Archive for October, 2007

Why do people ‘Hate’ math?

I was just reviewing the searches for my blog and I found that someone had typed in “Why do people hate math?”

My feeling is that perhaps people do not hate it so much as fear it or are intimidated by it. Our culture (western) is so dominated by the verbal we learn to think in words and feelings perhaps before anything else. Mathematics is simply another language for explaining and interpreting the phenomena in the world. However, it is a very straight forward and logical language that has rules, that often elude us because we are not taught these rules properly in school.

Serendipitously, I’m currently working on developing a course on teaching algebra to middle school students, both the SME (Subject Matter Expert) and myself decided that one of the biggest obstacles to really getting math, let alone algebra, is the proper development of “Number Sense.” If I could explain what number sense means to myself and the other ‘verbal’ people out there, I’d probably start by saying that Number Sense may be analogous to being able to understand the basic rules of structure in language. (Maybe, I need a better analogy. Anyone else out there want to help?) Here is a simple, simple comparison.

Word Sense: I know that a sentence must have a subject and a verb. I know that the verb tense/form must agree with the nature of the subject (I am, you are, he is, etc.)

Number Sense: (Or maybe number babbling) I know that when I add two positives together I get a positive. Conversely, I know that when I add two negatives I get a negative. When I add a negative and a positive… I’m really combining or matching the negative and positive and combining them. After you combine these pairs that each equal zero I take them away – and I’m left with the remainder of the greater number (either positive or negative). Oh, heck… just look at the picture I drew.

 

Illustration of additing pos. neg. numbers

If I were asked to explain this using pictures the first time, I think the concept would have sunk it a lot faster. I’ll bet dimes to dollars, if you were taught math more than 40 years ago all they did was simply put a set of problems in front of you. Maybe with the help (if you were lucky) of an astute teacher, they would explain what was happening in the problems or the pattern of solutions. But generally you were expected to figure it all out on your own. I didn’t learn math 40 years ago, but still, that’s how I felt it was taught. I went through the mechanics of solving the problems without really learning the rules of the language of mathematics.

Since, I didn’t understand the rules I could really only solve the simplest level problems in algebra. I sort of got the concepts, but as I moved into advanced algebra and calculus I’d often get lost. I was the “Queen of Partial Credit” on quizzes and tests. In the end in Calculus I barely scraped by with a C-. I could blame adolescent hormonal binges I was experiencing at the time, but looking back, I think that if I really sat down with the teachers and tried to understand math (from my own terms) I might have been able to do much better. I don’t think I really found the language of mathematics meaningful until I started applying it to my work in the form of ratios and proportions. Hexidecimal values and understanding the concepts of arrays and tables. But isn’t that the challenge that most teachers face, we must really coax the understanding and application of knowledge from our students regardless of who they are.

When I was actually teaching in the classroom, I really tried to understand how my students were perceiving a concept or what their general understanding or lack of understanding was. I really did try with certain complex subjects to relay the information to them in various ways or even ask them to explain why they thought they didn’t understand something. This morning at breakfast, my husband and I were talking about the difficulties of designing really good instruction. He puzzled about why it is so hard to teach… it doesn’t seem that hard, he said. More, it shouldn’t be hard to capture all that needs to be taught in writing. Yes, I explained, it’s easy to capture content int he form of raw concepts and information, but it’s the getting the student to understand and apply these things that is the hardest part. You can teach any monkey* to take a test, but getting people to make something with what they learn… that’s another challenge. I explained that teaching is an art that require not just book smarts and knowledge… it requires heart and the ability to read people and adjust your teaching to their needs.

*My apologies to all monkeys out there.

“You cannot fight water, you have to learn how to live with it.”

I cannot believe that a people as innovative, inventive, and resilient as the Dutch would not be able to deal with a problem like Global Warming and the rising of sea levels. The city of Amsterdam has such a wonderful history just in its development over the centuries. The Amsterdamers constantly shaped and rebuilt their city as it grew. They also spent a great deal of time, support, and money on public institutions such as elderly homes, hospitals, and orphanages early as the 16th and 17th centuries. Perhaps because they instinctively and shrewdly knew that the people are the heart of a city and it’s best to take care of the people so the entire city can prosper.

I found this article on a proposed ‘floating city.’ Amphibious houses and buildings would be built on flotation foundations that imitate the hull of ships. These houses are anchored in place by huge steel posts. As the water rises and recedes the house follows with it. This is great, but what about the beautiful buildings, palaces, of historic Amsterdam? What about the city itself? Could they possibly build strong enough hulls to keep these buildings afloat? Or would and could they relocate the city away from the rising sea. If you look at a map of the the region that projects the effects of a rise of 1 meter to the sea level, you can see what effect this will have on the Netherlands (map from http://flood.firetree.net/).

