Alexander Hoeft is from Hazelwood, Missouri (North County, St. Louis). He attends college at Missouri University of Science & Technology (formerly UMR or Rolla), studying Mechanical Engineering, with a minor in Computer Science. He is in his 10th semester, with 4 to go, because he started in remedial math. Next he took College Algebra, then Trigonometry, and then Calculus 1, 2, & 3. (Most students start at Calc 1.)
He still must conquer Differential Equations and other obstacles, but is determined to succeed. He does better when math is directly applicable rather than theoretical.
We learned about Alexander from Miles Collins, Stanford University graduate and co-founder of Swift Calcs, the free math tools that Alexander uses to ameliorate his dyscalculia.
In his 2nd semester, Alexander sought testing for learning disabilities and ADHD.
Here is Alexander's story:
Math was always challenging for me. Looking back, I didn’t realize how difficult it really was. It wasn’t until I got to college, that I realized that math isn’t this arduous for everyone else. I also noticed that challenges excite me, that I want to conquer them, and that they help me improve. It was then that I decided to seek out testing for LD and ADHD. Shortly thereafter, I decided to continue to pursue a degree in Mechanical Engineering.
After working to get myself tested, an adventure in it’s own right, I finally got my results: Dyscalculia, ADHD, and a healthy dose of pretty good numbers in every other IQ category (sans basic math operations). I then took my documentation to all of the relevant college officials and discussed what I learned about my disability. The most common thing I was told in all of these talks was, “They should have caught this earlier,” to which I generally responded, “You’re telling me; I’ve been living with it!”
So this got me thinking, "Has math really been that big of a problem this whole time?" I thought back to my earliest math-related memory. It was around first or second grade when my parents would give me small addition algebra problems where I would solve for a variable in my head. I always had to visualize the quantities and move them around in my head to get the answer, but after two or three minutes I would usually get it.
It didn’t seem to matter how many of these problems I did; I never got any faster at them, just more
likely to be correct. The pattern persisted when I got to times tables in third or fourth grade. With practice, I could get more likely to come up with the correct answer, but never more quickly and never by rote memorization.
Despite this, my conceptual understanding of math grew because it interested me. If a problem had actual numbers or algebraic operations, then it was time to grab a snack, because it was going to take awhile.
Maybe this is why they never noticed; I was doing just fine in most things. I didn’t get an IEP, or any special remediation, or assistance, or accommodations for homework or exams. About half the time, I didn’t get recess because I had to finish math homework from the day before.
The most important thing was that my parents supported me. They didn’t have any inherent ability to teach math or understand what my difficulties were, but they had patience and praise. They sat with me through my math homework nearly every night for hours. They encouraged me endlessly, building my healthy self-esteem with facts and accomplishments. I was special because I worked hard.
Armed with confidence, persistence, and ingenuity, I unknowingly set forth to compensate for the differences in how my brain works. I refined how I learned and changed what I learned. Since I found that I understood concepts, I explored the concepts behind the things I had the most trouble with. I researched and read until I found the most basic information and then generalized to the level of understanding of the thing I was trying to learn.
For example, for addition, I drilled down to how number systems are structured. From there, adding is just counting up until you reach the maximum number allowed in the system, then you increment the next digit by one. This still didn’t make math much faster, but I understood the questions being asked.
I was able to generalize these concepts to other aspects of math. While others understand the base ten system, they may struggle with the base 8 or hexadecimal system. For me, however, all systems are basically the same. I do the same process for adding in each base system. While I am slower in base ten, I am quite faster in all of the other bases.
Another tool I use is representing things in different ways so I am not working with pure numbers. I either break a problem down into simpler operations, or visualize an equivalent physical representation. I play to my strengths.
For example, I can't read an analog clock like everyone else, so I use math to calculate the time. It
takes a bit longer, but I get it done. First I take the hour hand back to the number before it. Then I take the number before the minute hand and multiply it by 5.
(But since I don’t remember many multiplication facts past past 5x2, I need some other way to do this. I add a zero onto the end of the number, multiplying it by 10; then I divide all of the individual digits by 2, giving me the same result.)
The holdup will be dividing by 2. This is where I visualize. I put dots on each number, 1 through 9, so that I can count the number of dots on each. They are all symmetrical, so when I divide by 2, I draw a line down the middle and count the dots on one side. If I split a dot, I put a 0.5 near the next digit and do it separately until I add all of the fractional dots in at the end. This requires a lot of concepts to execute, so my explanation here may be lacking.
With these skills, I have tackled greater and greater math-heavy courses. To date, I have quite a few
courses in the “pass” category. In actual math courses, I have Algebra, Trig, Calculus 1,2, 3, and Introduction to Numerical Methods. In other engineering courses, I have classes like Thermodynamics, Programming Data Structures in C++, and Mechanics of Solid Materials.
Does this mean I’m all better? Not by a long shot! This an uphill battle that doesn’t appear to have an end. But that's alright with me, because the best way to reach great heights is to climb a big hill. Race me to the top?