Weekly Student Work_Ann Rauschenberger

The purpose of this learning task is to see the student’s level of understanding of concepts of less than and greater than. This activity follows under the common core standard: “K.CC.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)” This activity is designed to elicit student thinking because the student will have to explain how and why he answered the way he did. Based on viewing the answers he marked and talking to him about his answers, the teacher would be able to tell the reasons for him choosing the answers. For example, if the student picked a number that was greater than the given group, the teacher might look further into his knowledge of the terms “greater than” and “less than”.

The student could approach this task in a couple of ways. For the first two problems, the student could count the number of dots in the given group. Then start with A, counting to see if it was less than the given group. The student would then move on to B, C, and D counting to see which one is less than the given group. This would be using the process of elimination by counting. The student could also use the size of the given object (dots in a rectangle). Looking at the answer choices and picking out the ones that are longer than the given number would lead the student to the correct answer as well. This could be done if the student was using a tool to help them measure the length of each choice (to simply see which one is shorter than the given number). For the third problem, the directions say to draw circles in and below the ten-frames to show the numbers. Students could individually count out while drawing circles until they reach the given number, or they could notice that the given frame will always have ten in it, so they only have to add a certain amount more to reach the answer.

I anticipate that Joe’s current mathematical thinking will result in him being able to solve these problems easily. However, there might be possible errors in his work as well. For the first question, I anticipate that he will count each dot to see which answer choice is less than the given set. For the second question, I anticipate that Joe might think choices A, B, and C are all correct, because they are all less than the given set. I think he might skip over the information that stated to find the set that had one fewer than the given set. For number three, I think Joe will count out the numbers each time he draws a circle to reach the number given. On the second problem in number three (writing 18), Joe might skip over writing circles in the ten-frame, and go right to adding eight more. Joe tends to work very quickly, and I anticipate the chance that he might miss something if he rushes too quickly.

The steps taken by the student to approach/solve the given problems:

Number One—

1.     I read the directions, "fill in the bubble next to the picture that shows a group less than 5."

2.     Joe used his pencil touching each dot, while silently mouthing each number as he counted. He chose the correct answer.

3.     I asked, “How did you know that was the right answer?”

4.     He responded, “Uhm ‘cause I counted to four. When you count 1, 2, 3, 4, 5…see four is smaller than five.”

Number Two—

1.     I read the directions, "fill in the bubble next to the picture that shows 1 fewer baseball than the set shown."

2.     Joe selected the correct answer without saying or showing any physical counting like in the first problem.

3.     I asked, “So how did you know how to do that?”

4.     He answered, “Like the same as I just told you before. Well it had five so I just counted back…I just counted back one because four is one fewer than five.”

Number Three—

1.     I read the directions, "draw circles in and below the ten-frames to show the numbers."

2.     Part 1: Joe started counting from one, drawing circles in each square in the tens-frame, and continued counting and drawing circles to reach 17.

3.     I asked, “How did you know how to do that?”

4.     He replied, “Uhm because I counted when I was drawing the circles.

5.     Part 2: Joe stated, “this is the same as that one (pointing to the previous problem) so I just have to put 8 under the ten-frame to make 18.”

6.     I responded, “Why do you have to put 8 under the ten-frame?”

7.     Joe said, “because if I already have 10 in there (points to ten-frame), ten plus 8 more is 18. Hey I only have to put one more than that one (pointing to previous problem) because that one had 17 and this one is 18.”

I’ve noticed that Joe sometimes has a hard time verbally expressing how he completed different tasks. While the majority of the time his answers are correct and he completes them fast, when asking him how he did it, he will answer with things like, “I don’t know I just did it”, or, "I just knew how to". However, during this interview, he seemed to have something to say.

My hypothesis for his current mathematical understanding is that a.) Joe’s mathematical understanding is at or above grade-level in determining numbers that are greater than and less than others, and b.) Joe is able to identify whether the number of objects in one group is less than the number of objects in another group.

To advance Joe’s thinking, I might give him more challenging problems that have the same concept as these. For example, I might give him a problem that asks for 3 fewer than, rather than one. Another way to advance his thinking would be to ask a question about the number 20 using the ten-frame. I would do this to see if he would know that two of the ten-frames would make 20, rather than counting and drawing out circles for each number.