“Where do these norms come from anyway?” That’s what Cathy Fosnot said in response to a question I asked her on voice.ed radio. I wanted to know what to do to help students who were well below their peers on the Landscape of Learning. (You can listen to the whole thing here.)
I was thinking about this again this past week when EQAO math results were released to the public. Spoiler: they aren’t great. And now everyone is in a snit. Blame is being placed on the teachers, the “new” way of teaching math, the curriculum and even the test itself.
I did a lot of reading this summer about developmental progression of the acquisition of math skills. And you know what? None of them strictly says, “By such and such age kids need to be able to do this….and that…” Instead, the research has shown that first this skill develops, and then that one, and as problems become more complex the student folds back (as Alex Lawson calls it) to earlier strategies and skills they trust.
When my children were small, I carefully monitored the expected milestones for physical and cognitive development. My daughter met each milestone at exactly the right time. Rolling over is supposed to happen at 5 months, and sure enough within a week of her 5 month birthday, she rolled over. Same for walking, running, accepting solid food, etc. When at age 18 months she did not have 20 words in her vocabulary, I signed her up for a speech assessment. Those milestones are normed. Lots of work has been done, lots of comparisons have been made, and now we know it is developmentally appropriate for 5 year olds to stand on one foot for 10 seconds or longer, and that they could be doing it before 5, but if they are 6 and can’t we need to talk to the doctor about it because something is not right.
But none of the math research seems to be that specific. I can’t look at a student and say, “Today he turned 8, in the next few weeks fractions are going to make sense to him.” The math skills develop sequentially: the child learns to add 1 digit numbers, then 2, etc.
But large scale testing, such as EQAO, isn’t like that at all. Instead, we test kids when they are in a certain grade. At times the difference between the oldest child in a single grade and the youngest can be a whole year. My daughter turned 6 in January, but another child in her class won’t be turning 6 until December. But someday (3 times to be exact) the two of them will be expected to take their EQAO on the same day. They are not marked on their achievement as it relates to their age. This test assumes that every grade 3 or 6 or 9 student is at the same developmental stage and should be tested in exactly the same way with the same tests and same testing conditions. Maybe this is closer to true when they get to high school, but I feel like I have a lot of anecdotal evidence, collected over 17 years of teaching grade 3 students, that would suggest grade 3 students are definitely not all at the same place developmentally in a lot of different areas.
So where do these norms come from? Well, in this case, they aren’t norms. They are raw scores that reflect the number of right and wrong answers a child gave. They say, “This child is meeting the standard for a child in this grade.” Or is not meeting the standard. Or is nearly meeting the standard.
I think the problem lies in the interpretation. We jump to the conclusion that a kid is behind, lagging in skills his peers have. Most teachers would be able to tell you this sort of information about the students in their class (and do – 3 times a year in massive essays about students a.k.a. report cards.) Hopefully all of us are getting better at identifying exactly which skills to work on to move individuals along the landscape or continuum.
When I look at the test results for my class last year, it will be too late for me to do anything for those exact people. They are in somebody else’s class now. But I can see that all or most struggled with this or that and examine my own practice to see what I can do to perhaps avert this result for the current group.
However, how well my students are doing, whether or not they are meeting grade level standards, is only one piece of the puzzle. I’m much more interested in what they can do, and what skill they need to develop next than I am in comparing them to all the kids in the province. My job is to teach the 20 kids in front of me. I’m just going to worry about them.
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