danielle_journal+6_+march+13,+3009

__Journal Assessment #6__

The first graders in my cooperating teacher’s classroom had math class this Friday because it was a switching day. During this math class students played around the world using dot cards and then were given a worksheet to work on. This worksheet had a front and a back. On one side of the sheet, students had to add up the sum of two dice and then draw another combination of dice that equaled the same amount. For example, in one box a student would see two dice each having four dots on them. They would have to figure out the sum of the two dice; that 4 + 4 = 8. Next to this box was another box separated by an equal sign. The students’ job was to find another way to make the number eight, besides using the numbers four and four. So students needed to pick one number between 1 and 6 because those are the lowest and highest numbers on a dye. After they picked one number they would draw that dye in the box and then count either up to eight or down from eight to determine what they other dye should be. Then the student would draw that second dye to create the same total. This part of the assessment was very easy for the majority of the class to complete independently. After I sat down to explain the task to students who needed help, they quickly completed this half of the worksheet.

This formative assessment was in the form of fill in the blank where students used their pencils to create dice combinations for five problems. This particular assessment allows the math teacher to obtain feedback from her students about whether or not they are understanding dot addition, as well as determining whether students understand that different numbers added together can create the same total. Many students were either breaking down the numbers that they saw in the first box to create their new combinations, or they used a variety of different numbers to make that same sum. For example, if a student saw four dots on each dye in the first box, they may have made the combination 1, 3, 4. While other students may have used entirely different numbers such as 5 and 3 or 6 and 2.

On the back side of the work sheet were problems similar to the ones on the front, however students needed a deck of dot cards to complete this side. Students would pick two dot cards out of their pile and draw the number of dots from their chosen card onto dice in the first box. Then, in the second box students would create a new dice combination, equaling the same sum in the first box. The example given on the sheet was once again the dice four and four. In the adjacent box were the dice, three, three, and two. If students were to count the dots on these dice, they would get the number eight. The same number that 4+ 4 equaled. Students would then notice that the two boxes equal the same amount, but have different numbers in them; so different combinations are possible to make the same number. After this example, students needed to continue this process for four other problems, identifying a sum, drawing the combination, and then figuring out another combination equaling that sum.

This side was more challenging for students to complete, however I asked students questions along the way to guide them. After students added together the dots on their cards for the first box, I would have them draw these dice and then ask them to pick any number between one and six. We would make sure that this number was less than the total of the sum of the dice in the first box, and then I would ask students to pick another number. I would have students add their two chosen numbers together; then ask them how many more was needed to get to the sum. We would continue to create dice until the struggling student created a combination that equaled the same total as in the first box. After, as students would move onto the next question, I would ask them what they should do first. They would walk me through the steps and I would stay with them to ensure their understanding of what was needed to complete this side of the worksheet. As I walked around students answers varied tremendously. Answers varied because of the cards chosen from each deck, as well as the number of dice that students’ used to represent each sum. All students used different numbers, ranging from one to six, but some used two dice, others used three, four or five dice to create their combinations.

This assessment has high validity and reliability because students’ answers could vary, however there were only so many combinations that could be created because the highest sum was ten on the front side and twenty on the backside. In addition, the numbers on each dye only ranged between one and six. In completing this assessment, students would have to understand how to add numbers correctly because they would not be able to fake their combinations adding up to the same total number. A students’ work would truly show this lack of understanding because they may be drawing as many dots as they want on each dye without understanding what these dye combinations are representing. Students either know how to add or they do not. This assessment is reliable because the teacher will be measuring the assessment consistently among the class. She is able to do this because even though the answers will vary, there are only so many definite combinations that form the sums that each problem is asking. This task is not authentic, however students will need to know which combinations of numbers create different sums in real life.

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