Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Sunday, April 6, 2014

Measurement, Memory, and Mathematics


“Five hundred twenty five thousand six hundred minutes/Five hundred twenty five thousand moments so dear/Five hundred twenty thousand six hundred minutes/How do you measure, measure a year?” –“Seasons of Love”

Yesterday, we took Alex to a family restaurant for dinner, and as soon as we sat in our booth, he realized that he had forgotten to wear his watch. In the past, he might have panicked that he didn’t have his watch to keep track of the time, and we would have had to leave immediately. However, he has learned to roll with things much better lately, staying calm and solving problems. First, he looked around the restaurant for a wall clock, but there was none to be found. Then, he decided he would just borrow one from us. In a scene reminiscent of “Goldilocks and the Three Bears,” he tried and rejected our watches. Ed’s watch had the wrong date, which was unacceptable, and my watch was too snug on his wrist. Finally, I handed him my cell phone with the digital clock showing on the screen, and this item, like Baby Bear’s porridge, chair, and bed, satisfied Alex, who found this substitute for his watch to be “just right.” Crisis averted.

As I have mentioned in previous blog entries, Alex makes sense of the world by measuring it and keeping records of statistics that matter to him. His favorite subject has always been math, and he possesses almost savant skills in working with numbers, enhanced by his amazing visual memory. From memorizing nearly 1500 digits of the irrational number pi to remembering people’s birthdates to calculating math problems mentally, he has a gift for remembering and understanding numbers. To assist him with measuring the important aspects of his world, Alex always keeps his measuring tools close at hand, which are among his prized possessions. Calendars, clocks, tape measures, calculators, and thermometers line his bedroom desk and chest of drawers, ready when he needs them. Because he relies upon them greatly, he has more than one of each type of measuring tool in case he mislays one of them and can’t find it. In addition, he keeps notepads and pens handy to record his measuring data.

When dealing with measurements, Alex values precision. If I tell him something costs six dollars, he will correct me and say, “Or $5.99.” If I tell him something will last about a week, he will ask, “Approximately a week or exactly six days?” When his behavioral therapist or music therapist arrives for his sessions, he immediately records their precise arrival time on a notepad as he consults his watch. Even though I have told him that they will be here around 1:00, he wants to keep track of the minute that they actually ring the doorbell. We have also learned not to dispute him when he proclaims certain information about when past events have occurred. For example, he likes to keep track of gasoline prices and will tell us how much gas cost in a particular year. Even when the figures seem a bit off, I never question them. Whenever I go online to check his accuracy, I discover that he is always right, and I find his keen knowledge of the history of gas prices a little eerie.

While some people with autism have amazing abilities to calculate days and dates, I don’t really think Alex possesses that skill. So-called calendar savants can be given a particular date and immediately figure out what day of the week that date was. Recently, my aunt and uncle came to visit from out of town, and Alex commented that my uncle had been born on a Sunday. My uncle didn’t seem to know what day of the week he was born, but trusting Alex’s confidence, he thought that fact was likely. After looking up my uncle’s birth date on a perpetual calendar in the almanac, I confirmed that Alex was right about what day of the week my uncle had been born. However, I suspect that Alex probably had also used the almanac as his source of data instead of calculating the day in his mind.

Nonetheless, Alex does possess outstanding mental calculation skills. A couple of weeks ago, I asked him how he had liked the dinner I had made. After quickly assessing his plate, he told me he liked it “91.6 percent.” Although we’ve grown accustomed to Alex’s percentage rating scale for meals, we were surprised by this odd figure since he usually rates foods in less specific figures, such as 90 percent or 85 percent. When we asked him how he had arrived at that number, he said, “Pasta 90 percent, sauce 90 percent, Italian sausage 95 percent.” As I was trying to add up and divide those figures, Ed, who is much better in math than I am (and from whom Alex has probably inherited his math skills), quickly confirmed the accuracy of Alex’s calculations.

Similarly, yesterday Alex was telling me that he had a “little voice” in June of 2004. Alex has a great fascination with people’s voices, especially those of children, whom he says have “little voices.” I suppose he was reflecting upon when his own voice changed. After I figured out how old he would have been in June of 2004, I commented that he would have been twelve and a half years old in June 2004. However, he corrected me by noting that he was thinking of when he was “12.482 years old.” Fortunately, he shows patience with my lack of mathematical precision, seeming almost bemused by my approximation.

At the restaurant yesterday when he was using my cell phone clock as a substitute for his forgotten watch, Alex noticed the message on the bottom of the screen and asked me what “232 service days left” meant. I explained that my phone service is “pay as you go,” and that I had paid for a year in advance and had that many days left before I need to renew my phone. He didn’t respond, but then he quickly said, “November 24th.” Ed and I exchanged a look and then realized that Alex had rapidly calculated back to the date I had renewed my phone contract. When he said that, I remembered that I had signed up for a year of phone service around Thanksgiving, so his comment seemed likely. A couple of minutes later, Ed, who had been contemplative, commented that Alex was right because he had mentally calculated to see if Alex’s date was correct. The two of them astonish me with how quickly they can figure out in their minds the problems I need some time and a calculator to solve. However, I am grateful that not only has Alex inherited Ed’s math skills but that he also finds using numbers entertaining and satisfying, a way to make sense of the world that sometimes overwhelms him.

