http://mathmojo.com/chronicles The Official Blog of MathMojo.com - helping public school, homeschooling, unschooling students, parents, teachers and adults learn math with easy and effective methods. Wed, 23 Jul 2008 02:21:06 +0000 http://backend.userland.com/rss092 en I've got lots more to post about bases, but right now I'm faced with a paradox - Hintikka's Paradox, to be precise.  Hintikka's Paradox comes from Deontic Logic, a form of Modal Logic. I first read about it in Raymond Smullyan's "Alice in Puzzleland' (a brilliant book about logic, and Alice ... http://mathmojo.com/chronicles/2008/07/22/hintikkas-paradox/ Continued from the previous post: The same person wrote a follow up comment: "you are not pretending i'm stupid!!!!! Okay is a base the number you can multiply by????? "example: base two is 2,4,6,8,10,12,14,16,18 ?????????i don't know what you mean!" Yeah, keep trying to convince me that you're stupid. From your grammar and ... http://mathmojo.com/chronicles/2008/07/03/bases-what-are-they-2/ photo by lsiegert A curious reader asked this question: What is a base?? I'm sorry but I'm in the sixth grade and never heard of a base and then all of the sudden it's in my homework. Will you please explain to me in easy fifth or fourth grade words what a ... http://mathmojo.com/chronicles/2008/06/30/bases-1/ Hey, you droogs, There was an interesting post on the Whallah! blog about an article in the Associated Press, concerning the education of math teachers in public schools. Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an ... http://mathmojo.com/chronicles/2008/06/27/why-teachers-cant-teach-math/ A mom recently wrote in to ask this question about standard and expanded notation. "How do you know when you are writing in standard form, expanded form? For example, is the expanded for of 30,048 30000 + 40 + 8 ? Or for 29,486, the expanded form = 20000 + ... http://mathmojo.com/chronicles/2008/06/19/standard-and-expanded-notation/ photo by jonathan229 I haven't been posting much. Sorry. Been in a kind of existential funk. But today I had to include this. It is a link to an article that was in our local paper today, about a heinous phenomenon in a local school. Apparently, some second-graders have ... http://mathmojo.com/chronicles/2008/06/07/now-play-nice-and-dont-plot-to-kill-your-schoolmates/ The previous post was about the value of learning conceptually before you start practicing for skill. There is an alternative argument that argues for the opposite. Many pedagogues try to plead the case that first you must teach the "basics" (meaning the basic skills, like the "multiplication facts") before you ... http://mathmojo.com/chronicles/2008/05/24/math-skills-versus-math-concepts-pt-2/ There seems to be a big "fight" about "which should you teach first, math skills or math concepts." A popular example is the "multiplication tables" versus the concept of multiplication (as repeated addition, for example). It's a pretty good bet to say that when memorizing things it's easier if you ... http://mathmojo.com/chronicles/2008/05/23/math-skills-versus-math-concepts/ "The essence of mathematics lies in its freedom. - Georg Cantor Not much math this time, but there is a math joke at the bottom. Today is our little dog's birthday. Our "little" dog is an eighty-pound Golden Retriever named Maia . (Our hundred-ten pounder is a Golden Retriever named Galileo.) ... http://mathmojo.com/chronicles/2008/05/14/maias-seventh-birthday/ Nice title, eh? Let me preface this with the admission that I know just about nothing about dyslexia. Clinically, I mean. The reason for this post is that Angela (Mother Crone) left a very interesting comment on yesterday's post concerning how mental math has helped her daughter, who is dyslexic. ... http://mathmojo.com/chronicles/2008/05/14/mental-math-and-dyslexia/