Week 1 Task 3: Pose questions about running Math Circles
Follow the link, then select File-Download - Bright, Brave, Open Minds: Course Introduction. Prepare for actual teaching: read the math circle philosophy and teaching suggestions, and pose two questions about the material.
My first question is what happens if the young children aren't 'curious' and are not interested in problem solving? How do we help them develop this curiosity, so that they will even want to participate in math-circles and think about problems?
My younger son (6) is perfectly happy with routine math excercises (addition, subtraction etc), but as soon as he sees an interesting problem, whether it be a word problem, or anything unusual or out of the ordinary (that doesn't follow the pattern of previous problems) he has an immediate temper tantrum with real tears and an "I can't do it, I can't do it" , "this is stupid" chant that he repeats over and over. I mention this, because I read your "math cirlce values" and there was a sentence that struck a cord with me. "Fear of authority can completely block a mental activity." I have gotten really frustrated with him when he has acted like this in the past, and I think it has gotten to the point where now perhaps out of fear that I will be upset with him, instead of even trying to think about the problem, he just immediately gets upset and starts throwing a tantrum even though I am not upset/frustrated and just patiently tell him to try to calm down so that he can think. Can you help me out with a way out of this mess? I want him to be excited when he sees an interesting problem, and to want to try to solve it, not to fear it (or me) and get a mental block. So what do I do?
Also, I was hoping you could address this same question during the live event tonight as well. I wonder whether I need to copy it to that section of the website. I will most likely not be able to participate tonight in the live event due to not being able to install the necessary software on my browser (I use firefox on linux and it didn't work when I tried it earlier).
Iskra, I will make sure your question goes to Julia. I am going through forums before the webinar to gather the questions. I think the Blackboard webinar software talks to Ubuntu with stable Firefox, but not other flavors. Just in case, check that you have Java and that it is allowed to run.
Iskra,
does your child love games? You may want to stop doing "formal" math for a while, so the unpleasant feelings will go away, and try something different. There are some great thinking games there, such as "Blokus" (mental rotation and strategy), "Chocolate fix" ( logic), Equate ( Scrabble analog but for math operations), and many others ( check this bookshelf for more ideas). It may be easier and more fun for both of you to talk about problem-solving approaches and terminology while playing games - and then transfer those ideas back to more formal activities. I can also recommend "Crayon Physics" - the player is asked to find three visual solutions for each problem: an "old school", an "elegant" and an "awesome" - a wonderful terminology for your future studies!
The website Math Pickle (http://mathpickle.com/K-12/$1,000,000_Problems.html) lists unsolved problems in mathematics that kids can work on - the site calls it "bringing failure to everybody." I've done some of them with kids as young as 5 and 6. It's so empowering for kids to know that even mathematicians struggle.
Rodi, you should write that to Gordon ( the author of the project) - he would be happy to hear that!
My kids are 3 years apart and I am wandering if it will be possible for them to collaborate or the older one will tend to dominate the discussion?
Kam,
you may certainly try to do it with both of them, and see how it goes. You may set a rule that you let the youngest go first, and ask the older one to "builld upon" what was said by the younger one.
I find that if I am working with a wide age spread, if I stick with topics that are not heavily arithmetic based, things go better. I also like to have multiple questions so that different kids can answer at different levels.
I'm wondering about adding tesellations to the Tiling activities. Do you have any suggestions for this?
Jen,
please feel free to modify the lessons any way you want. Exploratorium, Shodor, and Totally Tessanations provide some good resources.
How much preparation does it take to run a math circle?
It does not require a Ph.D in abstract algebra, if that is your question :) You may expect to spend an hour or so reading the lesson plan, collecting materials and writing down your guess about how the lesson will go. You may need some extra time prior to starting the math circle to set the place and time.
As pertaining to motivation, how do you help support motivation through lack of external rewards and good team environment when students are accustomed to a competitive, reward driven system? I agree that those things listed under "motivation" will help them develop intrinsic motivation, but when they are so used to extrinsic motivation (competition and rewards) they seem to flounder and disengage (at least initially) when those things are removed because they don't know how to function without them. How do we help them transition to intrinsic motivators?
Motivation is quite an interesting subject. Animal psychologists conducted the following experiment: A squirrel naturally loves running inside the exercise wheel, when given an opportunity. Imagine that you want the squirrel to spend more time inside the wheel, so you give it treats for extra time there. Paradoxically, soon the squirrel will stop using the wheel unless you give it a treat - you've killed the natural motivation and substituted it with an external one.
All children are naturally curious - and will stay so for quite a while unless given too many external rewards. Unfortunately, it is much easier to motivate a child with an external reward than to find a way to deeply engage a child - because external motivation does not require such a fine-tuned attention for each individual child. I would start by small steps:
- Observing your child and finding their internal motivations ( not in math, but in general)
- Creating regular "quiet" time and finding quiet, but intensely focusing activities
- Figuring out what makes your child agitated and craving external stimulation
If your child is old enough, you may start discussing all these questions with them, and looking for a solution together. You may explain to your child that people use external motivation to control others, so being depended on external motivation is not healthy in general. Your child may want to start looking for a way to obtain more personal freedom.
"Verbalization of solutions usually falls behind the ability to actually solve a problem." I agree this is true of most students, but I've found these abilities to be quite disparate in one of my kids. Besides pointing out differences between problems, do you have other specific suggestions for developing lagging verbalization of solutions skills? I'd be especially interested in how to delicately do this without putting words into the student's mouths or solving for them.
Dear Targhee,
thank you for your deep and thoughtful questions. The issue of verbalization is not easy - but many people, including adults, can do problem solving without much verbalization. In ancient Egypt, they used no explanation for a problem solution, except for a diagram. It may be encouraging for you and your child to take a look at "Proofs without words" book which illustrates the visual thinking in math.
1. Can you give any examples of kids inventing new notations that were useful?
2. What do you feel is the ideal timetable for this kind of thing? Should we be trying to meet as a math circle once a week, or spread it out over the year by meeting once a month?
3. You mentioned these eight lessons are one set of three sets of lessons. Are the other lessons available anywhere? Maybe in the book?
1.Kids are very inventive in finding their own notations. For example, take a look here in "count the squares" activity.
2. Once a week is what worked for us the best.
3. Unfortunately, those lessons are not in the proper format yet; each book we produce will contain material for one 8-week session, so the second session will be in the second book.
Hi! Here's my question: is there a guideline to how long we should let our kids struggle and work through the "stuck" phase on their own? I want to them to be able to have that feeling of success when they finally have that "a-ha" moment but I also down't want them to become so frustrated that they want to give up.
Keetgi,
If you take a look at the topics, you will see the "wait time" icon - I tried to give suggestions on the "wait time" for most of the problems. Please let me know if there is a specific problem you are asking about.
