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

Wednesday, February 11, 2015

On Relating to Other Intelligences, or On Numbers


It's common knowledge that people's minds tend to be inclined toward different sorts of knowledge and understanding: musical, mathematical, linguistic, spatial, kinesthetic, interpersonal, and so forth.  While people can generally function in the other areas, they are typically less proficient than other people so inclined.  Unfortunately, we often forget to account for this difference in understanding when we communicate.  The result (aside from poor communication) may be impatience or scorn on the part of the speakerand confusion, frustration, or anxiety on the part of the listener.  How, then, does one develop a sensitivityor might we say bilingualismfor other intelligences? 

I would venture that the first step to improving communication requires basic empathyinsight into the other person's struggles.  Part of this requires acknowledging intellectual differences as, well, differences rather than a sign of stupidity.  Empathy may not help much with the nitty-gritty of how to explain ideas better, but it can improve one's patience with the effort of communicating and thus ease some of the listener's stress.

First, an important note on what not to do: When conversing with a person weak in one's favored area, one ought not think that speaking with this person is akin to speaking with a child.  Yes, one needs to simplify concepts and word choices or to try different approaches, but this perspective tends to make one's tone come across as condescending.  The parallel is also imperfect because a child's mental processes differ from an adult's beyond a mere difference in areas of intellectual strength; young children, for instance, cannot grasp figurative language or abstract concepts well.  But that topic is a whole 'nother kettle of fish.

Instead, a more accurate analogy is conversing with a non-native speakersomething to which most people can likely relate in some way.  For the other person, one's jargon and assumptions of basic knowledge may be unfamiliar or may take extra time to process.  

To illustrate this, I can only draw upon my own experiences as an example.  As I do so, I hope the reader will keep in mind that this illustration could be applied to any other area of intelligence, as well.

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For me, numbers are a kind of foreign language, one I’m only partially familiar with.  As with a foreign language, I understand some words automatically; I can immediately grasp numbers one through five, for instance, as easily as I understand “¿Cómo estás?” and “adios.”  I can quickly regurgitate memorized answers to basic addition, subtraction, multiplication, and division questions involving numbers under 12.  Given time and perhaps paper, I can answer more complicated questions of the same.  Patterns are also easy to recognize when they’re ascending or descending in ones, twos, fives, tens...  But everything else?  Foreign.

Let's give this some context.  I’ve been studying Spanish off and on for some time.  Perhaps I hear or read a sentence, such as Sus ojos son azules y su pelo es marrón.  My thought process goes something like this: “Okay, azules--that’s blue.  Ojos… ojos… that’s either eyes or ears.  Must be eyes, if they’re blue.  Sus--well, without context, it could mean ‘your’ or ‘his’ or ‘hers.’  Anyway, somebody’s eyes are blue.  And… pelo, marrón… I should know those words… oh, hair!  Marrón… it doesn’t mean blondthat’s rubio.  Must be brown.”   There--translation more-or-less complete… but several seconds have gone by, and if other things have been said in the interim, I either missed them or, by hearing them, didn’t finish translating that first sentence. 

This example mirrors my thought process with numbersparticularly numbers I hear, but also with those that I see.

When I first glance at a page of numbers, it’s gibberisha foreign alphabet.  As I study individual components, I recognize the “language” as one might recognize Korean, Japanese, Chinese, Arabic, Hindi, or Russian text.  In the same way, I may identify the "language" of dates, times, recipe amounts, temperature, tech specs, construction dimensions, addresses, phone numbers, statisticsand the language of basic math, fractions, decimals, percents, algebra, geometry.  Higher levels of algebra, as well as calc and trig, look more like French or Italian to melanguages I've never studied, but whose cognates and Latin derivations make parts of some sentences recognizable.  

If I care to put in the energy, I may then “translate” the numbers and find their significance or the answer.  I may have to re-read some numbers multiple times so I can remember them well enough to compare them with another set of numbers elsewhere, as when I check out our finances or try to understand a news report that's loaded with comparative statistics.  

With spoken numbers, I have to process each one first into its physical, written shape, then into a sense (like a blurred picture) of the amountaccompanied by a judgement of whether that amount is high or low for the given things to which it is applied.  This judgement is complicated by a certain amount of number confusion.  When translating, I often mix up the words "thousand" and "hundred," so when I hear "twenty-five hundred dollars," I have to think about where the comma would go to get an idea of the amount, whether $25,000 or $2,500.  When given a second number, I often can't recall the first well enough to compare the difference unless they're both rounded or smallish numbers, or unless they're written down and I have a moment to compare the two side-by-side.

Thus, written or spoken, this processing of numerical information takes more time for me than it seems to for others.  Moreover, when time is pressed (as on timed tests or when others wait for me to reply or to finish my turn on a board game), it creates emotional stressas when a foreign language student faces an onslaught of information in a poorly-understood language.  Self-consciousness makes it all worse; I think of myself as being relatively intelligent, so I hate feeling judged for my slownessmy apparently stupidity.  In consequence, when feeling pressed, I will more likely rush and make mistakes or have frantically muddled thinking that slows me further.  I become tense and irritable and more prone to angry outbursts.

To copeand preserve my sanity and relationshipswhen I don’t have to process a difficult number, I don’t bother.  So when Joel rattles off the “really cool” statistics for his latest D&D character, describing stacking bonuses to AC, hit, or damageor when a student talks about statistics for his research paperI react based on the context or the person's tone because the numbers don’t register quickly enough in my brain for me to make sense of them.  Unfortunately, when the context doesn’t tell me what importance the numbers hold, I must ask the other person to slow down, repeat, explain their significance... or I change the subject. Again, I imagine foreign language students do much the same thing when they don’t understand a word or words.
    
