WEBVTT 00:00:00.430 --> 00:00:03.250 Hello and welcome to this episode of What in 00:00:03.250 --> 00:00:06.530 the World is Dyscalculia, the podcast that's 00:00:06.530 --> 00:00:09.869 all about the math learning disability. I'm your 00:00:09.869 --> 00:00:13.269 host, Dr. Honora Wall, Executive Director of 00:00:13.269 --> 00:00:15.890 the Dyscalculia Training and Research Institute, 00:00:16.489 --> 00:00:19.809 and this podcast is sponsored by Educalc Learning. 00:00:20.589 --> 00:00:27.250 You can visit either website www .vdtri .org 00:00:27.250 --> 00:00:32.179 or eduCalcLearning .com and find more information 00:00:32.179 --> 00:00:35.579 about dyscalculia. You can also listen to this 00:00:35.579 --> 00:00:38.679 podcast and share it with your friends and colleagues. 00:00:39.659 --> 00:00:42.060 And in this episode I wanted to talk about a 00:00:42.060 --> 00:00:46.439 question I saw recently in a chat group for math 00:00:46.439 --> 00:00:50.219 teachers. So some of the questions can be a little 00:00:50.219 --> 00:00:52.200 high -end but this one I think is accessible 00:00:52.200 --> 00:00:56.490 and I think this really helps me when I think 00:00:56.490 --> 00:01:00.229 about why are so many people struggling to help 00:01:00.229 --> 00:01:04.030 students with dyscalculia? So I'll tell you a 00:01:04.030 --> 00:01:05.730 summary of the question and then we'll get to 00:01:05.730 --> 00:01:09.109 what I think one of the issues is. The question 00:01:09.109 --> 00:01:14.129 asks teachers to discuss which they prefer and 00:01:14.129 --> 00:01:17.549 what kind of trends they observe when they either 00:01:17.549 --> 00:01:21.969 teach a formula to students or let them discover 00:01:21.969 --> 00:01:28.780 a formula. in the question the post says for 00:01:28.780 --> 00:01:32.500 example area of a trapezoid if you let your students 00:01:32.500 --> 00:01:36.260 discover the ways to evaluate the area of different 00:01:36.260 --> 00:01:40.500 trapezoids and then let them generalize a formula 00:01:40.500 --> 00:01:45.760 from that and the other case is telling the formula 00:01:45.760 --> 00:01:50.219 and then letting them remember and apply it and 00:01:51.389 --> 00:01:54.329 then further contemplation, what are thoughts, 00:01:54.530 --> 00:01:58.250 what are experiences, and what kind of motivation 00:01:58.250 --> 00:02:02.629 do we see? And are we developing an ability to 00:02:02.629 --> 00:02:07.189 solve any generic math problem by using either 00:02:07.189 --> 00:02:11.389 of these methods? And a couple of things I found 00:02:11.389 --> 00:02:13.930 interesting when I was reading this. First, it 00:02:13.930 --> 00:02:18.870 assumes that every single student could be given 00:02:19.080 --> 00:02:22.979 examples or samples and somehow derive a formula 00:02:22.979 --> 00:02:27.139 that would apply in any generic setting based 00:02:27.139 --> 00:02:32.259 on this figure. I have yet to see that kind of 00:02:32.259 --> 00:02:35.539 generalization happen for students who have dyscalculia. 00:02:35.719 --> 00:02:39.379 I'm not saying it couldn't. I'm saying in close 00:02:39.379 --> 00:02:43.099 to two decades it would surprise me very very 00:02:43.099 --> 00:02:47.139 much. Mostly because people who are neurodivergent 00:02:47.139 --> 00:02:50.539 don't make the same kind of leaps we are expecting 00:02:50.539 --> 00:02:53.759 when we're leading them to a certain outcome. 