WEBVTT Kind: captions Language: en 00:00:00.160 --> 00:00:04.880 Hello everyone and welcome to our session titled three by three? 00:00:04.880 --> 00:00:09.599 Exploring math for ELLs which stands for english language learners. 00:00:09.599 --> 00:00:14.160 My name is Amel Belmahdi and joining me is the lovely 00:00:14.160 --> 00:00:18.240 Keisha Deoraj. This presentation is for the OAME 00:00:18.240 --> 00:00:21.840 or Ontario Association for Mathematics Education 00:00:21.840 --> 00:00:25.199 2020 conference. Keisha and I would like you to know 00:00:25.199 --> 00:00:29.359 that we both met and heard about this conference from Ontario Tech University 00:00:29.359 --> 00:00:33.680 more specifically in a math for society course we took with professor Ami 00:00:33.680 --> 00:00:36.559 Mamolo who encouraged us to apply and assisted 00:00:36.559 --> 00:00:40.000 us along the way. Keisha would like to add something else 00:00:40.000 --> 00:00:44.559 to this part. In addition we'd like to acknowledge that Ontario Tech University 00:00:44.559 --> 00:00:49.920 is proud to be located on the lands and people of the Mississaugas of Scugog 00:00:49.920 --> 00:00:52.800 Island First Nation which is covered under the Williams 00:00:52.800 --> 00:00:56.239 Treaties. We are situated on the traditional territories of the 00:00:56.239 --> 00:00:58.960 Mississaugas a branch of the greater Anishinaabe 00:00:58.960 --> 00:01:05.340 nation which includes Algonquin, Ojibwe, Odawa and Potawatomi. 00:01:05.340 --> 00:01:08.159 If you have any questions or comments or if you would like to connect with us 00:01:08.159 --> 00:01:12.320 please do not hesitate to contact us anytime. We will do our best to get back 00:01:12.320 --> 00:01:15.600 to you as soon as possible. Please note that this slide will 00:01:15.600 --> 00:01:21.520 reappear at the end of our presentation. Throughout our time together you will be 00:01:21.520 --> 00:01:25.439 introduced to this session, learn about the outcomes of it and about 00:01:25.439 --> 00:01:28.960 english language learners. We will then focus on the barriers 00:01:28.960 --> 00:01:32.640 english language learners face in a mathematics classroom which hinder their 00:01:32.640 --> 00:01:37.360 performance and success. We will then discuss ways to overcome 00:01:37.360 --> 00:01:40.560 challenges these learners face when learning math. 00:01:40.560 --> 00:01:43.840 Then we will move into a personalized section before heading into the 00:01:43.840 --> 00:01:47.840 conclusion to summarize this session. Finally we will take you 00:01:47.840 --> 00:01:50.079 through additional resources and references 00:01:50.079 --> 00:01:54.240 along with some activities that you can access. 00:01:54.240 --> 00:01:57.920 English language learners of all types especially racialized ones 00:01:57.920 --> 00:02:01.119 face a number of challenges in the classroom including those 00:02:01.119 --> 00:02:05.119 related to language. Despite their intelligence often these students 00:02:05.119 --> 00:02:07.600 struggle to succeed in mathematics classrooms 00:02:07.600 --> 00:02:11.440 due to an imbalance in the teaching approaches both within the Ontario 00:02:11.440 --> 00:02:13.680 curriculum and for teachers who have never 00:02:13.680 --> 00:02:18.800 underwent the unique experiences of an english language learner. 00:02:18.800 --> 00:02:22.000 Throughout this engaging session participants will become better 00:02:22.000 --> 00:02:25.120 informed about some key issues facing these students. 00:02:25.120 --> 00:02:28.720 They will also explore how to improve their teaching and learning strategies 00:02:28.720 --> 00:02:32.400 to better suit these learners needs in a mathematics classroom. 00:02:32.400 --> 00:02:36.000 In particular we will examine how using technology to enhance 00:02:36.000 --> 00:02:40.080 culturally responsive instruction can help teachers communicate with 00:02:40.080 --> 00:02:43.680 attend to and respond to their students experiences 00:02:43.680 --> 00:02:46.800 and thus help pave the road for their success. 00:02:46.800 --> 00:02:51.360 English language learners face various challenges with regards to math. 00:02:51.360 --> 00:02:54.959 English language learners must learn another language along with 00:02:54.959 --> 00:02:59.440 content simultaneously. Contrary to common assumptions, 00:02:59.440 --> 00:03:02.720 language plays an important role in learning mathematics. 00:03:02.720 --> 00:03:06.640 Teachers are faced with creating math lessons which are comprehensible 00:03:06.640 --> 00:03:09.840 while ensuring learners have the language to understand what is being 00:03:09.840 --> 00:03:12.959 taught or asked of them and they have to be able to display 00:03:12.959 --> 00:03:15.760 their comprehension by speaking and writing. 00:03:15.760 --> 00:03:19.840 In addition to all of these educators have an added task of keeping 00:03:19.840 --> 00:03:22.959 all learners engaged through student-centered instruction 00:03:22.959 --> 00:03:28.080 with the integration of fun educational activities. 