Among the most unpopular subjects for boys in the Ontario curriculum are French and Mathematics. French, because many boys feel that there is little use putting effort into something that they feel they will never use. It isn’t an issue of difficulty but rather one of perceived relevance. Few boys have any fear of French, they just do not like it. As a Grade 9 mandatory credit required for graduation, the majority of Ontario schools offer it at what is called an Applied or Open level. Few students take it beyond the grade 9. Mathematics, on the other hand, is regarded by many boys as threatening. Being good at math is equatable with being smart. Being really good at math is therefore equateable with being very smart. As such, insecurities translate not being good at math into being stupid. Since insecurities invariably result in denial, then poor math results are justified by denying its importance and in many cases in a glorious failure that indicates no effort whatever was put forward. To work hard and do poorly or even worse to work hard and fail is more than tender egos can sustain. But a mark so low as to be clearly a result of no effort, that is a statement. It shouts out, you can’t fire me, I quit. It is a pathetic attempt to establish a sense of control over a situation in which ultimately you feel you have none. But while opting out of the game may be is perceived as the only viable recourse to protect threatened self-esteem, it comes at a cost.
Math is a unique subject within the curriculum in that emotions play a significant role in students’ attitudes towards it which in turn impacts their respective performance and perceived ability. It is also unique inasmuch as one often struggles to master a new concept only to find that when you suddenly get it, it is difficult to see why you didn’t see it all along. No other subject of which I am aware presents itself in this way. So, whereas emotions play a significant role in all aspects of school performance, their impact with math functioning is especially dominant and pervasive in terms of any self-assessment of intelligence.
On a personal note, I had no issues with mathematics in school until in high school I was taught it by a teacher that I disliked. He was also the physical education teacher and we had had a disagreement about the weightlifting club in which he had insisted on timing routines competitively. I felt that this was dangerous and resigned from the club. After that, our relationship was problematic with me thinking that he was wrong and him thinking that I had no right to question him. At any rate, I began to fall behind in math and the next year I experienced significant difficulties because the previous year had undermined both my foundational skills and my confidence in the subject.
Aware of my struggles, my father offered to help me. My father, who was an aeronautical engineer, had always been a strong math student and had won numerous scholarships as a youth in England. Upon sitting at the kitchen table and reaching for my textbook, my father began to review it and began to look puzzled. What grade is this again? he asked already knowing the answer and then proceeded to tell me that he had covered the same math in England when he was three years younger than I was. This was a response based upon spontaneous surprise on his part and he was entirely oblivious to my reaction to his reaction. My response was hidden within subdued silence. Internal to my own thoughts and feelings, I immediately resigned myself to the belief that my father had come to the conclusion that I was an idiot. During the lesson itself, I felt that he was exhibiting an unnatural tone of voice and exercising immense self-control as if speaking to somebody with subnormal intelligence. Each sentence from him resulted in growing pressure in my brain with the result that I developed intense headaches, took aspirins and could not concentrate. I barely squeezed through the year with a pass but resolved to stay well clear of mathematics in the future. I blame none of this on my father and realized long ago that my perception of reality formed my reality. He genuinely wanted to help and cared deeply for my feelings. My insecurities, however, ruled the day. As such, my recollections are so colored by emotions that I can no longer attest to the accuracy of events as much as I can to the subjectivity of my response.
At university I enrolled in a combined honors degree taking history and philosophy. The philosophy degree had a mandatory second year course in symbolic logic which I quickly found was like algebra on steroids. Apparently, honors math students took the course as an elective for fun. To me, it was a senseless succession of formulas and had nothing to do with the deeper issues that I thought philosophy was supposed to deal with. After several weeks of floundering, the professor asked me to come to his office. Harley, he said in a matter-of-fact voice, you are going to fail this course and you had better drop it. I left his office full of indignation as I realized fully that I couldn’t graduate without it. Damn him I thought, I will pass this course even if it kills me. I went to a local used bookstore and looked through the books in the hope that I might find something that would help me. I picked up a little volume entitled Immanuel Kant’s Introduction to Logic and studied it meticulously. I spent hours going over the problems and solutions for the course. Suddenly, I started to get it. Rather than being concerned about its deeper meaning, I came to the conclusion that I needed to look at it more like solving a puzzle or a crossword. Suddenly, it began to fall into place, and I found that I could do it. My mark improved and I ended up having a strong final exam. So surprised was my professor that he asked to see me. Well Harley, he said, how did you do it? I told him about picking up the book and how it had clarified things for me. Kant clarified things for you he asked in amazement. Yes sir, I responded and without thinking added that I had found his explanations clearer than the lectures. I later found that Kant was infamous for being especially obscure and so had insulted my professor without knowing it. As an addendum to this story, I should add that when I returned to McMaster on staff after completing my Ph.D, we became good friends and remained so until his death. I do not know if he ever remembered my undergraduate experience with him, but it never came up in conversation.
