On Friday, I wrote a bit about my personal experience in the education system as it pertains to learning math. To summarize: although some of my peers excelled, the way math was taught wasn’t a good match for my own learning style. I’m old enough to understand what kind of learner I am. I can’t just read something and know it. I need to live it: to see it, feel it, chew it on it. I learn by doing, not just by reading and memorizing.
I see the relationship between education and learning as a fast-moving river. Education gives you the tools to build a ship and sail it. When you learn, you’ve built something that works, and you can catch the current and sail into the sunset feeling pretty darn good. But what if the tools you are given are too big to hold? What if the building material for your boat floats for one person, and sinks for another? What happens then? (Answer: you don’t get to visit The Island of Understanding and you live in a state of stress, panic and wet shoes for your entire life.)
OMS Montessori is a Fishbowl patron, and they invited me to learn a bit more about how they approach the subject of math. I already had a bit of an idea, as I’d visited – and wrote about them twice before (here and here) but this was to be a more focused visit. I was eager to learn how can math be taught differently and how a different approach can improve outcomes for students.
To backtrack a bit: the OMS program is based on the philosophy of Maria Montessori, who learned that young children learn sensorily. If children manipulate materials with their hands, the information they learn from that experience is retained more quickly and more deeply. (Think, in the case of math, counting beads and blocks to introduce math concepts.) Maria Montessori’s observations took place decades ago (she was born in 1870) but they are now supported by current brain research. Her learning philosophy holds especially true for kids under the age of six.
Based on her ideas, Montessori (I’m talking about the school now) designed its own math materials, and they are used by students as young as 2 ½. Children move from a concrete sensorial experience to understanding more abstract concepts that don’t require beads and blocks. This is something that doesn’t happen right away, it’s a process.
Dave MacDonald, a Montessori teacher whose charges are between the ages of 6 and 9, showed me the materials that are used when teaching fractions, for example, adding, multiplying, dividing fractions with different denominators. When you are holding those little slivers in your hand the learning is visual and tactile, and it’s bumped up a level. The materials are also “self-correcting,” which means it’s easy for children to figure out they’ve made a mistake and fix it on their own.
“When you’re manipulating [the materials] yourself, you can truly understand why it works,” says Dave. “The teacher’s job is to introduce it, and then we step back and make sure they’re making the key discoveries they need to make.”
As students understand each level, the teacher tweaks and adds new layers when the student is ready for them, but the kids are essentially masters of their own “ah ha” moments.
The advantages of Montessori’s mixed-age groupings comes into play here too. The more proficient kids can help the others. Kids also watch each other and learn from one another during a lesson. “You see that a lot, particularly at the elementary level,” says Pat Garneau, the Director of the English Program. “This age group is particularly collaborative.”
Those are leadership skills emerging.
“Everyone is getting exactly what they need, at the time they need it,” says Dave. “We have a pretty complete picture of each student because we’re constantly assessing, constantly observing.”
So how does memorization fall into all of this? I remember sitting in our rows of desks, the whole class chanting the times tables while the teacher kept time. I asked Pat. “We know that if you memorize first without having that sensorial experience with the material, that your level of understanding is not as deep,” says Pat.
Both Pat and Dave – Montessori teachers – had their own math-related epiphanies during their teacher training. Like me, in their youth, they had memorized ways to find the answers without truly understanding what it all meant. (Think about the steps involved in long division for example.) Dave says there were people in his training group who were math phobic: “You could see them transform over the course of training because it all just made so much sense.”
Is every person a “math person?” In his eight years of teaching at OMS, Dave has only seen one case of a diagnosed math-related learning disability. “That said, there are people who pick it up more quickly, and there are people who struggle with it more,” says Dave. “We have the flexibility to give the students the support that they need, and because [each class grouping] is a three-year age span they get support, not just from the teacher but from their peers as well. So if a student needs more support in math, they will get it.”
So here’s the big question: How can we help our children get a solid foundation in math at home?
There are lots of things parents can do at home to feed little brains. The fact is that math is its own language and it needs to be practiced every day in ways that are physical and concrete. “The math has to be real,” says Pat. “It has to be every day. It has to be applied.” Math has to be part of everyday routines, not just something kids practice at school. So for example, parents of toddlers can ask their kids to count all of the spoons when unloading the dishwasher and put four cups on the table.
“The ability to think in abstract terms about math happens between the ages of 6 and 12,” says Dave. It’s helpful to remember that understanding a concept doesn’t happen for everyone at the same time. It’s a matter of giving kids the tools, the guidance, and waiting for it to fall into place. (And giving them the additional support they need if it’s not happening.)
Associating numbers with objects is also a great activity for young children. Pat points out that the act of counting to 20 is not math, it’s memorization. It’s important to teach kids what the numbers actually represent.
Pat told me that kids start to show a preference for math at five years of age. This is probably because they like it better, and they enjoy it because they’re better at it. If your kids are avoiding math, it’s worth paying attention. “When a child avoids doing something, it’s almost always because they find it hard,” says Pat. “So that’s telling you something. You need to break it down and explain it differently.”
If you’re enrolling kids in any program – or maybe they’re in the middle of one – ask the teachers about their approach to math. Does it match the kind of experience you want for your child?
If you’re interested in the Montessori approach to math you should check out the Math and Montessori Parent Night at OMS Montessori on Tuesday, January 12. (7 p.m. at 335 Lindsay St. in Alta Vista) You’ll be able to see the progression of learning from the toddler years to upper elementary years and gain a better understanding of the way kids learn the language of numbers. It’s also a great time to ask questions about assessment, about how they approach kids who struggle (this is HUGE) and how they help develop math confidence that lasts a lifetime. Or, if you can’t make it and you have questions about the Ottawa Montessori program, go to their website and set up a call or a tour.
I’d love to hear about your own math experiences. Do you feel like you got a good foundation in school? What about your kids?
