A fair number of children who have difficulty with algebra have difficulty much earlier with understanding subtraction and division, two areas that we had covered through stories in class. The children felt that they had practiced and were confident that they can create stories, interpret my stories into numbers. I decided to use an assessment that would require application of these concepts in real life using a weighing balance.
I started with one of their pencil boxes, passed it around and asked them to guess its mass. Once they had all recorded their guesses in their notebook we measured it (52 g). I then took 10 pens and put in inside the pencil box and repeated the process. I asked them to guess the mass of one pen. Then scale it with 10 pens. They came up with 90g-100g as their guesses. We then made the measurement (102 g) and I asked for the weight of one pen. As with the previous process the children started guessing. I told them they had already guessed and this time I would like a correct answer. The children could not walk back the path they had come and correct for the measurement they came up with interesting answers including some that were over 10 g. I tried to help them by walking through how I would do it with what the mass of 10 pens would be. I was intrigued that some children were confused by this process and some even managed to add the two measurements (152g). On digging deeper I realized that these children could only think of subtraction when a clear word 'remove' was part of the construction.
I had to move from
Pencil box mass is 52g. Pencil box with 10 pens mass is 102g. What is the mass of 10 pens
TO
Pencil box with 10 pens mass is 102g. To find 10 pens mass I need to 'remove' the mass of the pencil box, which is 52g.
To open up the puzzle (well it had become one) for children's participation, I asked the children to each list 10 kinds of items that they could put in the pencil box. With time I added clarifications that the items needed to be something they could find copies of and for a couple of children needed to reiterate that 'kinds' was different kinds of items and 10 pens didn't work. We then measured one of the item they had in mind and the children made their own stories with pencil-box+some number of objects * mass of one object that they had measured. This process involving addition and multiplication that all children find comforting. As they exchanged their stories and solved them they did get practice in handling what they had initially felt a very different problem.
Its actually interesting that I tried these out in different grades and how the numbers change appropriately. For children in 5th grade the number came out as a round number, for the children in 6th grade the objects we picked up had a touch of a fraction and when we did the same exercise in the 7th grades the weights gave some neat decimal numbers.
I started with one of their pencil boxes, passed it around and asked them to guess its mass. Once they had all recorded their guesses in their notebook we measured it (52 g). I then took 10 pens and put in inside the pencil box and repeated the process. I asked them to guess the mass of one pen. Then scale it with 10 pens. They came up with 90g-100g as their guesses. We then made the measurement (102 g) and I asked for the weight of one pen. As with the previous process the children started guessing. I told them they had already guessed and this time I would like a correct answer. The children could not walk back the path they had come and correct for the measurement they came up with interesting answers including some that were over 10 g. I tried to help them by walking through how I would do it with what the mass of 10 pens would be. I was intrigued that some children were confused by this process and some even managed to add the two measurements (152g). On digging deeper I realized that these children could only think of subtraction when a clear word 'remove' was part of the construction.
I had to move from
Pencil box mass is 52g. Pencil box with 10 pens mass is 102g. What is the mass of 10 pens
TO
Pencil box with 10 pens mass is 102g. To find 10 pens mass I need to 'remove' the mass of the pencil box, which is 52g.
To open up the puzzle (well it had become one) for children's participation, I asked the children to each list 10 kinds of items that they could put in the pencil box. With time I added clarifications that the items needed to be something they could find copies of and for a couple of children needed to reiterate that 'kinds' was different kinds of items and 10 pens didn't work. We then measured one of the item they had in mind and the children made their own stories with pencil-box+some number of objects * mass of one object that they had measured. This process involving addition and multiplication that all children find comforting. As they exchanged their stories and solved them they did get practice in handling what they had initially felt a very different problem.
Its actually interesting that I tried these out in different grades and how the numbers change appropriately. For children in 5th grade the number came out as a round number, for the children in 6th grade the objects we picked up had a touch of a fraction and when we did the same exercise in the 7th grades the weights gave some neat decimal numbers.
No comments:
Post a Comment