I have provided all of this personal material before proceeding with the book under review because I, like the author, found that my experiences with mathematics were grounded in emotion and insecurity rather than in
inherent ability. Insecurity generated inability and I had approached the subject and material as if it was a threatening IQ test that I was bound to do poorly on. Experiences in teaching at the primary, secondary and post-secondary levels have reinforced the fact that insecurity plays a major role in student performance. Equally, being good at mathematics is often a justification for students to feel that they have superior intelligence of near god like proportions. Fortunately, the University of Waterloo has offered the Euclid Math contest each year for senior high school students looking to university admission. The results of this test have served the useful purpose of giving math students a more accurate perspective of their own abilities and helping to bring them down to earth prior to entering university.
Since Mighton’s book was published, the institution of a no failure approach to the elementary school panel has resulted in significantly large numbers of boys being passed forward despite having failed to realize grade appropriate expectations in mathematics. As a result, I would estimate that the majority of boys finishing grade 8 are at least one year behind with others sometimes still entering high school 2-4 years behind. This has resulted in fewer males than females entering university and growing numbers of boys in modified academic programs with limited post-secondary options. When interviewing one boy some years ago I asked him about the sudden downturn in his math results. Well, sir, he said, it was in Grade 6 when I found out that I couldn’t fail math, I found it boring, and I didn’t like my teacher and so I thought, why put in the effort if they are going to advance me anyway. Given the absence of immediate consequences and the youthful insulation from the knowledge of long-term consequences, such actions can only be seen as purely rational within their context. No small wonder then that I have found that increasingly the profile of boys falling behind academically before entering high school is one of above average intelligence. How does one square above average intelligence with below average school performance? Simply put because marks are no accurate indication of intelligence or ability, merely of performance.
The 20 years since the appearance of The Myth of Ability have seen the exacerbation of what was already a significant problem but it is also true to say that the advocacy of a different approach to math and his J.U.M.P. or Junior Undiscovered Math Prodigies program has had positive results in some private and public schools that took the initiative to adopt it. However, the origins of the book and Mighton’s passion for the project are deeply personal. They relate to his own experience in learning mathematics and like my own personal memories involve a sense of failure and insecurity that later resulted in confronting and conquering that fear. From this came a greater understanding of and empathy for the students under our care. However, implicit in this is the assumption of a standard of performance external to the individual and an awareness of not meeting it. Current approaches have largely eliminated this and having not identified any deficit see no reason for corrective action. The overall effects of this approach are at least as damaging as the assumption of fixed intelligence and ability based upon performance.
Mighton relates how he had even as a child regarded mathematics as somehow being an index of intelligence:
“It seemed clear, from everything that I had read that a person born to do mathematics would never do badly on a test or struggle to learn a new concept. The thoughts and mental processes of a great scientist or mathematician were of an order entirely different from those of an ordinary person. As this belief sank in, I began to find math more difficult at school and my marks steadily declined. When I received a D (later belled to a C) in Calculus for the Life Sciences at university, I decided to drop the subject once and for all.”
At this point Mighton shifted his focus to creative writing. Though not in his own estimation especially gifted in this regard, through hard work and application he graduated later becoming a successful playwright receiving a Governor General’s Award. His career as a playwright was not particularly rewarding financially and he took on a number of part-time jobs, one of which was as a math tutor. On revisiting the subject, he found that without the pressure of the classroom environment he began to gain confidence in the subject and found it easier than he had remembered. Helping a number of young students, he found that he was able to build their confidence and gain significant success despite the fact that they had not demonstrated any initial ability or potential. One such boy went on to earn a Ph.D. in mathematics as a result of his response to being tutored.
“He worked hard and and soon developed an interest in mathematics. Because I hadn’t assumed that he lacked ability, and because I was lucky enough to work with him for a period of five years, I saw changes in his aptitude that few teachers ever see in their students. In Grade 13, my student did so well in the Sir Isaac Newton physics competition, he was offered a scholarship to Waterloo University even though he hadn’t applied there. He is presently completing a doctorate in Mathematics at another university.”
Mighton decided to return to university to take some mathematics courses and continued with the mathematics tutoring. He enlisted the support of a vice-principal who convinced her principal to start an experimental tutoring class of 15 students that Mighton and a few of his friends volunteered to work with. The successes in this program lead to the development of the JUMP program. One student, he noted, was able to advance from a Grade 1 level to a grade 9 level in Math after only a hundred hours of tutorials. Again, in case after case, Mighton found that building confidence and overcoming the fear of stupidity was a major factor in student success.