00:03:28.080 --> 00:03:32.159 First it is worth noting that the Literacy and Numeracy Secretariat 00:03:32.159 --> 00:03:36.000 states that research has revealed that although english language learners can 00:03:36.000 --> 00:03:40.400 develop basic conversational english it takes years to gain specialized 00:03:40.400 --> 00:03:44.080 academic english skills. Research also shows a positive 00:03:44.080 --> 00:03:46.640 correlation between low proficiency in languages 00:03:46.640 --> 00:03:50.560 and lack of success in mathematics especially for minorities like language 00:03:50.560 --> 00:03:54.560 learners. Second, relevant to comprehensible 00:03:54.560 --> 00:03:57.280 content, english language learners often find 00:03:57.280 --> 00:04:01.760 that language used in math problems is linguistically complex. They 00:04:01.760 --> 00:04:04.560 also encounter math word problems which contain 00:04:04.560 --> 00:04:08.480 unnecessary vocabulary words and unfamiliar symbols making it 00:04:08.480 --> 00:04:12.000 challenging for them to fully understand what is being asked or how to solve 00:04:12.000 --> 00:04:16.959 these types of problems. For many, including native speakers, math 00:04:16.959 --> 00:04:21.040 can be a dry boring subject. There are also many english language 00:04:21.040 --> 00:04:24.479 learners who once loved math and found it to be a favorite subject 00:04:24.479 --> 00:04:28.320 but are now not interested in it as language learners. 00:04:28.320 --> 00:04:31.440 This is not only because of the challenges associated with learning a 00:04:31.440 --> 00:04:34.560 new language but because of the way it is taught. 00:04:34.560 --> 00:04:37.759 Instruction may lack a student-centered approach 00:04:37.759 --> 00:04:40.080 taking on more of a teacher-centered approach 00:04:40.080 --> 00:04:43.360 where teachers stand in front of the class to instruct students before 00:04:43.360 --> 00:04:47.199 allowing them to take part. There is a meme I found which has an 00:04:47.199 --> 00:04:50.720 open license and although exaggerated I found it to be relevant in 00:04:50.720 --> 00:04:54.479 this context. It reads every time I see a math word 00:04:54.479 --> 00:04:57.759 problem it looks like this: If i have 10 ice 00:04:57.759 --> 00:05:01.360 cubes and you have 11 apples how many pancakes will fit on the 00:05:01.360 --> 00:05:04.639 roof? The answer is purple because aliens 00:05:04.639 --> 00:05:08.880 don't wear hats. English language learners usually find 00:05:08.880 --> 00:05:12.560 word problems challenging and this increases as they move forward 00:05:12.560 --> 00:05:15.600 educationally because these types of problems become 00:05:15.600 --> 00:05:19.120 more linguistically and conceptually complicated. 00:05:19.120 --> 00:05:23.199 Areas that pose issues include vocabulary syntax and grammar 00:05:23.199 --> 00:05:26.560 which depend on learner's comprehension of the math instruction 00:05:26.560 --> 00:05:30.479 and their ability to take part in discussions related to mathematics. 00:05:30.479 --> 00:05:34.160 So now it's your turn to be placed in a language learner's shoes to try and 00:05:34.160 --> 00:05:37.440 solve a math problem. I created a math problem in english and 00:05:37.440 --> 00:05:40.720 used Google translate to translate it into four different languages. 00:05:40.720 --> 00:05:45.360 So please excuse any errors that may have occurred with the translations. 00:05:45.360 --> 00:05:49.360 If any of these are in a language you speak, try to understand one which is in 00:05:49.360 --> 00:05:53.199 a different language and please do not use Google translate. 00:05:53.199 --> 00:05:56.800 You can now pause the video and take a moment to try 00:05:56.800 --> 00:06:00.080 and understand any of these. 00:06:01.039 --> 00:06:04.720 So now that you've tried taking a look, I'd like to say that it's not easy 00:06:04.720 --> 00:06:08.800 understanding the message is it? If you felt overwhelmed by the text on 00:06:08.800 --> 00:06:11.759 the slide which is unknown or unfamiliar to you 00:06:11.759 --> 00:06:15.600 imagine what your english language learners must feel like. 00:06:15.600 --> 00:06:20.319 Text on the left is in Arabic. The one in the middle is in Urdu. The one 00:06:20.319 --> 00:06:23.919 on the right is in Vietnamese and the one at the bottom is in Russian. 00:06:23.919 --> 00:06:26.880 All of these have different ways of being written with the closest to 00:06:26.880 --> 00:06:30.960 english being the one in Vietnamese due to the structure of the alphabet or 00:06:30.960 --> 00:06:34.400 its alphabetic system. If you paid close attention to the one 00:06:34.400 --> 00:06:37.039 in Vietnamese you may have picked up proper nouns. 00:06:37.039 --> 00:06:40.160 More specifically names like Safiya, Ramdane, 00:06:40.160 --> 00:06:45.919 Amine, Najma, Anab and Zeinab, You may have also noticed the word pizza 00:06:45.919 --> 00:06:49.360 being repeated a few times. Well let's look at what the problem says 00:06:49.360 --> 00:06:53.599 in english, I'm going to read this question out loud 00:06:53.599 --> 00:06:56.319 and then you can pause the video to read it again 00:06:56.319 --> 00:07:01.199 and try to solve this problem. So it reads: at a party 00:07:01.199 --> 00:07:04.880 there were 10 slices of pizza. Safiya ate two slices 00:07:04.880 --> 00:07:09.120 and Ramdane took five slices of which he gave two to his son Amin. 00:07:09.120 --> 00:07:13.440 Najma and her sister Anab came with two boxes of pizza that contained eight 00:07:13.440 --> 00:07:16.880 slices each. Wejdan ate four slices before giving 00:07:16.880 --> 00:07:22.160 three to her sister Zeinab, How many pizza slices were left? 00:07:22.639 --> 00:07:26.880 So you can pause the video take a moment to think about the answer or calculate 00:07:26.880 --> 00:07:32.319 the answer. Okay so if you came up with 12 slices, 00:07:32.319 --> 00:07:35.599 you are correct. There were 10 to begin with. 00:07:35.599 --> 00:07:39.360 Safiya ate two which left eight slices. Then Ramdane 00:07:39.360 --> 00:07:42.880 took five bringing us down to three slices. 