Please take some time to explore the stories below.
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Note that while some of the quotations below have been edited for readability, the researchers have done their best not to alter the meaning or content therein.
Steven is 14 years old and in grade 8 in a school in Ottawa, Canada. He was born in China and came to Canada in the mid-year of grade 5. Steven lived in Montreal for 3 years, before moving to Ottawa. In China, he studied mathematics in Mandarin. In Montreal, he studied mathematics in French, and then when he moved to Ottawa, he studied mathematics in English.
Solving "the Canada Way"
Steven said that some of the math procedures were done differently in China and in Canada. He grabbed a notebook and pencil and solved the same math equation (i.e., 168 divided by 12) using the algorithms learned in China (see the upper image on the right) and Canada (see the lower image on the right). He shared that it takes time to get used to “the Canada way”. When asked about the difference between the two algorithms, he explained, “Um, well, the major difference, I think, we just write the, like the second number 168 divided by 12 divided by in a different place and we write the answer, um, quotient? What we call it? The result of, the result of division, what we call it? Oh, yes, we write it in a different place. That's pretty much the main difference”. Steven was asked if he preferred one way over the other, and he stated, “Well, I'm more used to the China way, so I prefer it, but I also took some time to understand how to do it in Canadian way. Because teacher may not understand.…So I can use it to it, so I get used to it, very fast, very early”. Steven also talked about how one of his teachers in Canada said to him, “You do it in a different way". However, Steven explained to them he does not “understand how to do it in your ways”. Yet he displayed acceptance or acquiescence by learning the Canadian way, he stated, “/but/ then I figure it out" by relying on a book that showed him how to do it, “one by one, step by step”.
Math in China as "harder"
Steven described his mathematics experience in China as “harder” than what he experienced in Canada, and when asked why, he stated how they were not just solving a simple x equation, as he experienced in Canada. Rather, in China, he was solving "in-life problems with it [algebra]”, which he characterized, as “harder”. He stated that, in Canada, they spent a lot of time working on Algebra, when “I learned it a long time ago already. So, that's easy for me, but you know, what is it called, the graph? And those things? I didn't learn that much in China. So, yeah, that's more challenging”. Steven shared how the algebraic relations in the exercise book he used in China are “kinda like very complicated”. Steven showed a grade 6 math textbook that he used in China. When asked about the textbook, Steven explained that he purchased textbooks from China for grades 6, 7, 8, and 9, and he will get the exercise books for those grades soon. He uses these textbooks to support his mathematics learning in Canada.
Project work – help the other guy do their taxes
Steven felt that in Ottawa, they were required to do many projects for mathematics, and the students were not given clear instructions, he shared, “One of the differences is, in China and Montreal, we always do some calculations and something like that for homework, but now here, we mostly do project, after school...So, sometimes the math project is not well explained. Like, we don't have a clear instruction to follow and it's, well, very hard to say, is, it's just uh you don't have a clear instruction to follow so you cannot do it very well”. One example of a school project shared was on the topic of Financial Literacy. Steven felt the project was more of an English project than a math project, he said, “I think is more English ((direct)) than math. Because we write like five pages, and you rarely see numbers... Explain to teacher how you help the other guy how to do their tax”. Steven even shared that he created a probability game for math in Ottawa. He explained that the game was “kind of similar with the you know Battleship...This kind of similar with it, by add more probability choices... So yeah. I don't think that's a really good game so whatever”. One of the differences is, in China and Montreal, we always do some calculations and something like that for homework, but now here, we mostly do project, after school...So, sometimes the math project is not well explained. Like, we don't have a clear instruction to follow and it's, well, very hard to say, is, it's just uh you don't have a clear instruction to follow so you cannot do it very well. One example of a school project shared was on the topic of Financial Literacy. Steven felt the project was more of an English project than a math project, he said, “I think is more English ((direct)) than math. Because we write like five pages, and you rarely see numbers... Explain to teacher how you help the other guy how to do their tax”. Steven even shared that he created a probability game for math in Ottawa. He explained that the game was “kind of similar with the you know Battleship...This kind of similar with it, by add more probability choices... So yeah. I don't think that's a really good game so whatever”.
