tag:blogger.com,1999:blog-2036014053389751696.post7593655720297466951..comments2024-08-07T08:29:41.242+01:00Comments on Colin Foster's Mathematics Education Blog: Mixing the dimensions in models of numberColin Fosterhttp://www.blogger.com/profile/12463017049484632672noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2036014053389751696.post-8569074776632364802023-01-02T12:28:37.543+00:002023-01-02T12:28:37.543+00:00I have been thinking the same thing about algebra ...I have been thinking the same thing about algebra tiles, I have found it particularly problematic when trying to use them to model completing the square, they 'work', I think, only when dealing with positive terms (x^2 + 2x + 10) but for expressions like x^2 - 4x -10 you need to have tiles representing positive and negative areas and lengths. This type of representation seems more complicated than just learning the transformation from the perfect square. Anna Pickovernoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-42965287144441339352022-12-23T10:47:51.738+00:002022-12-23T10:47:51.738+00:00Not fractional powers but negative powers!
Linear...Not fractional powers but negative powers! <br />Linear models are also very important.Christine Lenghausnoreply@blogger.comtag:blogger.com,1999:blog-2036014053389751696.post-67139309283397570382022-12-23T10:02:49.744+00:002022-12-23T10:02:49.744+00:00There are many ways to view this. I see it as the ...There are many ways to view this. I see it as the generalisation for any base. So base 10, x^2 would be the hundreds column, x the tens or if it was base 2, x^2 would be the 4 column and x would be 2. The first (most right) column, before fractional powers, is ones.<br />If we had students that wanted to go deeper on the maths we could explain the different dimensions. For most of the students I teach the area model has been a game changer in terms of their understanding and success.Christine Lenghausnoreply@blogger.com