# Order And Value : Transitioning For Integers By Laura Bofferding

793 Words
Apr 18th, 2016
4 Pages

The article I read for this assignment was, Order and Value: Transitioning to Integers by Laura Bofferding. In this article Laura Bofferding conducted an interview with 61 first graders to see what they knew about integers/ negative numbers. It was interesting to read about the different responses that the students gave her when she asked them a series of questions.

Through this article, I learned about six different models that explained the way the first graders were thinking when they were asked to count backwards until the smallest number. The first model is called whole mental model, in which the students order the negative numbers next to the positive number. For example, -2 will go next to 2 in the number line. When the students were asked to count backwards to the smallest number the students often stopped at 1 or 0. Another model discussed in the article was called, continuous zero mental model, which the students kept repeating 0 when counting backwards. This model of thinking made the researchers think that the students were open to the possibility that there’s other numbers that exit after the number 0. In the absolute mental model, the students used negative numbers to order the numbers apart from the positive ones, but they thought -9 was bigger than 3. In addition, the students did not give any value to the negative numbers. In the order nothing model, the students treated the negative numbers as 0. They thought that the farther the number was away from zero…

Through this article, I learned about six different models that explained the way the first graders were thinking when they were asked to count backwards until the smallest number. The first model is called whole mental model, in which the students order the negative numbers next to the positive number. For example, -2 will go next to 2 in the number line. When the students were asked to count backwards to the smallest number the students often stopped at 1 or 0. Another model discussed in the article was called, continuous zero mental model, which the students kept repeating 0 when counting backwards. This model of thinking made the researchers think that the students were open to the possibility that there’s other numbers that exit after the number 0. In the absolute mental model, the students used negative numbers to order the numbers apart from the positive ones, but they thought -9 was bigger than 3. In addition, the students did not give any value to the negative numbers. In the order nothing model, the students treated the negative numbers as 0. They thought that the farther the number was away from zero…