Have you ever had a teacher tell you the following?
"If you can solve the questions, then I will give you more, and they will keep getting harder and harder and harder until I crush you."
Neither had I, until yesterday.
I'm taking a class on problem solving. Unlike the prescriptive learning style of other classes (read: you demonstrate, I repeat), in order to learn problem solving you need to challenge your mind (read: you blindfold me and stick me in a hole of unknown size at an undisclosed site and leave me for dead, and I find my way out. Alone.) I am the most frustrated and the most content that I have been in a long time. My sleep is being replaced with a scratch pad. That's okay. That's what espresso is for.
Here is a logic problem that my teacher gave us to try. I have already heard this one and I know the answer. Since I can't enjoy it, I thought I'd pass it along to you.
You are alone in the basement of a house. In the basement there are three identical light switches. One of the switches can turn on a light bulb, which is located in the attic. The other two switches are broken and have no function. Your mission is to determine which of the three switches turns on the light bulb. You can flick as many switches as many times as you like, but you can only go to the attic once to check. How do you do it?
Many people ask questions like, "Can I phone a friend?" or "Is there a window in the attic." The answer to these, and any other "Can I..." or "Is there..." type questions is always NO.
Have fun with this one! It's a mind bender. It helps to think outside of the box.
Enjoy!
Tuesday, September 14, 2010
Wednesday, September 8, 2010
Over the Edge
You're in the front seat of a roller coaster car, waiting impatiently for it to load with passengers. Your heart beats wildly and your pupils are dilated - your sympathetic nervous system is pushing its boundaries. Even though the car is not yet moving, excitement rushes through your body. After all, you love roller coasters. Right?
The car shudders to life and turns onto the conveyor that will pull it up the first hill. There's no turning back now. You're committed, whether you like it or not. As the mechanical chain pulls you and the other passengers up, you can't help but think, "What have I gotten myself into?" As you get to the top, you peer over the edge. The view from the top doesn't quite mentally prepare you for the thrills, screams, and fear that lie ahead. But, as you know, you are going over. Hang on tight, and try to enjoy the ride.
After a few years of a chemistry and biology degree, I had a change of heart and decided to give mathematics a try. So I signed up for four university mathematics courses, three of which are upper level courses. This morning, as I headed to my course on Problem Solving, I had that gut-dropping feeling that I get on the way up the highest roller coaster hill: I want to get out now, please. Why would I sign up for this? What was I thinking?
During the first few minutes of class, the teacher said exactly what I was feeling. He told us that if we didn't try then we couldn't fail. For many students the prospect of failing is more frightening than the prospect of giving up. If you give up, you will never know if you have the ability to accomplish something. But if you fail, you know that you can't do it. End of story.
Then we started with the problems. My heart beat loudly and strongly and I began to sweat. I felt like a teenager trying to impress someone of the opposite sex who was, quite frankly, out of my league. Instead of getting discouraged, I loved every minute of it! I sat and puzzled and puzzled and puzzled... and didn't come up with a single solution (yet.) But even though I couldn't get to the solution, my euphoria verified to me that I belonged in this math class. I had the adrenaline rush of the nerd world.
I don't know how many hills and valleys make up this roller coaster, but I'm holding on tight for now. And here we go, over the edge.
The car shudders to life and turns onto the conveyor that will pull it up the first hill. There's no turning back now. You're committed, whether you like it or not. As the mechanical chain pulls you and the other passengers up, you can't help but think, "What have I gotten myself into?" As you get to the top, you peer over the edge. The view from the top doesn't quite mentally prepare you for the thrills, screams, and fear that lie ahead. But, as you know, you are going over. Hang on tight, and try to enjoy the ride.
After a few years of a chemistry and biology degree, I had a change of heart and decided to give mathematics a try. So I signed up for four university mathematics courses, three of which are upper level courses. This morning, as I headed to my course on Problem Solving, I had that gut-dropping feeling that I get on the way up the highest roller coaster hill: I want to get out now, please. Why would I sign up for this? What was I thinking?
