with all of these articles (like here, here, oh, and yes — here), how can one not be aware and contemplative of the EQAO scores, specifically in Math. As a grade 6 teacher, and as one of the many others who saw the Ontario results, the question, “What happened?” has been eating away at me for days. Since then, “What happened?” has morphed into “What do I do now?”
Because, if not now, when?
However, before I discuss my thoughts, and, spoiler alert: There is no one answer, I should probably do my best (within my knowledge) to give some information.
The Concept of “50%”:
I can see how the concept of “50% achieve” in Mathematics on EQAO a little deceiving. Remember, these are those students who achieved level 3 or higher on the assessment. It does not mean that 50% “failed”. In fact, if we compare to the description on the provincial report card, a “C”, or, level 2, is:
“The student has demonstrated the required knowledge and skills with some effectiveness. Achievement approaches the provincial standard.”
So, in reality, this student has not failed. They are approaching provincial standard. I am positive when more specific scores are available, educators will find that many students will be ‘hovering’ in the mid/high level 2 range, and thus, in theory, students who are considered ‘moveable’. Another question arises: Why are these students not moving into the “level 3” category, and what do we do to help them get there?
The concept of “rote memorization”:
Now, let’s jump to another point that comes out in media. As per Robyn Urback’s article, “rote memorization” seems to one solution that keeps popping up.
So, sure. Let’s go with that idea. Let’s ‘play’ as if we go ‘back’ to teaching rote memorization of mathematical facts.
Here we go.
OK. So, what mathematical concepts (because, they are concepts!) can we actually memorize? The first thing that comes to mind is multiplication tables. I noticed in the comments sections of these articles was a concern that students could ‘not make change’. Many people commenting were discussing specific instances where they were at the checkout, and the person working was stumped. Sure, a concern for many. We need to go back and memorize so that we don’t have this guffaw at the store.
Also, working flexibly with money and money amounts is something that is perfected with experience. Those who work in the retail industry are going to have mental shortcuts for finding change, and are only going to become fast and fluent when they are constantly doing so. The real-life experience is what makes people ‘fast’ at giving change and working with certain amounts.
So, we memorize our multiplication tables. Heck, why not use what we know about multiplying, and apply it to division (it is just the inverse, right? Oh no! Wait, that won’t do. Did you just learn math by making a connection between the relationships of operations?). We can do the same for memorizing our addition and subtraction facts. How high do we go? Do we memorize a certain number by a grade? For example, we all now up to our 12 times tables by grade 6? That would be my first question.
Well that fixes that! What else can we memorize? Oh, some polygons! A triangle has 3 sides, it looks like this:
See? You memorized it. Now you know triangles. I can do the same for other regular 2D polygons and 3D figures.
Now I can have you memorize some formulas. Perimeter and Area for starters.
But what about the other strands and areas of mathematics students are to experience, and are to learn? Interpreting data, for example. I am not too sure how to have that become rote. Every graph is different with different information, so strategies for reading and understanding the information given in a graph is going to change. What about patterning? Patterns change and morph, they can grow or shrink. Sure, a simple pattern might be “decreasing by two each term”, but what about more complex, and geometric patterns? You need to look at them, think, and analyze them. Again, I can’t give you a one time formula to memorize and you know patterns. For the sake of argument’s sake, there are math strands in the Ontario Curriculum that cannot be sheerly memorized.
Assessment Itself: What are we wanting to assess?
If we continue the idea of making math completely rote, what would an assessment like EQAO look like now? How would EQAO be laid out? What would be the purpose of the assessment? Would it literally be a table of addition, subtraction, multiplication, and division questions? Would timing and speed be valued as well (meaning we add a timing element?).
Or, are we wanting to know exactly how a student is learning and understanding in mathematics? If I go rote teaching, then really just making sure they have it memorized. Even then, someone will forget the formula, second guess their memory. Will scores be that much different? Maybe. What exactly am I testing at this point? Memory, or a student’s ability to process, problem solve, and use what they know about math in a new context? Their application capabilities? What is going to give me more information as an educator into a student’s understanding, and ability to process and apply math?
So, to get a little broader picture, I guess a word problem could be added.
Shavi bought $16.55 worth of goods at a store. He gave a $20.00. How much change should he receive?
No matter how much practice and memorization the student has done, what are they going to do now? If we have just been rote memorizing straight up math facts, some things are going to happen here:
- They will struggle with what operation needs to be required here. There is language that needs to be comprehended and deconstructed.
- Even with rote memorization, the decimal will be the hardship. No child can be expected to memorize whole numbers and all possible decimal number operations, too. If I round the 16.55 to 16, subtract that from 20, my math will be wrong. Suddenly they are going to need a strategy – yes, a strategy, to solve this effectively and efficiently.
So — here is what I am getting at: Rote learning and memorization will not solve the EQAO problem. Math is a fluid, flexible concept — it ebbs and flows depending on the situation the math is in. One strategy will not always be the best dependant on what is happening. Rote memorization will not be the answer to all mathematical quandaries. Will automaticity and fluency of math basics help? Absolutely. Will teaching completely in this manner ‘fix’ the issues of the scores? Probably not.
What We Can Do Now:
So, now I have two things to say:
- If math were completely rote in schools, would assessment practices such as EQAO garner any worthy information other than it was memorized or not;
- If testing for a student’s mathematical thinking and application skills is what we are interested in as educators, and as a society at large, then rote memorization is not going to ‘fix’ very much, if anything.
What does need to happen?
Well, clearly many things. If anything, the latest results tell us we need to keep looking deeper. We are not going to have any one answer anytime soon. We need to look at 3 big areas: How students learn mathematics most effectively, how teachers know, understand and present math, and the developmental reality of conceptual attainment in mathematics. There is a developmental piece for how students learn math – are we addressing this enough? Maybe we need to really look at the curriculum and the test itself.
Either way, as a society, as educators, we need ask ourselves what are we looking for when we standardize test. Are we looking for patterns into student thinking, application, and connecting ideas? Or do we just want to make sure they can recite the multiplication table without skipping a beat?
How do I really effectively test a student’s actual mathematical understanding? Once I have figured that out, what does it implicate for the teaching and learning of mathematics?
Mathematical balance is a phrase that pops into my head. Giving students time to investigate mathematical concepts, but also giving them time to practice and become comfortable working with the ‘mathematical basics’. As of the 2005 Ontario Math curriculum, this has always been the process of math instruction. Never does it say “no longer do we teach multiplication tables!”. A balance of both conceptual and explicit instruction is needed; and teachers need to know when to do which depending on the student’s needs. Most of all, we want our students thinking.
If anything, EQAO makes us bring questions to the table, and requires us to really talk about what we need to do as educators.