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Hello and thank you for listening to the mathematics teacher educator journal podcast. The mathematics teacher educator journal is co sponsored by the Association of mathematics teacher educators and the National Council of Teachers of Mathematics. We will be discussing Gianni and Jasmine Stanford's article pre service teachers mathematical visual implementation for emergent bilinguals, published in the September 2018, issue of the mathematics teacher educator journal. We will begin by summarizing the main points of the article and discuss in more depth the lessons they shared in their article, their successes and challenges, and how these lessons relate to their other work. My name is Eva Sennheiser, and I'm talking with Jie Zhang Yi, can you take a minute to introduce yourself?
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Yes, I'm Dr. E, and assistant professor in mathematics education at Iowa State University. I teach both secondary and elementary pre service teachers. But my main part is secondary. And my research agenda is focusing on emergent bilinguals mostly IELTS so in our English language learners in the US, but also Korean language learners in South Korea. So my research is about how to teach mathematics for emergent bilinguals and how to support pre service and in service teachers of a teaching reverse mathematics for emergent bilinguals.
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All right, well, thank you for joining us. And let's get started. Can you start off with a brief summary of the article including the results?
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Yes, but I'm not sure if I can make it brief. I'll try. Okay, so this is a multiple case study involves emergent bilinguals, pre service teachers and mathematical problem solving. So by the way, I used the ABS emergent bilinguals. Throughout this paper instead of URLs, or the URLs are most commonly used term in the US. I prefer to use ABS emergent bilinguals. Because URLs, the term doesn't show the student can speak a list of one language already. So I want to emphasize the bilingualism, they have to have the SF view rather than emphasize the mere fact that they are learning English. So I want to use emergent bilinguals. Yeah, so we designed this study to investigate pre service teacher learning about teaching mathematical problem solving for EBS. So our focuses the one particular strategy and how to use visuals. So we use the one on one setting. So we have three cases, that means three paradox reserve teachers and emergent bilinguals. So in each pair, there is one middle school mathematics pre service teacher in one Middle School in a bilingual. So the pre service teacher, they developed a lesson plan using the given problem, which has highly in high level cognitive demand. And they actually teach the lesson with the real students the assigned in bilingual. So we measured how they modify the problems and what instructional strategies they implemented to support their emergent bilinguals and how they fluctuated their teaching and learning. So they had five sessions with their emergent bilinguals. And intervention was provided after each teaching. So we used shovel and chocolate, seven key strategies for ELS to provide the intervention of research based strategies. And one of the research based strategies was how to use visuals. And this paper is particularly about the ps4 strategies. So although using visuals is very common strategy to teach abs, even without any training, teachers and people can think of our visuals is a good strategy, emergent bilinguals. But not all visuals are the same. So this intervention was designed with three different versions of the tools embedded in the same math word problem. And the problem is written in Korean because none of the preserve teacher could read or understand Korean. So the first version had only text, only Korean text. So the preserve teacher had no idea what it says and what information are there and how to solve it. And the second version has the one picture with the word problem, but only related to each context. So there is no mathematical information to preserve, teachers could gain so they try to make some guesses, but ultimately, they can solve it. The third version has the parameters and representations. So take any pictures and numbers. So it conveys not only contextual clues, but also mathematical information. So with these visuals, the old priest or a teacher could figure out what the problem was about what it means and how to solve it, or though they did not understand the language. So after this intervention, we found all preserved, teachers started using the tools differently and it using more Various representations and try to add mathematical information. So this was my study.
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Okay. I'm going to try to figure out if I understood what you said correctly. So you had three pre service teachers you worked with, and they each worked with one emergent bilingual child. Yes. Now, was the study conducted in the United States? Yes. So the children were English learners, they are
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all English language learners. But
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the Korean intervention was something you did with the teachers. That's not the thing they did with the children, right? They're trying, yes. During the intervention with the pre service teachers, and you chose Korean, so that none of them would have access to it at all, because none of them speak Korean. And so they would encounter a problem that they didn't know what the problem was about. And then you added different kinds of visuals to kind of talk about what each visual adds to understanding the problem.
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Yes. Okay.
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And then I think what you said is, you found that after this intervention, the pre service teachers, when they worked with the children, they used more and different kinds of visuals in their own teaching.
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Yes, they did.
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Okay, just making sure that I followed. So who should read this article,
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definitely teacher educators, or someone who is designing teacher preparation program, because this intervention involved build experience. So I think it's not only for one method class is for a whole teacher preparation program. And also, I believe it is beneficial for in service teachers, as well.
