I include both the English and French Immersion versions as there was a difference in the results. In English, 82% of the students were right whilst in French, only 68% were right. The most common wrong answer for the French Immersion students was 'mètre'. When I have shown this to some adults who know a bit of French but not a lot, they have also chosen 'mètre' as they did not know what 'clé' meant but knew that 'maison' meant house so figured that metres would be the best answer. Students are not allowed to use English-French dictionaries in the EQAO tests but I wonder if these French Immersion students would have performed better even if a picture of a house key was included?
Here is another interesting question:
Recent tweets from Steven Strogatz revealed his concern that students do not know about analogue clocks. In this question, 68% of the students were right with French Immersion students slightly higher than their English counterparts (76% to 67%). I wonder if this difference a result of the clock being more frequently used as a tool for developing the language in French Immersion classes. I also wonder if telling the time is best taught not as a separate unit but as an ongoing life skill throughout the day, throughout the year. A simple act of taking 30 seconds to stop the class and get them to look at the clock to tell the time, done five or six times throughout the day could have a massive impact on student learning. I've shared some ideas on why analogue clocks are fantastic tools for developing Mathematical thinking previously in this post.
This question also reveals a common misconception:
Only 57% of students got this correct. Over a quarter of the students chose 240 minutes. This does not surprise me as I often see a common counting misconception where students are asked to count up (or down) by ones from a start number (bolded) and write:
157, 158, 159, 200
or
300, 259, 258, 257
I call this microwave math as I think it develops from situations such as looking at the decimal clack on a microwave, putting in your food, pressing '3 0 0' then start and, WOW! The next number is 259!
So how to address this misconception? Well, firstly we need to acknowledge it exists and not assume that all students (even if they can tell the time) know that there are 60 minutes in an hour. I have seen some teachers write the number of minutes alongside each hour number on their classroom clock, and then ask questions such as, 'It is two hours to lunch. How many minutes is that?' I have also seen some teachers use a double number line with hours on top and the corresponding minutes below. Such strategies done at frequent intervals throughout the year could go a long way to fixing this common misconception.
A final question which is revealing, is this one:
Here, just less than half the students (49%) got this correct. The most common wrong answer was the top one (one-quarter litre, one-half litre, 1 L, 2 L). I wonder how many of these students misread (or are used to seeing) it as a smallest to greatest question? If so, then at least they were kind of correct! What is more problematic are the students who chose one of the middle two answers. For the second one (chosen by 12% of students), I would assume that they are thinking greatest to smallest as this list has 2 L followed by 1 L. Do these students also think that one-quarter litre and one-half litre are therefore bigger than two litres? For the third option, again assuming that the students are thinking greatest to smallest (on account of 2 L being followed by 1 L), do these students think that one-quarter litre is greater than one-half litre? If so this reminds me of the McDonald's-A&Ws math misconception:
So how do we address this misconception? For students to really understand measurement, they need to spend a lot of time practically measuring things. They MUST experience measuring with rulers, tape measures, scales, or, in this case, by pouring water into containers to see the difference between one litre, one-half litre and one-quarter litre. It is actually a great way to develop fractional understanding too (How many quarter cups of water do you need to fill a full cup?)
One final thought: I wonder if any students were confused by the notation used i.e. 2 litres written as 2 L? I only mention this as I am not sure how often (if ever) I use an upper case L to stand for litres. I either write litres out in full or use a lower case l.