During the first few minutes of class, the teacher said exactly what I was feeling. He told us that if we didn't try then we couldn't fail. For many students the prospect of failing is more frightening than the prospect of giving up. If you give up, you will never know if you have the ability to accomplish something. But if you fail, you know that you can't do it. End of story.
Then we started with the problems. My heart beat loudly and strongly and I began to sweat. I felt like a teenager trying to impress someone of the opposite sex who was, quite frankly, out of my league. Instead of getting discouraged, I loved every minute of it! I sat and puzzled and puzzled and puzzled... and didn't come up with a single solution (yet.) But even though I couldn't get to the solution, my euphoria verified to me that I belonged in this math class. I had the adrenaline rush of the nerd world.
I don't know how many hills and valleys make up this roller coaster, but I'm holding on tight for now. And here we go, over the edge.
Monday, September 6, 2010
Back To The Grind
It's 8:46pm on Labor Day. My dishes are drying in the rack as I listen to the low rumble of my dryer as it sucks the last bit of moisture out of my clothes. Binders, stocked with crisp new paper, lay by the door in anticipation of tomorrow morning's excursion to school.
Good bye free time. You were fun. Hello assignments, midterms, and espresso. Gotta love espresso. Best thing next to Ritalin.
One summertime luxury that I miss during the semester is the ability to cook complicated, time-consuming recipes. During midterm season time, money, and patience are limited in supply and cannot be doled out in front of the stove. However, I am not willing to compromise nutrition. Here are some tips for the student (or busy mom) that I have learned thus far:
1. A slow cooker is the BEST invention in the history of all inventions.
2. Many recipes (chilies, soups, dips, pasta sauce, etc) taste the best on the second day. This is a great excuse to make lots and have leftovers.
3. Buy seasonal, local produce. It's cheaper, more nutritious, it tastes better, and the environment will thank you. Many summer fruits are still in season in September, and winter vegetables such as winter squash may start coming in at the end of the month.
4. Canadian Living magazine's recipes are seasonal, quick, delicious, and use common ingredients that most people have on hand. Also, I have been impressed by every single recipe that I have tried from Anne Lindsay.
5. Try to set aside one day a week for each of beef, pork, chicken, fish, and vegetarian cuisine. This helps to ensure diversity in your diet.
6. Having pizzas or lasagna in the freezer to pop in the oven is a great idea. Let's face it: some days are exhausting. It's okay to take a break from cooking once in a while.
I'd like to know: what can you teach me? What is your favourite weeknight meal?
Have a great semester!
Good bye free time. You were fun. Hello assignments, midterms, and espresso. Gotta love espresso. Best thing next to Ritalin.
One summertime luxury that I miss during the semester is the ability to cook complicated, time-consuming recipes. During midterm season time, money, and patience are limited in supply and cannot be doled out in front of the stove. However, I am not willing to compromise nutrition. Here are some tips for the student (or busy mom) that I have learned thus far:
1. A slow cooker is the BEST invention in the history of all inventions.
2. Many recipes (chilies, soups, dips, pasta sauce, etc) taste the best on the second day. This is a great excuse to make lots and have leftovers.
3. Buy seasonal, local produce. It's cheaper, more nutritious, it tastes better, and the environment will thank you. Many summer fruits are still in season in September, and winter vegetables such as winter squash may start coming in at the end of the month.
4. Canadian Living magazine's recipes are seasonal, quick, delicious, and use common ingredients that most people have on hand. Also, I have been impressed by every single recipe that I have tried from Anne Lindsay.
5. Try to set aside one day a week for each of beef, pork, chicken, fish, and vegetarian cuisine. This helps to ensure diversity in your diet.
6. Having pizzas or lasagna in the freezer to pop in the oven is a great idea. Let's face it: some days are exhausting. It's okay to take a break from cooking once in a while.
I'd like to know: what can you teach me? What is your favourite weeknight meal?