Special things called abacus
When asked about his experiences with mathematical tools, Steven shared, “In China, we have special things called abacus...I, I know how to use it, but teachers don't teach it in class...I learned it by like, going somewhere else...I, I brought it to the school [in Canada] sometimes, and, still, my classmates be like, “It's a calculator”. But it's not...it really does help a lot...how to do math. I have a backwards in my head [I have it in the back of my head] and I calculate there...And I calculate with it”. Steven mentioned that he did not share his use of the abacus with his teachers in Canada because “they didn’t ask”. But given his use of the abacus to make calculations, he often wrote the answer without showing his work, which led his teachers to ask him to show his work, he explained, “Sometimes, we do uh you know, two-digit times two digit. That's easy for me. So, I just write the answer. Teacher be like “Uh show your work, please” ...And so I’m gonna calculate them one by one, step by step. And I will write it down”. Here, the abacus is an invisible tool that Steven uses but his teachers are not aware of it. Therefore, he is required to show the steps taken to solve the problem.
That [vocabulary] bothered me a lot
When asked about his mathematics experience after coming to Canada, Steven said, “I spent a whole year studying French [in Montreal]. It was a very hard language…The good news is the math there is so easy. Like, for me, I, I thought it's like for, grade two or three or something.... so, I didn't have any pressure on math. Just sometimes we did something in a different way, like division... and yeah, math is if I understand, if I can read the French and I understand it. I can do it”. However, a difference in mathematics that Steven experienced in Montreal was related to mathematics vocabulary, he shared, “um, just other difficulties I found is the vocabulary...Yeah. So, you see, all the mathematic language those things have a different name, very different”. Steven shared an example related to Geometry and shared how the names of shapes were easier in China because the name described the shape, he explained “like, you see the octagon, we just say shape with eight sides. And that's super easy to learn. You just count one by one”. However, Steven finds similarities in the way geometry is taught in both countries, he shared that “both teachers would draw the shape on the board, and they would explain how to calculate the perimeter or area”. Another example shared was concerning the term prime number, which he found confusing, he said “in French, it’s nombre premier. And the, the word premier is like same as first. So, I'm getting pretty confused there”. Still, Steven felt that he was at an advantage when he moved to Ottawa, as the vocabulary words he learned in Montreal were like those he learned in Ottawa, he explained, “Also, I have an advantage is that every time it comes a new word, maybe my classmates didn't know, but I can tell from French...So uh, I can know a word by ah using French strategy. So, like, one word is, it tells nothing English but it's very similar from another word in French so I can tell it easily”. In general, Steven felt that he did not experience challenges concerning language in moving from Montreal to Ottawa, he said, “you know, English and French is kind of similar...so it’s kind of easy”. He also felt that some of what he learned in grade 7 in Montreal, he was learning in Grade 8 in Ottawa, he said, “Also, I have a, like, I don't know if it's my feeling or it’s true is that we learn the kind of same thing as grade 8, as a, grade 7 in Montreal”. However, when Steven was asked to share what advice he would give a teacher welcoming a new student from China, he said; “Um, my advice is teach more uh vocabulary, math vocabulary in the class. And also, every student from China even they're not very good at math, they should be, they should uh could easily afford the math here [Seems to mean that they could easily understand and do the math here]. So, the first thing that block them is probably the vocabulary. Hmm. Yeah, after the vocabulary, um, just, um make, make them do more, a little bit exercise with it. And ((that’s it)), that's done...That [vocabulary] bothered me a lot”.
Maya is 18 years old and attended her senior year and first year of university in Ottawa, Canada. She lived and studied in Saudi Arabia most of her life, except for when was in grade 5, she came to Toronto, Canada and studied there for 6 months. In Saudi Arabia, Maya learned mathematics in Arabic until grade 7, and from grade 8 onwards, she learned mathematics in English.
Why is everybody so scared?
When asked if she experienced any differences between learning mathematics in Saudi Arabia and in Canada, Maya described how in Saudi Arabia she took the International General Certificate of Secondary Education (IGCSE) curriculum, which was taught to students in Year 10 - 11 in the UK to prepare them for university. So, they would “dive a lot more” into topics like deriving and integration, which she “didn't notice being taught in senior year” in Ottawa. Such topics were first presented to her at university when she took the calculus and vectors course required for her program, she explains, “We started deriving just a bit and I was like, wait, I took this before...I always hear like, oh, calculus is such a scary subject and I was like, is it? Like, what is it about? Like, why is everybody so scared? … And then it was like, oh, deriving and I was like, oh, it's deriving like, “what's scary about it? So, because I've had like, knowledge about it, it was really easy and I got like an 88 in that class, and it was during summer and it was three weeks... But we went over it more in Saudi in grade 8 and in my 11th grade. We had a lot of integration and deriving problems. And I practiced it a lot because it was a very, like, relevant topic. And so, I had more of a basic knowledge behind it than any other student would who was studying here [in Canada]”.