The article notes that there are efforts to design buildings that are up to 100 meters in height that are adaptable to this floating way of life. These engineers have simply adjusted their building principles to meet the demands of the elements. It’s really quite astounding when you think of it, the ingenuity and effort that makes such ideas and plans reality. It makes one feel quite good to be human.

Netherlands 1 meter sea level rise

Houseboat in Amsterdam

A Houseboat in Amsterdam

Shift happens – now what are we going to do about it?!!!!

I read somewhere that the first Industrial Revolution (at the end of the 18th and beginning of the 19th) may have been a result of a surplus of educated or informed people solving mechanical problems (of course, now I can’t find the article where I read that and I may be paraphrasing it incorrectly). Also, during the Great Depression many people who would have taken white collar or higher-paying jobs went into teaching and education because of the steady pay.

So maybe the United States won’t be in such bad shape in the long run despite the job shift and outsourcing. Perhaps people who once worked at major corporations would move into public service jobs or roles where they could use their smarts to innovate new processes or products. It might actually suck that they would have to take a cut in pay. On the other hand, I don’t really see anyone in this country realizing that they need to do anything to react or prepare for the shift of even more jobs to China and India. I worked in Corporate America and my impression was that most people would just hunker down and wait and hope for the better. If they were canned they looked elsewhere, but honestly, it seems that the safe havens for the jobs we were educated and trained to do are becoming fewer and fewer.

I’ve seen the “Shift Happens” slide set about a year ago, but it frustrates me that I SEE OR HEAR ABOUT NO ONE who is working to help people in this country deal with the shift. The slide set the idea forth… “We are currently preparing students for jobs that don’t yet exist.” That’s great… NOW DO SOMETHING ABOUT IT! Perhaps I’m just to far removed from what is actually happening, and there are educators or people in the system (despite the bureaucratic and political muck and mire) who are forming a plan of action. I can only hope.

If we were to do something about it. I think we’d have to take a hard look at our own educational system and see what we are doing right (and wrong). Maybe starting with the most successful and brightest young people today who are either successful and poised for success. We look at how they passed through the educational system and evaluate how we can make this happen for more or all students. In general we should look at why we’re failing to educate students…. and not just by looking at test scores. Things that are measurable are the easiest things to fix, and often they don’t reach the crux of the problem and the heart of the solution. Besides, when institutions are given targets they will often not follow logical or correct paths to meeting their numbers. They will bend and shape the numbers (students, customers, patients, etc.) so that they “appear to be successful.”

Instead of just looking at test scores maybe we should be asking questions like: Does this individual know how to solve multifaceted problems? Could this individual pass a behavioral interview at a job? Is this person succeeding at what he or she is good at (trade, skill, art, craft, etc.)? Also, we need to start making technology and the best teachers available to everyone regardless of their neighborhood or demographic. We start expecting every child to succeed not just at tests but succeed at attaining a higher level of education. Maybe it’s me, but believe that the educational system we have today has failed us and will continue to fail us. We’re all like alcoholics on the way to recovery. We’ve realized that there is indeed a problem. Now what are we going to do about it?

[Youtube=http://www.youtube.com/watch?v=fhnWKg9B2-8]

What I learned on my vacation – it’s easier to be green

  1. We can live in cities and still respect the environment and use less natural resources and decrease our carbon footprint
  2. Markets (traditional) are good
  3. Trains are good

aladyonbike.jpg
We can live in cities and still respect the environment

Amsterdam has a hundreds of years of history or dedication to the smart and responsible growth of their city. I hope that this Dutch ingenuity serves them well with the coming changes to the global landscape. I was in the grocery store and I noticed that they sold chocolate pudding in cartons. When I read the calories per serving I nearly flipped, but I guessed that if you’re riding your bicycle everywhere then you can afford to eat a few hundred calories worth of chocolate pudding.

EVERYONE RIDES BICYCLES IN AMSTERDAM! It’s really neat to see. Families cart small children and dogs in little trolleys or carts in front of their bikes. There are cars on the streets, presumably commuters from the suburbs, but I was astounded and impressed by how bicycle culture is the ‘transport culture’ in this city. If only we could build up or separate the bike lanes in Portland to make them more safe for bikers. Also, I noticed that there wasn’t a lot of macho-mountain bike culture going on or people dressed ridiculously in tight Speedo shorts and brightly colored biker wear, instead you find just a bunch of normal people riding their bikes. I’ve decided that my next big purchase is going to be a used city cruising bike. I live just a few minutes bike ride from the local grocery store so why not.

