1 00:00:00,000 --> 00:00:06,960 Hello everyone and welcome back to What in the World is Dyscalculia, the podcast that 2 00:00:06,960 --> 00:00:10,160 is all about the math learning disability. 3 00:00:10,160 --> 00:00:16,620 I'm your host, Dr. Honora Wall, and the podcast is produced by Educalc Learning. 4 00:00:16,620 --> 00:00:24,280 You can find out more about Dyscalculia at educalclearning.com or at our non-profit 5 00:00:24,280 --> 00:00:33,920 www.thedtri.org which stands for the Dyscalculia Training and Research Institute. 6 00:00:33,920 --> 00:00:39,960 And I'm going to jump in today because I just had a session with a student that really highlighted 7 00:00:39,960 --> 00:00:48,960 a lot of things I want to talk about for classroom teachers, interventionist, tutors, and home 8 00:00:48,960 --> 00:00:49,960 school parents. 9 00:00:49,960 --> 00:00:56,480 I'll be running into this situation that I have today. 10 00:00:56,480 --> 00:01:03,000 And I will preface by saying that most of the situation I ran into today was a conflict 11 00:01:03,000 --> 00:01:09,720 between my prior knowledge as a math educator and the student's lack of prior knowledge 12 00:01:09,720 --> 00:01:15,640 because they're the student and how there's that disconnect between the two. 13 00:01:15,640 --> 00:01:22,960 It is really difficult as an educator to get into the headspace of the student who's hearing 14 00:01:22,960 --> 00:01:29,000 all these terms and doing all this work, learning these concepts for the first time. 15 00:01:29,000 --> 00:01:37,120 We know exactly what we mean when we're talking about these math topics and presenting a lesson. 16 00:01:37,120 --> 00:01:43,400 So it can be hard to know when the student really understands what we're trying to say 17 00:01:43,400 --> 00:01:45,720 and when they don't. 18 00:01:45,720 --> 00:01:53,840 When you work with students who have neurodivergence, dyscalculia, dyslexia, dysgraphia, ADHD, high 19 00:01:53,840 --> 00:01:58,960 functioning autism, or I guess I should say autism in general, I was working with a student 20 00:01:58,960 --> 00:02:04,080 who has high functioning autism and dyscalculia. 21 00:02:04,080 --> 00:02:11,520 These students have a quality I find quite frequently just because I see it a lot does 22 00:02:11,520 --> 00:02:14,360 not mean that they're tied together. 23 00:02:14,360 --> 00:02:16,360 That is an important distinction. 24 00:02:16,360 --> 00:02:23,160 But I do see it quite a bit and it is a great quality in a student and it can be a difficult 25 00:02:23,160 --> 00:02:26,920 or sometimes frustrating quality for a teacher which is why I wanted to talk about it. 26 00:02:26,920 --> 00:02:28,600 So here's the quality. 27 00:02:28,600 --> 00:02:35,840 The quality that I find prevalent in this population of learners is that they're not 28 00:02:35,840 --> 00:02:43,560 interested in taking your first explanation as the answer, they need to know more. 29 00:02:43,560 --> 00:02:50,320 They have so many more questions than a neurotypical student who is more likely to say, okay, I'm 30 00:02:50,320 --> 00:02:54,120 going to do X, I'm going to do Y, and then I get answers E and I move on. 31 00:02:54,120 --> 00:02:58,840 Or I got to do it because they said this is what to do and they move on. 32 00:02:58,840 --> 00:03:02,080 No, neurodivergent students have a lot more questions. 33 00:03:02,080 --> 00:03:07,280 They need to know Y and the way you explain the Y to everyone else is not going to be 34 00:03:07,280 --> 00:03:11,240 satisfactory for these students so they're going to have more Ys. 35 00:03:11,240 --> 00:03:17,880 And I have had students I work with who find that their classroom teachers do get frustrated 36 00:03:17,880 --> 00:03:19,880 and say things like you have to get it. 37 00:03:19,880 --> 00:03:21,440 I just told you what it was. 38 00:03:21,440 --> 00:03:23,720 Or say, okay, that's too many questions. 39 00:03:23,720 --> 00:03:25,480 The class has to move on. 40 00:03:25,480 --> 00:03:26,720 Ask me later. 