get’ how important it is for students to understand what they are working on in mathematics lessons. Why? Because when we were at school, we were one of the 10-20% of students who understood mathematics. Therefore, it is difficult for us to stand in the shoes of students who experience mathematics as a torturous, irrelevant 'school thing' that must be endured, a pursuit we never truly understood nor ever will.

Let me paint a scenario for you ...

Let’s say I’m a student who struggles with mathematics. I’m writing down a new mathematical procedure that makes no sense.

I’m unable to use my own thinking to give me any sense of how and why this procedure works. To me, it’s just another ‘maths thing’ I have to follow, another ‘If I follow the teacher's instructions and remember them, I'll have a chance of getting the correct answer’. However, ‘Houston, We Have A Problem’ because there are another 259 other ‘maths rules and routines’ I need to remember ‘that the teacher taught’, and very few of them make any sense to me. And “Oh my gosh, there’ are still another 35 minutes to go before I can walk out that door and rejoin my real world!”

As already implied, I believe the above scenario applies to most students.

Yet, if we present mathematics to students in ways that have them using their thinking BEFORE they see the procedures, then this game of ‘trying to remember what the teacher said’ changes. Dramatically!

Clearly, it is more time efficient to present tasks to students that allow them to understand; not easier tasks, but rather, tasks that are presented in a way that requires them to ‘think their way through the activities’ before they see the procedures. When we do this, student engagement skyrockets and hence time is saved.

2. Better Understanding = Less requirement for practice = Time saved

This is related to #1 but touches on a different aspect. The mantra of proceduralism seems to be ‘give students enough practice and eventually they will understand’. With a well-run Understanding-first approach, students need to work through less problems to gain proficiency. Improved understanding saves time.

3. Increased Student Agency = Increased Work Efficiency = Time saved

When we foster agency in students, they work more efficiently. They are more engaged. Efficient workers are time-efficient workers.

The Understanding-first, Procedures-second approach empowers teachers to authentically engage their students. Below are three ways the approach authentically engages students:

1. By prioritising understanding to a level of importance that at least equals the need for procedural knowledge. In this way, we prevent students from working through tasks they do not understand. In short, we stop turning students off mathematics! We increase student engagement. We save time.
2. By enabling students to take ownership of their learning. We do this by using more student-centric activities, that give studnents a sense of control over their learning. Research has found that when students take ownership of their learning, it results in ‘perceived competence, an internal locus of control, mastery motivation rather than helplessness, self-efficacy, and an optimistic attributional style’ (Jang, Reeve, Deci, 2010). In other words, student engagement is increased, and time is saved.
3. By incorporating more ‘investigative’ styles of activities. Well-designed investigative activities (which can be 5-15 minutes long) require students to draw on their own logic rather than forcing them to have to remember, with little conceptual understanding, ‘what the teacher said’. These short investigations focus on the underlying concepts leading to understanding, engagement, agency and ultimately, a saving of time.

Call to Action 

Did this article provide you with any takeaways? Are you sceptical? Have you experienced saving time through using some conceptually-based activities? Or do you assume that any conceptually-based approach, by default, is more time intensive?

Please share in the comments.