Thursday, May 12, 2016

Poor Math Questions and Misunderstandings

My daughter sent me this article, Parents are Freaking Out Because They Can't Answer a 7-year Olds Exam Question, the other day concerning a Twitter posting about a math problem that was frustrating students, parents, and lots of people on Twitter obviously. Here's the problem:

The issue is there are two answers that could be correct: 65, if you use the 'work backwards' method, subtracting out the 17 that just got on from the 63 and then adding back the 19 that got off.  The other answer is 46, which results from simply subtracting out the 17 that just got on from the 63 currently on the train.  The teachers exam rubric/'test key" stated the correct answer as 46.  Hence - all the confusion, because that would mean the 19 was an unneeded number.

The real problem here, and it is NOT an isolated situation, is that this question is very poorly worded, and thus open to both interpretations. The work-backwards approach assumes that the question is asking for how many people were on the train at the beginning of the trip BEFORE the 19 people got off the train.  The second interpretation assumes the question is asking for how many people were on the train before the 17 got on but AFTER the 19 got off.  Both interpretations are right because the question is so vague - but, as the student obviously found out, the 'test key' accepts only one interpretation.

Poorly worded questions or problems on math tests or in math books are very common and a cause of much frustration and angst on the part of students, parents, and teachers. As a teacher I experienced it often in the textbooks and assessments my students had to use/take. Having worked in the math publishing arena for several years, when creating math lessons, assessments, etc. it is VERY easy to word things in a confusing way, making them subject to multiple interpretations.  Without "vetting" and piloting questions, this can become a huge issue, thus where the problem lies - the creators of today's assessments and textbooks - i.e. the publishing companies - do not always invest in proper editing and piloting of problems to ensure that there is no confusion, misunderstandings, multiple interpretations, etc. That is time and cost prohibitive. 

Poorly worded questions wouldn't be that big a deal if in fact, as this problem asks, the students worked actually counted for something. If their showing of work included their method and interpretation,  and based on their method, the teacher was able to say that yes, in fact, your answer is correct based on your interpretation of the question asked, regardless of the key, then the poorly worded question would just be a minor issue.  But - as this is more than likely a standardized exam with only one acceptable answer, the students' explaining and justifying of their interpretation and work has no bearing on the actual expected outcome.  A true disservice to our students.

Ideally - students won't be exposed to these ambiguous types of questions. But - in a perfect world, even if these types of questions slip through the cracks, a students' explanation of what they interpreted the question to be asking, and the proof of their method to support their interpretation, would be counted as correct - i.e. 65 is a correct solution, even if the "key" says it's 46 because the student was able to explain and justify their answer to support their interpretation.  That's a true assessment of student understanding - not an "set answer" to a crap question.  So - first, let's push for better assessments, but more importantly, let's accept logical, well-reasoned explanations to poorly asked questions because there-in lies true learning.

By the way - a better worded question, if the answer was to be 46, would have been: "How many people were on the train AFTER the 19 left and BEFORE the 17 people got on?  Or - even, "How many people were on the train RIGHT BEFORE the 17 people got on?