41 00:03:26,720 --> 00:03:31,760 And I completely get that especially if you have a large classroom, you're trying to meet 42 00:03:31,760 --> 00:03:34,160 a pacing chart or just get through a lesson. 43 00:03:34,160 --> 00:03:35,680 You know the homework you need to assign. 44 00:03:35,680 --> 00:03:39,120 You have to talk about all the things that are going to be on the homework. 45 00:03:39,120 --> 00:03:45,640 So it can take longer to work with students who have more questions. 46 00:03:45,640 --> 00:03:48,440 And sometimes we don't know the answer to their question. 47 00:03:48,440 --> 00:03:51,600 That's exactly what happened to me today. 48 00:03:51,600 --> 00:03:54,080 And I start this lesson. 49 00:03:54,080 --> 00:04:00,880 This particular student of mine is a homeschool student who came to me recently with high 50 00:04:00,880 --> 00:04:10,320 functioning autism and dyscalculia and is old enough, he's 18, old enough to have had 51 00:04:10,320 --> 00:04:13,840 a whole lot of math and were doing mostly grade level work. 52 00:04:13,840 --> 00:04:19,960 But he also did not have the foundation for it because with the dyscalculia using a traditional 53 00:04:19,960 --> 00:04:25,400 math curriculum, he just really had not progressed past second or third grade math. 54 00:04:25,400 --> 00:04:30,920 Which is very common, the worksheets and the traditional curriculum for second and third 55 00:04:30,920 --> 00:04:36,240 grade are a train wreck for students with dyscalculia and without the right support 56 00:04:36,240 --> 00:04:38,360 systems it's just not going to happen. 57 00:04:38,360 --> 00:04:40,720 And that is what the case was here. 58 00:04:40,720 --> 00:04:46,320 So when I met this student a few months ago, I said all right we're going to jump in to 59 00:04:46,320 --> 00:04:54,880 grade level as much as possible, fix the foundation as we go and get this math curriculum complete. 60 00:04:54,880 --> 00:05:01,720 So, today we were talking about complementary and supplementary angles. 61 00:05:01,720 --> 00:05:08,360 All right, if two angles happen to be complementary that is a technical term that means the two 62 00:05:08,360 --> 00:05:13,720 angles add to exactly 90 degrees. 63 00:05:13,720 --> 00:05:18,800 Maybe they are two angles that are part of a right angle, maybe they are two angles that 64 00:05:18,800 --> 00:05:21,720 are not connected to each other. 65 00:05:21,720 --> 00:05:30,400 Maybe you have a graphic of an angle or the two angles, maybe you have a word problem 66 00:05:30,400 --> 00:05:33,960 that just lists the degrees. 67 00:05:33,960 --> 00:05:38,200 You can see this working a lot of different presentations. 68 00:05:38,200 --> 00:05:43,960 But at the end of the day, complementary means two angles add to 90 and supplementary means 69 00:05:43,960 --> 00:05:46,160 two angles add to 180. 70 00:05:46,160 --> 00:05:51,520 I was thinking this would be pretty straightforward, this would be a breeze. 71 00:05:51,520 --> 00:05:56,240 The calculator work, we've already talked about angles, we've already talked even a 72 00:05:56,240 --> 00:06:00,680 little bit about the unit circle and what degrees are, where they come from, what does 73 00:06:00,680 --> 00:06:02,160 that term mean. 74 00:06:02,160 --> 00:06:05,720 We've talked about the semicircle, the 180 degrees. 75 00:06:05,720 --> 00:06:08,040 We've talked about different types of angles, acute up too. 76 00:06:08,040 --> 00:06:14,360 So I thought we had a lot of prep and groundwork laid and this would be a pretty straightforward 77 00:06:14,360 --> 00:06:15,360 extension. 78 00:06:15,360 --> 00:06:20,440 And I could not have been more incorrect in that assumption. 79 00:06:20,440 --> 00:06:27,560 Here we got to with this lesson is that, you know, if you have an angle that's, let's 80 00:06:27,560 --> 00:06:34,160 say 62 degrees and you have to find the complement, the work you do is to grab your calculator 81 00:06:34,160 --> 00:06:38,280 and put in 90 minus 62. 