Well, it is four in a row for teachers, as once again you successfully predicted the most common student misconception to the following question on straight line graphs. But it was a close one!
Indeed, the most popular student misconception was to select C), attracting 40% of incorrect answers. Why did students go for this? The majority of students seemed to be mixing up the roles of the gradient and the y-intercept as their explanations reveal:
because the line has to pass through -2 on the y-axis and the gradient is positive meaning the line will go uphill from left to right
The intercept is -2, and the gradient is positive since it is coming from the bottom left up to the top right.
But a significant 33% of incorrect choices were for A). And this is a different misconception, with students either muddling up which way the line is sloping:
It has to be A because it is the only one where it is going in a negative direction and it crosses 1 at the y intercept
Or assuming that the -2x must be something to do with the x-intercept:
On the y axis it equals 1 and on the x axis it crosses over on the -2
And my personal favourite:
because it is deal with it !!! It also is going diagonally right which means the y intercept is gonna be positive
Finally, we cannot discount the popularity of D), which accounted for 27% of incorrect responses. This is perhaps the most worrying, as it is two misconceptions rolled into one:
the y axis has to go through -2 and the gradient has to be 1 this graph shows this
The y-intercept is -2 and the line crosses equal distance between the centre so I think they are the same numbers.
A final point worth making is that students who tried to substitute values into the equation to support their argument often went wrong:
y=1-2x and when x=0 -2*0=0 and 1-0 =1 which is where the line intercepts the y axis but then when x=1 -2*1=-2 and 1–2 changes into 1+2=3 which means the line goes over on to the positive side
Because 1-2x is e.g. 1-1(x2)=-1 and so on that means the line will descend rather than ascend
This may suggest that unless students are confident with substitution, dealing with negative numbers, and solving the subsequent equation, their best bet is likely to be to focus on the equation of the line itself.
In summary, once again I feel this adds weight to my belief that it is not simply the case that students can or cannot do a topic, in this case straight line graphs. They either can do it, or cannot do it for several different reasons. The choices of answers, combined with their explanations, reveal clearly whether the misconception is with the gradient, the intercept, the equation itself, substitution, or simply the negative sign. Only by knowing the specific ailment can we propose the appropriate cure.