70% Of Capable Students Are Failing Mathematics. What Can We do?
OK, so the title is a tad sensational. I get it. But stay tuned. Although I cannot prove the validity of the title, I have more than a vague hunch that, indeed, 70% of students are failing maths that they are capable of mastering.
What countries, I hear you ask? Let’s start with Australia, but we can probably safely assume this applies to school students of most western countries. First, I’ll argue that 70-ish% of school students are performing at a level that is congruent with their belief ‘I’m hopeless at mathematics’. Second, I’ll draw on some research that allows us to conclude that most of this 70% of students are capable of succeeding at the mathematics they are struggling with. The unintentional ‘How did you fare with school mathematics?’ survey
For four decades, once people discovered I was a maths teacher, they would commonly unload their school maths experience onto me. This is despite me never having asked them to do so!
Poignantly, the most common response was along the lines “I was hopeless at maths”. At least a hundred people must have summarised for me their school math experience, and at least 70% have been of the type ‘I bombed at maths’. |
Granted, this is far from solid research. Nor is the sample space large. Nevertheless, when I share this anecdote with other maths teachers, they tend to agree that of the many people who also share - uninvited - their maths experience, 70-ish% state they never understood maths at school … they hated maths … they bombed at maths.
But does this mean that all 70% failed?
In case anyone is suggesting ‘Just because an adult says they were hopeless at school maths doesn’t mean they failed’, let me state the following for the record:
- People are generally good readers of whether or not they are good at something, especially mathematics.
- The 30-ish% of people who said they were good at maths were equally eager to share their experience.
- I find it implausible that someone would claim to have been hopeless at school maths when in reality, they performed well.
My conclusion, therefore, is that a majority of people fared poorly with mathematics when they were at school.
What types of maths?
What types of mathematics did this majority of responders struggle with? Was it with Yr 12 topics such as locus, matrices, imaginary numbers and integral calculus?
No! Clearly, those who claim to have 'bombed out' never made it to the higher levels. Rather, they failed to cope with simple topics such as fractions, decimals, percentages, basic algebra, Pythagoras, indices, right-angled trigonometry and pretty much anything with a formula.
What we are talking about here is junior high mathematics! And when we break junior high maths into concepts, we discover that none of it is difficult! Nevertheless, it seems that 70-ish% of people found their junior high school mathematics to be a perplexing experience.
No! Clearly, those who claim to have 'bombed out' never made it to the higher levels. Rather, they failed to cope with simple topics such as fractions, decimals, percentages, basic algebra, Pythagoras, indices, right-angled trigonometry and pretty much anything with a formula.
What we are talking about here is junior high mathematics! And when we break junior high maths into concepts, we discover that none of it is difficult! Nevertheless, it seems that 70-ish% of people found their junior high school mathematics to be a perplexing experience.
Houston, we have a problem!
Spoiler Alert: Assumptive leap coming!
I see no reason why our 70% figure of adults who bombed at school maths - in the past - would not correlate to current high school students. Why wouldn't it correlate? I don’t see anything that suggests that students' responses to school mathematics has radically changed over recent decades. In other words, I'm proposing that a majority - perhaps 70% - of current high school students struggle with junior high mathematics. |
It must be stated that all this is despite the extraordinary efforts of hard-working, determined mathematics teachers who are genuinely doing their best to make a difference in their classrooms.
My teaching experience - which has been somewhat unique - backs up this figure. Sure, I was the teacher for 50+ maths classes and had some 100 others under my care as a Department Head. However, a more poignant window into what is going on for students in mathematics lessons comes from casual (substitute) teaching.
Early in my professional career, I spent a decade being nomadic. This resulted in me spending one or more lessons inside some 200 maths classrooms across South Australia, the Northern Territory and New South Wales. An eye-opening experience, to say the least! My experience backs up the hunch that 70-ish% of students are not coping with junior mathematics.
Again, this is far from solid research. However, my hunch remains strong.
My teaching experience - which has been somewhat unique - backs up this figure. Sure, I was the teacher for 50+ maths classes and had some 100 others under my care as a Department Head. However, a more poignant window into what is going on for students in mathematics lessons comes from casual (substitute) teaching.