82 00:06:38,280 --> 00:06:42,360 The answer is the measure of the complementary angle. 83 00:06:42,360 --> 00:06:43,360 Okay. 84 00:06:43,360 --> 00:06:52,400 Well, the student really got stuck on why do we care if angles are complementary or 85 00:06:52,400 --> 00:06:53,680 supplementary? 86 00:06:53,680 --> 00:06:55,720 Why do you need to know this? 87 00:06:55,720 --> 00:07:04,840 In what format will you ever use this either in math or in life? 88 00:07:04,840 --> 00:07:07,600 What is the point essentially? 89 00:07:07,600 --> 00:07:12,120 And this is where I think there's an interesting disconnect. 90 00:07:12,120 --> 00:07:18,360 There's big movement in education right now to do kind of the problem-based learning and 91 00:07:18,360 --> 00:07:22,440 put students in a situation where they have to kind of try some things and figure it out 92 00:07:22,440 --> 00:07:25,640 and that is going to develop conceptual understanding. 93 00:07:25,640 --> 00:07:28,840 And that's true for a lot of things and for a lot of students. 94 00:07:28,840 --> 00:07:36,880 I don't find it to be effective in the way we want for students who are neurodivergent 95 00:07:36,880 --> 00:07:42,280 because their conceptual understanding is different and unique. 96 00:07:42,280 --> 00:07:46,800 It is not weak, it is not lower level, it is not incorrect. 97 00:07:46,800 --> 00:07:49,760 It's just different. 98 00:07:49,760 --> 00:07:54,680 And this is a population that will test you as an educator. 99 00:07:54,680 --> 00:08:01,360 They will stretch you and you will have to work in a different way, a unique way. 100 00:08:01,360 --> 00:08:05,000 You're going to have to dig deeper to answer their questions. 101 00:08:05,000 --> 00:08:07,120 I'll give you a spoiler alert. 102 00:08:07,120 --> 00:08:11,840 We got to the end of the session and I said, I will keep searching to try to find an answer 103 00:08:11,840 --> 00:08:19,840 that works for your question but I really don't have one that is satisfactory at this 104 00:08:19,840 --> 00:08:21,720 time and we had to move on. 105 00:08:21,720 --> 00:08:23,280 We'll come back to it later. 106 00:08:23,280 --> 00:08:28,480 If I find a good way to answer the question, I'll let you know in a future podcast. 107 00:08:28,480 --> 00:08:33,560 But for you, you can get this kind of question teaching any topic so I don't want to get 108 00:08:33,560 --> 00:08:37,640 too hung up on what's a good answer for complementary or supplementary. 109 00:08:37,640 --> 00:08:43,000 It's going to happen to you in all sorts of math topics. 110 00:08:43,000 --> 00:08:50,680 So what I really need for you to know is that this is very normal for neurodiverse students. 111 00:08:50,680 --> 00:08:55,120 They have more questions, they need more and different answers. 112 00:08:55,120 --> 00:08:58,200 Telling them the same answer over and over again will not work. 113 00:08:58,200 --> 00:09:04,000 Saying it the way it works for every other student you've worked with will not work. 114 00:09:04,000 --> 00:09:07,440 Saying it just the way it makes sense to you will not work. 115 00:09:07,440 --> 00:09:10,520 You're going to have to keep trying some new things. 116 00:09:10,520 --> 00:09:16,440 And if you have the time and space to do it, it's a really interesting conversation. 117 00:09:16,440 --> 00:09:21,320 You get to think about math in a very different and unique way and you get to think about 118 00:09:21,320 --> 00:09:28,760 the application of math concepts in an interesting and unique way that you have not had to do 119 00:09:28,760 --> 00:09:31,560 before. 120 00:09:31,560 --> 00:09:39,120 If you're finding that it's a source of frustration or aggravation, you want to reflect on your 121 00:09:39,120 --> 00:09:41,160 thoughts about math and your understanding of it. 122 00:09:41,160 --> 00:09:46,320 We can understand math and still not understand how to ask or answer a question about it. 123 00:09:46,320 --> 00:09:47,320 That's okay. 124 00:09:47,320 --> 00:09:48,320 That happens. 