My deepest fear was graphs...
Another difference Maya experienced between the two education systems (i.e., Saudi Arabia and Canada) was related to graphs. Maya described how she hated graphs prior to coming to Canada because she did not have any knowledge of them: “My deepest fear was graphs because we were never taught about it. And I was like, oh my God, I hate graphs. I'm so scared of graphs... … I didn't feel like if I was confronted with a mathematical graphical question, I would be able to solve it. And that makes me scared. I'm like, you're intimidating me. I don't know how to solve you”. However, her hate for graphs changed when she took the grade 11 Functions course in high school, in Canada. She explained, “So, when I came here [to Canada], there was the functions course that was the 3U [grade 11], that had a lot to deal with graphs and how to write graphs and draw them and whatnot, which we did not go over at all. ... But I felt like it was easy, although it wasn't like taught and I didn't have any knowledge in graphs, if anything, I didn't like them before. But then suddenly, I was like, oh wow, this is really fun. I don't know why we were never taught about it. So yeah, we weren't taught about graphs, but I did really enjoy it. And I didn't find it as hard.... and I was like, graphs is the best subject and best topic ever. I love graphs... [Also], the “e” or the “ln”, we never talked about that also before, and I saw them on my calculator when we would like, take exams, and I was like, wow, I wonder when I'm ever gonna be taught about this, and then when I came here [to Canada], they were like, graphing, the like, “e” graphs or the “ln”. And I was like, oh, my God, you can graph those? I didn't know that. So that was like another discovery for me to find out about...Desmos was a blessing, like till now I still use it with my calculus classes and whatnot to kind of like, help me visualize the graphs. And when she would like insert, she’d [the teacher] be like, oh, like, this is the website, and you just insert your graph and then it shows up and I was like, what do you mean it just shows up? Like it just like, it just makes it for you? This is beautiful. It was just, it was mind blowing. And, yeah, I use that a lot. I completely forgot about it. But yeah, I use the Desmos Graphing Calculator a lot”.
How they want you to phrase it
Maya also talked about the difference in how she practiced for tests or exams in Saudi Arabia and in Canada. She explained, “So, in Saudi Arabia, it was basically just past papers [copies of previous exams], I did not need more than that. It was, as long as you go through them and you practice them, I would print like a bunch of sheets on my printer, and just try to go through them with like, the topics. And that's like, that should guarantee you as long as you get the hang of how like, they want you to phrase it and how to solve it. That should be good. You're okay”. “Here [in Canada] there wasn't a specific kind of way you needed to follow your answers. Like, I was getting used to it, was basically like, you look at the paper, and you kind of like, memorize it, there was no like, older tests here or anything I could, you know, get my hands on. So, I had to use YouTube and look up kind of the topics and write my own notes, and::, like, relearn them before the test so I could like, go through more examples, because I didn't know what examples they would get. It wasn't like, oh, they would get this type or that type. Whereas in the past papers, it was like, oh, it's gonna be like this, like, this is the way it's going to be phrased. If it's phrased like this, that means it wants this or like, if it's phrased like that, this is what it wants. Where here, it's just like, randomized and I'm like, oh::, my God, I don't know what expect. So, I had to go through everything /And yeah/, just basically surf the internet until like, I felt content enough to go into the RST”. “Google, YouTube, any, any website I could get my hands on that gives more notes or exercises that I could find. Like, I would just put in the topic and then like exercises or like anything, and if I'd find like PDFs or something. I tried to like download them and try to solve them, reflect upon them and whatnot. And mostly the worksheets, because I know, they would say like, this is how you're supposed to get like your main foundation. So as long as you have these topics, it should be okay. And then there's like the midterms we already did, to try to go over them just in case there was something similar that might be in the in the RST or whatnot”.