00:07:42.880 --> 00:07:46.319 Then we got 16 more slices from Najma and Anab 00:07:46.319 --> 00:07:49.599 which brought us up to 19 slices and then 00:07:49.599 --> 00:07:53.599 from there Wejdan ate four bringing us down to 15 00:07:53.599 --> 00:07:57.039 before she gave three to Zeinab which then brought us down to 12 00:07:57.039 --> 00:08:02.720 slices and that was what was remaining. Having this in a language you are fluent 00:08:02.720 --> 00:08:05.599 in helped make the question easy to understand and solve. 00:08:05.599 --> 00:08:09.039 Thus it wasn't your lack of math skills but your lack of understanding the 00:08:09.039 --> 00:08:12.560 language used in the question which hindered your ability to solve the 00:08:12.560 --> 00:08:16.000 problem in the previous slide. 00:08:16.160 --> 00:08:19.520 Various solutions will be discussed in the subsequent slides and areas of 00:08:19.520 --> 00:08:23.520 discussion include STEP, educator collaboration, considering 00:08:23.520 --> 00:08:26.560 learners needs, implementing cooperative, interactive and 00:08:26.560 --> 00:08:30.160 engaged learning, integrating technological devices, 00:08:30.160 --> 00:08:34.560 strategically asking questions, teaching academic vocabulary, providing 00:08:34.560 --> 00:08:39.760 enough time for learning, and grouping and pairing effectively. 00:08:39.760 --> 00:08:44.720 In a video Nada Aoudeh mentions using STEP as a teacher support to assist 00:08:44.720 --> 00:08:48.560 educators in determining objectives and pinpointing where learners should 00:08:48.560 --> 00:08:51.200 begin and getting to know their objectives. 00:08:51.200 --> 00:08:54.240 STEP is a framework that assesses language acquisition 00:08:54.240 --> 00:08:57.920 and the literacy development of english language learners across the Ontario 00:08:57.920 --> 00:09:00.800 curriculum. For the next few points I'd like to 00:09:00.800 --> 00:09:04.720 start by saying that both Nada and in TIPS for english language 00:09:04.720 --> 00:09:09.040 learners in mathematics grades 7 8 9 applied and 10 applied 00:09:09.040 --> 00:09:12.800 also emphasize the importance of educators collaborating with one another 00:09:12.800 --> 00:09:16.160 especially with those who support english language learners 00:09:16.160 --> 00:09:19.920 to adopt some teaching techniques which will help language learners in a 00:09:19.920 --> 00:09:24.080 mathematical setting. the TIPS for english language learners 00:09:24.080 --> 00:09:27.120 in mathematics also mentions that by working collaboratively 00:09:27.120 --> 00:09:30.320 teachers can plan and exchange information with one another 00:09:30.320 --> 00:09:34.399 regarding students development and cater to each student's needs. 00:09:34.399 --> 00:09:38.399 They can also exchange notions relevant to effective ways of assisting certain 00:09:38.399 --> 00:09:42.080 students in becoming familiar with the concepts and vocabulary used 00:09:42.080 --> 00:09:45.519 in mathematics. To incorporate cooperative 00:09:45.519 --> 00:09:49.360 interactive and engaged learning, teachers can involve students in various 00:09:49.360 --> 00:09:52.320 activities. Some examples are mentioned by Christina 00:09:52.320 --> 00:09:56.000 Robertson which include making math journals in order for the learners to 00:09:56.000 --> 00:09:59.600 process what they have learned and record any questions that they may have, 00:09:59.600 --> 00:10:03.680 translate math symbols into words to formulate complete sentences, 00:10:03.680 --> 00:10:07.360 and this is also a way for instructors to check students comprehension of the 00:10:07.360 --> 00:10:10.640 math problems. Students can discuss and exchange 00:10:10.640 --> 00:10:14.959 problem solving strategies by digging into how other students came up with the 00:10:14.959 --> 00:10:18.480 solutions to problems. Teachers should also allow 00:10:18.480 --> 00:10:21.600 students to create their own math problems similar to ones learned in 00:10:21.600 --> 00:10:24.720 class and allow them to switch with a partner 00:10:24.720 --> 00:10:27.680 to answer their partner's questions and this 00:10:27.680 --> 00:10:33.839 reinforces student learning. 00:10:34.560 --> 00:10:39.519 Korenova and Veress-Bagyi argue that mobile technology and constant use of 00:10:39.519 --> 00:10:42.959 applications and gamification is crucial in aiding with the shift from a 00:10:42.959 --> 00:10:46.320 student's negative perception of math to a more positive one. 00:10:46.320 --> 00:10:49.839 So i'm going to talk about some applications that are beneficial 00:10:49.839 --> 00:10:54.959 for language learners in math. First Seesaw is an application that promotes 00:10:54.959 --> 00:10:57.600 student engagement which was created to empower 00:10:57.600 --> 00:11:01.120 students to create reflect share and collaborate. 00:11:01.120 --> 00:11:04.320 In using this learners can display what they know 00:11:04.320 --> 00:11:09.760 by recording videos displaying drawings and uploading drawings, texts, PDFs, web 00:11:09.760 --> 00:11:13.839 links and photos of their work. This allows students to create and track 00:11:13.839 --> 00:11:17.360 their e-portfolio all of which and along with their 00:11:17.360 --> 00:11:20.399 learning progress can be shared with others. 00:11:20.399 --> 00:11:23.440 A study done by Jarvis and Martin in 2018 00:11:23.440 --> 00:11:28.320 found that Seesaw positively impacted student parent and teacher relationships. 