“Great is the Lord! He is most worthy of praise! No one can measure his greatness.” Psalm 145:3

Wednesday, January 4, 2012

Number, Please

Since he got his new graphing calculator last week, Alex has been carrying it with him around the house—from the family room to his bedroom to the kitchen to the bathroom. In addition, he has been filling notebooks with numbers he’s written. One morning, we discovered that he apparently had run out of paper in his bedroom, so he decided to write numbers on his bedroom wall. [A little household tip: thankfully, a cotton cosmetic square soaked with rubbing alcohol takes dry erase marker off painted walls.] Another evening, Ed noticed that Alex had written numbers on his legs and tummy. [Another tip: anti-bacterial soap, which contains alcohol, takes ballpoint ink off skin.] Not surprisingly, when I went to check his Internet searching history on his laptop the other day, he’s been researching numbers.

Here are a dozen number-related sites Alex has investigated online this week:

1. He Googled “big number random generator.”

2. He also checked out “math videos” on Google.

3. In addition, he typed, “count from 0 to 100 & beyond” into Google.

4. Similarly, he searched for “numbers 0-500” on Google.

5. Later, he expanded his Google search for “numbers tables 0-10,000.”

6. The last search I discovered on Google was “2091,” which may seem like a random big number. However, I’m sure he was thinking of it as a year because in 2091, he will turn 100 years old.

7. From Google, he went to You Tube, where he found a video called “Random Number Generator.”

8. You Tube also amused him with a musical video called “Numbers Song 1-1000.”

9. Another You Tube music video he watched was entitled, “The Big Numbers Song.”

10. His Google searches enabled him to find a site that had a prime numbers
table.

11. He also spent some time at homeschoolmath.net, where he looked at free rounding worksheets and free number charts.

12. Finally, combining his interest in math and foreign languages, he visited a
website that taught how to count from 0 to 100 in more than twenty different languages.

Since I never particularly liked math, I’ve never quite understood Alex’s love of everything about numbers. However, I’m pleased that he still possesses a curiosity about learning and has developed the skills needed to research topics he finds interesting, both of which ensure that he will continue to learn and develop his mind.

“And I will make a covenant of peace with them, an everlasting covenant. I will give them their land and increase their numbers, and I will put my Temple among them forever. “ Ezekiel 37:26

Sunday, July 11, 2010

Careers

In watching Kids’ Week on Jeopardy with Alex last week, I noticed something interesting about these bright upper-elementary students: their proposed career choices. They listed rather impressive possible jobs, such as marine biologist, cardiologist, anthropologist, and even President of the United States. While Alex hasn’t quite decided what career he wants to pursue, and we haven’t determined what God has planned for him, he has offered some interesting choices through the years. One scientific career Alex has discussed is meteorology. His interest in weather makes this a natural choice. I always find it interesting that he says that he wants to be “a meteorologist” and not a weatherman; he takes the science seriously. He is probably one of the few kids who knows and understands the Fujita and Saffir-Simpson Scales for tornadoes and hurricanes. His greatest fascination with weather, though, is in record temperatures. He enjoys looking up these extremes online, including recently finding The Weather Channel videos reporting record highs and lows posted on You Tube. I can almost picture him standing out in the elements with The Weather Channel meteorologist Jim Cantore, reporting some extreme weather condition, but then I remember how much lightning scares him and think he’d more likely be working safely indoors with severe weather expert Dr. Greg Forbes instead.

When Alex was seven years old, he wanted to be an astronomer. He studied the planets, stars, and constellations, reading all the books he could find about them. Also, he loved astronomer Jack Horkheimer’s nightly five-minute Star Gazer show so much that Ed would wake him to see it shortly before midnight, and then Alex would happily return to sleep. One evening, we took him to see Valparaiso University’s telescope and observatory, and one would have thought we had taken him to Disney World because he was so excited. First, college students explained the Summer Triangle and allowed people to view it through the telescope. The brief description made such an impression on him that he still can list the three stars that comprise the triangle: Altair, Deneb, and Vega. The second part of the presentation took place in the observatory, where a student detailed the features of each planet. He described the eight planets and then asked if there were any questions. In the dark room, I suddenly heard a child’s voice beside me blurt out, “How about Pluto?” I was surprised that Alex spoke up, but I was pleased that he had been paying attention and wanted to know more. The student graciously explained how Pluto didn’t fit with the other planets, told Alex his question was a good one, and satisfied a curious possible future astronomer.

Probably his most consistent career choice through the years has been mathematician. Math has always been Alex’s favorite and his strongest subject. He can easily do math problems in his head accurately, often more quickly than most people can do them on a calculator. An idol of his is Professor Yasumasa Kanada, a mathematician at the University of Tokyo, who has set world records for calculating digits of pi using supercomputers. One of Alex’s proud accomplishments is that he has memorized nearly 1500 digits of pi. Once when he was twelve years old, I came home from school to find one of his legs covered in black. As I looked closer, I could see that it was ink, and upon even further inspection, I could make out numbers. Curious as to what he’d been doing (and also wondering where his father was when he was doing this), I asked him what was on his leg. He proudly replied, “The first 100 digits of pi.” I then asked him why he’d written them on himself, and he nonchalantly responded, “Because we ran out of paper.” I had to hand it to him: the boy was smart and resourceful. This incident reminded me of John Nash in the movie A Beautiful Mind writing formulas and equations on windows with a grease pencil; perhaps someday Alex will figure out something as equally brilliant as Nash’s game theory that won him the Nobel Prize. In the meantime, we try to encourage his interests and enthusiasm as we wait for God to lead him to his destiny. Also, we try to keep plenty of paper on hand, as well.

“For I know the plans I have for you, “declares the Lord. “Plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11