Challenge 3: Video Responses

Derek: When solving the question Derek is very thoughtful. Derek gets the right answer for this question, but he explains it by saying that he multiplied it all together and then added one. For the next question, Derek gets the wrong answer. He understands that you start with the first number and then add up. For the subtraction problem, Derek understands that you start with the larger number and take the smaller number away from that. He uses his fingers to count down. Derek used the same method for the word problem, but he was unable to solve the problem. Derek seems to understand the general processes of addition and subtraction. Derek also understands number concepts regarding which numbers are larger or smaller.

Elizabeth: Elizabeth knows simple addition facts from memory. Elizabeth also has an understanding of how numbers relate to one another. She shows this when she uses the first answer of 6 to “guess” the answer of 7 for the question about how many apples would there would be if she had 3 and her instructor had four. When using the cows in the video, Elizabeth shows that she is able to count and corrects her mistake when explaining her answer. Elizabeth says that she counts in her mind, so she understands that you take one number and count up to add. When there were 6 cows out and 4 in the barn, Elizabeth gets the wrong answer but she shows that she understands the problem when she says that she did not count to 6 but started at 7 and counted up. Elizabeth also shows that she understands that subtraction is taking away with the last problems.

Jim: Jim understands that subtraction is taking away numbers. He says that he “took away 6 and 5” to get the answer of 4 apples. Jim tries to do all of the problems in his head without using his fingers. For the addition problems, Jim does not understand how to get the answer and either guesses or says that he has not been taught that. Jim has trouble explaining how he gets his answers. He says that he just thinks about it. Jim does understand how numbers are related. When asked how he got the answer 3 for the last problem, Jim says that 3 comes before 4. This makes sense since he was asked to take away 1 from 4.

Lauren: Lauren was taught the number and dot method, and she uses this in addition problems. She understands that she counts the “dots” that are on the numbers and add them together. Lauren has these dot methods memorized. Lauren understands that subtraction is taking away numbers. She is able to count backwards in her mind. Lauren understands that you start with the high number and take away the smaller number. Lauren is very good at problem solving and uses her fingers to count up the difference between two numbers and finds how many pieces of candy a boy should put back for a word problem.