Hello and welcome to the latest podcast of What in the World is Dyscalculia presented
by Educalc learning.
I'm your host Dr. Nora Wall and I want to talk today about the importance of precision.
So when I'm writing math standards for my students, when I'm developing my materials
and when I'm talking to other educators, I really want to change the conversation from
the word fluency to the word precision.
Now fluency, especially the term math fluency, is a big part of math standards and a big
part of the mathematical achievement conversation.
And typically when people talk about math fluency, they're talking about that memorization
piece, that being very fast with an answer, that idea of either doing the math in your
head or doing it really quickly, going through those worksheets at a crazy pace.
Hopefully none of our listeners are using timed math worksheets ever.
We know for a fact through published research that the only thing timed math tests are directly
tied to is developing math anxiety.
They have not been shown to increase fluency or later math achievement.
Just stop.
Just don't do them anymore.
Get rid of them.
What I really would like you to do is think about precision.
And that way we're changing our conversation away from the fluency, from the speed, we're
moving away from the confidence in the right answer, and we're looking more at being precise,
checking our work, being accurate.
Whatever we think the answer might be, we're going to verify before we put down that right
answer.
We want to be precise with all of our work.
The earlier you can work precision into your math conversations, the better your students
are going to do in high school and college math.
Because in our elementary math, we're looking at fluency because we're focusing on the four
operations, add, subtract, multiply, divide.
And we want students to do that over and over and over again.
Near the end of elementary, now we're looking at taking those four operations and using
them in unique situations following the specific rules for those operations and fractions,
for those operations and decimals.
We get into middle school.
Now we want to know about those four operations and like terms.
But we're building off of that basis of those operations.
Once we get into higher level math, now we're looking at formulas.
We're looking at doing all of our operations repeatedly within one question.
We're looking at procedures.
And we're looking at the roots of graphing.
We're looking at extension of exponents and the basis of roots, not just the square roots
but cubed roots.
We're doing a lot more conceptual work, which actually is much easier for students with
dyscalculia than our early math is.
We just have such a barrier in the early math subjects.
And that stops our students from finding success in the beginning.
And it definitely blocks them from getting into the higher level math classes.
They should be in later.
Let me use this moment to plug grade level work.
All students should be doing grade level work.
Yes, you will have to plug in some holes on occasion.
Yes, you will have to help fix a foundation every once in a while.
But no, sixth grade students should not be given a fourth or a third grade book and told
to master that before they can move on.
Get into grade level work.
Okay, back to our topic.
What do I mean by using precision in math?
Well, here's an example I used in a conversation with someone recently.
I'm going to paraphrase what I explained or the way I explained this term in a recent
conversation.
When students are thinking about their math problem, let's say they're finding the perimeter
of a shape.
The mental process goes something like this.
They're asking themselves, okay, perimeter is adding?
No, wait, multiplying?
No, adding, adding, adding, okay.
This side is five.
This side is three, five plus three is seven.
Is it eight?
I think it's eight.
No, it's seven.
So we can see that the mental process of thinking about what they're supposed to do is very
confusing for students who have this learning difference, this learning discrepancy in the
field of math.
They don't have a lot of confidence in whether or not they have the right answer.
And that comes in part from their lived experiences with math and in part from the neurological
pathways from recalling that information, the parietal lobe is losing information over
time.
So they're not entirely positive if it's adding or multiplying.
They think it's one of those two.
Is the answer seven or is it eight?
It's somewhere right in that ballpark.
That kind of confusion completely erodes the stability of the neurological connections,
if I can put it that way.
What the human brain wants is to have a question, confirm the answer, and then once it has
confirmation, it strengthens the neurological connections to that right answer.
And it lessens, kind of weakens, kind of lets go of the connection to the wrong answer.
When we leave students in this area of questioning, is it adding, is it multiplying, is it seven,
is it eight, am I in the right ballpark?
I'm just going to try something.
We are not giving them that confirmation.