Online... I did what I could
Maya also described how her experience learning mathematics online, due to the Covid 19 pandemic, changed her perspective towards mathematics. She shared that when she took the 4U [Grade 12] Advanced Functions course, the first couple of weeks, which were in person, went very well for her, but that quickly changed when they went online. “But then it was the second quarter, around Christmas break, everybody went back to online learning. And, if there's one thing about me is that I cannot study online. I can't do it. I cannot understand. I can't focus. It just doesn't work with me…. So, that's where like my grade, like, completely plummeted, and I went to down to like, 70s, 60s, and I was like, what? Like, I never got like this mark on math like, this is not me. This is not who I am. And I knew it wasn't like the subject, it was just like the difficulties of like online teaching, and just me not understanding, specifically. But then I obviously had to like pull myself out of it and say, you know, like, it's just a couple more weeks, I have to get my grade up. This is my last year, like I have to, and I ended up with like an 84 or something by the end of the class. But like it still haunts me how much online could like affect from like 90 to 60. I was like, traumatizing. But it wasn't as bad. I feel like if I were to retake it in class., I would have gotten a higher grade. But it was fine, at the end. It was like an 80 something so I don't mind. It's okay. I did what I could”.
Sarah and Ghazel are sisters. Sarah is 13 years old and in grade 7. Ghazel is 12 years old and in grade 6. They were born in Baghdad, Iraq, and moved to Turkey when they were very young. In Turkey, Sarah attended grades 1-4 and Ghazel attended grades 1-3. When they came to Canada, Sarah was in “the middle of grade 4”, and Ghazel was “in the middle of grade 3”. In Turkey, they studied mathematics in Turkish, and when they moved to Ottawa, they studied mathematics in English.
We were like glued together
Sarah explained how in Turkey they had the same teacher for grades 1-3, and that same teacher taught them all subjects except for English. She also shared how she preferred math in Turkey. She explains, “It was kind of easy…and like the questions were easy and I really like it. Um, it was not much different in Canada. When I came here, I was in grade 4, it was like the same, kind of similar, you know, plus, adding, stuff like that. It was easy. It was, it was similar. But like, I enjoy Turkey more”. When asked why she enjoyed Turkey more, Sarah said, “I don't know... It’s just that I would rather like, do math in Turkey...Um, in Turkey we don’t really like do, um like here [in Canada], we don’t really do partners and stuff, like we do our own thing ...And I don’t like it...But in here [in Canada], we do like partners, like, the teachers, the teacher tell us what to do, and then we do like the first question, the second questions and then we do partner, so it can help us. But like in Turkey, this is the thing that I don’t like about Turkey is that no like partners...And I like it here. And like I don't know. I just feel like Turkey is better. There's not a specific thing but it’s that like, I don't know, I think, I would like rather Turkey”. “I don't think in Turkey they had like groupwork...Yeah, and then also in Turkey, we used to have like, you know, seats, like together... Yeah. We're like glued together like actually two, one chair, one chair like they're actually together. And like we used to sit as, it was, it used to be fun... And like if it was two and two, and like every day we like, maybe I'm in the back, I come like to the front and then to the front every day... So, we don't get bored from the same seat”. Whereas in Canada, Sarah said, “Um, they're just like by, by themselves. Like the same seat, the whole year... Yeah, but like there's like I sit by myself. It's like, what two, like, it's not that really far from the other seat. It's like only like, yeah, 22 centimeters. It's not that far... But when we want to like do work together... Like from now, they like allowed us, like in the lunchtime, they allowed us to sit with our friends. Like, sit in another seat. And like, you know, get like closer not like before we used to wear masks, and not like do a lot to do anything and stuff. And also, um, when we want to do like group work, they allowed us to like get the seats together. And then when we're done, we can just separate it and then sit in our own seats”.
An actual apple
When asked if they used the same tools for math in Canada, Sarah responded, “It's kind of similar. It's like the same questions. Like they explain, they help you, they, you know, give you a chance to do your own work so they can understand if you like, understand or not. It's kind of the similar, it's like the similar questions, you know, but it's just that like, I would prefer Turkey more. I don't know. I just feel like it's closer to like...Like, I feel like it's more fun. Like, I don’t know. I feel like it's more fun. I don't know because I live like eight years there. Or something. Like before I even started school. I went there like when I was like five, six, or something... School was more fun because like maybe it was because it's grade four, and like two, and three. Like, they gave us like props to use with maths, and like they gave us like apples to use or candy to use. So it was more fun for kids, but here now it’s grade seven, six, five so like we have to like do it on our own, and like if we have and all that you know like-, pretty hard...Yeah, it's like they give us, well I was like, like I told you from grade one to grade four, like in grade two they used to like give us like apple you know, candy to like count like one plus one, like they gave us apple plus apple like actual apple.... We would like, you know, it would be more fun to us like to love it more. They would like think that way”. “In grade, like, in grade four [in Canada], they used to don't do that... Yeah, they used to not do that. They used to not like get actual apple and candy to make the kids love math and stuff. They just used the board. Like give us sheets”.