The JUMP program developed and evolved as a not-for-profit initiative to help students achieve success in math encompassing both lessons plans, texts and teaching strategies. Central to the mission was and is the overcoming of the mythology surrounding mathematical ability.
“Twelve or 13 years in oversized classes, in a system predicated on the idea that only a few students will excel: these factors are not considered to be complicit in the problem. Failure in this system stands as irrefutable proof, even for the person failing, that one was born not to succeed.”
And again:
“Based upon my observations of hundreds of students, I predict that with proper teaching and minimal tutorial support, a Grade 3 class could easily reach a grade 6 or 7 level in all areas of the mathematics curriculum without a single student left behind.”
“The JUMP program was specifically developed to help children who have fallen behind catch up quickly. I would never claim it is the only way to teach mathematics, or even the best….I would claim, however, that whatever method is used, the teacher should never assume that a student who initially fails to understand an explanation is therefore incapable of progressing.”
Much of the rest of the book is filled with specific examples of teaching strategies. As already indicated, the JUMP program has developed detailed teaching plans and text materials that have been adopted by some math teachers in both the public and private system prepared to try new things.
With all of the problems identified by MIghton over 20 years as to the teaching of Mathematics, changes in the operating educational philosophy have further exacerbated unresolved issues by adopting a guaranteed pass/no failure that insulates students from their actual grade level performance and provides no immediate consequences. Whereas it is true that failure can result in students giving up on certain subjects or school in general, the solution to this is not in eliminating failure and thereby standards. Indeed, it is hard if not impossible to define success where failure is not a possibility. Bypassing learning difficulties and lowering expectations rather than confronting and overcoming them has become the solution. Clearly, however, these practices have done nothing ultimately to solve the problem. Rather, problems are pushed further into the future where solutions become increasingly difficult if not impossible. In doing so, the accumulative impact as to postsecondary options and adult life in general become more ominous.
Much is said in neurology these days about brain plasticity. When I was in elementary school, I can remember teachers repeating that the brain was like any other muscle that improved with exercise. Having said that, I think that most of us translated this as being an admonishment to work harder not an encouragement to become smarter. Intelligence was largely viewed as fixed both by those who supposedly lacked it as evidenced by their school performance and those who possessed it by virtue of their accomplishments. Just as some are led to believe that they are intellectually different or inferior in this regard, I have found that there is a certain investment among both students and teachers who excel in this area to believe in their inherent superiority. Such a belief is after all most reassuring for those who can subscribe to it. I have met numerous teachers throughout my career who firmly believe that ability and intelligence are fixed. As such, they perceive their role to be akin to sorting eggs into small, medium, large and extra-large. Between those who adopt this attitude and others who believe that genuine accountability in learning should be ignored in the interest of ensuring ‘success’, the lives of many students as well as their potential for intellectual development have been seriously jeopardized.
The shift over from the sorting of eggs approach to every player is a winner has solved nothing. Indeed, it has resulted in a generation of students with increasingly high opinions of themselves vulnerable at any time to the threats posed by an unrelenting reality. Whereas such threats can be largely minimized within the artificially constructed school environment, they cannot long resist the adulthood that follows. The creation of an artificial reality is no preparation for the adult reality for which preparation is required. The shock resulting from this lack of preparedness fuels not only depression and hopelessness, but also anger and resentment. As such, an already weakened social fabric is subject to stresses that further threaten its existence.
The challenges facing the present generation require a strength of character and stamina to endure hardship that is increasingly not evident. I have recently heard of the younger generation being referred to as strawberries in that they are easily bruised and more recently as snowflakes in that they dissolve upon contact. The general recognition of this should be a cause for the re-examination of its causes as well as a call for action to address it as a problem with dire implications both individually and collectively.
The confrontation of difficulties in a constructive manner within the school environment as Mighton has advocated has implications far beyond the simple matter of mathematics. At its core it represents the ongoing struggle within each of us to confront challenges through effort and determination in the belief that with effort and endurance we can grow, develop and realize our undiscovered potential rather than succumbing to a sense of insecurity and futility. Empowerment, that often-used term these days, cannot be given but must be nurtured. In the final analysis, it comes from within and is developed on the basis of meeting challenges and difficulties successfully. This is genuine self-confidence as opposed to the simple egotism of blatant arrogance. Human life has never been lacking in challenges as it has never lacked suffering, pain and tragedy. Equally, some portion of happiness, joy and fulfilment are also characteristic of human existence. The unifying theme is, was and always will be that of struggle. As such, passivity achieved either through denial or resignation is the ultimate obstacle to survival as it is the anathema of the human spirt.