tag:blogger.com,1999:blog-7168278597203252936.post1641351128996490044..comments2010-03-29T14:11:01.418-07:00Comments on Haley Bly MathEd117: Two Types of Understandinghaley johnsonhttp://www.blogger.com/profile/17726556132560508433noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7168278597203252936.post-9320419322564406662010-01-20T11:34:24.286-08:002010-01-20T11:34:24.286-08:00By reading your summary of Skemp's article i f...By reading your summary of Skemp's article i felt like you completely hit every important part of his explantions when it comes to how we understand as students. The only difficulty I had while reading your blog was the length. I felt like a summary should be more precise and to the point but I still enjoyed reading it overall.Alicia C.https://www.blogger.com/profile/10094861801813712798noreply@blogger.comtag:blogger.com,1999:blog-7168278597203252936.post-35452321619496682172010-01-19T21:12:32.349-08:002010-01-19T21:12:32.349-08:00First of all, I really like how you went into grea...First of all, I really like how you went into great detail about the advantages and disadvantages of instrumental and relational understanding. I think your most interesting point was when you mentioned the difficulty for teachers to make that jump from the current teaching techniques, which are more focused on instrumental learning, to a new innovative way of teaching focused on relational understanding. I liked how this statement sort of implied that the newer teachers, and us who are studying to become teachers, need to step up to the plate and take on this responsibility in order to improve mathematical learning for our students.<br /><br />The only statement of yours that gave me some pause was that you mentioned that the level of difficulty of relational understanding may exceed the student's ability. I think this may be a bit of a misconception. Although Skemp explains how developing relational understanding is at first more difficult, I believe that this is partly due to the fact that we have grown accustomed to an instrumental way of thinking when it comes to mathematics. I think that if students began mathematics viewing it from a relational understanding perspective they would be able to catch on relatively easily because they wouldn't know any other way. This relates to the idea that you can't teach an old dog new tricks, because change is hard. However, if there is nothing to change maybe it would be easier then we might think.Steve Ohttps://www.blogger.com/profile/10863128023863358741noreply@blogger.comtag:blogger.com,1999:blog-7168278597203252936.post-73176481306902185302010-01-19T21:02:30.294-08:002010-01-19T21:02:30.294-08:00You did a great job including the advantages and d...You did a great job including the advantages and disadvantages of both methods! I especially like how you said relational understanding is "harder to understand but easier to remember." Well said!<br />I think that for somethings maybe it is ok to teach instrumental mathematics,maybe just to give some variety. I guess I just think that leaning too much either way would be bad. What do you think?Miss Abbeyhttps://www.blogger.com/profile/17349252983883013242noreply@blogger.comtag:blogger.com,1999:blog-7168278597203252936.post-70496093250888107092010-01-18T16:08:38.413-08:002010-01-18T16:08:38.413-08:00Wow, you do a wonderful job of capturing so many o...Wow, you do a wonderful job of capturing so many of Skemp's arguments about the pros and cons of the two types of understanding! I can tell you really understand this part of the paper.<br /><br />The first part of the paper where you define the two types of understanding was confusing to me. I always think of these two terms as describing what someone knows about mathematics. The way that these terms are used in the beginning, however, seems to indicate that they are ways of teaching mathematics. Which way do you think Skemp uses the terms?Dr. Daniel Sieberthttps://www.blogger.com/profile/08368158973200343666noreply@blogger.com