First let me appologize for being late with this. - 2 reasons; getting grades done this past weekend and organizing a group from her ein Blackstone going to the MIT SPLASH this weekend.
Anway here are my thoughts on the the 2 topics raised by the readings:
From an image of science education that emphasizes content and process goals to science education that stresses goals examining the relation between evidence and explanations.
This also relates to the second topic question:
Reflect on any one of the above trends in relation to your classroom teaching and the DataTools investigations that you are implementing
In teaching math one of my focues is on having students be able to justfiy their answer, providing factual evidence and well thought thru and explained reasons.
For example a recent problem I assigned was a situation where 9 data values were collected, but one was lost. The problem was to identfy the missing data item given some descriptions of the statistical properties of the total sample.
As a step along the way in this process I ask students to find the range of the data set and explain how they know that is the range. Since range is an easy thing to compute I typically just get the answer, 7. When pressed to explain how they get the answer I get 9-2 = 7. (Which is typically what is asked for in math class when students are asked to "show their work") Then I press again asking why did you subtract 2 from 9, and I then get that the definition of range is you subtract the minimum from the maximum value. Now we are close, and at this point I would actually accept this as an answer, but the real insight I am looking for comes from recognizing you are making the assumption that the missing data point is between 2 and 9. Coming to that realization drives the student to decide if that is a reasonable assumption and it also bounds the search for the missing data, which is where the problem continues.
I see this as the true value of inquiry based problems in math. They are not closed you have to become aware of what you know, what you assume and the rules and reasons of the mathmatical manipulations you are performing.
Does it make sense to do what you are doing? What more do I need to know, how can I justify my answer are the things I look to bring to my lessons by using stessing inquiry in assignments.
Anway here are my thoughts on the the 2 topics raised by the readings:
From an image of science education that emphasizes content and process goals to science education that stresses goals examining the relation between evidence and explanations.
This also relates to the second topic question:
Reflect on any one of the above trends in relation to your classroom teaching and the DataTools investigations that you are implementing
In teaching math one of my focues is on having students be able to justfiy their answer, providing factual evidence and well thought thru and explained reasons.
For example a recent problem I assigned was a situation where 9 data values were collected, but one was lost. The problem was to identfy the missing data item given some descriptions of the statistical properties of the total sample.
As a step along the way in this process I ask students to find the range of the data set and explain how they know that is the range. Since range is an easy thing to compute I typically just get the answer, 7. When pressed to explain how they get the answer I get 9-2 = 7. (Which is typically what is asked for in math class when students are asked to "show their work") Then I press again asking why did you subtract 2 from 9, and I then get that the definition of range is you subtract the minimum from the maximum value. Now we are close, and at this point I would actually accept this as an answer, but the real insight I am looking for comes from recognizing you are making the assumption that the missing data point is between 2 and 9. Coming to that realization drives the student to decide if that is a reasonable assumption and it also bounds the search for the missing data, which is where the problem continues.
I see this as the true value of inquiry based problems in math. They are not closed you have to become aware of what you know, what you assume and the rules and reasons of the mathmatical manipulations you are performing.
Does it make sense to do what you are doing? What more do I need to know, how can I justify my answer are the things I look to bring to my lessons by using stessing inquiry in assignments.
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