Explore or Be Direct?

0:00Hello and welcome to this episode of What in the World is Discounculia, the podcast that's all about the math learning disability. I'm your host, Dr. Hanora Wall, Executive Director of the Discounculia Training and Research Institute. And this podcast is sponsored by Edge Account Learning. You can visit either website www.vdti.org or edgeaccountlearning.com and find more information about Discounculia. You can also listen to this podcast and share it with your friends and colleagues. And in this episode I wanted to talk about a question I saw recently in a chat group for math teachers. So some of the questions can be a little high end, but this one I think is accessible. And I think this really helps me when I think about why are so many people struggling to help students with Discounculia.

1:02So I'll tell you a summary of the question and then we'll get to what I think one of the issues is. The question asks teachers to discuss which they prefer and what kind of trends they observe when they either teach a formula to students or let them discover a formula. And in the question, the post says for example, area of a trapezoid, if you let your students discover the ways to evaluate the area of different trapezoids. And then let them generalize a formula from that. And the other case is telling the formula and then letting them remember and apply it and then further contemplation, what are thoughts, what are experiences. And what kind of motivation do we see and are we developing an ability to solve any generic math problem by using either of these methods.

2:08And a couple of things I found interesting when I was reading this. First, it assumes that every single student could be given examples or samples and somehow derive a formula that would apply in an generic setting based on this figure. I have yet to see that kind of generalization happen for students who have Discounculia. Saying close to two decades, it would surprise me very, very much. Mostly because people who are neurodivergent don't make the same kind of leaps we are expecting when we're leading them to a certain outcome. So they might generalize all sorts of interesting things about a trapezoid. Literally none of them might have anything to do with deriving a generic formula based on given examples. So we can either teach students that skill which takes a lot of time, effort and planning that most of our pacing charts don't incorporate or we can leave them struggling, which is what commonly happens to many students with a math disability.

3:26In the second case, giving the student a formula showing them how to work it will that lead to solving other generic math problems. I have to say also in a couple of decades of doing this work, I don't know of any student with Discounculia who would really care if it's going to lead to some other generic problem solving tip they want to know how to solve the problem in front of them. Then they want to solve as many similar problems as they can because students with Discounculia are exceptionally hard working and they want to know how to do this work. They want to be let in the math class door so that they can succeed with these topics. Another thing people with Discounculia like is to know what's going to be on the homework, how do they do that so that they can practice effectively at home. They want to know exactly what's going to be on the test Friday or the quiz Thursday or the midterm or final so they can prepare for exactly that.

4:36That is the goal they're trying to reach, usually because that's also tied to getting their diploma and then later getting a college degree so it's a wonderful goal. I will say anecdotally a lot of my students come to enjoy parts of math after we get them that success. So it's not that they are never going to enjoy math or want to apply things in new situations. It's that within the K-12 system are we really giving them time to do that? Are we actually rewarding their curiosity and interest or are we verbally rewarding that in class? Oh, what a great way to think about that problem and then still failing them when we give them a test that was not aligned to our lessons, our instruction or our space to practice. That is where my pragmatic view comes into play. If you've heard any of the other podcast episodes or watched some of the reels we have out on social media, you know that I'm a very pragmatic view because people are trying to reach goals.

5:42And I think that their goal should be set by them. It's their life trajectory, it's their educational path. We can help them explore more goals and objectives once we've gotten some mastery and rebuilt a little bit of confidence. So let's get back to that original question that I saw in the chat. How do I feel about either method? Well, I think for the vast majority of students in a classroom, maybe not vast, I might even say 40%. Students who have a pretty good math foundation and are enjoying geometry and have strong visual spatial skills and great working memory, they might be able to raffle with an example and a set of examples on their own and see if they can figure out a formula that would go with it. And that is great. If they also have the skill to know when and how to apply that in other settings, that's a really nice bonus.

6:45I think if there were highly common for students to do that on their own, we would probably have better national math scores, especially among adults. But that's a longitudinal conversation for another day. I think that when we find students in class are struggling with whatever method we're doing, we need to try some other methods. There is no one perfect way to teach math. There's no one perfect way to teach anything, frankly, because learning depends on the learner on the student. Not simply what we know and how we deliver it. It is how that message is received, how it's understood, how it's coded, where it is stored in long-term memory, if at all, and how the retrieval process works. So for my money, if I have a student in class who's still struggling, I'm not going to keep relying on telling them that they need to figure it out because I've given them this amazing method.

7:49Whether it's the case A or case B from the question in the chat. I'm going to simply throw all this beginning at the wall and see what sticks for that student. And I'm going to let them drive the work because they are the one who needs to show change in their understanding. Really, that's the goal of education. If we look at the beginning of the school year versus the end of the school year, what is the change in knowledge over time? And that's only partially determined by me as the educator. It's mostly determined by the student as the learner. And we read some of Hagatsky's amazing work. We know that this happens in a system, a back and forth, working with a more knowledgeable other who can help us grapple with our questions and help build deeper understanding. However, we open the door to that understanding. Whether it's fumbling around on our own, trying to find a formula that we can apply or if it's starting with a direct and explicit formula so that we know what to do and now we can explore with confidence.

9:02So educators, whichever method your school or district or co-teacher is promoting right now, see if it works and for the students who it does not work for, have some other tools in your toolbox. Don't rely on any one method, rely on finding methods that works. Oh, hey folks, that goes back to that growth mindset we all like to talk so much about. So let's apply that in our classrooms and in our tutoring sessions. For my money, I usually work with students who are in someone else's classroom and I need to find a way to help them succeed where they are. So I'm going to go direct and explicit and then we're going to apply that to all of the homework, classwork, practice worksheets, different practice programs and in our test prep. So the student knows what to do and can then spend their time effectively training how to do that skill in a variety of circumstances.

10:09But that's just me and there's a million other methods out there that you might have found more success or at least equal success in. I'd love to hear about what's working for you. You can email me, Hanora at thedtri.org or you can message me on any of the social media platforms or find me on LinkedIn. And I'm off to a great conference right now. I'm very excited. I'll be doing some recordings, both of the podcast and of some social media reels from South by Southwest EDU. And if you will be there in March of 2026, I hope you come find me. And if not, I will see you online. If you have questions about Discalculia, if you'd like to train your team or yourself, feel free to reach out. And thank you for listening to What in the World is Discalculia.