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<\/a><\/p>\nThe first thing that Cindy does in her journaling is make her own thinking explicit (which I love). \u00a0She is stepping me through her thinking and the questions that arose for her. \u00a0This is actually a major step for many students who are confused – are they able to even know what they are confused about?<\/p>\n
She writes: “I know the problem probably deals with the parallel line theories that we dealt with.” and then lists the types of angles we studied and then with a big “OR” says “maybe it has something to do with the sum of the angles of parallelograms and triangles?” \u00a0Little does she know that what she is doing is practicing synthesizing different pieces of prior knowledge – is it overwhelming to her? – possibly, but she went there and that’s so great! \u00a0I wanted her to know that I was excited that that she even thought about the sum of the angles so I gave her some feedback about those ideas.<\/p>\n
She wrote down what she knew about the sums of the angles which we had also studied.<\/p>\n
She writes her first equation to think about: “5x-5\/=180” using one of the angles in the top triangle. \u00a0I would’ve loved to know where that was coming from. \u00a0What made her write that? \u00a0She then notes that “but it wouldn’t work because if x is the measure of the angle than the equation should be set to 180”<\/p>\n
There is so much that this tells me about her confusion. \u00a0She is not understanding what the expression 5x-5 is supposed to be representing in the diagram I think, or she isn’t connecting what x is “not representing” (the angle) and the whole expression is representing too. \u00a0She also is confused about between the sum of the whole triangle’s angles and just that one angle.<\/p>\n
She then looks at the two expressions she is given, 5x-5 and 4x+10 and I think<\/em> makes a guess that they are corresponding angles – she doesn’t give any reason why they are corresponding. \u00a0She just asks the question. \u00a0But the cool thing is she says “Let’s try it.” \u00a0I love that. \u00a0Why not – I am always encouraging them to go with their ideas and the fact that she tries it is wonderful. \u00a0The funny thing is she does end up getting the same value for the two angles so she asks: “Does this mean that this is correct?” and then “What do I do for “6y-4?” and still has not connected many of the ideas line the fact that these angles are a linear pair and that’s where the 180 comes into play, or even why the angles were corresponding in the first place. \u00a0So many questions that she still has, although I am encouraged by her thinking and risk-taking.<\/p>\n This journal entry allowed me to have a great follow-up conversation with Cindy and she was able to talk to me about these misconceptions. \u00a0I’m not sure I would’ve had this opportunity to clarify these with her if she had not written this journal entry and then she would not have done so well on the problem set the following week. \u00a0I just love it! \u00a0Let me know if you use journals and if you feel the same clarifying or communicative way about them too.<\/p>\n See my website for lots of sample entries and also other blogposts and resources about journaling if you are interested.<\/p>\n <\/p>\n\n