So they have less of an opportunity to confirm the right answer, to strengthen that neurological
framework.
That confirmation and strengthening has to be immediate.
So doing the work and then reviewing the work later at the end of the day, end of the class,
the next day, whenever a test is returned, the moment is lost.
So the confirmation needs to be immediate.
And that's where requiring precision benefits our students immensely.
Have the students focus on being precise by making them use their resources.
So when you're leading this class, you can ask questions like, okay, we need to find
the perimeter of this shape.
James, check your notes on this.
If I'm finding perimeter, do I want to add or do I want to multiply?
Which is it?
Excellent.
Yes.
That's right.
Now, if I look at the sides, first I'm going to add five plus three.
So let's check.
Tell me what you get if you use the number line, if you check it on the calculator, depending
on the grade level in the program, you might be using one or the other.
Tell me what you get when you check your answer.
Okay, great.
Awesome.
Now, remember, perimeter needs to be around the whole thing.
So I've got to do that again.
I have these two other sides.
So let's do that.
Now, tell me what you get.
Walking the student through, checking their references, checking their resources, confirming
the proper approach, confirming the right answer, this forces them to use those resources
and develop that habit.
Now they have the right operation and they have the right answer and they can complete
this question.
We're building really strong work habits.
We don't expect them to do it on their own because these are students.
They're learning how to do these things on their own.
You are not doing it for them.
They need to do independent work.
You are prompting them and ensuring they go back to use their resources.
This is going to reaffirm in their brain what information to keep, what information to get
rid of.
And when we do this consistently, we only use the correct operation.
We only find the correct right answer.
So over time, the brain only has that pathway of the correct response to follow because
we have utilized our time to help the student let go of the incorrect pathway.
The only thing ever is the correct path, the correct operation, the correct response.
And over time, you're going to see that that really builds a better understanding of math
facts.
Then you're going to see some kind of fluency develop.
It will be different for each student depending on who they are as a learner.
But that's where you're going to get that extra growth.
I promise if you do this precision approach in your classroom consistently, you're going
to find that your students are doing better on their standardized tests.
You're going to see that growth that your administrators are looking for.
You're going to see that growth over time because you have supported them correctly.
You've made the right framework in your classroom.
Now a lot of times, students can resist this focus on precision.
They don't want to use their resources because they know they're supposed to use mental
math or they think they are.
They've been in classrooms before where this was not allowed.
They're not sure if they're cheating or not.
They don't want other people to see them using a resource.
This is where it becomes vital for you as the educator, as the person in charge of the
room to say, you might be right about that.
I want you to look at your notes and double check for me before we go on.
You can frame that however you want.
You can say, I want you to double check your notes to make sure we're precise.
You can say, I want you to double check your notes to make sure that you have the right
notes written down.
You can say, I want you to double check your notes so that when you're studying for the
test later, I know you have the right information to study.
However you want to frame it, but require that precision.
Make sure that we're confirming the correct work and the correct response.
We don't accept incorrect work because we make sure that we know what we're doing before
we turn that work in.
If you're outside of the field of education, we do this in the workplace all the time.
If you had a big meeting with your boss, if you had a big meeting with a new client or
investor, there's no way you would walk into that meeting with your best idea.
You would make sure you had the right information before you got started.
So we're really using that same approach.
We're just putting it into the classroom.
So make sure you're using precision and you're focusing on precision over fluency.
That's going to be your most important step.
And if you have any questions about this or other approaches, please reach out to me at
any time.
You can find me at Honora, H-O-N-O-R-A at educalclearning.com.
Make sure you're checking out our brand new 501c3, the DysCalculia Training and Research
Institute.
You can find that at www.thedtri.org.
And I look forward to hearing your feedback.
If you're using precision in the classroom, please email me.
Let me know how it's going.
I would love to hear from you.
Thank you for listening to What in the World is Dyscalculia.
This is Dr. Honora Wall and I will see you again soon.