View related sites
Do you allow students to use a textbook when solving problems at the board?
Yale University, late 1820s.
Andrew Jackson is the President. (Who? I know. He managed to dismantle the Bank of America and forcibly removed most members of the Native American tribes in the South to Indian Territory. He also signed a treaty with Great Britain and survived an assassination attempt.)
At Yale, however, history was about to be made in a different manner entirely.
In 1825, blackboards and chalk began to be used at Yale for the first time. This meant that, instead of using textbooks as references, students were expected to come to the board and reconstruct knowledge from scratch, drawing their own diagrams. Even worse, they were asked to do so without the help of the textbook at all.
Students of the Yale second-year mathematics class were not happy. (We think that tech rebellion is new; it’s not.) While they were content to solve problems on some topics of study at the chalkboard, they drew the line at tricky conic sections. They went on strike and simply refused to do it.
Thirty-eight students out of a class of eighty-seven were suspended; the Faculty contacted the students' parents, and the students were pressured into signing a statement of concession:
“We, the undersigned, having been led into a course of opposition to the government of Yale College, do acknowledge our fault in this resistance, and promise, on being restored to our standing in the class, to yield a faithful obedience to the laws (of Yale College).”
The incident was known as the Conic Sections Rebellion of 1825.
However, the matter did not end there. The students continued to be quietly revolting.
1830. Another policy change: students now had to draw their own reference diagrams for exams rather than be allowed to refer to diagrams in their textbooks. The students took action again. A number of students staged a rebellion in which they refused to take the exams at all. The Second Conic Sections Rebellion ended with even more conflict: forty-three of the ninety-six students were excluded and blacklisted by Yale.
Have you ever come up against this type of stubbornness in pupils – the kind of bullish refusal to complete a mathematical task that stops all fruitful work in its tracks? Has it ever been the result of a policy change like the one at Yale, where students felt that the circumstances under which they were being asked to work had become grossly unfair?
Did your sympathies lie with the students at Yale, the teachers; both; or neither?
Rebellious students can be tough. When teaching maths, we may face resistance to our subject as well as our behaviour management; students may already hate the subject and feel strong emotional reactions to it before they have even reached our classrooms.
When students refuse to engage with mathematical ideas, how do you respond?
Ignacio et al (2006) report that ‘many pupils generate negative attitudes towards mathematics in the course of their academic life, and on occasions present an authentic aversion to the discipline’.
We often refer to these sorts of ideas as the affective domain. The affective domain is much more than just an attitude towards something: it may comprise of beliefs, values, and emotions or feelings, too. One possible model, showing how these facets are interconnected, is given below.
How does maths make you feel?
One possible response is given below:
‘On the eighth day God created mathematics. He took stainless steel, and he rolled it out thin, and he made it into a fence, forty cubits high, and infinite cubits long. And on this fence, in fair capitals, he did print rules, theorems, axioms and pointed reminders. “Invert and multiply.” “The square on the hypotenuse is three decibels louder than one hand clapping.” “Always do what’s in the parentheses first.” And when he was finished, he said, “On one side of this fence will reside those who are good at maths. And on the other side will remain those who are bad at maths, and woe unto them, for they shall weep and gnash their teeth.” Maths does make me think of a stainless steel wall—hard, cold, smooth, offering no handhold, all it does is glint back at me. Edge up to it, put your nose against it, it doesn’t take your shape, it doesn’t have any smell, all it does is make your nose cold. I like the shine of it—it does look very smart, in an icy way. But I resent its cold impenetrability, its supercilious glare.’ (Buerk 1985, p. 59, cited in Grootenboer & Lomas, 2015)
If maths feels like a wall for students, should we be surprised when sometimes they give up and sit down next to it? Is this defiance, or something else?
How can we help them see it differently?
In the case of the Great Conic Section Rebellion (Parts 1 and 2), it is a shame that a compromise could not have been reached. If a student in your classroom refused to work on a problem at the board, yet gave clear reasoning for doing so, there may be flexibility for discussion there – or there may not. Your classroom rules, the school’s policies, your relationship with the pupil will all come into play here. But the ability to recognise when pupils have emotional walls or boundaries – stated differently: principles – and aren’t just misbehaving appears to be significant when asking them not only to think about mathematics, but also to develop a (hopefully positive) relationship with it.
When is mathematical rebellion understandable, and what can we do about it?
Join the conversation: You can tweet us @CambridgeMaths or comment below.