# Precision in student work

At the end of the school year, I gave my students a problem set related to the law of sines where many students engaged in approximation at various points. I noted two types of precision issues in their work.

1) Looking at the following pattern 19.1, 19.03, 18.95 and concluding that the rule is that sin(A)/a, sin(B)/b, and sin(C)/c are approximately equal. I think that in this instance students are paying excessive attention to precision, rather than trying to conclude an overall rule.

2) sin(60) = .9 For the purposes of this assignment and most trigonometry problems, it seems that a one digit approximation is not sufficiently precise. (Although the student who gives a 10-digit expansion also seems to be missing something)

What do you think is the actual issue represented by these two examples?

What knowledge/ skills are necessary for students to be appropriately precise when giving approximate answers? How do I build this capacity in my students?

• Could you clarify (1)? For instance, do you mean that you gave students a triangle and had them calculate $\frac{\sin{A}}{a}$, $\frac{\sin{B}}{b}$, and $\frac{\sin{C}}{c}$, which came out to 19.1, 19.03, and 18.95, respectively? Perhaps, if this is the case, you could try specifying that students round to the nearest whole number in the directions for the activity? Jul 4 '15 at 16:13
• Students here in the US receive many years of mathematical training in which these ideas are never discussed, followed by their first course in a quantitative science (usually chemistry), in which the concept of significant figures is introduced. If you're teaching students who haven't taken chem yet, it's not surprising that they have no clue about this.
– user507
Jul 4 '15 at 18:51

I've seen people (more often in the sciences than math, though it's certainly appropriate in math) work with numbers with errors (1.04$\pm$0.1) and expect students to report calculations correctly---that is, is accurately as possible given the uncertainty in the original data.