Have a great semester!
Wednesday, September 1, 2010
Don't be a square. Get well rounded.
I have just ambitiously signed up for four math courses which begin next week.
Am I terrified?
Yeah, a little bit. But I am also very excited. Multivariable Calculus, Real Analysis (as opposed to imaginary analysis.... seriously!), Problem Solving, History of Math. I'm not ashamed to admit it: I like numbers. Quantities and algebra weave through my mind like verbiage in the brain of Mordecai Richler.
Okay, maybe I'm no mathematical Mordecai. But I still love algebra.
Unfortunately, mathematics have become esoteric. Recreational mathematics doesn't exist for the general population. People don't tend to whip out geometric proofs to kill time at the bus stop or solve matrices at the beach while relaxing in the sun. Why? It's too hard. It's no fun. I wasn't good at it in high school. It isn't useful.
Does this approach to math look familiar?
So how do we raise our kids?
Do we only encourage the children who excel at sports to be active? NO. Everybody needs physical activity to be healthy.
Do we only encourage the children who excel at music to be creative? NO. Everybody needs to develop creative intelligence through music, art, creative writing, drama, or some other media.
Do we only encourage the children who excel socially to develop their interpersonal skills? NO. Everyone needs to practice social skills to build and maintain relationships.
But math and science... that's a different story for many kids.
It's pretty easy to make the above activities fun for kids. Start a band. Enroll in dance class. Join a sports team. Have a playdate. Join a summer camp. But math and science often get labeled as "hard work" and "no fun," discouraging kids from developing healthy curiosity and reasoning skills which are so important for adult life. Math is more than numbers: it teaches logic, pattern recognition, categorizatoinal skills, inductive and deductive reasoning, and many more essentail skills.
Here are ten simple, inexpensive, and FUN ideas to encourage recreational science and math in your household with your kids:
1. Tangram puzzles - seven pieces should be assembled into a square. It's not as easy as it looks. These usually go for about a buck, or you can google and print your own. LESSON: Spatial mathematics.
2. Mix cornstarch and water together to make a thick paste with properties of both solids and liquids. We call this a non-Newtonian fluid. (NOTE: Do this outside and use a hose to rinse off any surfaces that it gets on. DON'T pour it down the sink!) LESSON: types of matter.
3. Go for a walk in a park or at the beach at low tide and see how many local plants or animals you can name. Some parks have free interpretive programs in the summer. LESSON: local ecosystems.
4. Try Sudoku. Puzzles range from easy to very difficult and are often free in your local newspaper or on the internet. The aim is to get the numbers 1-9 in each of 9 columns, 9 rows, and 9 3x3 grids. LESSON: deductive reasoning.
5. Mix a little baking soda and vinegar. Add food colouring to the vinegar for a prettier explosion. LESSON: chemical reactions.
6. Put some milk in a shallow dish. Add a few drops of food colouring to the surface to make a pretty, splotchy pattern. Then add a few drops of dishsoap to see the colour spread like magic.
LESSON: surface tension.
7. Make a lava lamp. Fill a bottle 3/4 full with water. Add a little food colouring. Fill the rest of the bottle with canola oil and a little salt and put the lid on. LESSON: density.
8. Head out to a dark place with a warm blanket and do some star gazing. Search for your favourite constellations. If you go in mid-August, look for meteors (shooting stars). LESSON: astronomy.
9. Next time you are at the beach or river, look at the types of rocks. Are there smooth stones which were eroded by the ocean? Do the rocks have visible layers or shiny crystals? Is there moss growing on the rocks? Are there coloured rocks (other than grey)? LESSON: geology.
10. Google brain teasers and riddles, most of which push your mathematical and reasoning skills. LESSON: analysis and reasoning.
So maybe your kids don't want to take a course multivariable calculus or Einstein's relativity. But math and science (just like physical interaction, social skills, and creative activities) are part of a healthy, balanced, and enjoyable lifestyle. Enjoy! And remember (in the words of one of my chemistry profs), it's all about the journey.
