After reading this article, I realized that the analysis of attributes isn't anything new. We've been doing this all throughout our schooling. Whoever came up with the idea breaking a question down into parts "a, b, and c" must have read this article. Many of the questions that I assign to my class will usually start off by assessing their basic knowledge of a particular topic, and then the question will by modified by changing single attributes. I suppose the difference is that in a text book, modifications usually make a question more difficult whereas, Brown & Walter may not agree that an attribute change needs to result in an increase in difficulty.
The three problems that I have chosen have been taken out of the Math Makes Sense 8 textbook.
1)
a) List the attributes of the problem: Copy the shapes, copy them on to grid paper, the shapes are squares, the squares are different colours, find the area of each square, rotate the squares so that they line up with the grid paper, count the grid paper squares to find the area, state which square has the greater area.
b) Possible ways to alter the attributes: What if the squares were triangles? What if one of the squares was a triangle? What if you didn't have grid paper? What if they were measured in different units? What if you were allowed to trace the shapes? What if you had to find the perimeter?
2)
a) List the attributes of the problem: Write two equations, the equations should represent what is happening on the number line, the equations should have an operation, the operation should be multiplication, the number line is in whole numbers, the whole numbers are partitioned into 5 equal segments, the amount being skipped is 4/5. 4/5 is shown visually with a red line, the number line is horizontal, the number line starts at 0.
b) Possible ways to alter the attributes: What if the partitions (1/5's) were not visible? What if the jumps were 2/10? What if you had write an equation using addition? What if you had to write an equation using division? Can you get to the same end point counting in 1/3's? If so, what equation would you use? What if the jumping starting at 1/5? How would that alter the equation?
3)
a) List the attributes of the problem: A jacket is for sale, the regular price is $89.99, after 4 weeks the price reduces by 25%, after 6 weeks the price is reduced an additional 15%, the price is only reduced if the item has not sold, tax is not included in the price, there are 2 taxes added on to the price, PST is a tax, PST is 5%, GST is a tax, GST is 6%, the manager is the one who reduces the price.
b) Possible ways to alter the attributes: What if another jacket when on sale for 40% off after 4 weeks? How would this be different then a 25% reduction followed by a 15% reduction? What if you were buying the jacket for a child and there was no PST? How much more money would you save if you purchased the jacket 7 weeks after it went on sale rather than 5 weeks?
Hi Dave,
ReplyDeleteI like your comment about the analysis of attributes not being new. That said, I personally had not really thought to formally about what it as a process, and likely would not have used that terminology had I done so. I think part of our education in education is learning the formalization of what many of us do naturally, and empowering us to take more into our own hands - as per this case. Your attribute alterations for each of the examples you gave seem fine from my perspective. I particularly like the `no PST for the children' example.
Dave,
ReplyDeleteI agree with Sophie that this notion of attributes is nothing new. I feel as though this could also be referred to as scaffolding. Often, if a problem is too difficult stated as is, the problem can be much more approachable when a sort of scaffold is provided. I really like your alterations for your second problem. I think it gives students the opportunity to abstract the problem of fractions.
Ah. I didn't mean to publish that yet.
ReplyDeleteOne question I have about determining the attributes of a problem, is whether the authors recommended ways to identify the attributes? For an experienced teacher like yourself, this task is presumably extremely familiar. But for a teacher in their first year of teaching, it might not be a familiar notion at all!
Hi Dave,
ReplyDeleteI like your comment about the analysis of attributes not being new. That said, I personally had not really thought to formally about what it as a process, and likely would not have used that terminology had I done so. I think part of our education in education is learning the formalization of what many of us do naturally, and empowering us to take more into our own hands - as per this case. Your attribute alterations for each of the examples you gave seem fine from my perspective. I particularly like the `no PST for the children' example.
Interesting changes to these problems. Would you say the results are still typical 'school math word problems', or do they take kids to a different level of mathematical/ problem-solving thought?
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