Also, most of the cities in Spain have recycling containers labeled on their streets. Huge containers that stand about 5 feet high. Alicante, I noticed, was nearly immaculately clean. There was no or little garbage strewn on the streets. Also, power must be expensive in Spain because no one uses an electric dryer to dry their clothes. Where ever you go, you can see laundry left out window sills to dry. In nicer neighborhoods, the apartments all have inner courtyards with balconies and common areas for hanging up clothes. In addition, I noticed that all the hotel rooms we stayed at require the insertion of a room key to start the power in the room. This insures that power won’t be lost from lights or appliances left on. I did notice that there were no digital clocks in the rooms.
jamon.jpgMarkets are good (I wish we had more of them)

In all three cities we visited in Spain we visited a public market of some sort. In Barcelona and Alicante we walked through the Mercado Central. The markets were amazing, brightly colored booths with spices, meats, and candies. I did find a sweets vendor that was selling several kinds of metallic non-pareil (sp?) decorations for cakes, as well as many kinds of dried and candied fruits. I was kind of pissed off that I couldn’t spend more time in the Barcelona market, but we were on a mission and could not stop. As we walked through the Mercado in Alicante, Eric puzzled, how can all these vendors could make any money if they were selling the same products right next to everyone else. I made the assumption that it was a combination of personal relationships merchants made with their customers as well as the general volume of people who would come to the market over anywhere else because the selection was good. No one is going to offer crap if they have to compete with all the other vendors. The reputation of the market as a great place to purchase goods holds firm with the people. The meat market here, is a horror fest for most vegetarians, but for those of us who partake, it sure beats having to settle for the water injected chicken at the Win Co. The fish and seafood vendors sold everything from snails, tuna steaks, something that looked like baby geoducks, and octopus. Also, I was able to buy and eat some of the most delicous Empanadas and Ensaymada (sweet bread) I’ve had in my life from the bakery vendors.

mercado.jpg

Alicante Mercado Central

Alicante Mercado Central

The front of the Mercado Central in Alicante

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Trains are good

In Spain we traveled everywhere by train. When traveling between big cities it seems like most people in Spain use the train system. Now, I’m no scientist but I suspect that using this mode of transport is easier on fuel consumption that a couple hundred people driving their SUV’s from city to city. No doubt with fuel prices being what they are here, who would? I liked riding the train, it was pleasant, quiet, nice and I had the opportunity to finish knitting a whole pair of socks.


More about good things people are doing to reduce their carbon footprints:
Smart Growth (NRDC) – http://www.nrdc.org/smartgrowth/default.asp

Link obsession… Vista

Window Vista Debacle:

How Google Maps Can Help Vacationers

I used Google Maps incessantly before and while I was on vacation. I don’t have a live GPS locating device so I actually made hi-resolution images of the maps I made ahead of time and then uploaded them to my iTouch device. While it isn’t a good idea to whip out your iTouch in a busy square or in public while touring in a foreign country (actually, pulling out a map in a place where you’re conspicuous or subject to being targeted like a busy square or a train station isn’t that safe either), you can easily sit in a quiet cafe or hotel lobby and check your map while sipping a cup of coffee or tea. I did this a few times in Amsterdam.

Also, if I wasn’t too sure about a place to stay I would look it up online if I could. Many hotels have been rated by travelers. Though sometimes you have to scroll through lists of sponsored links/reviews to get to actual reviews by live people. I wonder if some tourist agencies will get the picture and hire people to write fake but real-sounding consumer reviews.

One thing I did notice, few shops and businesses have actual websites in Europe also, not many were listed by name in Google or other online directories. Who knows, maybe if more people use the web to research their trips then businesses at tourist destinations will start creating a web presence. I think having a web presence is just starting to catch on in some European Countries. If there were places I really liked I did actually write a review for them in Google Maps. I posted reviews for a few that had no previous reference or even names listed in the internet.

Successfully Loaded my Maps on my iTouch

Dinner at La Sidereria Escondida

Walking past the Sidereria during the day

Menu (what I can remember)

  • Preserved/cured beef
  • Six kinds of cheeses including a buttery blue cheese called Cabrales
  • Smoked fish pate
  • Potatoes with langistino and eel with aioli
  • Blood pudding
  • Chorizo cooked in cider
  • Breaded and fried beef (pork) with fried potatoes and a blue cheese sauce
  • Bread
  • Chocolate mousse
  • A large bottle of cider for each person


People in Spain eat really late and the stay up all night. That’s what siesta is for. Eating and drinking is just a background for social life. I noticed in Madrid there were a lot of older people (past their 40′s) out late, not just in the Tapas places or bars, but coming out of the theater. At the Sidereria we met a couple with children who were hanging out with us until the late, late hours of the evening. Their children were staying at their grandparents for the evening.

I sometimes feel that we in America are incredibly insular (to the nuclear family) that there’s not a lot of socializing going on in general unless you’re younger. Maybe that’s why we’ve been leaning more towards being social online. Online is nice, but somehow, at least to me, it’s still lacking of the intangible rewards of being in the actual presence of others. But what do I know? I’m really introverted by nature.

The night we arrived our host Miguel and his mother treated us to a wonderful late dinner that included White asparagus with aioli (garlic mayonnaise), cheeses, bread, ham and a savory dish of snails (Caracoles). The snails were actually quite good and actually not unlike mushrooms in texture.

eatingsnails.jpg

Eating Snails Alicante Style


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