125 00:09:48,320 --> 00:09:55,840 We are not robots and a lot of what we're talking about is ephemeral esoteric topics. 126 00:09:55,840 --> 00:10:02,160 I tried to get as close as possible by utilizing, okay, well, if you need complementary angles, 127 00:10:02,160 --> 00:10:03,720 you might need that in building. 128 00:10:03,720 --> 00:10:10,720 Let's say you had a house and the wall was at an 80-degree angle and it really needs 129 00:10:10,720 --> 00:10:12,920 to be at 90 for strength and stability. 130 00:10:12,920 --> 00:10:19,560 So what are you missing, a complementary angle of 10 degrees would help shore that up, things 131 00:10:19,560 --> 00:10:20,560 like that. 132 00:10:20,560 --> 00:10:25,680 But it didn't really satisfy the student in a way that he felt comfortable with the homework 133 00:10:25,680 --> 00:10:33,960 I needed to assign, which was simply what is the complement to a 62-degree angle? 134 00:10:33,960 --> 00:10:38,880 Another interesting point, and I bring this up because this will impact the way you teach 135 00:10:38,880 --> 00:10:40,760 as well. 136 00:10:40,760 --> 00:10:46,160 When I was introducing this lesson, I gave the definition that I thought would make the 137 00:10:46,160 --> 00:10:52,440 most sense complementary means two angles that add to 90 degrees. 138 00:10:52,440 --> 00:10:57,720 Supplementary means two angles that add to 180 degrees. 139 00:10:57,720 --> 00:11:02,440 We talked about it, we wrote it down, we got into our examples, and at the top of this 140 00:11:02,440 --> 00:11:07,200 worksheet you would be given an angle, like I said, the 62 degrees, and you had to find 141 00:11:07,200 --> 00:11:08,880 the complement. 142 00:11:08,880 --> 00:11:14,840 So the work then becomes 90 minus 62. 143 00:11:14,840 --> 00:11:20,040 Even if we had written out the equation, 62 plus x equals 90, you still would have solved 144 00:11:20,040 --> 00:11:22,880 by subtracting 90 minus 62. 145 00:11:22,880 --> 00:11:28,600 Well then at the bottom of the worksheet there were other questions. 146 00:11:28,600 --> 00:11:32,520 Classify the angles as complementary, supplementary, or neither. 147 00:11:32,520 --> 00:11:37,200 And then you were given two angles, let's say 44 degrees and 17 degrees. 148 00:11:37,200 --> 00:11:45,080 You had to add them and decide whether or not they added to 90 or 180 and what kind 149 00:11:45,080 --> 00:11:48,360 of special term that would give it. 150 00:11:48,360 --> 00:11:54,120 So as he's writing down the notes so that he can do this work on his own later, this 151 00:11:54,120 --> 00:11:56,720 was really a sticking point for him. 152 00:11:56,720 --> 00:12:02,200 He was trying to write down what is my formula, how could he explain to himself later, his 153 00:12:02,200 --> 00:12:03,480 future self. 154 00:12:03,480 --> 00:12:09,440 His notes have to be a message to his future self on how to do this work. 155 00:12:09,440 --> 00:12:17,400 And my definition, complementary adds to 90, did not match the work being done. 156 00:12:17,400 --> 00:12:25,320 If you have an angle, you are going to do 90 minus that angle to find the missing complementary 157 00:12:25,320 --> 00:12:27,520 angle. 158 00:12:27,520 --> 00:12:30,960 I said complementary angles add to 90. 159 00:12:30,960 --> 00:12:33,560 The work I told him to do is subtraction. 160 00:12:33,560 --> 00:12:38,680 For people who do not have a math learning disability, this is part of a fact family 161 00:12:38,680 --> 00:12:39,680 situation. 162 00:12:39,680 --> 00:12:40,880 These are inverse operations. 163 00:12:40,880 --> 00:12:43,400 You add and the backwards of that is subtract. 164 00:12:43,400 --> 00:12:44,400 They go together. 165 00:12:44,400 --> 00:12:49,120 For a student with dyscalculia, they do not go together. 166 00:12:49,120 --> 00:12:58,240 These are completely individual, unrelated, separate tasks. 167 00:12:58,240 --> 00:13:03,080 And having the definition adds to 90 does not automatically correlate to solve with 168 00:13:03,080 --> 00:13:04,080 subtraction. 