00:02:54.360 --> 00:02:56.580 So they might generalize all sorts of interesting 00:02:56.580 --> 00:03:00.080 things about a trapezoid. Literally none of them 00:03:00.080 --> 00:03:03.360 might have anything to do with deriving a generic 00:03:03.360 --> 00:03:08.000 formula based on given examples. So we can either 00:03:08.000 --> 00:03:11.620 teach students that skill, which takes a lot 00:03:11.620 --> 00:03:14.139 of time, effort, and planning that most of our 00:03:14.139 --> 00:03:19.150 pacing charts don't. incorporate, or we can leave 00:03:19.150 --> 00:03:22.189 them struggling, which is what commonly happens 00:03:22.189 --> 00:03:27.150 to many students with a math disability. In the 00:03:27.150 --> 00:03:29.969 second case, giving the student the formula, 00:03:30.150 --> 00:03:34.729 showing them how to work it, will that lead to 00:03:34.729 --> 00:03:38.229 solving other generic math problems? I have to 00:03:38.229 --> 00:03:41.189 say also, In a couple decades of doing this work, 00:03:41.330 --> 00:03:43.990 I don't know of any student with dyscalculia 00:03:43.990 --> 00:03:46.810 who would really care if it's going to lead to 00:03:46.810 --> 00:03:49.849 some other generic problem -solving tip. They 00:03:49.849 --> 00:03:52.909 want to know how to solve the problem in front 00:03:52.909 --> 00:03:57.330 of them. Then they want to solve as many similar 00:03:57.330 --> 00:04:01.050 problems as they can because students with dyscalculia 00:04:01.050 --> 00:04:04.250 are exceptionally hard -working and they want 00:04:04.250 --> 00:04:07.340 to know how to do this work. They want to be 00:04:07.340 --> 00:04:10.860 let in the math class door so that they can succeed 00:04:10.860 --> 00:04:15.020 with these topics. Another thing people with 00:04:15.020 --> 00:04:18.379 dyscalculia like is to know what's going to be 00:04:18.379 --> 00:04:22.040 on the homework. How do they do that so that 00:04:22.040 --> 00:04:24.680 they can practice effectively at home? They want 00:04:24.680 --> 00:04:27.100 to know exactly what's going to be on the test 00:04:27.100 --> 00:04:31.199 Friday or the quiz Thursday or the midterm or 00:04:31.199 --> 00:04:37.230 final so they can prepare for exactly that. That 00:04:37.230 --> 00:04:39.529 is the goal they're trying to reach. Usually 00:04:39.529 --> 00:04:42.990 because that's also tied to getting their diploma 00:04:42.990 --> 00:04:46.750 and then later getting a college degree. So it's 00:04:46.750 --> 00:04:50.370 a wonderful goal. I will say anecdotally a lot 00:04:50.370 --> 00:04:54.689 of my students come to enjoy parts of math after 00:04:54.689 --> 00:04:57.689 we get them that success. So it's not that they 00:04:57.689 --> 00:05:01.050 are never going to enjoy math or want to apply 00:05:01.050 --> 00:05:03.949 things in new situations. It's that within the 00:05:03.949 --> 00:05:07.610 K -12 system Are we really giving them time to 00:05:07.610 --> 00:05:11.490 do that? Are we actually rewarding their curiosity 00:05:11.490 --> 00:05:15.310 and interest? Or are we verbally rewarding that 00:05:15.310 --> 00:05:17.230 in class? Oh, what a great way to think about 00:05:17.230 --> 00:05:20.670 that problem, and then still failing them when 00:05:20.670 --> 00:05:23.170 we give them a test that was not aligned to our 00:05:23.170 --> 00:05:26.189 lessons, our instruction, or our spaced practice. 