00:11:28.320 --> 00:11:32.079 It also allowed instructors to assess whether learners understood 00:11:32.079 --> 00:11:35.200 class concepts taught or needed further instruction 00:11:35.200 --> 00:11:41.200 and it was easy to use. Next geogebra is a free open source math 00:11:41.200 --> 00:11:46.480 software with a purpose to connect statistics, algebra, calculus, and geometry. 00:11:46.480 --> 00:11:50.160 The program includes a plethora of support materials such as downloadable 00:11:50.160 --> 00:11:53.519 manuals, lessons and detailed tutorials. In a 00:11:53.519 --> 00:11:57.839 study conducted by Shadaan and Leong with 53 participants, most of 00:11:57.839 --> 00:12:00.480 them agreed that this application is exciting, 00:12:00.480 --> 00:12:03.519 engaging, effective as a learning tool and helpful 00:12:03.519 --> 00:12:06.720 with visualization. 00:12:06.800 --> 00:12:11.200 Third Photomath. Photomath drives learning mathematics. 00:12:11.200 --> 00:12:15.440 It can assist students and others in interpreting all types of math questions 00:12:15.440 --> 00:12:20.480 from arithmetic to calculus in order to facilitate learning and understanding of 00:12:20.480 --> 00:12:24.240 math concepts. Users of Photomath can utilize their 00:12:24.240 --> 00:12:28.480 phones to scan a math problem to receive clear detailed and in some 00:12:28.480 --> 00:12:32.160 situations different solutions to the question. 00:12:32.160 --> 00:12:36.639 It also provides animated solution as well as smart calculator and graph 00:12:36.639 --> 00:12:40.160 features suiting visual learners and allowing others to further 00:12:40.160 --> 00:12:46.160 delve into the math realm. Another application is Pokemon Go which 00:12:46.160 --> 00:12:50.800 is a common application based game that uses GPS systems within phones to 00:12:50.800 --> 00:12:55.360 display Pokemon in the real world. With this students can learn about and 00:12:55.360 --> 00:12:58.800 use probability when they use their Pokemon to battle. 00:12:58.800 --> 00:13:05.200 So when they battle usually a Pokemon with higher combat power wins however 00:13:05.200 --> 00:13:08.880 there are some cases where Pokemon with lower combat power wins 00:13:08.880 --> 00:13:12.800 so students can use these statistics and situations 00:13:12.800 --> 00:13:18.399 and apply them to probabilities. Distances can also be calculated between 00:13:18.399 --> 00:13:23.279 Poke stops as well as catching sessions. In addition learners can compare and 00:13:23.279 --> 00:13:28.000 contrast Pokemon statistics such as height, weight and other measurements 00:13:28.000 --> 00:13:32.079 that are relevant. Furthermore students can learn about 00:13:32.079 --> 00:13:36.320 conversion. Pokemon Go usually displays data in kilometers but 00:13:36.320 --> 00:13:40.240 research has shown that users have increased their search 00:13:40.240 --> 00:13:44.800 on Google to convert kilometers into miles. Learners can be 00:13:44.800 --> 00:13:47.839 encouraged to track the number and type of Pokemon they 00:13:47.839 --> 00:13:51.600 encounter daily which can then be used in class to discuss ratios and 00:13:51.600 --> 00:13:55.279 percentages. Now Keisha will discuss the last few 00:13:55.279 --> 00:13:58.000 applications. 00:13:58.160 --> 00:14:03.120 Thanks Amel. Geometry Pad is an interactive notebook that students can 00:14:03.120 --> 00:14:06.800 use to create fundamental geometric shapes, explore and 00:14:06.800 --> 00:14:10.720 change their properties, and calculate metrics. The shapes are 00:14:10.720 --> 00:14:14.000 displayed on a scrollable and zoomable workbook with a 00:14:14.000 --> 00:14:19.760 four quadrant grid. Then there's the Khan Academy application which is affiliated 00:14:19.760 --> 00:14:22.880 with the well-known Khan Academy Youtube channel. 00:14:22.880 --> 00:14:26.000 You can use the app to study math, science and more 00:14:26.000 --> 00:14:30.480 at your own pace. There are over ten thousand videos and explanations 00:14:30.480 --> 00:14:36.079 with math and science content mapped to National Council of Educational Research 00:14:36.079 --> 00:14:40.720 and Training and Central Board of Secondary Education 00:14:40.720 --> 00:14:44.079 syllabi which are two educational authorities in 00:14:44.079 --> 00:14:49.680 India. Brainscape is a web and mobile education platform 00:14:49.680 --> 00:14:53.199 that allows students to study adaptive flashcards. 00:14:53.199 --> 00:14:57.120 The website and mobile application allows students and corporate trainers 00:14:57.120 --> 00:15:01.519 to create electronic flashcards and to find flashcards created by other 00:15:01.519 --> 00:15:04.560 users and publishers from around the world. 00:15:04.560 --> 00:15:09.920 Lastly there is the CK-12 foundation which is a California-based non-profit 00:15:09.920 --> 00:15:13.839 organization that aims to increase access to low-cost 00:15:13.839 --> 00:15:18.519 K-12 education across the United States and abroad. 00:15:18.519 --> 00:15:22.480 CK-12 provides free and customizable K-12 00:15:22.480 --> 00:15:26.160 open educational resources aligned to state curriculum 00:15:26.160 --> 00:15:30.079 standards. I'll hand it back over to Amel now. 00:15:30.079 --> 00:15:36.240 Thank you Keisha. Finally Nada Aoudeh and TIPS for english language 00:15:36.240 --> 00:15:40.000 learners in mathematics state that it's important for educators 00:15:40.000 --> 00:15:44.480 to ask students questions in an intentional but strategic manner 00:15:44.480 --> 00:15:48.800 and ways of doing this is by using concept checking questions, 00:15:48.800 --> 00:15:54.720 CCQs or information checking questions, ICQ's. This is crucial because some 00:15:54.720 --> 00:15:57.920 students may come from an environment where students are not allowed to ask 00:15:57.920 --> 00:16:01.920 teachers for assistance, make eye contact or express their own 00:16:01.920 --> 00:16:04.800 thoughts. In a blog post Christina Robertson 00:16:04.800 --> 00:16:08.880 states that teaching academic vocabulary is significant to a student's math 00:16:08.880 --> 00:16:11.839 learning. Teaching vocabulary involves more than 00:16:11.839 --> 00:16:15.120 teaching specialized math words like percent or fraction. 