tag:blogger.com,1999:blog-2084641237928654834.post3067231180903291105..comments2017-12-15T03:38:41.639-05:00Comments on Algebra, Essentially: What's the Big Idea with Algebra 2?Emily Allmanhttp://www.blogger.com/profile/08966304042607333303noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2084641237928654834.post-62051420753327148612012-09-24T07:18:26.954-04:002012-09-24T07:18:26.954-04:00Very impressive and knowledgeable blog.Algebra is ...Very impressive and knowledgeable blog.Algebra is a major component of math that is used to unify mathematic concepts. Algebra is built on experiences with numbers and operations, along with geometry and data analysis. Some students think that algebra is like learning another language. This is true to a small extent, algebra is a simple language used to solve problems that can not be solved by numbers alone. It models real-world situations by using symbols, such as the letters x, y, and z to represent numbers.Algebra Answershttp://math.tutorvista.com/algebra/algebraic-equations.htmlnoreply@blogger.comtag:blogger.com,1999:blog-2084641237928654834.post-9312087728321096562012-09-15T22:03:51.788-04:002012-09-15T22:03:51.788-04:00Steve, I like where you are going with these quest...Steve, I like where you are going with these questions. To me, I think that algebra is about logic and communication of patterns. We observe the way quantities relate to each other and use abstraction to communicate patterns of behavior. We quickly discover that some relationships are easier to describe than others. Why is that? <br /><br />Human behavior, for example, while it does follow some predictable patterns, is not in and of itself predictable. Some numerical relationships, on the other hand, are especially easy to describe: like the relationship where two quantities are always the same (y = x). I think it is no mistake that in Algebra I, we mention numerical 'relations' only briefly in order to define the truly utilitarian 'function.' We start our students off with simple, highly-predictable, injective relationships between two quantities... and then take them as far as they will let us.<br /><br />I think statistics shows us a wonderful marriage of the power of algebra combined with the less uniform patterns we observe in other life relationships around us. We observe, gather data, and attempt to fit a uniform pattern of behavior to our model. How close is close enough? Let the statistics decide.<br /><br />Thank you for providing me with more food for thought. It's this kind of stuff that keeps me up at night!Emily Allmanhttps://www.blogger.com/profile/08966304042607333303noreply@blogger.comtag:blogger.com,1999:blog-2084641237928654834.post-52763427057637307952012-09-15T20:01:14.195-04:002012-09-15T20:01:14.195-04:00I really enjoyed the thought behind your post and ...I really enjoyed the thought behind your post and the conclusion(s) you came up with. I particularly like the three everyday-language questions you pose here. <br /><br />I have taught Algebra 1 more than any other subject, and I wonder what the Algebra 1 Big Idea would be. I talk about relationships when discussing this with my students, but I tend to refer to relationships between people. I am interested in thinking further on whether I could expand my discussion to include ideas. <br /><br />I am curious if in your framing of the Big Idea you think it could refer to relationships between two people? (Or other types of relationships perhaps, like relationships between species in Biology or some such thing. I'm just thinking out loud here.)Steve Grossberghttps://www.blogger.com/profile/11066953723761392075noreply@blogger.com