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You talked a little bit about it, but let's isolate again, what is the important problem or issue that you address with your study
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is well known that there is a mismatch between the student population and teacher population in the US. So many students are really diverse, it is time, culturally and linguistically that we do not have enough teachers for failure where this diverse background. Yeah, that's one thing. Also the teachers lack of resources to teach emergent bilinguals many teachers don't have experience as emergent bilingual. So I think this is, yeah, it could be my personal opinion. But I think because English is the most popular language and most used in the world. English speakers don't have much experience as emergent bilinguals, like, other non English speakers, and I mean, yes, yeah. So that's one thing. And also, when they learn about how to teach emergent bilinguals I believe teachers only care only the general principles. So just use visual that's good strategy, but they don't know how to utilize the general principles. I believe general principles and strategies do not really help teachers when they actually have to use it.
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Are you saying that you're trying to put these teachers into a situation where they can experience what emergent bilinguals experience?
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Yes, because even if they have a good strategy, with good intention, if they do not really understand their students, it will be hard for them to utilize the strategy and effective way. So if they really don't know how emergent bilinguals feel, and they experienced in English only classroom, it'd be hard for them to provide them knows charity in a really good way.
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Okay. So also in your summary, in the beginning, you talked a little bit but let's explore a little further How does this article build on existing work in the field? And what particular theories are you building your work on?
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Yeah, obviously, yeah, I use the previous research relates to emergent bilinguals. So for example, I used to shovel in Chavez, the review kangaroo and they they review the main previous articles related to your URLs and they found the seven key strategies and I use to design my intervention and also for my analytic framework, I used the two previous study, one is minor at all and the other is marked in yellow. So they proposed different types of results. Although these studies are not particularly for image bilinguals they provide this kind of guideline how to analyze visuals. So not all these are the same. So my use the term progressive formalization, to show the different abstraction or permutations of visuals. So based on these studies, I categorize the visuals so I first categorized the visuals into visuals without mathematical information and visuals with medical information and for the visuals with mathematical information I further divided into three sub categories, informal people, more For more. So this serves as my analytic framework so I could analyze the visuals the pre service teachers use for their emergent bilinguals. Do you think we could
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try to talk through an example of what these different visuals have? So I think in your paper, it's about a classroom, right? And so what would a visual look like that has nothing to do with the mathematics? For example, though, math word problem with the visuals that I used for this intervention was from Korean textbook with this color for me this color is so for a second version, I
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use the original visual the text, I actually used that one picture with kind of classrooms creation with some baskets there some students are there's some boys and girls are there. So that picture shows. So what context is in this problem? It's classroom setting. That's it, it doesn't show how many female students are there, how many males center there, and actually, this problem is of a fraction. So they have to actually find the number of female students based on the given fractional information, but it doesn't have any fraction and not real numbers of its students. So they can use this as visuals without mathematical information. Okay, yeah. So the third version has a picture of a classroom. So this gives a classroom setting and there's also give picture with caption, so the caption is absolutely a fraction. So with a picture of boy, there is a caption to third, and there is a picture of her. And question mark. So people can think in the classroom, the number of buoy is two third of all students said, What is the number or the fraction of the female students, so it's easy to find it one third, something like that. And also there is a table with picture with caption so people can think. And also there is fractions and question mark, also variable x. So people can figure out what this fraction or numerical symbol you present.
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So we had one picture that just had like a random classroom image, one that had some kids in it, but it wasn't clear what the question was. And then the last one had specific information that related to the question, is that correct?
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Yeah, it was hard to explain without showing the picture. Yes. Well, people
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can go to the article to like, look at the pictures, right?
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Yeah. Yes. Is this the example of the visuals with mathematical information? Right.
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I think this sounds like such a powerful experience to me. Because, you know, we're not often ourselves in a situation where we don't know what's going on, and really seeing how a visual can help you understand. The mathematics is really powerful in this article, so I think it's a really cool intervention. All right. So what was your research question? And what did you find?
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So my research question is to what extent does an immersive Borneo language intervention for pre service teachers designed to highlight the power of visuals in understanding mathematics influence their perspectives and practices with regard to teaching mathematics for emergent bilinguals? So what was the question?
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So what's the research question? And then what was your finding other finding?