00:16:15.120 --> 00:16:18.959 It includes teaching the differences between the mathematical definition 00:16:18.959 --> 00:16:22.959 and other definitions of the same word. Take for example 00:16:22.959 --> 00:16:29.040 table and quarter. These both have math specific and math non-specific meanings. 00:16:29.040 --> 00:16:32.720 It is also essential that students are given enough time to process what they 00:16:32.720 --> 00:16:35.279 are learning and a way to do this is by providing 00:16:35.279 --> 00:16:39.120 students with enough practice time not only for homework but also in the 00:16:39.120 --> 00:16:42.639 classroom. During class it's important that 00:16:42.639 --> 00:16:46.639 students work collaboratively as well as in pairs or groups to support 00:16:46.639 --> 00:16:50.959 students in learning math and for language learning. Based on the 00:16:50.959 --> 00:16:53.440 TIPS for english language learners in mathematics, 00:16:53.440 --> 00:16:56.880 some options for educators to pair english language learners 00:16:56.880 --> 00:17:02.240 would be with peer tutors who comprehend math, english and the student's native 00:17:02.240 --> 00:17:05.439 language, with other math learners who are fluent 00:17:05.439 --> 00:17:08.160 in english or to pair stronger students with a 00:17:08.160 --> 00:17:12.480 weaker one. For example a student who is good at math with one 00:17:12.480 --> 00:17:17.360 who's a bit weaker in math and needs assistance. 00:17:17.600 --> 00:17:22.799 Now I'm going to pass it over to Keisha. In her talk Dr Lisa Lunney Borden 00:17:22.799 --> 00:17:26.240 discusses the ways in which the structure of the Mi'kmaq language is 00:17:26.240 --> 00:17:29.760 constructed which is relationally. This impacts 00:17:29.760 --> 00:17:33.039 Mi'kmaq students ability to understand mathematics in an 00:17:33.039 --> 00:17:38.160 english context which is not structured in a way that is relational. 00:17:38.160 --> 00:17:42.160 Just because students come to school speaking in english doesn't mean that 00:17:42.160 --> 00:17:45.440 they are thinking in english is one of the main points of 00:17:45.440 --> 00:17:49.360 her lecture. Let's take a look at this video together. 00:17:49.360 --> 00:17:53.120 Other big thing that I learned and this was something I often did was 00:17:53.120 --> 00:17:58.240 I asked what's the word for or is there a word for right and when 00:17:58.240 --> 00:18:01.600 you're asking questions like that what you're getting at is ways of 00:18:01.600 --> 00:18:05.200 thinking. And you'll see two words up here on the slide 00:18:05.200 --> 00:18:12.240 Aklasie'witasi and Lnuitasi. Lnuitasi is our people's ways of 00:18:12.240 --> 00:18:16.640 thinking. Mi'kmaq people call themselves lnu. 00:18:16.640 --> 00:18:25.280 Us. Our people. Europeans call them Mi'kmaq. Mi'kmaq actually means my kin 00:18:25.280 --> 00:18:32.160 and it's actually ni'kmaq but you know. So Mi'kmaq people call themselves lnu 00:18:32.160 --> 00:18:36.240 and Lnuitasi is our people's ways of thinking. Aklasie'witasi is 00:18:36.240 --> 00:18:41.120 anglophone or European ways of thinking. And one of the teachers in the study 00:18:41.120 --> 00:18:44.320 talked about how these things come into conflict 00:18:44.320 --> 00:18:48.640 because teachers think because kids come to school speaking english 00:18:48.640 --> 00:18:52.240 they're also thinking english and they're not. 00:18:52.240 --> 00:18:56.799 They're using the world view that's embedded in their own language. 00:18:56.799 --> 00:19:01.039 They're using the world view the grammar structures that's embedded in their own 00:19:01.039 --> 00:19:04.400 language. And so when kids come to school speaking 00:19:04.400 --> 00:19:08.720 english it is a mistake to also assume they are thinking english. 00:19:08.720 --> 00:19:13.200 And one couple really good examples come out when you start asking 00:19:13.200 --> 00:19:20.400 what's the word for. For example "flat". What's the word for "flat"? I asked an 00:19:20.400 --> 00:19:24.720 elder that one time. I was doing a paper as part of my doctoral work trying to 00:19:24.720 --> 00:19:29.600 find mathy kinds of words. I wanted to research mathy words. So I 00:19:29.600 --> 00:19:32.400 was asking about shape and space and number 00:19:32.400 --> 00:19:35.440 and I said to her you know what's what's the word for flat because we use that 00:19:35.440 --> 00:19:39.520 often. We talk about the face of a cube is a flat surface 00:19:39.520 --> 00:19:46.080 right. And she said well how would you use flat? And I said well 00:19:46.080 --> 00:19:53.039 what about the bottom of a basket? It's flat. She said no. 00:19:53.039 --> 00:19:57.200 It's what lets it sit still. It can sit still. 