Data Collection and Analysis

Adding and Subtracting

I gave students a worksheet on adding and subtracting integers at the beginning of my research, after completing the exercises on number lines, and after completing the real world applications. On the graph, 0 is the beginning worksheet, 1 is after number lines, and 2 is after real world applications.

Both 8th and 9th hour made large improvements after we did the number line work. I believe this is partially because students had a tool they could use daily. I put number lines on their desks, which gave them something to work with. They didn't make as much of an improvement after doing the real world applications. This may be due to the fact that I had already utilized this throughout the year. The difference from the first test point to the second test point was found to be statistically significant with a p value of .0001. The difference from the second test point to the third test point was found not to be statistically significant with a p value of .8735

Multiplying and Dividing

There wasn't as much of an improvement in multiplying and dividing. In fact 9th hour got worse the last test point. This may be due to that class period being rushed that day. I also think my real world applications were not as applicable in this section as they were in the adding and subtracting section. There was an improvement after the number line work. I think the number line helped them re- conceptualize why a negative times a negative is a positive and why a negative times a positive is a negative. It gave them a concrete way to check. The difference in the means from test point 0 to test point 1 was not found to be statistically significant with a p value of .3843. The difference in the means between test point 1 and test point 2 was not found to be statistically significant with a p value of .9723.

This set of data is how the operations with the negative signs affected our Algebra unit on factoring. I calculated this by taking the number of answers they got wrong due to signs divided by the total number of problems. I had three check in points. Check in point 1 was our first quiz over factoring. Check in point 2 was our second quiz over factoring. Check in point 3 was our unit test on factoring.

There were some common themes in my daily observations. One thing I noted often was the apathy in my class. Some days, students were engaged, but often they weren't. I had some students who refused to participate all throughout the unit. I definitely think this affected my data, because low student engagement would cause them to not learn as much as if they were completely engaged.

Another common trend was how quickly students were answering questions. They would often not think critically about their answer but shout out the first thing that came to mind. I didn't initially intend for reflection to be part of the research, but it naturally came up because of them shouting out an answer. We started working on reflecting on our answers and using our tools to think critically about our answers.

Students seemed the most engaged when they were all able to participate in some way and communicate with their classmates. If only one student got to answer or they were working alone, they weren't as interested. I tried to make sure I was getting everyone involved in order to get higher engagement.

I saw a much larger improvement in the addition and subtraction lessons than in the multiplication and division lessons. They were already pretty good with multiplication and division, so there wasn't as much room to improve. They really struggled with addition and subtraction, so I saw large improvements. They relied on the number line a lot more during the practices with addition and subtraction. Some of them already seemed to recognize how to use this tool, so I think they were more comfortable with it.

Factoring Unit

Daily Observations

As the graphs show the students started out missing a lot of questions due to signs. However, as we practiced more and more they seemed to get better. At the end they weren't doing as well with the signs, but I think that is because we were focusing more on multiplication and division instead of addition and subtraction where the real issue was. The difference in the means between quiz 1 and quiz 2 was statistically significant with a p value of less than .0001. The difference in the means between quiz 2 and the test was not statistically significant with a p value of .2475.

I analyzed the data in three different ways. I did worksheets over adding and subtracting and multiplying and dividing to see how the students were doing. I did daily observations. I analyzed their tests and quizzes, in the factoring unit, to see how they handled negative signs, while working on Algebra skills.

I gave students a worksheet on multiplying and dividing integers at the beginning of my research, after completing the exercises on number lines, and after completing the real world applications. On the graph, 0 is the beginning worksheet, 1 is after number lines, and 2 is after real world applications.