Ghazel is Sarah’s younger sister. Ghazel is 12 years old and in grade 6. In Turkey, Ghazel attended grades 1-3. When she came to Canada, Ghazel was “in the middle of grade 3”. In Turkey, they studied mathematics in Turkish, and when they moved to Ottawa, they studied mathematics in English.
They teach us in a really cool way
“Um, in Turkey, it was really fun. As I said, they give us a lot of props to use as a grade three. Um, and they also like, teach us in a, in a fun way. Like, they count the numbers in a fun way... They teach us in a really cool way. And, the best part is, um, for my grade three, they give, like us, um, like a chance to like, like say something or, like, if you're, you don't want to like answer the question, you're allowed to because you’re grade three but if it's grade four, like you have to answer because you're in grade four and you need to learn to, like, know what to say to like grade five or six or seven. And, yeah, just what my sister said like in math, it's like really easy, and, because they teach us in a good way, and they also like give us terms on the board, and they give you time and, yeah, it's just like that”.
Here they don’t actually want to teach you that much
“Here [in Canada], like grade five, I mean in grade four and five and six, and six. Um, so like, but here, they teach you on the board and then after they give you the sheet to like just do it. Like and then, but there [in Turkey], they like have to actually teach you for you to do it. But here, they, you know what they say? They say try your best like, they don't actually, like, want to teach you that much for you to actually do it. Unless you're in grade eight or nine, obviously”. “They [in Turkey] um, they like, um, they, they take two days or three to teach, to teach like a whole lesson, about that thing. So, the other days, other days of the week, you, when they give you a sheet you know how to do it. It's not like just 20 minutes of telling you what it is, it depends on if everyone understands…Maximum is three days. Unless like a person didn't understand. Yeah, because they don't want someone to feel like, they're like, like, they don't know what to do and the other students are doing it and they just did it fast and give their sheet to the teacher and other students are still like, um “I don't know what to do”.
Obviously, I'm doing it for myself
“Math, here [in Canada]. Um, is like, okay. Because I really like math and, in any country, I would definitely do math, because it's like my favorite subject. So like, um [giggles] so like, I would like learn it fast cause like, obviously, it's like all like obviously is going to be hard but I try to learn it as fast as I can, because like, these days we have EQAO [provincial assessment]... Yeah, so, cause like the, the last days of like school, so like we have to do EQAO because it's the last day, the last year of grade six. So, like, I do a lot of math and I change, like I, I just, at school, I try like, on my free time I try to like practice for it because I don't want to, like let my parents down. Obviously, I'm doing it for myself but, I want to like be a doctor one day so I'm trying to like work hard on my things”.
Activity of relief: Hula hoops and asteroid
One math activity that Ghazel shared which was different in Turkey was related to addition, “Oh, I have one. Like we had this activity every week. We had like hula hoops that we put on the garden…So we had these hula hoops that we did in math, but like the teacher gives us a math question like “what's two plus two?” because they used to give us easy ones just because it’s a game. So, they give us like two plus two, and then um, like how much, how much hula hoops there is. Like we jump, because two plus two is four so we jump four hula hoops. And it's like, they don't go as hard ones because obviously we can't put a hundred hoops, hula hoops in the like, hallway, right? So, we just put like easy numbers because like we need to jump like easy numbers, numbers to 20 hula hoops because we had a really, really big hall outside in the garden, in the field…There was like a spinning wheel. We had like a little spinning wheel. It had like stickers on it and the grade twos decorated it. Yeah. Like us. And then we'd like spin it and whatever, we used to have like numbers to 10. And it only used to be plus because we can't really add, we can't really add much numbers. So, we did like two plus three, which is, which gives you five. So, um, we jumped five or like people like to guess. And the teacher standing beside the steering wheel, and he spins in whichever number he lands on…We spin it two times, like one for the first number, like let’s say 4, and then…we spin it the second time, say, four plus the second number…and then we counted and then we jumped the hula hoops, like we jumped the answers”.