Examining the Exam, part 2: thank Que mambam

I have corrected the rest of my Class V maths exam and tabulated the results. I expect that when many of you in Canada see the bar graph below, you will be horrified because 29 students did not attain the 40% pass rate and no student scored in the 90's. You may assume that I am an awful teacher (I'm not), that I have lazy students (I don't), or that my test was unreasonably difficult (it wasn't). As I will explain, these results actually represent remarkable improvement and plenty to be proud of:



First, let's talk about core computational skills. I was ecstatic when I corrected the exam's division component. It included questions to be answered with remainders and others demanding full decimal expansions:



Twenty-one students earned a nine or ten (/10) in this section, demonstrating genuine mastery. At the beginning of the year, none of them could divide, very few could perform multi-digit multiplication reliably, and several still struggled with addition and subtraction.



Many of those who earned 10 out of 10's paid several Sundays for them, attending extra help sessions on their only day off (recall that Bhutan has a 6-day school week.) I am intensely proud of how much time and effort they put in. Even better, they are proud of themselves...

Samdrup: When you go back to Canada and have Canadian students, will you tell them about us?
Me: Of course.
Samdrup: Will you tell them how there was one girl named Samdrup who didn't know any division at first but then she got perfect at it?



One of my mottos is "celebrate success, analyse errors." While I dance a jubilant jig for Samdrup and all my masters of division, see if you can figure out why the following question stumped all but a few students:



The first thing you should have noticed is that it is a word problem. In English. As this sweet little note shows, my students are very much ESL learners:



The greater challenge, though, was that the question contained a distractor, namely the picture of the soccer ball. I included the image hoping it might help some students decode the words "World Cup football field" but it was a gamble. Blame frugality in the cyclostyling room or a more general cultural aversion to whimsy, Bhutanese students aren't accustomed to encountering non-essential images in maths class. Seeing the soccer ball, they felt they had to do something with it. Many students counted the number of panels shown touching its perimeter and wrote "9 units." It isn't a bad answer but is it good enough to predict success in Class VI?



"Social promotion", moving all students to the next grade level irrespective of their achievement or lack of it, is the current fashion in Canada. Teaching in Bhutan has allowed me to see the alternative. At TYLSS, students must earn at least 40% in Maths, English, and Dzongkha and 35% in Science and Social Studies to be promoted to the next grade level. The other Class V teachers and I predict that only about half of our students will be in Class VI next year.

Midway into correcting the exams, I heard the distinctive lekzo heave ho of collective manual labour. I left the staff room to investigate. It turns out it was just my students hoisting a giant prayer flag.







Hard work, planning, and cooperation can accomplish just about anything. Whatever class my students are in next year, they will need those three things to continue their progress. My teaching has been successful if it has instilled those values and an abiding desire to think more clearly. That's what mathematics all comes down to. It is not about a bar graph of marks or even the ability to multiply or divide. Math is about structuring your thoughts in ways that eliminate confusion in order to illuminate what's really going on.