00:19:57.200 --> 00:20:01.520 And I said well what about the table? It's flat. 00:20:01.520 --> 00:20:07.919 Pata'wti. You can put things on it. That's what pata'wti means. It's not 00:20:07.919 --> 00:20:11.600 about the flatness it's about the purposefulness of it. 00:20:11.600 --> 00:20:14.720 And Mi'kmaq language like many indigenous languages across the country is 00:20:14.720 --> 00:20:20.720 constructed relationally. It is about relationships. Relationships 00:20:20.720 --> 00:20:24.320 are at the core. If i'm on the inside looking out a 00:20:24.320 --> 00:20:27.919 window I use one word. If i'm on the outside 00:20:27.919 --> 00:20:31.039 looking in a window I use a different word. 00:20:31.039 --> 00:20:36.080 Because it's not about the window it's about the relationship and the 00:20:36.080 --> 00:20:41.440 purposefulness of the window. So I kept asking well what about a flat 00:20:41.440 --> 00:20:45.360 tire? And my friend who was sitting with me, my colleague, 00:20:45.360 --> 00:20:48.480 he said, I would say it's out there because it's really not the flatness 00:20:48.480 --> 00:20:51.200 that's the problem it's the fact that it's losing air that's a problem. 00:20:51.200 --> 00:20:55.760 Right? And so he would actually say oh my tire's losing air 00:20:55.760 --> 00:21:00.240 when he's speaking english. So his children would describe a flat tire not 00:21:00.240 --> 00:21:05.679 as flat but as a tire losing air. That's the problem. 00:21:05.679 --> 00:21:11.679 And you know calm water, I ask, no that's really the negation of rough. Like 00:21:11.679 --> 00:21:14.559 it has to be able to move in order to be calm. 00:21:14.559 --> 00:21:17.919 The closest word I've got so far is like a plank. 00:21:17.919 --> 00:21:21.360 So there is a word for plank like a board and so 00:21:21.360 --> 00:21:24.880 they that's kind of the closest we've agreed on that that would be a good way 00:21:24.880 --> 00:21:30.720 to describe something that's flat because it's relational. It's purposeful. 00:21:30.720 --> 00:21:34.080 Another day we were we were working in our 00:21:34.080 --> 00:21:37.440 our study groups after school and one of the teachers arrived 00:21:37.440 --> 00:21:42.159 and she said what's the word for middle? And she said it just like that. She was 00:21:42.159 --> 00:21:46.480 very frustrated and I could tell. And I said what's going on. She's like I 00:21:46.480 --> 00:21:48.480 need to know if there's a word for middle. 00:21:48.480 --> 00:21:51.600 I had a child who was sent for an assessment 00:21:51.600 --> 00:21:54.640 and the person doing the assessment said he had 00:21:54.640 --> 00:21:58.080 auditory processing disorder. When he was asked to 00:21:58.080 --> 00:22:02.080 point to the object in the middle he could not do it. 00:22:02.080 --> 00:22:05.840 And her argument was he didn't know what middle meant. 00:22:05.840 --> 00:22:12.400 Right? And so we had this conversation. I know you can't read that slide. It's 00:22:12.400 --> 00:22:16.720 okay you don't need to. The conversation is really two Mi'kmaq 00:22:16.720 --> 00:22:19.200 teachers and this resource teacher who wanted to 00:22:19.200 --> 00:22:24.320 know about the word for middle talking back and forth about different 00:22:24.320 --> 00:22:29.840 kinds of words that you might describe, different contexts of kind of a sense of 00:22:29.840 --> 00:22:34.000 something that might be in the middle but by the end of it it was really, yeah 00:22:34.000 --> 00:22:36.480 right it's not a word you would typically use. 00:22:36.480 --> 00:22:41.919 Right? And so the teacher had in fact done some work with the 00:22:41.919 --> 00:22:45.360 student where they played monkey in the middle and they had 00:22:45.360 --> 00:22:48.640 students line up and taking different turns with someone standing in the 00:22:48.640 --> 00:22:52.159 middle and suddenly the child was easily able 00:22:52.159 --> 00:22:57.120 to point to the middle. He had come from a fluent Mi'kmaq speaking 00:22:57.120 --> 00:23:02.159 home. He was a Mi'kmaq speaker. He was learning english as a second language 00:23:02.159 --> 00:23:05.840 and he didn't know what middle meant. So here 00:23:05.840 --> 00:23:11.280 he was being diagnosed with a disability when in reality he just didn't know the 00:23:11.280 --> 00:23:17.120 meaning of the word. And so this was an important idea. 00:23:17.120 --> 00:23:22.799 Understanding when words don't exist in the indigenous language can help us to 00:23:22.799 --> 00:23:26.240 think about how maybe kids might not have a conceptual 00:23:26.240 --> 00:23:30.480 understanding of something that we might take for granted in english 00:23:30.480 --> 00:23:34.480 and and it's important to be mindful of this. 00:23:34.480 --> 00:23:39.840 I wrote this story in my dissertation. I was involved. I was in the room while 00:23:39.840 --> 00:23:43.679 this conversation was going on. Several years later I was teaching a 00:23:43.679 --> 00:23:46.159 room full of Mi'kmaq pre-service teachers 00:23:46.159 --> 00:23:51.039 and we were doing polygons and I wanted them to talk about the lines of symmetry 00:23:51.039 --> 00:23:53.760 of the polygons that happened to pass through the 00:23:53.760 --> 00:23:57.760 midpoint of the sides. And I did as I had always done with my 00:23:57.760 --> 00:24:01.360 good teacher move I said what would you call this point? 00:24:01.360 --> 00:24:04.400 Expecting the room to say middle so I could say yes. 00:24:04.400 --> 00:24:07.919 Mathematicians call that the midpoint isn't it lovely 00:24:07.919 --> 00:24:12.000 except it was a room full of Mi'kmaq speaking pre-service teachers. 00:24:12.000 --> 00:24:15.120 No one said middle. 