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I hope that this parallel helps readers have a little more patience and understanding with people who become stressed whenever numbers (or musical terms or emotions or other aspects of the various intelligences) come up in conversation.  The speaker would do well to slow down or explain it in alternate ways, and the other party will keep up a lot more cheerfully.

Readers, do you experience the same difficulty processing numbers? Following "easy" dance steps? Understanding music? Something else? Share it in the comments below.



Friday, August 9, 2013

On Patience



Though my temper has improved with age, I still don’t consider myself particularly patient.  I struggle to press on when I can’t “get” mathematics, complete a project just right, or comprehend some techno-jargon I need to help me accomplish something on the computer.  I “tire” inexplicably quickly or find myself blurting angry and sometimes inappropriate words, or I simply give up or ask someone else to see to it.  If that’s not an option, I may take a little break to get over my impatient huff before I try, try again, accompanied by more muttering and an increasing desire to break things.


Similarly, I struggle to be polite when people approach me to make extended small talk with whom I did not wish to form an acquaintance or when I am clearly attempting to read.  I also find it hard to be a polite, patient listener with people who rehash the same topic multiple times in one conversation or who inevitably veer every conversation into their uninteresting hobbies or boasts.  


As a child, I also felt impatient with adult conversations that excluded me but that still required my presence nearby.  Regrettably, I did not display this impatience very subtly: those times when shyness didn’t prevent me, I’d pull my mom’s hand or whine “I want to go!”  As I got older, that turned into subtle pokes or toe-trodding accompanied by significant glances, a finger pointed at a clock, or a suggestive yawn.  


(I congratulate myself that I can now last much longer--and actually enjoy the company--more than I ever did, and when it’s time to go, I’ve (mostly) learned the polite hints and phrases that (I hope) do not give offense when I take my leave.  Unfortunately, my patience still dwindles and I neglect my company whenever I’m too eager to escape them to work on a project or read a book.  I must work on this.)


Historically, with the exception of mathematics, I’ve had the least patience with interruptions to my solitude, particularly when reading.  Thankfully, my mother’s and husband’s training of me has civilized my tongue and behavior a great deal, but it remains a frequent struggle.

Given my obvious flaws in this area, I felt surprised when, some time ago, my boss commented on my work with a certain student and remarked that I had “the patience of Job.”  


I do?  Huh!


Naturally, I felt quite flattered by the compliment, but it seemed to me I’d simply done what I’d been hired to do; I hadn’t thought my patience extraordinary or even difficult.  The compliment also made me feel a twinge of guilt, for I keenly remembered how, in various other circumstances, I felt terribly impatient and not remotely Job-like.  


This set me wondering about what had made the difference in my attitude.  Obviously, it wasn’t a knowledge that impatience was wrong and unloving; I’d been taught that since childhood, and a part of me had always acknowledged my impatient words and actions as wrong even as I did them.  Experience testified that impatience never glorifies God, edifies others, or makes me feel better about a situation, but the knowledge could rarely curb my impatience completely.  How, then, was I patient in certain circumstances, and how could I make myself more patient in others?


On reflection, I immediately noticed that I turn impatient when my expectations and desires are thwarted, and then when my selfish wish to progress to some situation other than reality turns me resentful, irritable, hasty, and short-tempered toward the things and people before me.  

Conversely, I noticed that my impatience fades away when, during an unwelcome interruption or setback or delay, I take a breath to seek God’s perspective and to then alter my expectations according to His priorities and to the present circumstance.  


In other words, to obtain patience, I have to first relinquish my death-grip on my original desire; rather than selfishly regretting my own neglected desires, I have to focus on the other people involved, being considerate and extending God’s love toward them.  If I face a task rather than people, God still expects me to seek and share His eternal perspective on it so that my attitude can be right and patient before Him and any witnesses.


The kind of patience this selfless submission produces is nothing like the forced grin-and-bear-it attitude of someone who knows she should be patient but who still harbors resentment about it.  Acceptance of God’s will and of reality produce a true contentment in all circumstances, such as Paul describes (2 Cor. 12:10, Phil. 4:11).  It works—and I find myself able to address the person or task before me with more grace and patience—because when I submit and change my goals in that way, the situation appears as part of my plan rather than an interruption or barrier to it.


Perhaps I shouldn’t be surprised that the key to patience turns out to be the same as many other Christian virtues: selflessness.  I should have remembered that “Love is patient...” (1 Cor. 13:4), for love is by definition other-centered rather than self-centered: it considers and works to meet other people’s needs rather than our own needs and to obey God’s will rather than our own will.   


I sure am thankful for the Lord’s patience!  “The Lord is not slow to fulfill his promise as some count slowness, but is patient toward you, not wishing that any should perish, but that all should reach repentance” (2 Peter 3:9).  In the same way, I know I should strive to be more patient (Rom.12:12, 1 Thes. 5:14).


When I feel I haven’t the strength to give up my own desires, I try to remember (not always successfully) that selflessness gets easier with practice, so I coax myself to practice just this once--just once more--and again... and thankfully, we have a God who is quite willing to help us if we only ask Him.. and don’t reject His help...  


Yeeaaaah... maybe I’ll master patience by the time I’m ninety.







This is an extended, personalized version of a devotional to appear Monday on my church's blog at http://firstcongregationalhutch.wordpress.com/.