"Many parents have asked me:
What is the point of my child explaining their work if they can get the answer wright?
My answer is always the same.
Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics."
- Jo Boaler - https://www.youcubed.org/
Dr. Jo Boaler is considered to be one of the premier voices in mathematics teaching and learning and wrote one of the most interesting books I've read in a long time called "Mathematical Mindsets" - among others that I have also enjoyed. I encourage parents and teachers to go to her website and take a look - there is so much there to challenge thinking about what teaching mathematics is about and how to engage kids in really learning about math rather than just 'doing' math!
This week there was a firestorm of opinion slaking through Alberta over the 'terrible' performance of grade 9 students on the Provincial Achievement Test. I followed this story with great interest - I have never taught grade 9 Math but, as a grade 5/6 teacher for 20 years, I am very familiar with the concept of 'timed' math tests since they used to be a part of the Grade 6 PAT for several years too. As I listened to the outrage and upset and finger pointing at elementary teachers who apparently 'avoid' teaching children how to count and form numbers - among other things, I have some wonders after listening to a week's worth of upset...
I wonder why a timed test?
In the days when I was a student, and when I was a young teacher, we used to give timed math facts tests to students in elementary school - for awhile, we called them Mad Minutes after a program that was popular at the time, and we pretty much gave the tests every day to kids. Each test would be focused on one or two concepts - adding, subtracting, multiplication, division - or a combination of adding/subtracting or multiplication/division - at least, towards the last couple of months of the school year. Tests would offer fewer questions in the beginning, and would gradually increase in complexity as the year progressed with the idea that students would get faster at answering questions over the course of nine or ten months. Including the at-minimum 5 minutes it would take for kids to set up for the tests (distribute the photocopies and have kids find pencils and erasers), and the 5 - 10 minutes per day we took to check and correct the answers, we would spend approximately 60 - 75 hours each school year trying to get our kids faster at filling in the same facts over and over.
One thing I noticed over the years was that kids really didn't get much faster if they wanted to be accurate; if they sacrificed accuracy then they were faster but not successful. Once they knew their facts, they knew them - they didn't get faster at recording the answers on paper, probably because recording the answers on paper took the same amount of time regardless of how quickly you knew the answer. And your answers had to be legible so they could be marked. I used to wonder about those timed tests - and how much time was devoted to practicing for one PAT. Was that the most important thing to assess in learning mathematics - how fast they could fill in the blanks? I wondered where the kids would use their quick regurgitation of math facts when they became adults?
Having learned all my math facts did not make me any less of a mediocre (at best) algebra and trigonometry student in high school and, e other than trying to figure out how much six pairs of socks will cost when shopping, I haven't used my instant recall of math facts too much at all as an adult either. I do use a calculator to add multiple, large numbers - although I am sure I could eventually get the right answer if I tried to add them mentally - it's just that the calculator makes my work faster and more accurate.
So I wonder about the concept of timed testing - are we finding out what we really want to know about what students understand about math?
I also wonder about the nature of the timed test - 1.5 minutes per question to complete multiple step/multiple operations questions that include reading - not basic recall of facts at all but applying concepts and strategies in a timed situation - I wonder about that too.
Kids learn to apply multiple strategies to questions from Kindergarten (first we sort blocks into appropriate groups, then we add them, for example) but we don't give them a time limit because we want to know what they can do, how they reason and make sense of the world through a mathematical lens, not how fast they can think. Adding, subtracting, multiplying, dividing, finding square roots and converting to fractions from decimals are all mathematical strategies students learn to do and use - trying to do them all as quickly as possible within one question in a 15 minute time span just may not be a quality indicator of student achievement...
Several years ago - back in the early 2000's - I had an opportunity to join a very brilliant group of teachers of mathematics to become part of a team that wrote elementary grade level mathematics text books for the "Math Makes Sense" series, an approved Alberta curricular resource. I learned much more than I could ever have contributed to the process for the Grades 3/4/5 text resources, about teaching mathematics but also about understanding what mathematics was all about. What I know is that we have to have a balance in teaching math, just like we have to have a balance between reading and writing when we are teaching literacy. Students need to figure out numbers and then understand they are reliable - 6 is always 6, 6 x 2 is always 12. They also need to know how to use that information in a practical sense and apply it to any and all situations - filling in pages of questions on copied sheets will not make them faster once they know a math fact is always a math fact, and adding up long columns of numbers when you can't really relate to how many 11,654 is, let alone 11,654 + 12,123 will not solve the problem of how many tiles to purchase for a bathroom renovation when you are 35 years old.
Because, to my way of thinking, this is the crux of the math dilemma - we need to teach kids math so they can carry it with them into real life and make sense of mathematical things - like area and perimeter, interest on mortgages, doubling or halving a recipe, how to order shingles for the roof or calculate your rate of pay for a summer job that needs to cover your university tuition. Some of our kids will definitely become engineers, computer programmers and commodities brokers. Regardless, they will all need to know a number is a number, concrete and useful and easily manipulated to make life more simple and sensible.
Timed tests? I wonder if they tell us much more than it might be hard to read a bunch of multi-step questions, calculate and record the answers in a very short time frame. I am not convinced they make us faster at recording answers we already know - it takes us the same amount of time to record the answers, even with much practice.
I understand why the public is upset - on the surface at least, the results don't look so good. But I wonder if it just might be possible the results aren't really showing what we want to know - which is how successfully students can manipulate numbers and ideas to demonstrate understanding of their relationships to each other and other mathematical concepts.
I also wonder about all the kids who have learned to dislike mathematics and opted out of amazing careers to avoid math altogether...as a mother, I learned the hard way that this is sometimes the way kids feel about math - and I am determined to offer a different way of seeing and thinking about math at EHS. No timed tests but lots of opportunity to cement knowledge of numbers, recall what we know and make sense of how numbers connect to shape and space, known and unknown, parts and wholes. That's the real challenge of mathematics - learning to see numbers as real and useful and fun rather than blanks to fill in on a page. At least, in my opinion :)
Lorraine Kinsman
Principal
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