00:24:15.120 --> 00:24:21.840 People said center. They said go halfway. a'qataig that's how you would say that in Mi'kmaq. 00:24:21.840 --> 00:24:25.440 It was consistent with how they would say it in Mi'kmaq and I 00:24:25.440 --> 00:24:27.679 said would you call it the middle and they said 00:24:27.679 --> 00:24:32.159 I guess you could maybe but it was a pretty lackluster response 00:24:32.159 --> 00:24:36.000 and then I started to laugh to myself and then I told them this story 00:24:36.000 --> 00:24:39.279 and then the rest of the class we had a wonderful class about how 00:24:39.279 --> 00:24:44.320 language impacts math learning and man was a never a rich discussion but I tell 00:24:44.320 --> 00:24:48.080 you that story because we have to be always mindful 00:24:48.080 --> 00:24:51.600 that sometimes it's something really simple that's causing a problem 00:24:51.600 --> 00:24:57.120 in kids understanding and for me even though I had written about 00:24:57.120 --> 00:25:01.279 it I still forgot because even though we're trying to 00:25:01.279 --> 00:25:04.480 change our practice we've had a really long apprenticeship 00:25:04.480 --> 00:25:08.240 in a different way of doing mathematics so we really need to be mindful of what 00:25:08.240 --> 00:25:11.440 we're doing. To begin to wrap up our presentation I'd 00:25:11.440 --> 00:25:16.159 like to provide a personal perspective of the way that language has 00:25:16.159 --> 00:25:22.400 impacted my own mathematics learning. Even the students who are not 00:25:22.400 --> 00:25:26.960 necessarily english language learners may have difficulty with mathematics in 00:25:26.960 --> 00:25:29.760 the classroom because it's important to note that english is 00:25:29.760 --> 00:25:32.480 different in different parts of the world. 00:25:32.480 --> 00:25:36.080 My family is from Guyana which is located in South America. 00:25:36.080 --> 00:25:40.159 Having been colonized by the British it is considered part of the Caribbean 00:25:40.159 --> 00:25:44.240 thus the language that is spoken there is Creolese and it is a beautiful 00:25:44.240 --> 00:25:48.559 rich mixture of African, East Indian, Arawakan and of 00:25:48.559 --> 00:25:53.919 older Dutch languages. Though Creolese is not officially considered a different 00:25:53.919 --> 00:25:57.760 language, there are enough differences between it 00:25:57.760 --> 00:26:01.520 and the Canadian english that I grew up hearing 00:26:01.520 --> 00:26:06.000 to have caused a lot of issues in my experience as a first generation 00:26:06.000 --> 00:26:09.520 Canadian and as the first person in my family to 00:26:09.520 --> 00:26:14.880 experience education outside of a Guyanese lens. 00:26:14.880 --> 00:26:21.039 A lot of the issues that Amel spoke to especially the ones related to 00:26:21.039 --> 00:26:25.440 definitions within and outside of a mathematical context were 00:26:25.440 --> 00:26:29.200 ones that I faced even though I am not technically an 00:26:29.200 --> 00:26:34.159 english language learner. For example you'll see some phrases 00:26:34.159 --> 00:26:37.919 written on the screen. The way that my parents would talk about 00:26:37.919 --> 00:26:41.440 multiplication is very different from the way I learned about multiplication 00:26:41.440 --> 00:26:44.000 at school. 00:26:44.159 --> 00:26:48.159 Instead of saying 6 multiplied by 9 equals 36 00:26:48.159 --> 00:26:53.360 my parents and grandparents would say 6 9s 36. 00:26:53.360 --> 00:26:57.840 Though seeing that on paper makes a little bit more sense 00:26:57.840 --> 00:27:01.279 now in hindsight you can imagine that as a 00:27:01.279 --> 00:27:04.960 student in grade 3 it was very confusing to hear 00:27:04.960 --> 00:27:08.880 a different thing at school and a different thing at home. 00:27:08.880 --> 00:27:15.600 Another key difference is three by three which is coincidentally the name of our 00:27:15.600 --> 00:27:18.960 presentation. Three by three is nine is something that 00:27:18.960 --> 00:27:23.600 my parents would say. And when talking about division six into 00:27:23.600 --> 00:27:28.000 twenty four is four. Again seeing these in text 00:27:28.000 --> 00:27:31.919 on the screen might aid in your assistance 00:27:31.919 --> 00:27:35.600 or seeing this text on the screen might be 00:27:35.600 --> 00:27:40.880 an aid to you as you try to decipher this difference in language 00:27:40.880 --> 00:27:44.240 but I wasn't provided with that as a student 00:27:44.240 --> 00:27:48.720 in a grade three classroom. Even previously today 00:27:48.720 --> 00:27:53.200 as I was preparing to meet with Amel to record this presentation 00:27:53.200 --> 00:27:59.200 I asked my dad, hey dad what's 144 divided by 12. 00:27:59.200 --> 00:28:03.039 In his mind and through the way that he was taught mathematics 00:28:03.039 --> 00:28:06.720 he actually did his division by multiplying. 00:28:06.720 --> 00:28:14.159 His answer to me was well 12 12s 144 so the answer is 12. 00:28:14.159 --> 00:28:18.320 Hearing math explained one way in school and another way at home 00:28:18.320 --> 00:28:21.440 caused a lot of confusion for me growing up. 00:28:21.440 --> 00:28:25.440 As a student I wish that my teachers had taken the time to understand where my 00:28:25.440 --> 00:28:30.720 family and I were coming from literally and figuratively and mirrored 00:28:30.720 --> 00:28:35.120 our use of the english language rather than force me to comply with what 00:28:35.120 --> 00:28:38.640 was deemed the quote-unquote right way of speaking 00:28:38.640 --> 00:28:43.760 about mathematics. At the core of this is one of the key 00:28:43.760 --> 00:28:48.320 principles that we all have as educators which is really just to get to know your 00:28:48.320 --> 00:28:52.960 students and that will be extremely helpful in your pursuit of 00:28:52.960 --> 00:28:56.880 helping them improve their mathematics. Thank you so 00:28:56.880 --> 00:28:59.200 much Keisha for taking us through that and sharing your 00:28:59.200 --> 00:29:02.559 personal story. So something I want to do as well 00:29:02.559 --> 00:29:06.320 is to share my own personal story which ties into a little bit of what 00:29:06.320 --> 00:29:11.520 Keisha discussed earlier. It is essential that math educators cater to different 00:29:11.520 --> 00:29:17.360 types of math learners. Take for example my personal story. 