tag:blogger.com,1999:blog-413213147692532190.post6283545909543950243..comments2024-03-15T03:38:22.132-06:00Comments on Real teaching means real learning: Math concepts first, tricks second.Davehttp://www.blogger.com/profile/13790571271386459698noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-413213147692532190.post-26710088724454296422011-02-13T13:42:17.526-07:002011-02-13T13:42:17.526-07:00Great point, Dave - looking for the consistent cog...Great point, Dave - looking for the consistent cognitive frameworks inherent in the mathematical concepts can often serve to reveal the developmental problems of teaching 'tricks' in math.<br /><br />GOOD tricks are simply distillations of the methods that can be used interchangeably with the 'expected' algorithms in appropriate contexts... they highlight, not conceal, student understandings.<br /><br />In your FOIL example, a student that understood the concept of 'everything times everything else' would be able to transparently apply the 'trick' across a wide range of situations without losing sight of the ball.<br /><br />Math is, after all, an ongoing game of 'I wonder if...?'<br /><br />Have a good one!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-413213147692532190.post-57291238057531578362011-02-13T12:50:26.364-07:002011-02-13T12:50:26.364-07:00Don't know where this comes from, but this is ...Don't know where this comes from, but this is a quote I often share with my learners:<br /><br />"People who know what to do and people who know how to do it will always be working for those who know why it is being done."<br /><br />Your post is interesting because we are trying to apply the same idea to developing teaching approaches. No short cuts - just progress. Check out my colleagues blog at http://mathhombre.blogspot.com/2011/01/planning-for-engagement.htmldelta_dchttps://www.blogger.com/profile/18024582157985654525noreply@blogger.com