tag:blogger.com,1999:blog-25541994.post3738686370473689817..comments2022-12-25T04:15:37.293-05:00Comments on D-Ed Reckoning: Testing Higher Order Thinking Skills -- Part TwoKDeRosahttp://www.blogger.com/profile/06853211164976890091noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-25541994.post-47983174170031601502009-01-06T13:56:00.000-05:002009-01-06T13:56:00.000-05:00Your last step does not conserve matter.Your last step does not conserve matter.KDeRosahttps://www.blogger.com/profile/06853211164976890091noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-27872282771357415012009-01-06T13:27:00.000-05:002009-01-06T13:27:00.000-05:00I was very surprised no-one has challenged this. T...I was very surprised no-one has challenged this. The teaspoon of red dye added to the water is 100% red dye. The teaspoon of mixture then taken to add to the red dye is not 100% water. Therefore there is less water in the red dye than there is red dye in the water. So 100a, -10a, +10b is not equal to 100b, +10a, -7b+3a.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-25541994.post-36955603012307090792007-04-28T17:58:00.000-04:002007-04-28T17:58:00.000-04:00The way I understand the problem is this. Because...The way I understand the problem is this. Because the two glasses end with the same volume as they started with, the net effect of the movements is that some dye molecules have been transferred from dye glass to water glass and have been replaced by an equal number of water molecules that have been moved in the opposite direction. The concentration of dye in water is therefore equal to that of water in dye. This works even if you know nothing about molecules and see a quantity of liquid as a single entity.duffer davehttps://www.blogger.com/profile/14836338827364833975noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-68661343561481354972007-02-24T13:23:00.000-05:002007-02-24T13:23:00.000-05:00Linda, you might want to work that out again. It ...Linda, you might want to work that out again. It is impossible to have a different mix in the glasses. Instead of liquid pretend that each glass has ten marbles in it. Now take three red marbles out of the one glass and put them in the other glass. Now take out any three marbles from the other glass and put them back in the first. No matter what marbles you pick the mix will always wind up the same.KDeRosahttps://www.blogger.com/profile/06853211164976890091noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-72502438979750216332007-02-24T12:48:00.000-05:002007-02-24T12:48:00.000-05:00If you move the dye to the water glass, then take ...If you move the dye to the water glass, then take an amount equal to that, and add it to the dye glass, the quantities will be the same, but the mix will not.<BR/><BR/>The dye glass will have:<BR/><BR/>dye amount - 1 teaspoon dye + one teaspoon of dye and water mixture<BR/><BR/>The water glass will have:<BR/><BR/>water amount + 1 teaspoon dye - 1 teaspoon of dye and water mixture<BR/><BR/>There will be fewer water molecules in the dye glass than dye molecules in the water glass.Linda Foxhttps://www.blogger.com/profile/15024201252345608291noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-48558380651636085572007-02-20T23:02:00.000-05:002007-02-20T23:02:00.000-05:0042, I had the same problem.I knew that it ended up...42, I had the same problem.<BR/><BR/>I knew that it ended up with the same amount of liquid is each glass, but it seemed wrong that what I put back in the dye glass wasn't the opposite of what I took out. (but it did reflect the opposite of what I left in the other glass, I guess.)NDChttps://www.blogger.com/profile/13189451707001084048noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-20489244731682904242007-02-20T12:58:00.000-05:002007-02-20T12:58:00.000-05:00Hi 42.That is more than simple number conservation...Hi 42.<BR/><BR/><I>That is more than simple number conservation, and not intuitive unless you've worked the math yourself or have otherwise learned it.</I><BR/><BR/>I think you can solve the problem using simple number conservation. But, I agree its not intuitive and must be learned through some means, such as being taught.<BR/><BR/>Think of it this way. No matter how you rearrange the water and dye in the end you must have some amount of dye in one glass and that amount minus x in the other glass. If both glasses end up with the same amount of liquid at the end then the amount of water in the (total minus x) glass must always equal x and thus the ratios will always be the same.<BR/><BR/>Here's one example that's closer to Piaget's. Make two rows of differently colored clips. Now rearrange the clips in whatever manner you wish. Keep on rearranging the clips for a full minute. Now mak both rows equal to ten clips again using whatever methos suits you. Is the percentage of foreign clips in each row the same?<BR/><BR/>How about a problem that can't be worked out using math.<BR/><BR/>I start out with a container with of 1 liter of oil and another container with 1 liter of vinegar. beside me is a box full of different quantity measuring spoons. I randomly select ten spoons and without looking proceed to use each spoon in turn and take a quantity of liquid from container one and put it into container two. Then I take the next spoon and take some liquid from teo and put it into container one. I repeat this procedure until I run out of spoons. At the end I pour an amount of liquid from the more full container into the less full container so that I have equal amounts of liquid in each container. Is the percentage change of foreign liquid in each container the same?KDeRosahttps://www.blogger.com/profile/06853211164976890091noreply@blogger.comtag:blogger.com,1999:blog-25541994.post-37549802017455432682007-02-20T11:21:00.000-05:002007-02-20T11:21:00.000-05:00Ok, maybe I just don't have flexible higher order ...Ok, maybe I just don't have flexible higher order thinking skills =), but I didn't find the liquid example intuitive or a good example of number conservation. If a spoonful was taken from each pure liquid and then added to the opposite glass, it would have been obvious each had the same amount and percentage of foreign matter, and a clear example that changing the "piles" didn't change the total amount. <BR/><BR/>For me the issue was the fact that the pure dye was added to the water and then the mix was added back to the dye. I was surprised when the ratios came out even. This had nothing to do with understanding that the total amount of dye and water was unchanged no matter how it was distributed, or understanding that each glass would end up with the same amount of liquid it started with (just a different mixture), but knowing that even with the manner of redistribution, there would be the same amount of foreign matter in each. That is more than simple number conservation, and not intuitive unless you've worked the math yourself or have otherwise learned it.Forty-twohttps://www.blogger.com/profile/09318394490833830613noreply@blogger.com