tag:blogger.com,1999:blog-812794395259173668.post4314305930176660638..comments2024-01-16T20:55:12.331-05:00Comments on Drawing On Math: Expressions with Absolute ValueTina Cardonehttp://www.blogger.com/profile/00549943329133396794noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-812794395259173668.post-3093742032269969092015-11-01T08:50:24.269-05:002015-11-01T08:50:24.269-05:00Tina,
This is such a great example of being curio...Tina, <br />This is such a great example of being curious around what students are thinking. I loved how you involved the students in conversation around the mistake to see such an interesting difference. I am sorry I missed the original post because I have a bit of a different thought around the mistake in the first question versus the second just based on what my the elementary students may have experienced....<br />We do a lot of work with small arrays combining to form larger arrays such as (3x2)+(3x6)=3x8 and use dot images to nudge students to thinking about groupings of dots to bring out the properties of operations. In all of this work, we use the notation similar to what I did above to reflect students' thoughts on "I did this first and then I did this second, and then I combined the two outcomes." So, I see this notation feeling a lot like your second problem, simply because of "doing something first" with the first set of parentheses, then "doing something next" with the next set and then combining or subtracting after. <br /><br />Thinking about that process in the first question, I immediately think that students lose that sense of order somehow. Again, with the elementary, if they do add or subtract from "something they solved as a set" it is typically after because their thought process lends to that. For example, in figuring 9x4 a student may do (10x4)-4 or (5x4)+(4x4). In neither case do they need to deal with a number standing alone before the parentheses. <br /><br />I don't know if any of that makes any sense at all or if it is really even relevant...heehee! I was just thinking of the primary exposure to the notation that my students would have when they leave elementary. <br /><br />Great stuff to think about! ~Kristinkgrayhttps://www.blogger.com/profile/00385187692877248447noreply@blogger.com