169 00:13:04,080 --> 00:13:09,800 So we really had to dig into that and how to put the right kind of notes for each section 170 00:13:09,800 --> 00:13:12,120 so he knew what to do. 171 00:13:12,120 --> 00:13:21,840 And also discuss a very little bit of the duality, the front and back, top and bottom, 172 00:13:21,840 --> 00:13:26,280 add subtract, the relationship between inverses. 173 00:13:26,280 --> 00:13:30,520 That is why students with dyscalculia also have a lot of trouble with directions and 174 00:13:30,520 --> 00:13:37,640 also have a lot of trouble with those prepositions above, below, front, back, left, right. 175 00:13:37,640 --> 00:13:43,440 These are all difficult concepts because we teach them and think of them as being related 176 00:13:43,440 --> 00:13:46,120 terms. 177 00:13:46,120 --> 00:13:48,840 And for students with dyscalculia, they are not. 178 00:13:48,840 --> 00:13:54,640 It is very much like saying you could have an orange or you could have an octopus. 179 00:13:54,640 --> 00:13:55,640 What? 180 00:13:55,640 --> 00:13:57,760 They are not related at all. 181 00:13:57,760 --> 00:14:01,600 And that is a very different way of thinking about this as an educator. 182 00:14:01,600 --> 00:14:07,720 We might think of things as going together as a unit, doing and undoing each other. 183 00:14:07,720 --> 00:14:13,200 That is not how our students with dyscalculia interpret these concepts. 184 00:14:13,200 --> 00:14:18,520 So just a heads up on some of the things you will definitely find working with neurodivergent 185 00:14:18,520 --> 00:14:19,600 students. 186 00:14:19,600 --> 00:14:23,560 When they're asking questions and they say, but why, but why, but why? 187 00:14:23,560 --> 00:14:24,960 It doesn't make sense to me yet. 188 00:14:24,960 --> 00:14:29,000 I need it to make sense before I can move on. 189 00:14:29,000 --> 00:14:33,920 You really need to take everything that you are thinking about the topic and throw it 190 00:14:33,920 --> 00:14:39,880 up in the air, separate it all out like confetti and start talking about it individually and 191 00:14:39,880 --> 00:14:43,160 separately and differently and try a few things. 192 00:14:43,160 --> 00:14:48,520 And don't be afraid to tell students, you know, that's a really interesting question. 193 00:14:48,520 --> 00:14:52,760 I'm not sure if I'm answering it the way you're looking for an answer. 194 00:14:52,760 --> 00:14:55,800 I'm not sure I understand exactly what you're asking. 195 00:14:55,800 --> 00:15:00,440 Let's dig into this a little more and see if we can get somewhere with it. 196 00:15:00,440 --> 00:15:05,680 Maybe we'll get somewhere that lets you feel better about the topic and understanding it. 197 00:15:05,680 --> 00:15:10,640 We might just get to a point of, listen, for the top half, you're going to do 90 minus. 198 00:15:10,640 --> 00:15:13,480 And for the bottom half, you're going to add and see if it's 90 or not. 199 00:15:13,480 --> 00:15:15,360 Yes or no. 200 00:15:15,360 --> 00:15:19,840 Sometimes we do have to get to that very specific direct instruction. 201 00:15:19,840 --> 00:15:27,960 Do this, do not do that and save the rest of the understanding for a longer or a future 202 00:15:27,960 --> 00:15:33,080 discussion because we have to come up with better explanations. 203 00:15:33,080 --> 00:15:36,080 We have to find that, that route together. 204 00:15:36,080 --> 00:15:40,760 And I do find a lot of students are willing to accept that. 205 00:15:40,760 --> 00:15:44,360 If you are willing to say, listen, I'm not sure, I'd like to find out. 206 00:15:44,360 --> 00:15:46,280 I'm going to research it a little bit. 207 00:15:46,280 --> 00:15:49,280 I'm happy to have this conversation with you later. 208 00:15:49,280 --> 00:15:52,040 Right now we just need to get this part done. 209 00:15:52,040 --> 00:15:53,040 Then that's okay. 210 00:15:53,040 --> 00:15:56,120 It's when we say, no more questions. 211 00:15:56,120 --> 00:15:57,120 Talk to me later. 