00:29:17.360 --> 00:29:20.799 My family comes from Algeria which is in north Africa 00:29:20.799 --> 00:29:24.640 and my parents learned math a little differently than the way I learned it. 00:29:24.640 --> 00:29:28.480 My dad excelled in math and it was one of his favorite subjects 00:29:28.480 --> 00:29:34.640 and it still is until now. Growing up, being born and raised here, anytime I had 00:29:34.640 --> 00:29:38.480 issues solving problems I would ask my parents for help but 00:29:38.480 --> 00:29:42.880 there were times, many times actually, where I believed that their method of 00:29:42.880 --> 00:29:46.720 answering questions was inaccurate because they solved the 00:29:46.720 --> 00:29:49.760 problems so they got the correct answer but they 00:29:49.760 --> 00:29:53.440 did it in a different way, a way that was unfamiliar to me that I 00:29:53.440 --> 00:29:58.159 didn't learn in school. So as I grew older I realized that there 00:29:58.159 --> 00:30:00.880 isn't only one way to solve math problems. 00:30:00.880 --> 00:30:05.120 There can be various different ways. Educators should welcome these various 00:30:05.120 --> 00:30:08.240 approaches and allow students to take control of their own learning 00:30:08.240 --> 00:30:11.679 by teaching them these different methods and allowing them to choose what best 00:30:11.679 --> 00:30:15.360 suits them. So now that we are reaching the end of 00:30:15.360 --> 00:30:18.559 our presentation, to wrap it up I just want to share with 00:30:18.559 --> 00:30:23.279 you some resources that I created. One of which is a kahoot so that way you 00:30:23.279 --> 00:30:26.960 can test your comprehension and what you've learned during our 00:30:26.960 --> 00:30:29.840 session. It's not long. It's about eight questions 00:30:29.840 --> 00:30:34.159 and I am going to share with you the link. 00:30:34.159 --> 00:30:38.080 So here is the kahoot activity and if you're not familiar with it, 00:30:38.080 --> 00:30:43.200 if you just go to this link above, so if you just pause this video and type 00:30:43.200 --> 00:30:48.480 this link, you should be able to click play, which is right over here and 00:30:48.480 --> 00:30:54.080 engage in the quiz. Another resource that I created for your 00:30:54.080 --> 00:30:59.039 own reference and educational purposes 00:30:59.039 --> 00:31:02.640 is this padlet. 00:31:02.880 --> 00:31:06.480 Please explore the padlet I created. Feel free to use 00:31:06.480 --> 00:31:10.799 any of the resources, to share the padlet, to share the resources, 00:31:10.799 --> 00:31:14.640 to add your own, and to also post your own comments. 00:31:14.640 --> 00:31:20.320 You'll also find a link to over 190 open educational resource mathematics 00:31:20.320 --> 00:31:23.440 textbooks that you can use for your own teaching 00:31:23.440 --> 00:31:27.440 and for your students learning. I really encourage that you check those 00:31:27.440 --> 00:31:30.000 out and see if there's anything that will be helpful 00:31:30.000 --> 00:31:32.880 for you. I'm sure you will find something and it is the first 00:31:32.880 --> 00:31:38.640 comment on the top left when you go on it and i'm gonna share my screen for 00:31:38.640 --> 00:31:42.880 this part as well. So here it is. So if you just 00:31:42.880 --> 00:31:46.000 type in this link you will find this nice padlet 00:31:46.000 --> 00:31:51.360 filled with resources most of which were used in the 00:31:51.360 --> 00:31:55.440 presentation today and here's the link for the open resource mathematics 00:31:55.440 --> 00:31:58.640 textbooks. So if you are intrigued and want to 00:31:58.640 --> 00:32:01.440 learn more about english language learners along with the problems and 00:32:01.440 --> 00:32:03.840 solutions associated with their math acquisition 00:32:03.840 --> 00:32:07.200 here are some additional resources at your disposal so you can pause this 00:32:07.200 --> 00:32:10.480 video and save these or better yet just go on the padlet and 00:32:10.480 --> 00:32:16.320 you'll find all of these there. As we start ending our presentation as 00:32:16.320 --> 00:32:19.360 discussed earlier we mentioned that our contact 00:32:19.360 --> 00:32:21.760 information will reappear again at the end. 00:32:21.760 --> 00:32:24.799 So here it is. Please feel free to pause this 00:32:24.799 --> 00:32:28.320 and take note of our contact information so you can 00:32:28.320 --> 00:32:32.799 touch base with us anytime and again as mentioned we will do our best to get 00:32:32.799 --> 00:32:35.919 back to you as soon as possible and we would love to hear 00:32:35.919 --> 00:32:39.600 from you anything you had to have to say any questions concerns or 00:32:39.600 --> 00:32:46.159 comments, positive or you know room for improvement would be greatly appreciated. 00:32:49.120 --> 00:32:53.279 Finally we would like to thank you for sticking in and tuning into our 00:32:53.279 --> 00:32:57.600 presentation. Here are our references for this session 00:32:57.600 --> 00:33:00.640 and once again I would like to thank you so much for joining us 00:33:00.640 --> 00:33:03.840 and I hope you have a great day a great week 00:33:03.840 --> 00:33:09.200 great break. Thank you so much and stay safe.