Online Course: Numeracy and LD - Definitions of Math Difficulties and Disabilities

Learning to Acheive: A Professional's Guide book coverUse this discussion thread to explore your thoughts on definitions of math difficulties and math learning disabilities from the Numeracy Instruction and Adults with Learning Disabilities online course.

Post a 'Reply' with your thoughts, using the following questions to guide your reflections:

  • How might your current understanding of math disabilities or math difficulties impact your instructional practice? Why?
  • What questions would you like to discuss with peers? What topics or ideas would you like to learn more about?

To enhance your understanding: Read and reply to other participants' posted plans. Check back to this page, or subscribe to this post to read and reply to others' responses or thoughts on your plan.


How might your current understanding of math disabilities or math difficulties impact your instructional practice?

My job as a math instructor in adult education allows me to see adults every day that struggle with math and math topics.  The majority of the time my adult learners have not been diagnosed with learning disabilities. The majority of my learners definitely have math difficulties. Many times my students have had negative experiences with mathematics in the past. It is my goal to make math a positive learning experience and change the ideas that adult learners have about mathematics.

My understanding of math disabilities is not vast, however, my understanding and experience with people who have math difficulties is great. As a math instructor I try to relate mathematics to my student’s interest and daily lives. If I can make a connection and make the math relevant to the student they tend to have more interest in learning the material.  If you have ever taught math I almost guarantee that you have heard the question “why do I need to know this?” Again, if you can make it relevant they are more likely to relate.  I also try to have my students do more than just worksheets. We get up and out of seat and measure things, make human number lines, play card games, etc. I attempt to make learning math fun.

I would like to discuss with my peers ideas about more interactive ways to teach mathematical concepts. We have to do more than just repetition on paper. How do other instructors get their students to “buy in” or to relate? 

One of the things I do with my students is talk about a growth mindset, particularly when it comes to math.  It isn't that they "aren't good" or "can't do it", etc, rather that they haven't learned it yet, or haven't explored it in a way that makes sense to them yet.  Jo Boaler created a MOOC (massive online open course) through Stanford that talks about math and mindset.  It is broken into 6 modules that each take about 20 mins to complete.  The students usually take away a few points from it, and I try to reference it when they are coming to a frustration level in their learning.  It is free!

I have also tried to be better about having my students explain to one another how they solved a problem.  I do this by having them work problems on the board or work in groups.  They all have different ways to come at problems and it seems to help those who struggle to hear these different options.  This has also helped me learn how to solve problems using several different strategies.

One area I would like to work on is helping students remember procedures, especially when it comes to algebra.  We often talk about the differences between procedural math versus conceptual math.  Sometimes they are missing something in the concept, and others it is in the procedure.  When it comes to procedure, I would like to be able to better help them store the steps in long term memory.

(I need to say that clicking through from email is a nice, smooth process now!   We'd better be careful... we'll have *everybody* joining these discussions ;)) 

Are there specific procedures you'd like ideas for?   I've worked a lot of "Sue Jones methods" out, with these principles: 

A.   It should (whenever possible) actually make sense, even if there is a mnemonic included. (Duly note that no, the quadratic formula isn't likely to make sense at all...) 

B.   It should be in digestible chunk size. 

C.   When possible, it should have a "look" and a "feel" - and a reason for that.   I see students do creative things that look and feel right, and have nothing to do with the math... the visual-motor part of algebra is underrated.  When students see 5x = 20 and the motor memory kicks in and they put the fraction bar & 5 under each side, good things are happening... 

Yesterday I was pleased when a fellow came in to tell me that no, he hadn't fallen off the face of the earth (hadn't seen him last two weeks of semester in tutoring lab) -- he'd gotten an 87 on the "Math Literacy" final by focusing on what he knew and then doing best he could on the rest.   

He also said that "The quadratic formula is forever etched upon my brain."  He started with the vertex formula and "etching" that on his brain (a.k.a. "symbol imagery" -- taking a snapshot of it, covering it up... then reconstructing it until it's automatic)  which is -b / 2a ... then added the +/- square rooty part.   

So, he figured out chunking into smaller pieces and symbol imagery, and applied it successfully.  (Have I mentioned he's really smart... but too many symbols in a row become meaningless to him?  I'd shown him some 'reduce visual confusion' strategies like rewriting (a + b) (3a - 4b)) as if it were a regular 2-digit by 2-digit multiplication problem.   For most people that would have been more confusing but for him it "clicked.")   

I know some teachers who are *dead set* against "tricks" to help remember formulas.   I think it's highly overrated and oft done at the exclusion of any understanding at all, but that if done well, being confident w/ the formula can help a student build the conceptual understanding.   