212 00:15:57,120 --> 00:15:58,120 You're asking too much. 213 00:15:58,120 --> 00:15:59,120 You need to already know. 214 00:15:59,120 --> 00:16:02,200 Now they feel very cut off and that closes the door. 215 00:16:02,200 --> 00:16:08,720 We're limiting the access because of our own experiences, our own frustrations or our 216 00:16:08,720 --> 00:16:14,000 own needs to get some other things done or our own feelings of insecurity, not knowing 217 00:16:14,000 --> 00:16:20,360 how to answer the question that is being asked, not being able to get a satisfactory answer. 218 00:16:20,360 --> 00:16:22,920 And I know that this is true of a lot of educators. 219 00:16:22,920 --> 00:16:30,360 I hear this from teachers at conferences and conventions and during the Q&A and I hear 220 00:16:30,360 --> 00:16:33,080 from the students what they hear from their teachers. 221 00:16:33,080 --> 00:16:35,040 We know teachers are frustrated. 222 00:16:35,040 --> 00:16:41,120 So I want you to understand what to do about that frustration where some of it comes from. 223 00:16:41,120 --> 00:16:48,000 That's just really exciting and different conversation. 224 00:16:48,000 --> 00:16:52,040 It's not the conversation you've had in math class for the last 20 years of your teaching 225 00:16:52,040 --> 00:16:53,280 career. 226 00:16:53,280 --> 00:16:56,880 This is different and be open to that. 227 00:16:56,880 --> 00:16:58,880 And be ready for the surprise. 228 00:16:58,880 --> 00:17:03,400 I truly felt that this would be one of our easier lessons. 229 00:17:03,400 --> 00:17:05,960 I mean, heck, we're using a calculator. 230 00:17:05,960 --> 00:17:09,680 It's only two words and there's only two things to do. 231 00:17:09,680 --> 00:17:13,040 It equals 90 or it equals 180. 232 00:17:13,040 --> 00:17:14,040 That's it. 233 00:17:14,040 --> 00:17:15,040 Those are the only two options. 234 00:17:15,040 --> 00:17:17,920 I thought this would be very straightforward. 235 00:17:17,920 --> 00:17:24,920 And as I said, it was exceptionally difficult to come up with a good explanation that made 236 00:17:24,920 --> 00:17:29,200 my student feel better and more confident about these terms. 237 00:17:29,200 --> 00:17:35,280 I believe he feels confident with the work, but now I'm going to see. 238 00:17:35,280 --> 00:17:40,160 After he's done these worksheets on his own, do his notes still make sense? 239 00:17:40,160 --> 00:17:43,960 Is he still able to complete this work or does he still get stuck because of that conceptual 240 00:17:43,960 --> 00:17:44,960 piece? 241 00:17:44,960 --> 00:17:51,360 Personally, I do not know of any research that's being done in this field yet. 242 00:17:51,360 --> 00:17:54,520 I'm not sure what the research question would even be. 243 00:17:54,520 --> 00:18:02,800 Maybe just a case study or qualitative examination of neurodivergent students and their feelings 244 00:18:02,800 --> 00:18:05,960 about math concepts. 245 00:18:05,960 --> 00:18:10,040 If you've come across anything like that, you have some research for me, please share 246 00:18:10,040 --> 00:18:11,040 it. 247 00:18:11,040 --> 00:18:13,040 I would love to know more. 248 00:18:13,040 --> 00:18:21,400 You can send it to me at Honora, H-O-N-O-R-A at educalclearning.com or Honora at the 249 00:18:21,400 --> 00:18:22,560 dtri.org. 250 00:18:22,560 --> 00:18:25,280 And of course, check out the two websites. 251 00:18:25,280 --> 00:18:30,400 If I do come across some good information in this area, I will put them up as blog posts 252 00:18:30,400 --> 00:18:36,200 and put the links to research or articles on those websites so that we can keep sharing 253 00:18:36,200 --> 00:18:44,680 information about the math learning disability and help our students with any type of neurodivergence. 254 00:18:44,680 --> 00:18:50,200 Thank you very much for listening to the What in the World is Discalculia podcast. 255 00:18:50,200 --> 00:18:54,400 This has been your host, Dr. Honora Wall, and I look forward to speaking with you again 256 00:18:54,400 --> 00:19:02,400 soon.