the teaching tree

May 1, 2009

jeremy and emily factor a quadratic

jeremy and emily factor a quadratic

I’m here at Cafe Wifi, with my triple latte and chocolate scone, thinking about my algebra students sitting there listening to me (or not), and I wondered: What about teaching a concept or giving out a problem, using the students themselves as tutors, in the following way:

Say a couple of students already know how to do something; for example, factoring the difference of cubes. They each explain it to someone, then those two explain it to two others, while the first two explain it to two other others.

As new students learn the skill, they move from the “don’t know” side of the room to the “know” side, with the explaining taking place at the interface where the tables are. From time to time, the newer knowers must explain it back to the early knowers to check they know it, and to gain insight into how the process changes.

Within a short number of generations, the whole class knows and the “don’t know” section is empty. Mission accomplished.

One concern is when a student doesn’t get the explanation and then gets bogged down trying to explain it to the next person. Maybe helping with that could be the role of the teacher, if there’s even one present.

Any comments on how you think this might or might not work? It wouldn’t have to be limited to math classes, right?


twitter problem archive, part deux

February 13, 2009

small stellated dodecahedron

small stellated dodecahedron


the second set of my daily twitter math problems, #26-50. answers can be found by scrubbing my twitter feed at

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Problem 26 (dan’s prime code):
Label the letters with first 26 primes; A=2, B=3, . . . , Z=101. What’s the value of DANSMATH? (eval. as in algebra)

Problem 27:
Review ‘dan’s prime code’, then find the (real) word whose prime code is closest to a million. (rules: two tweets max, closest=1.5, next5=1, rest=0.5.) Read the rest of this entry »

twitter problem archive 1-25

December 26, 2008

icosahedron with 'sierpinski gasket' faces

here is a list of my first 25 daily math problems; follow me at

remember there’s a 140-char lim on tweets so some r “dense” stmts. thanks to barry fulk @fulkb for pulling these from my twitter feed. 

there are also answers if you scrub my twitter feed; please leave a comment if you want me to post them here. 

– – – – – –
@dansmath daily twitter problems Nov/Dec 2008:
– – –
One dansmath point for each correct answer. First to a million wins!
– – –
Problem 1:
2x^2 + 5xy – 12y^2 = ( ? )( ? )
– – –
Problem 2:
Write 391 as the difference of squares, then factor it as such.
– – – Read the rest of this entry »

twitter daily contest?

November 22, 2008

new – i’m not sure how long i’ll keep these up, but i am posting quick contest problems on twitter, such as factoring puzzles and the like. winners are limited to the first few each day. one was to factor 391 as the difference of squares; the answer is 17 times 23 when the dust settles. do you know what that means? follow me at for more updates!

dansmath on xtranormal

November 15, 2008
welcome to dansmathworld

welcome to dansmathworld

i have just scripted, animated, produced, and uploaded a promo for my site and podcast through a webapp called xtranormal, the self-titled “text-to-movie” company.

it was a fun and painless experience: i just typed in the dialogue, dragged in some camera angles, looks, and backgrounds, uploaded to the xtranormal page, and easily put the video on my youtube as well.

watch my shameless self-promotion now!

dansmath interview

September 19, 2008
dan in front, algebra in back

dan in front, algebra in back

recently i was interviewed by bill palmer of iProng magazine about my website and podcast. you find it at ; you click it, you download it as pdf, you read it, you know all about me! please feel free to comment here, or at , or in itunes!

who else is a math nut?

August 30, 2008
dan inside a polyhedron

dan inside a polyhedron


i am often accused by others of being, of all things, a ‘math nut.’ i accept the label, but wonder if it is said in admiration or with sarcasm. does anyone have thoughts, events, or stories to relate about this?