Alright, so we are now into the start of February, and I have some new thoughts about proportions. First I have just finished reading the Billings article on proportional reasoning, and i found it fascinating. This is due to the fact that she recommends using a “no numbers first” approach to introducing proportions to middle school students. Her argument for this is that this allows instructors to better understand where their students are in terms of their initial proportional reasoning skills. Thus this is an excellent way to both administer a diagnostic assessment to gather useful data on our students, but also to use as a formative assessment(s) to gauge how well our students are grasping the concept.

Furthermore, she argues against teaching, initially, the cross multiplication strategy/algorithm used to commonly solve proportional problems. The basis of this follows from the fact that students will then simply memorize the procedure for dealing with proportions, without necessarily comprehending the logical reasoning behind why proportions work the way they do.

Also, we did an in class activity on Day 7 (1-28-15) in which I had the opportunity to “play teacher” to the class. For this activity, we were tasked with identifying, in a series of 7 problems, which set of solutions had more “blueness” too them. What I had to do was illicit student responses and get them to explain their reasoning behind which answer they believed to be right in a ‘pure’ mathematical sense. Overall, the activity was fun, but as I explained on my thoughts about that day’s activity, I felt like it is difficult to simultaneously divorce your own experience and knowledge from the problem and keep and open mind when dealing with an actual class of middle school students who do not really have a firm grasp on what proportions are. Hence my solution to clear up some confusion is to be explicit in my questions on formal and informal assessments as to whether or not I am looking for a proportion or an actual integer or something else. That being said, a good bonus question or formative assessment would be to investigate whether our students can correctly identify which contexts require proportional reasoning compared to integer or other kinds of reasoning abilities.

Thanks for taking a few minutes to read my thoughts on proportions and teaching the topic. Hope something is useful/thought provoking.

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clear, complete, consolidated +

coherent, content – I think an example of the kind of problem you’re talking about at te end would be good. OK to be your first take or an approximation of it. Think about what your main argument is here.

I usually don’t give these kind of notes, but elicit is very different from illicit.

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I think you did a great job when you were the “teacher” in class. That was a difficult discussion to lead we all were not really sure how to do this activity without using fractions. I know I had trouble. I kept thinking that the idea crossing out would work but then when John pointed it that this is really not a method that should be used because you are changing the factions whenever you do this. Also the idea that 1 blues = 2 blue when it came to blueness was really difficult for me to grasp at first. Overall I think that your post does a good job to talking about the activity as well as the reading.

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You did a great job when you were the “teacher”. It was hard for us, as students, to explain our reasoning of how we came up with the answer. Then you had to write it up on the board for the whole class to understand. Then the class really got into the problem, and you still stuck with your “teacher mood” and wrote everyone’s reasoning on the board whether it was right or wrong! Great job!

The hardest part of the whole class, was trying to remember that we do not know fractions yet as students and we are discovering them in the problem. I know that was hard for me to not use fractions as an explanation.

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