tag:blogger.com,1999:blog-2036014053389751696.post3168389866086717339..comments2024-08-07T08:29:41.242+01:00Comments on Colin Foster's Mathematics Education Blog: Crocodiles and inequality signsColin Fosterhttp://www.blogger.com/profile/12463017049484632672noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2036014053389751696.post-64946512909184156092023-05-15T09:07:00.259+01:002023-05-15T09:07:00.259+01:00Really interesting. With your alternate vertical ...Really interesting. With your alternate vertical lines, and visually linking equality with inequality, I think there is also the potential to link the horizontal lines - an equal sign becomes an inequality by the two lines getting closer together at one end and therefore further apart at the other - no need for the crocodile, but still exploring the visualAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-75835058863352797052023-03-29T16:32:26.436+01:002023-03-29T16:32:26.436+01:00Really interesting thoughts, Colin. I wonder to wh...Really interesting thoughts, Colin. I wonder to what degree relating inequality signs to magnitudes hinders when we get to negative numbers, though. Is thinking of 3<4 in terms of 'smaller' and 'bigger' problematic when we get to -4<-3, when -4 is a 'bigger' negative than -3?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-34649522889620418832023-03-20T13:02:14.090+00:002023-03-20T13:02:14.090+00:00Thanks as ever for an interesting and thoughtful b...Thanks as ever for an interesting and thoughtful blog. I would say it is okay when it makes things more fun (with obvious caveats to avoid racism or engendering unhelpful beliefs for life). I think its main use is when introducing ideas - I remember learning the game of chess from a book where pieces talked to one another, which I liked. <br /><br />Informal terms: to be controversial (ignorant?) I actually think we should use the terms "top of a fraction" and "bottom of a fraction" - I think they are just as precise, and IMHO clearer. I think informal terms can be helpful to aid understanding, but there is a big potential danger of then not recognising standard terms (with "top" and "bottom" above I these should be the standard terms) or being confused by having two terms for the same thing (since a very reasonable assumption is that if they were the same, there wouldn't be two terms!)<br /><br />Using own terms I think is helpful for a sense of ownership, and particularly good in say exploring a problem where the student spots some property, and it's really helpful to give it a name. In the debrief, I think it is helpful for the teacher to map these to any standard terms/concepts e.g. "parity", "odd function". Anonymousnoreply@blogger.com