Am I terrified?
Yeah, a little bit. But I am also very excited. Multivariable Calculus, Real Analysis (as opposed to imaginary analysis.... seriously!), Problem Solving, History of Math. I'm not ashamed to admit it: I like numbers. Quantities and algebra weave through my mind like verbiage in the brain of Mordecai Richler.
Okay, maybe I'm no mathematical Mordecai. But I still love algebra.
Unfortunately, mathematics have become esoteric. Recreational mathematics doesn't exist for the general population. People don't tend to whip out geometric proofs to kill time at the bus stop or solve matrices at the beach while relaxing in the sun. Why? It's too hard. It's no fun. I wasn't good at it in high school. It isn't useful.
Does this approach to math look familiar?
So how do we raise our kids?Do we only encourage the children who excel at sports to be active? NO. Everybody needs physical activity to be healthy.
Do we only encourage the children who excel at music to be creative? NO. Everybody needs to develop creative intelligence through music, art, creative writing, drama, or some other media.
Do we only encourage the children who excel socially to develop their interpersonal skills? NO. Everyone needs to practice social skills to build and maintain relationships.
But math and science... that's a different story for many kids.
It's pretty easy to make the above activities fun for kids. Start a band. Enroll in dance class. Join a sports team. Have a playdate. Join a summer camp. But math and science often get labeled as "hard work" and "no fun," discouraging kids from developing healthy curiosity and reasoning skills which are so important for adult life. Math is more than numbers: it teaches logic, pattern recognition, categorizatoinal skills, inductive and deductive reasoning, and many more essentail skills.
Here are ten simple, inexpensive, and FUN ideas to encourage recreational science and math in your household with your kids:
1. Tangram puzzles - seven pieces should be assembled into a square. It's not as easy as it looks. These usually go for about a buck, or you can google and print your own. LESSON: Spatial mathematics.
2. Mix cornstarch and water together to make a thick paste with properties of both solids and liquids. We call this a non-Newtonian fluid. (NOTE: Do this outside and use a hose to rinse off any surfaces that it gets on. DON'T pour it down the sink!) LESSON: types of matter.
3. Go for a walk in a park or at the beach at low tide and see how many local plants or animals you can name. Some parks have free interpretive programs in the summer. LESSON: local ecosystems.
4. Try Sudoku. Puzzles range from easy to very difficult and are often free in your local newspaper or on the internet. The aim is to get the numbers 1-9 in each of 9 columns, 9 rows, and 9 3x3 grids. LESSON: deductive reasoning.
5. Mix a little baking soda and vinegar. Add food colouring to the vinegar for a prettier explosion. LESSON: chemical reactions.
6. Put some milk in a shallow dish. Add a few drops of food colouring to the surface to make a pretty, splotchy pattern. Then add a few drops of dishsoap to see the colour spread like magic.
LESSON: surface tension.
7. Make a lava lamp. Fill a bottle 3/4 full with water. Add a little food colouring. Fill the rest of the bottle with canola oil and a little salt and put the lid on. LESSON: density.
8. Head out to a dark place with a warm blanket and do some star gazing. Search for your favourite constellations. If you go in mid-August, look for meteors (shooting stars). LESSON: astronomy.
9. Next time you are at the beach or river, look at the types of rocks. Are there smooth stones which were eroded by the ocean? Do the rocks have visible layers or shiny crystals? Is there moss growing on the rocks? Are there coloured rocks (other than grey)? LESSON: geology.
10. Google brain teasers and riddles, most of which push your mathematical and reasoning skills. LESSON: analysis and reasoning.
So maybe your kids don't want to take a course multivariable calculus or Einstein's relativity. But math and science (just like physical interaction, social skills, and creative activities) are part of a healthy, balanced, and enjoyable lifestyle. Enjoy! And remember (in the words of one of my chemistry profs), it's all about the journey.
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