00:05:27.370 --> 00:05:31.430 That is where my pragmatic view comes into play. 00:05:31.569 --> 00:05:35.160 If you've heard any of the other podcast episodes 00:05:35.160 --> 00:05:37.620 or watch some of the reels we have out on social 00:05:37.620 --> 00:05:40.199 media, you know that I have a very pragmatic 00:05:40.199 --> 00:05:42.519 view because people are trying to reach goals 00:05:42.519 --> 00:05:47.220 and I think that their goal should be set by 00:05:47.220 --> 00:05:50.100 them. It's their life trajectory, it's their 00:05:50.100 --> 00:05:54.420 educational path. We can help them explore more 00:05:54.420 --> 00:05:59.500 goals and objectives once we've gotten some mastery 00:05:59.500 --> 00:06:04.170 and rebuilt a little bit of confidence. So, let's 00:06:04.170 --> 00:06:07.269 get back to that original question that I saw 00:06:07.269 --> 00:06:10.769 in the chat. How do I feel about either method? 00:06:11.310 --> 00:06:13.870 Well, I think for the vast majority of students 00:06:13.870 --> 00:06:17.389 in a classroom, maybe not vast, I might even 00:06:17.389 --> 00:06:20.470 say 40%. Students who have a pretty good math 00:06:20.470 --> 00:06:23.750 foundation and are enjoying geometry and have 00:06:23.750 --> 00:06:26.110 strong visual spatial skills and great working 00:06:26.110 --> 00:06:29.209 memory, they might be able to rappel with an 00:06:29.209 --> 00:06:32.149 example and a set of examples on their own and 00:06:32.149 --> 00:06:34.670 see if they can figure out a formula that would 00:06:34.670 --> 00:06:39.129 go with it. And that is great. If they also have 00:06:39.129 --> 00:06:41.490 the skill to know when and how to apply that 00:06:41.490 --> 00:06:44.550 in other settings, that's a really nice bonus. 00:06:45.250 --> 00:06:48.269 I think if it were highly common for students 00:06:48.269 --> 00:06:50.649 to do that on their own, we would probably have 00:06:50.649 --> 00:06:52.970 better national math scores, especially among 00:06:52.970 --> 00:06:58.170 adults, but that's a longitudinal conversation 00:06:58.170 --> 00:07:04.610 for another day. I think that when we find students 00:07:04.610 --> 00:07:07.589 in class are struggling with whatever method 00:07:07.589 --> 00:07:10.110 we're doing, we need to try some other methods. 00:07:10.930 --> 00:07:15.839 There is no one perfect way to teach math. There's 00:07:15.839 --> 00:07:18.379 no one perfect way to teach anything frankly 00:07:18.379 --> 00:07:22.199 Because learning depends on the learner on the 00:07:22.199 --> 00:07:25.500 student It is not simply what we know and how 00:07:25.500 --> 00:07:28.540 we deliver it It is how that message is received 00:07:28.540 --> 00:07:32.860 how it's understood how it's coded Where it is 00:07:32.860 --> 00:07:36.060 stored in long -term memory if at all and how 00:07:36.060 --> 00:07:39.899 the retrieval process works? so for my money 00:07:40.199 --> 00:07:42.579 If I have a student in class who's still struggling, 00:07:42.860 --> 00:07:44.879 I'm not going to keep relying on telling them 00:07:44.879 --> 00:07:47.120 that they need to figure it out because I've 00:07:47.120 --> 00:07:49.980 given them this amazing method, whether it's 00:07:49.980 --> 00:07:54.279 the case A or case B from the question in the 00:07:54.279 --> 00:07:57.420 chat. I'm going to simply throw all the spaghetti 00:07:57.420 --> 00:08:00.379 at the wall and see what sticks for that student. 