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Creating A Need To Learn

A Teaching Strategy That Boosts Student Engaged in Mathematics
Richard Andrew  

Imagine teaching an equations unit in which students:

  • Beg you for your algebraic method. (You read that correctly)!
  • Choose the questions that they work on.
  • Progress at their own pace.
  • Gain instant and repeated success.
  • Beg you for your algebraic method. (Again, you read that correctly)!

If you are a mathematics teacher, then there’s a fair chance you enjoy teaching young students how to solve equations.

And there’s also a fair chance you like to help remove the fear that many of your students have of algebra.

However, when it comes to teaching students how to solve equations - or re-teaching those who coped poorly with equations in previous years - it is common for the unit to go pear-shaped during the first couple of lessons. In other words, students commence the unit on shaky ground and never quite recover, many of them winding up disillusioned and convinced that solving equations is stupid, meaningless and not for them.

Don't believe me? Allow me to describe (what I believe to be) a common scenario:

  • You deliver your introduction to the solving of equations.
  • You - perhaps - show the students a scary-looking equation that is well beyond their capability, to make the point that a method for solving equations is required.
  • You then write a simple one-step equation on the board and proceed to show them your preferred method for solving the one-step equation.
  • And here's where the problems begin! Within approximately seven milliseconds, a small war develops. Many of the students fight you in regard to having to use your method. They don’t want to use it. They don’t see the need to use it. They complain, they whinge - if not outwardly, then on the inside - because the answers to these one-step equations are obvious. So why should they follow your longer method?
  • Two lessons later, the unit should be unfolding nicely. Students should be finding this ‘new-to-them kind of mathematics’ enjoyable and satisfying. They should be gaining success with two and three-step equations.

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  • However, on the contrary, many don't get it at all and many have switched off. You have an affinity with these students, but now the rapport between you is fading. The engagement and compliance in the room are way less than they should be. Some students who have always been onside are displaying signs of discontent.
  • Of real concern is that your algebraic method - the one you know is efficient and ideal for students to follow - is not being followed universally. Many students are only half-following it resulting in incorrect answers and adding to their disillusion.
  • This isn’t the first time you’ve seen an equations unit disappear down the gurgler - it has happened before.
  • There has to be a better way.   
Now OK, your situation may not be quite as bleak as the one described above. However, before you dismiss this article as irrelevant to you, check the bullets below to see how your experience of teaching equations compares to what is possible:

What an Equations Unit Could Look Like:

  • A 5-10 minute introduction that captures the students’ interest.
  • Students then work through an activity which:
    • Has students choosing the questions that they work on, with some constraints.
    • Allows students to progress at their own pace.
    • Allows students instant and repeated success.
    • Keeps all students occupied.
    • Has students ‘pleading’ with you for your algebraic method.
    • I’ll state that again - rather than resisting using the algebraic method you teach them, students actively demand/plead/beg you to show them your method. (This isn’t an exaggeration.)
    • The work is both teacher-directed (you are busy, giving lots of input to individuals, groups of students and to the whole class) as well as being student-centred (students experience some freedom re their progress).
    • Differentiated instruction occurs naturally as it is a byproduct of the approach.
    • Student engagement (in most situations) is ‘through the roof’. The worst-case scenario is that some students are not very engaged, yet significantly more engaged than normal and feel somewhat surprised at their ability to succeed with this apparently difficult type of mathematics.
Note that the above outcomes are mostly a result of the approach being based on creating a need in students to learn your algebraic method.

How does your experience of teaching equations match up against these bullets? Are you intrigued, interested? If yes then sign up for this free tutorial showcasing, in detail, the Need-Levels-Choice approach to solving equations. 

About the Need-Levels-Choice Approach to Solving Equations

  • Yes, the Need-Levels-Choice approach works, folks, and from experience, enables the 'What an equations unit can look like' bullets above.
  • The approach is easy to implement.
  • The approach guides teachers explicitly so as to maximise the chance of success and to prevent some pitfalls that can occur when it is not implemented correctly.
  • I’m repeating this because it is important - the approach is based on the idea of creating a need to learn in students.

The Ideal Algebraic Method

The algebraic method needs mentioning.
There’s quite a bit of noise in mathematics teacher circles about what the ideal algebraic method is. I think the algebraic method is less important than people think. It is important that you believe your algebraic method is the ‘best method’ and it’s important that it makes sense to students and is easy to follow. Beyond this, it is the pedagogy, i.e. the approach that incorporates the algebraic method, that is more important.

Critically, the key question is this: “Does the approach you are using instill in students a desire to learn your algebraic method?”

In regard to an algebraic method, the Need-Levels-Choice tutorial demonstrates some principles of presenting a method so that it makes sense to students. But other than that there is no emphasis on which method is best to use. The choice of an algebraic method is yours to make.

Why isn’t the tutorial part of this page?

Great question! There are three strong reasons why this is an article about the approach and not the tutorial itself:
  1. The tutorial needs to be followed closely. People typically skim-read articles but are more likely to follow the tutorial closely if they sign up for it.
  2. The tutorial needs some explaining - hence this article. 
  3. Most teachers will not view a linear equations tutorial as high need. This article aims to present the case that all teachers can benefit from the Need-Levels-Choice approach - even those who have taught equations ‘a hundred times’.

Call to Action 

Did the article raise some interesting points for you? Are you tempted to undertake the Need-Levels-Choice tutorial?
If you do undertake the tutorial, make sure you complete the feedback at the end. We’d love you to share your experience of implementing the Need-Levels-Choice strategy.