Early in my professional career, I spent a decade being nomadic. This resulted in me spending one or more lessons inside some 200 maths classrooms across South Australia, the Northern Territory and New South Wales. An eye-opening experience, to say the least! My experience backs up the hunch that 70-ish% of students are not coping with junior mathematics.
Again, this is far from solid research. However, my hunch remains strong.
But all people are capable of K-12 maths - What the ?!?
And yet, cognitive scientist Daniel T Willingham states in his article Is It True That Some People Can't Do Math?, that 'the vast majority of people are fully capable of learning K-12 mathematics' (Willingham, 2010, p. 1).
My reading of the article is that even though Willingham references K-12 mathematics, he’s really referring to junior mathematics. Quote: Virtually everyone is fully capable of learning the numeracy content and skills required for good citizenship: an understanding of arithmetic procedures, algebra, geometry, and probability deep enough to allow application to problems in our daily lives. His statement is rigorously argued and research-backed.
My reading of the article is that even though Willingham references K-12 mathematics, he’s really referring to junior mathematics. Quote: Virtually everyone is fully capable of learning the numeracy content and skills required for good citizenship: an understanding of arithmetic procedures, algebra, geometry, and probability deep enough to allow application to problems in our daily lives. His statement is rigorously argued and research-backed.
The first part of the title (70% of students are failing at mathematics they are capable of mastering) ...
I’ve argued, albeit in an unusual way, that 70-ish% of students are failing at mathematics. And by inference, Willingham provides the research to state that most of these 70-ish% are fully capable of the mathematics they struggle with and fail at (junior high maths).
The second part of the title … (What can we do?)
We have established that there is a problem. The question is, what can we do about it.
Mathematical Understanding is Key
As I establish in the article, Why Students Need To Understand Mathematical Concepts Before We Teach Them Procedures and in articles on the Understanding-first approach (linked below), the key to having more students perform better in mathematics is to improve their understanding of the concepts underpinning the procedures they are working with.
It shouldn’t take an Einstein to conclude that a lack of mathematical understanding is the obvious reason for students not coping with mathematics; specifically, a lack of conceptual understanding of the concepts any given piece of work requires them to deal with.
As I argue in Why Compartmentalising Is A Bad Idea When Teaching Mathematics, one factor contributing to our 70% of under-achievers is the over-compartmentalising of mathematics.
If we are to avoid having WAY too many students spending WAY too much time in WAY too many lessons not understanding the maths that is in front of them, then we need to present mathematics so that students are able to understand, conceptually, what’s going on ... and to understand it as soon as possible after students encounter new-to-them mathematics.
It shouldn’t take an Einstein to conclude that a lack of mathematical understanding is the obvious reason for students not coping with mathematics; specifically, a lack of conceptual understanding of the concepts any given piece of work requires them to deal with.
As I argue in Why Compartmentalising Is A Bad Idea When Teaching Mathematics, one factor contributing to our 70% of under-achievers is the over-compartmentalising of mathematics.
If we are to avoid having WAY too many students spending WAY too much time in WAY too many lessons not understanding the maths that is in front of them, then we need to present mathematics so that students are able to understand, conceptually, what’s going on ... and to understand it as soon as possible after students encounter new-to-them mathematics.
Related Articles
Why Students Need To Understand The Concept Before We Teach Them The Procedure - here
Why We Need An Understanding-first, Procedures-second Mindset When Teaching Mathematics - here
The Understanding-first, Procedures-second Approach In Action - Three Examples - here
Why Compartmentalising Is A Bad Idea When Teaching Mathematics - here
The Case For NOT Teaching Procedures - here
Call to Action
I agree I argue my case in this article using an unusual strategy. However, I'm convinced the conclusions are likely close to the mark and worth pondering.
I'd love to hear your views - whether you are vehemently opposed to the arguments put forward here, or wildly in agreeance, or somewhere in between.
Fire away ...
I'd love to hear your views - whether you are vehemently opposed to the arguments put forward here, or wildly in agreeance, or somewhere in between.
Fire away ...