00:08:00.540 --> 00:08:03.060 And I'm going to let them drive the work because 00:08:03.060 --> 00:08:08.759 they are the one who needs to show change in 00:08:08.759 --> 00:08:10.660 their understanding. Really, that's the goal 00:08:10.660 --> 00:08:13.120 of education. If we look at the beginning of 00:08:13.120 --> 00:08:15.079 the school year versus the end of the school 00:08:15.079 --> 00:08:18.560 year, what is the change in knowledge over time? 00:08:19.600 --> 00:08:22.480 And that's only partially determined by me as 00:08:22.480 --> 00:08:26.860 the educator. It's mostly determined by the student 00:08:26.860 --> 00:08:31.740 as the learner. And we read some of Vygotsky's 00:08:31.740 --> 00:08:35.480 amazing work. We know that this happens in a 00:08:35.480 --> 00:08:38.620 system, a back and forth working with a more 00:08:38.620 --> 00:08:42.080 knowledgeable other who can help us grapple with 00:08:42.080 --> 00:08:45.200 our questions and help build deeper understanding. 00:08:45.820 --> 00:08:47.980 However, we open the door to that understanding. 00:08:48.500 --> 00:08:52.100 Whether it's fumbling around on our own trying 00:08:52.100 --> 00:08:56.059 to find a formula that we can apply or if it's 00:08:56.059 --> 00:08:59.039 starting with a direct and explicit formula so 00:08:59.039 --> 00:09:01.220 that we know what to do and now we can explore 00:09:01.220 --> 00:09:06.039 with confidence. So educators, Whichever method 00:09:06.039 --> 00:09:11.860 your school or district or co -teacher is promoting 00:09:11.860 --> 00:09:16.000 right now See if it works and for the students 00:09:16.000 --> 00:09:19.500 who it does not work for Have some other tools 00:09:19.500 --> 00:09:23.399 in your toolbox. Don't rely on any one method 00:09:23.399 --> 00:09:28.440 Rely on finding methods that works. Oh, hey folks 00:09:28.440 --> 00:09:30.399 that goes back to that growth mindset We all 00:09:30.399 --> 00:09:33.720 like to talk so much about so let's apply that 00:09:33.600 --> 00:09:36.639 in our classrooms and in our tutoring sessions. 00:09:37.940 --> 00:09:40.940 For my money I usually work with students who 00:09:40.940 --> 00:09:43.559 are in someone else's classroom and I need to 00:09:43.559 --> 00:09:46.259 find a way to help them succeed where they are. 00:09:46.980 --> 00:09:50.220 So I'm going to go direct and explicit and then 00:09:50.220 --> 00:09:53.559 we're going to apply that to all of the homework, 00:09:53.940 --> 00:09:57.539 classwork, practice worksheets, different practice 00:09:57.539 --> 00:10:01.100 programs and in our test prep so the student 00:10:01.100 --> 00:10:04.299 knows what to do and can then spend their time 00:10:04.299 --> 00:10:07.580 effectively training how to do that skill in 00:10:07.580 --> 00:10:10.759 a variety of circumstances. But that's just me. 00:10:11.480 --> 00:10:14.059 And there's a million other methods out there 00:10:14.059 --> 00:10:17.000 that you might have found more success or at 00:10:17.000 --> 00:10:19.639 least equal success in. I'd love to hear about 00:10:19.639 --> 00:10:22.860 what's working for you. You can email me, hanora 00:10:22.860 --> 00:10:28.600 at the DTRI .org or you can message me on any 00:10:28.600 --> 00:10:31.120 of the social media platforms or find me on LinkedIn. 00:10:33.430 --> 00:10:36.090 And I'm off to a great conference right now. 00:10:36.090 --> 00:10:38.769 I'm very excited. I'll be doing some recordings, 00:10:39.389 --> 00:10:41.789 both of the podcast and of some social media 00:10:41.789 --> 00:10:45.990 reels from South by Southwest EDU. And if you 00:10:45.990 --> 00:10:49.490 will be there in March of 2026, I hope you come 00:10:49.490 --> 00:10:52.870 find me. And if not, I will see you online. If 00:10:52.870 --> 00:10:56.009 you have questions about dyscalculia, if you'd 00:10:56.009 --> 00:10:59.889 like to train your team or yourself, feel free 00:10:59.889 --> 00:11:02.620 to reach out. And thank you for listening to 00:11:02.620 --> 00:11:05.019 What in the World is Dyscalculia.