Challenge 3

Initial Thoughts-

Jim did not seem to understand the concepts of addition and subtraction. He was not able to add. One of the two problems he answered correctly was the first one, which asked, "How many do you have if you take away 4 from 6?" He said he "took away 5 and 6," leaving him with four. This shows that he does understand that numbers go in a sequence, and 5 and 6 come after 4. When asked other questions, such as 7+6 and 8+5, Jim guessed random numbers. He was also asked "4-1" and he was correct, saying that "3 comes before 4." Again, this shows that Jim knows the concept of number sequence, but probably only up to about 6 or 7.

Lauren understood the concepts of addition and subtraction. She knew that 7+6=13, by "counting." She next said that 9+6 was 16, and when explaining how she reached that answer, she realized is was actually 15. She understands number sequence, and understands the concept of adding. Lauren could also count backwards, from at least 12 and possibly higher. She understood that subtracting meant taking away, which required counting down.

Elizabeth understands some basic addition, although she had difficulty explaining procedure. For example, she knew that 3+3 was 6, but could not explain it on her own without a prompt. Later, she answers that 4 cows+2 cows is 5 cows, but then changes her answer to 6 when counting out loud. Elizabeth typically tried to answer the questions "in her mind" but when she checked her work using her fingers, she was often able to correct her mistakes. She seemed to understand the concept of addition, but not subtraction. She was not able to answer the subtraction problems correctly. She did not seem to understand that "taking away" was subtracting, which meant counting backwards. She did seem to understand number sequence.

Derek seems to understand the concepts of addition and subtraction. He understands counting sequence, and can count backwards and forwards. However, he said he did not like "high numbers" and probably does not feel comfortable with adding and subtracting past 15. He understood that subtraction meant taking away, and was able to count backwards successfully.