Math - show your work?
Although there are a few cases where I think multiple choice questions can work for math, I think they are often inappropriate for two primary groups of students: (1) students who are very capable often work backwards to see which answer "works" without having to know the concept or process being tested; (2) students who are struggling with basic concepts who cannot work the problem to the end often cannot find the answer in the possible choices...so in the end, it is often a frustrated guess. It is my opinion (which could certainly be flat wrong) that this weakness applies to both teacher-written and professionally-developed math exams (SAT, ACT, etc). Boot camps "teach" how to score high on these exams.
Asking the student to "show your work" is essentially setting up an essay question type dilemma, with an even more unstructured format!
I have tried both MC and "short answer/show your work" and definitely get a better effort from the low- and medium-capable students when they are able to show their work and get partial credit...but it takes SO much time. For the very capable math students, requiring them to come up with their own answer, and offering the chance for partial credit if work is shown has also produced positive results for me. Those students have to be more prepared and are not rewarded for "breaking the code".
Besides "make GOOD multiple choice math questions", does anyone have a strategy for teaching (fundamental) math?
I completely agree. I want my students to show me they are capable of pattern recognition and abstract reasoning. If I ask them to factor a polynomial, I want them to verify their answers by applying the FOIL method or the distributive law as many times as necessary. If they need to determine the domain or range of a real-valued function, they need to rule out division by zero, square roots of negative numbers, and logarithms of nonpositive numbers. I want them to be rigorous. They need not write a formal proof for an introductory abstract algebra class, but they should be familiar with the nomenclature, the axioms, and the rules of inference. Just memorizing formulas or theorems is not enough, I want them to articulate why their answers are right.
I would like to give partial credit for a good effort, but find it difficult to be consistent. How much effort is "close enough"? So, I mark it wrong if it is wrong (even if they got 9 out of 10 steps right), then allow them to fix it and resubmit it for a "second chance". It is okay to make mistakes in math as long as you learn from them, that's my motto. However, this creates even more work for myself when I see the homework a second time.
I agree. I want to see how they came up with there awnser.
Well said Judy. Really love the way you approach learning.
I am a math teacher and I expect my students to show all work always. Math is not about answers. It is about the thinking, questioning, and actively doing.
Having students show their own work can be helpful in that students can be shown where in the process things broke down and you can give partial credit for answers.
I agree that showing your work is most important in math. It shows the students what they did right, and if they made a mistake they can go back and check what they did wrong. It is a total learning experience either way!
Yes, this is true Tracy. In some disciplines, we need students to elaborate on their answers in order to effectively assess their performance.
I agree that using short answers/show your work uses a lot of time to correct. But in math it's important to know that they understand and can apply the concepts and what better way than to see all their work. I think by forcing a student to be right or wrong can be frustrating for them. If they merely added or subtracted incorrectly on a problem that was more complex, I think partial credit encourages them to try harder. Sometimes just the sheer effort of having to show all their work makes them slow down and think about the questions. Knowing that they can't use "multiple guess" also encourages them to be better prepared. In accounting when I give MC exams the students do worse than when they have to complete problems. I think the dilemma with short answers is consistent grading.
I think that showing your work always let you know if the person knows what the really are doing.
Hi Paul,
You are correct. With multiple choice, it is hard to ensure that the student understood the material 100% as they do tend to work backwards. What I do is assess their true understanding using their homework where the students are required to show their steps which shows me that the students understand. Then I provide a multiple choice quiz on the concepts asking students to outline their work versus working backwards. I have found this to work much better for me.
Thanks!
