4 ms·

> I find I can reliably challenge most advanced math students in the United States just by serving them problems from grade-level standard curriculum textbooks

by jibiki 17y ago

> I find I can reliably challenge most advanced math students in the United States just by serving them problems from grade-level standard curriculum textbooks from Singapore. If it's not asking too much, can you give some examples? Are these contest-style problems, or computational problems?

tokenadult 17y ago
These Singapore Primary Mathematics series placement tests http://www.singaporemath.com/Placement_Test_s/86.htm http://www.singaporemath.com/Placement_Test_s/86.htm give some idea of problem types at different grade levels. They are not exhaustive, of course, as the distributor of the books doesn't want to give away all their content for free online.
- jibiki 17y ago
  Thanks, those are great. "A bell rings every 25 minutes while another bell rings every 40 minutes. Suppose they rang together at 6 a.m., when will they ring together again?" Very cute. Do you find that students prefer such problems to the normal "plug and chug" type? (Also, when you say "advanced math students", what age are you talking about?)
  - smanek 17y ago
    Really? I wasn't that impressed with them: they were mostly arithmetic - not actual math. Most of the questions I saw were just annoyances dealing with fractional/decimal arithmetic. There were some interesting word/figure problems, but the difficulty in those usually lay in doing the arithmetic by hand.
    - tokenadult 17y ago
      I wasn't that impressed with them: they were mostly arithmetic - not actual math. Same request as the friendly request above to which I responded: what resources would you suggest for examples of "actual math" appropriate for elementary-age students. I use a great variety of problem sources, published in both English and Chinese, to teach various learners of elementary math supplementary lessons, which is my current occupation. But one can never have too many sources of problems, so what sources do you suggest? There's no "ceiling" of difficulty level, because I have early-elementary-age students who are already well along in secondary-level math, so I have to keep looking for more challenging material all the time for my most advanced students.
      - smanek 17y ago
        Hmm, that's a fair question. I tutored high school kids (14-17) for a while, and I would generally tailor things to their interest. Basically, I tried to relate the math to solving a real problem they might be interested. Limits to money problems (e.g., could you retire on a Million dollars? Now take into account inflation, interest, etc)., differentials to sports/computer-games (plot the trajectory of the ball), random riddles, etc. I'm not really sure how well that would translate to younger kids though ... My elementary school aged nephews/nieces tend to enjoy geometry problems (find the pattern ...), 'shortcuts' (FOIL, etc), and morphisms, but I fear my experience with kids that young is too limited to draw any general conclusions.
      - Arun2009 17y ago
        See the following for general pointers. They may not be the exact material you want though. http://www.artofproblemsolving.com/ http://www.artofproblemsolving.com/ http://www.amazon.com/Art-Craft-Problem-Solving/dp/0471135712 http://www.amazon.com/Art-Craft-Problem-Solving/dp/047113571... I wish I had access to people who were really good at problem solving when I was in my pre-university days. The intention is not to really become an ace problem solver, but to give the brain a real good workout.
        tokenadult 17y ago
        I concur with the recommendation of the Art of Problem Solving website for all ages of problem-solvers. That's where I first took up the screen name I also use here on HN.
alain94040 17y ago
Here is an example from the typical French high-school graduation question: http://xmaths.free.fr/TSTI/exos/exercice.php?nomexo=TSTIpbacexA1 http://xmaths.free.fr/TSTI/exos/exercice.php?nomexo=TSTIpbac... If you wanted to graduate this year, this is the problem you had to solve: http://www.maths-express.com/bacs/2009/FranceSjuin2009.pdf http://www.maths-express.com/bacs/2009/FranceSjuin2009.pdf (in PDF, easy to read). (even if you don't speak the language, it's math, so you can probably figure out what the questions are, the formulas themselves are universal)

by jibiki 17y ago

tokenadult 17y ago

These Singapore Primary Mathematics series placement tests http://www.singaporemath.com/Placement_Test_s/86.htm http://www.singaporemath.com/Placement_Test_s/86.htm give some idea of problem types at different grade levels. They are not exhaustive, of course, as the distributor of the books doesn't want to give away all their content for free online.

jibiki 17y ago
Thanks, those are great. "A bell rings every 25 minutes while another bell rings every 40 minutes. Suppose they rang together at 6 a.m., when will they ring together again?" Very cute. Do you find that students prefer such problems to the normal "plug and chug" type? (Also, when you say "advanced math students", what age are you talking about?)
- smanek 17y ago
  Really? I wasn't that impressed with them: they were mostly arithmetic - not actual math. Most of the questions I saw were just annoyances dealing with fractional/decimal arithmetic. There were some interesting word/figure problems, but the difficulty in those usually lay in doing the arithmetic by hand.
  - tokenadult 17y ago
    I wasn't that impressed with them: they were mostly arithmetic - not actual math. Same request as the friendly request above to which I responded: what resources would you suggest for examples of "actual math" appropriate for elementary-age students. I use a great variety of problem sources, published in both English and Chinese, to teach various learners of elementary math supplementary lessons, which is my current occupation. But one can never have too many sources of problems, so what sources do you suggest? There's no "ceiling" of difficulty level, because I have early-elementary-age students who are already well along in secondary-level math, so I have to keep looking for more challenging material all the time for my most advanced students.
    - smanek 17y ago
      Hmm, that's a fair question. I tutored high school kids (14-17) for a while, and I would generally tailor things to their interest. Basically, I tried to relate the math to solving a real problem they might be interested. Limits to money problems (e.g., could you retire on a Million dollars? Now take into account inflation, interest, etc)., differentials to sports/computer-games (plot the trajectory of the ball), random riddles, etc. I'm not really sure how well that would translate to younger kids though ... My elementary school aged nephews/nieces tend to enjoy geometry problems (find the pattern ...), 'shortcuts' (FOIL, etc), and morphisms, but I fear my experience with kids that young is too limited to draw any general conclusions.
    - Arun2009 17y ago
      See the following for general pointers. They may not be the exact material you want though. http://www.artofproblemsolving.com/ http://www.artofproblemsolving.com/ http://www.amazon.com/Art-Craft-Problem-Solving/dp/0471135712 http://www.amazon.com/Art-Craft-Problem-Solving/dp/047113571... I wish I had access to people who were really good at problem solving when I was in my pre-university days. The intention is not to really become an ace problem solver, but to give the brain a real good workout.
      - tokenadult 17y ago
        I concur with the recommendation of the Art of Problem Solving website for all ages of problem-solvers. That's where I first took up the screen name I also use here on HN.

alain94040 17y ago

Here is an example from the typical French high-school graduation question: http://xmaths.free.fr/TSTI/exos/exercice.php?nomexo=TSTIpbacexA1 http://xmaths.free.fr/TSTI/exos/exercice.php?nomexo=TSTIpbac... If you wanted to graduate this year, this is the problem you had to solve: http://www.maths-express.com/bacs/2009/FranceSjuin2009.pdf http://www.maths-express.com/bacs/2009/FranceSjuin2009.pdf (in PDF, easy to read). (even if you don't speak the language, it's math, so you can probably figure out what the questions are, the formulas themselves are universal)