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So my finding is this specific intervention with a using the pony language, and also specific instructional strategy visuals with three different bergeon helps them understand how emergent bilinguals feel and experience in your school. And also what is Australian and one use of visuals actually help them understand the mathematical situation. So they can see the power of visuals, and each one has more power, and each one actually helped them understand the math. So after this intervention, the prison teacher could apply the learning in their teaching real fast. So my finding is, first, his intervention works. His intervention changes their perspective. It helps they're improving their teaching strategy teaching practice for emergent bilinguals. And also the one on one setting and the concurrent setting. So they had this intervention ways their teachings period, their field experience. So in their actual interview post survey, they said, this is really helpful for them so they could apply what they learned immediately so they are healthier understanding and improving your teaching. And the most powerful strategy they learned was this strategy, how to use visuals. So there was my finding.
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I think you have A table in your paper that shows that after this intervention, they used a lot more visuals, right?
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They use the more visual itself. And also they used more visual to with mathematical information. And even in that category they used to more pre formers tastes of visuals rather than informer. One
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if I understand, right, they that was five interventions. And after each intervention, they plan the lesson right to do with the child. And so you looked at the lessons, they plan to see how many visuals they included?
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Yes.
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All right. So if you had to sum up what is the new contribution of your paper, what
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would you say there was no previous study about connecting the types of visuals with teaching math for emergent bilinguals. So this is definitely new contribution. And also, this paper clearly provides an idea for designing and activity will program to educate pre service teachers and even user of teachers for teaching masty emergent bilinguals.
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Let's say that there's a whole bunch of people like me, who want to use your intervention. What advice would you give advice? Okay,
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so I think the setting is kind of important. So before you show any visual, you have to give the direction first. This is what I did. So before I showed the first version, I asked them, okay, this is a math problem, but it's for me this grow to be easy to try to solve it, and then show
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it and then you show them the Korean text.
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Yes. So they have more kind of impact. So they expected they could solve it, when they sit on language, new way. So they knew the math, they have all the mathematical knowledge to solve that. But because their language they couldn't shop,
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so what was their reaction when you show them this Korean text?
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Oh, it was actually hilarious. So they laughed about it a lot. And they knew they couldn't solve it, they could understand it, but they try to make some sense does the connecting the numbers, but they knew that's not working?
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This podcast is actually really timely for me, because next week, I'm doing a presentation where I'm doing something similar to you. We're gonna watch a Chinese lesson. Yeah, and nobody in the audience is gonna be speaking Chinese, I assume, I don't know. But I assume. And we're going to talk about how accessible the content of this lesson was. And the content is very accessible because of the figures on the board. It's you kind of know what they're talking about. And we're going to talk about how same idea how to give access to language learners, and putting people into this position of not understanding the language. So I was thrilled when I read your paper, I'm like, Yay, this is something I can use. And I'm imagining how to use it in like my everyday life because obviously I do not speak Korean or Chinese. So I'm wondering how I would go about especially if I were monolingual How would I go about finding a problem like this? That then I could work with? And this isn't so your problem? Yeah. But like, do you have more like if people are interested in more problems? Could they contact you? Would that be something you'd be interested in talking to people
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Yes, so I use these methods and in several of my presentations, or insert a teacher in a PD and I have several different version because not many emergent bilinguals are beginning level so they actually understand to understand so I'm English, but even if so my different version has only about one or two words. Oh, that's
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cool.
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Yeah, keywords so even if they understand the context, they cannot solve it because they key mathematical information is now written in English.
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Wow, that's really awesome. Yeah,
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so I try to make it authentic. So after each version of visual I asked them how they felt and why they couldn't solve it. So they have some time to digest their feeling and the reason why they couldn't solve it and why they are emergent bilinguals could solve it and why they are kinda feel outsider in their classroom.
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I have a different question. And I'm not sure this is going to be part of the podcast, but I'm really curious about the term emergent bilingual. I'm not a super big fan of it myself, because I feel like it limits the languages to two and I think many people speak more than two languages. Yes,
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it's true. Actually, one of them bilingual in my study is was trilingual. She could speak Japanese, Korean and English.
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Yeah, I think especially students who learn English often come from homes where they already spoke more than one language. Yes, I just don't know. There's a good time. But I thought it's interesting because it doesn't matter what term you use. You have to explain why you're using that term right?
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I think so. I think El Toro el, they're fine. When you use EBS, I believe we have a specific reason why. And also sometimes I put multilingual with parenthesis. So emergent bilingual apprentices, multilingual to respect
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Yeah, I think that would be I like that one. I think we're through except if you want to add anything,
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I think so. I hope many people many educator read this article and try this method. And if you do, please let me know how it works.
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Yeah, I think this is gonna be very exciting.
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Thank you. Thank you for this opportunity. That's also is really good experience for me.
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Well, thanks for publishing the paper. For further information on this topic, you can find the article on the mathematics teacher educator website. This has been your host, Ava Sennheiser. Thanks for listening and goodbye.