It's Time To Stop Our Mathematics Students From Playing The Memory Game!

What is the Memory Game?

The Memory Game is a term I coined to describe the school mathematics experience of students who lack a conceptual understanding of much of the work they undertake in lessons.

Let's break down that last sentence by adding a personal spin to it.

Let's say I am a student who has always encountered school mathematics in a?Procedures-first setting. To me, mathematics always seems to be about learning how to answer the next type of question. I seem to be forever learning new procedures and routines for answering an ever-increasing number of question types.

Not surprisingly, in most units of work, I simply don't 'get it'. Basically, I don't understand what I am doing as I replicate what the teacher has instructed me to do. I mean, I can often get the right answer on the early attempts. But I have no idea why THAT particular procedure needs to be applied to THAT type of question. And I rarely understand the mathematical process anyway. To me, it mostly seems like trickery, like pulling rabbits out of mathematical hats.

For example, I have no idea what is going on when I'm following the routine to add and subtract fractions with different denominators, nor when following routines to convert between fractions, decimals and percentages.?

Not surprisingly, I'm hopeless with application questions involving multiple steps. As for rates and ratios? Nope! Solving 3-4 step equations? Forget it! I'm currently in year 9 and when we tackled Trigonometry and Coordinate Geometry it felt like I fell to a new low in mathematical understanding.

Almost anything involving a formula is beyond my reach. I can usually do questions when I first copy the teacher's instructions but then, a few lessons later after we've been taught more procedures for the same topic, I find it really difficult to know which procedure to apply where.

Before a topic test, I do a couple of questions for each question type, but when I'm doing the test, I get them muddled.

To me, mathematics lessons are about remembering many things that I simply do not understand. It's like I'm playing a Memory Game, but I don't know the rules.

Whew!

The above description of the fictional low-achieving-maths-student is, I believe, representative of many, if not a majority of students.

And if this is true, then too many students are being asked to remember a great many procedures of which they have little understanding.

The above describes the outworking of the approach we all know too well, the approach most of us endured during our school and university years. I refer to that approach as a Procedures-first, Understanding-second approach.

The less we understand, the more we are forced to rely on memory

When was the last time you tried to read a complex (non-fiction) book that you didn't understand? Or tried to learn how to use some new software from tutorials that made no sense to you? Without understanding, learning the content becomes exponentially more difficult.

However, when we understand the connections within whatever we are learning, there is much less we need to remember. That's because when we UNDERSTAND what we are learning, we can use LOGIC to tie it all together in ways that make sense to us.

Conversely, when we DON'T understand, we can't make the connections, and so there is exponentially MORE we need to remember. After all, without understanding, we do not have the luxury of logic to make sense of the new information.

In summary, the less students understand the concepts underpinning the routines and procedures we teach them, the more they have to remember ... and the more that school mathematics becomes a meaningless Memory Game to those students.

Memory is important

I am not suggesting that memory has no place in the study of mathematics. Memory is obviously important in the learning of anything. What I am suggesting is to minimise (eliminate?) situations where students are required to replicate mathematics that they do not understand. When we stop forcing students to replicate mathematics that they do not understand, we stop forcing them to play the Memory Game.

Most students play the Memory Game when working with simple maths!

Consider the current students who are playing the Memory Game - the students who struggle with maths; the ones who lack understanding of what they are doing when working through their tasks. What will they say when, as adults, they are at a BBQ and meet a mathematics teacher?

Here's what they'll say ... "Oh, I sucked at maths when I was a school!" (Or any one of many similar phrases.)

And, BTW, my 40 years of anecdotal research tells me that 70% of adults enthusiastically tell us they sucked at school maths.

What sort of mathematics did these people struggle with? Vectors? Matrices? Integral calculus? Imaginary numbers?

Nope! They never made it that far. These people struggled with basic algebra, Pythagoras' Theorem, right-angled trigonometry, straight-line graphing, almost everything with a formula, and of course, fractions, decimals and percentages.

Due to their lack of conceptual understanding, they had to play the Memory Game with junior-high mathematics!

And when we break down junior-high maths, we find that nothing in junior maths is actually difficult - assuming students understand the related concepts.

(But of course, when students?do not understand the concepts that underpin the routines and procedures they are learning, then?junior maths becomes extremely difficult, frustrating, boring, meaningless and stress-inducing.)

Junior-high mathematics ... impossibly difficult or dead easy?

I'll rephrase those last two paragraphs ... Junior-high maths is, at the same time, impossibly difficult and dead easy depending on whether students understand the related concepts. And the students in the impossibly difficult camp are the ones playing the Memory Game.

High school teachers never played the Memory Game!

Fun Fact #1:?We high school mathematics teachers didn't need to play the Memory Game at school. We - almost all of us - never struggled with mathematics. Therefore, we weren't forced into the Memory Game.

Fun Fact #2:?Therefore, through no fault of our own, we mathematics teachers are arguably the least capable people on earth to relate to what it is like for our memory-game-playing-students - those who lack conceptual understanding, students who feel disempowered and disenchanted in maths lessons!

Just for the record - I am not criticising teachers. I know many exceptional teachers whom I would refer to as Procedures-first teachers. In any case, much of great teaching is about lesson structure and quality relationships with students regardless of the approach used.

Nevertheless, I stand by the ideas expressed here about the Memory Game. The Memory Game operates to some level in all maths classes. And the Memory Game is fuelled by approaches that prioritise the teaching of procedures in the hope that understanding follows the sufficient practice of those procedures.

The transition to Understanding-first, Procedures-second is not difficult

Numerous, relatively simple tweaks can transform a Procedures-first approach into one more aligned to Understanding-first (here are four examples).

Your comment ...

What are your takeaways? Do you suspect there are too many students at your school playing the Memory game than you'd like? Do tell ...