## 3 Ways Teaching Conceptually Can

Save You Time In The Mathematics Classroom

There has been an increasing demand for Mathematics teachers around the world to adopt a conceptual approach, where teaching for understanding is the primary aim. However, the shift from a traditional procedurally-based approach to one that is conceptually-based is a significant one for teachers to make. This shift has been made more difficult by several misconceptions that surround conceptually-based teaching.

One of the strongest misconceptions is that teaching conceptually is more time consuming than teaching procedurally. This is a misconception simply because a well-run, highly structured conceptually-based approach will do the opposite; it will actually

One of the strongest misconceptions is that teaching conceptually is more time consuming than teaching procedurally. This is a misconception simply because a well-run, highly structured conceptually-based approach will do the opposite; it will actually

*save*time in the classroom.## 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 Hybrid Conceptually-Based Approach, which acknowledges the need for students to understand what it is they are working on as well as the importance of procedures.

## Three Ways Teaching Conceptually Can be a Time Saver for Teachers

Below are three reasons why a well-run, (hybrid) conceptually-based approach can be a time saver for teachers.

## 1. Better Understanding = Less time working with confusion = Time saved

It can be argued that many students - perhaps the majority - struggle with rules and procedures 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 difficult.

This may sound obvious, however, we mathematics teachers tend to be handicapped in our ability to truly ‘get’ just how important it is that students understand what it is they are working on in maths class. Why? Because when we were at school we understood maths - we rarely experienced lessons in which we had 'no idea what was going on'. It is therefore difficult for us to stand in the shoes of students who do experience (many lessons) in which they are not understanding the work. Hence, I suspect that this issue - of students not understanding what they are working on - is more critical than most of us realise.

This may sound obvious, however, we mathematics teachers tend to be handicapped in our ability to truly ‘get’ just how important it is that students understand what it is they are working on in maths class. Why? Because when we were at school we understood maths - we rarely experienced lessons in which we had 'no idea what was going on'. It is therefore difficult for us to stand in the shoes of students who do experience (many lessons) in which they are not understanding the work. Hence, I suspect that this issue - of students not understanding what they are working on - is more critical than most of us realise.

## 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 to me. In other words, I’m unable to use my own thinking to give me any sense at all of how and why this procedure works. To me, it’s just another ‘maths thing’ I have to follow, another ‘If I remember this routine the teacher told me to use, and if I use it in the right situation, then I have a chance of getting a 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 said’, and very few of them make any sense to me. And “Oh my gosh, there’s still another 35 minutes to go before I can walk out that door and rejoin the world!”

As already implied, I believe the above scenario applies to way more students than we think.

If we can present mathematics to students in a way that has them using their own thinking BEFORE they see the procedures, then this game of ‘trying to remember what the teacher said’ can change. Clearly, it is more time efficient to present tasks to students that allow them to understand; not easier tasks, 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.

As already implied, I believe the above scenario applies to way more students than we think.

If we can present mathematics to students in a way that has them using their own thinking BEFORE they see the procedures, then this game of ‘trying to remember what the teacher said’ can change. Clearly, it is more time efficient to present tasks to students that allow them to understand; not easier tasks, 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 (hybrid) conceptual approach, understanding is present in the first place. Therefore, students don’t need to work through as many problems. In this way, better understanding provides another time saver for teachers.

## 3. Increased Student Engagement = Increased Work Efficiency = Time saved

When students are engaged with their learning, they work more efficiently on the task at hand. This, as a result, saves time in the classroom.

The (hybrid) conceptual approach is designed to empower teachers to engage their students more authentically. Below are 3 key ways the Hybrid approach authentically engages students:

The (hybrid) conceptual approach is designed to empower teachers to engage their students more authentically. Below are 3 key ways the Hybrid approach authentically engages students:

- By focusing on ‘understanding first, and procedures second’. In this way, we avoid the situation in which students work through tasks they do not properly understand, and subsequently become frustrated and disengaged with the subject. In other words, using an 'understanding first, and procedures second' mindset we increase student engagement and save time.
- By enabling students to take ownership of their learning via quality activities that are more student-centred. 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.
- By incorporating more ‘investigative’ styles of activities. Well-designed investigative activities (which can be of short duration up to several lessons) require students to draw on their own logic rather than forcing them to have to remember, with insufficient conceptual understanding, ‘what the teacher said’. When this occurs student engagement is increased and time is saved.

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## Call to Action

Did this article present to you any ideas in a fresh light? Are you skeptical? (Yes, btw, is an OK answer!) Have you experienced saving time through the use of a successful conceptual approach? Or have you always assumed a conceptual approach, by default, is more time intensive?

If you’d like to read more about the (hybrid) conceptual approach check out this article.

If you’d like to read more about the (hybrid) conceptual approach check out this article.