The sheer knowledge of the difference between disabilities and difficulties is going to go a long way in seeking new approaches for teaching new math strategies to these types of students.  Like Missy, most of my students fall into the catagory of those with "math difficulties."  I have experimented this semester with some tactics in making math more friendly and relevant and after this course, I hope to build on what I currently do.  Jo Boaler was mentioned by another student in this course and I am a big fan of some of her creative approaches to making math friendly and relevant.  I open every math class with a "Math Talk" which I learned about from Boaler's book, Mathematical Mindsets (2016) and from Making Number Talks Matter (2015) by Cathy Humphreys & Ruth Parker.  Without going into great detail, the activity goes something like this:  the class mentally solves a fairly easy math problem and then the students share and discuss how they saw in their minds a way to solve it.  Most of the time there are two, three or more different ways students break the problem apart and come up with an answer, giving everyone the opportunity to see different approaches (You Tube has some great videos of this). Boaler tells a story about how a group of London's Black Cab taxi drivers' brains were studied during their extensive training and she relates how the brain "grows" and becomes more able to retain information.  I told my math class that story on the first day of the semester and I think my students may have been inspired by it, because when asked how they're doing, a frequent reply is, "My brain is growing."  Most of us who go into the teaching profession are encouragers by nature, but no where is it more important than in math class.  I'm loving learning more about those who need a special kind of encouragement; those with disabilites and difficulties.  I'm eager to learn more.

  • How might your current understanding of math disabilities or math difficulties impact your instructional practice? Why?

I have only worked with adults who have a low IQ or definite disability as long term students. We played many games, used as many creative manipulative as I could find (for simple addition, we did m&m math, then marshmallows, pretzels, beads, beans, cubes, pencils, whatever caught her attention- usually food was a good bet).             For my GED students, I only saw them a few times each, when we showed up at the study table at the same time. I always tried to make everything relatable. I would find out their interests and make the task applicable to their hobby: recipes/cooking, linear measuring/construction, etc. Usually food was a good thing, because everyone eats something. Measurements, fractions, percentages, proportions all worked out with food (I brought in edibles) After a few times, it usually stuck.                                   I am fortunate to have an empathy and a flexibility that allow me to find a key with some success.


  • What questions would you like to discuss with peers? What topics or ideas would you like to learn more about? I think I need to be exposed to other practices to increase my arsenal of resources. I would enjoy hearing some different ideas. 

I teach all areas for the GED test and it seems about 90% of the adult students come in saying I just can't get that math.  It is usually those basic concepts of middle school math (fractions,decimals, percents, and proportions) that had stumped them; therefore, they tend to say, "I might as well forget that algebra."  The challenging part of instruction is getting those students to believe that they really can do the math.  I tell them anytime I present money problems, they get it.  Most students come in with difficulties in fractions and that is where I like to begin.  Once they have grasped the concept and fluency of performing the operations with fractions, they feel success for the first time in dealing with the challenges of math.  Getting those fractions under their belt makes teaching decimals, percents, and proportions so much easier because they are related.

Keeping students from getting frustrated though isn't easy.  Sometimes my students when they get frustrated will tell me they are going to take a break from what we're learning and then will come back the next day with a fresher look at the challenge.  This works, but this is what my students have taught me.  I have learned from the students "ways" to deal with teaching.  Yet, I want to learn more from my peers as to methods of keeping these students from feeling overwhelmed. They need to have more successes, developing their own self-efficacy.

I liked how the article stated all strands should be introduced to all learners at all levels.  How true!  I look forward to reading more on this.


Carolyn_Hendrix May 17, 2016 - 9:39am 0 Likes

Part 2

How might your current understanding of math disabilities or math difficulties impact your instructional practice?

How might your current understanding of math disabilities or math difficulties impact your instructional practice?

My current understanding of math disabilities and math difficulties is broad and runs deep.  I have a child who was diagnosed with a learning disability in math (dyscalculia).  He was in elementary school at the time and I was working on my master’s degree while teaching GED and Workforce development classes.

I sought information from every avenue available to me so I would be able to help him.  I have utilized that information over the years to assist my GED students

I have put the things learned to practice in my GED classes. I use peer-to peer, modeling, manipulatives, questioning etc.  I have the students show their work so that I can see how they arrived at the answer.  I ask them to explain to me how they arrived at the answer.  I ask them if their method works every time.  I have them show me by making up three to five more problems of their own and solving them in the same way.  We talk through problems, especially word problems.

When students struggle with math concepts and skills, I will remind myself how frustrated they must feel. I want to think of all the possible ways to encourage them and to instruct them.  I am turning to my peers for help in the proper ways to encourage these frustrated students and the most effective ways to instruct them.

I had a fourth grade student who was diagnosed by a pediatric neurologist with dysgraphia.  We used graph paper for multiplying 2 digits by 2 digits.  Thinking back, he probably should have just used a calculator.  That was a difficult thing for him to do, just like long division.  Maybe this fell into the category of visual-spatial ability.  He was such a bright young fellow.  He had wonderful comprehension skills.

In West Virginia, over the past 12 years,  we've opened 40 some SPOKES (WV WORKS) programs. The vast majority of participants have learning phobias/difficulties. As a non-traditional learner/teacher I'm pleased to be included in and learn from this pilot. My biggest barrier is lack of focus and time. Work first is the focus for all participants. Thus, there's seldom more than a cursory recognition of barriers and approach.