Wednesday, November 26, 2008

Reasoning and Communication

November 13th

Today I posed two different questions, an open and a closed. I wanted to once again see how these two questions compared in terms of what information it gave me about student understanding. I am noticing also, that open questions are giving me a lot of assessment information on student reasoning and communication skills, something that closed questions do not give me. Here are the two questions:

Mrs. J has a cell phone. She has a plan that allows her to talk for 1000 minutes a month. She gets her bill at the end of the month, and as she is scanning through, she spills coffee on it, blurring out some of the numbers. She notices that she talked for 345 minutes the first week, 210 minutes the second week, and 534 minutes the fourth week. The amount of minutes she was on her cell phone for the third week was missing. How many minutes was Mrs. J talking during week three? If she pays 5 cents a minute for her phone, how much was her bill?

#2. Mrs. J’s cell phone plan allows her to talk for 1200 minutes. As she is scanning her bill she notices that she talked the most in week four, the least in week two and about the same in weeks one and three. If Mrs. J has about 100 minutes left at the end of the month, what are some of the possible times Mrs. J could have talked in those four weeks? Mrs. J’s cell phone bill totaled 129.95. Knowing that she only pays 5 cents a minute, how did she know this was not correct? Explain.

I took about ten minutes to explain the two problems and entertained any questions students had. I gave students the entire class to work on the problems, where I collected their work and then compared their answers. As expected, the open question tasks allowed students greater access to the problem as every one of them was able to come up with appropriate answers, some even went as far to play with the numbers to see how many different combinations they could come up with. Students also did well with the closed question, but four out of ten students did not come up with an appropriate answer to the problem. Many, perhaps six of them had difficulty deciding what it was they had to do and they became frustrated, which may have contributed to the incorrect solutions. Using the open questioning technique, it required students to show me how they went about figuring out the problem. As a result of this, I was able to assess their level of thinking, reasoning and communication. I found that only three of my ten students were performing at a level four based on the rubric used in the CRT’s. All other students were scoring a level three with one student scoring a level two. This concerned me, but after doing this activity, I now see where I have to focus my teaching for this time being. I need to work with these 7 students to help them build their communication and reasoning skills. I intend to do this by using more open ended questions having the content scaled down a little so they will only need to focus on communicating their thinking and not on how to actually do the problem. This type of information would not have been gathered, nor would I have been able tole to realize I needed to work more closely with seven of my students to improve their reasoning and communication skills, if I had to only rely on the closed question.

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