The pre-assessment and the post-assesment were both graded the same way. Each question was worth 1 point, the pre-assessment, being out of 3, and the post-assessment being out of 5. Students were not able to receive half credit on any question. The students either answered the question with the proper steps of PEMDAS and had the correct computation for each part or they did not. Even if they did the order of the PEMDAS model correctly, yet had their arithmetic wrong, then their whole answer was wrong and received a 0. The opposite was also true, even if students did PEMDAS wrong, but completed their wrong lines of thinking with correct computation, they still received a 0. The standard is looking to see whether or not students understood that there was a particular order to do operations in math and which order to do them in. If they cannot demonstrate the were able to do so in the problem, then it was wrong. Additionally, students were able to use a small calculator with basic mathematical functions on both the pre and post, so I do not think computational errors were acceptable and thus did not receive partial credit for using the order of operations correctly. Students were able to use their calculator to check their work and even compute addition, multiplication, subtraction and division operations. Only 100% accuracy on each question was acceptable.

To further assess whether students were on track to achieving the goals and objectives I outlined I consistently used formative assessments.

Formative assessments that I used were worksheets. Students were given homework and once they were turned in I graded them on the same 0 or 1 point scale per question with no partial points. I would return all my students work within a day or two. Because I returned all my students' work I really do not have many examples of their original work. This formative assessment was really helpful to see where students were, but the downside was that students could have copied another students' work or students just might not turn it in (which is what a couple students did).

Additionally, I used exit cards a couple times. Each exit card I asked students if there was something they still found confusing and something they really like or understood well. Names on the exit cards were also not required so students would not feel embarrassed if they did not understand a particular concept. Students were really specific in telling me what they did not understand so I made sure that I addressed their point of confusion to the whole class.

Another formative assessment I did was warm-ups at the beginning of every class. I went around and stamped the piece of paper they did their warm-ups on so it held them accountable for doing them. They received a stamp based on effort and were required to correct their work. At the end of the 6 week grading period, my supervising teacher reviews all their stamps and gives them a grade. The warm-up questions reviewed concepts from previous lessons so when I stamped warm-ups I could gage which students were struggling with a particular concept and which students got it. The warm-ups were the most useful formative assessment. Students knew they had to work quietly and on their own and because they were graded on participation students really had no inclination to copy another's work. The warm-up questions typically related to the previous lesson's objective.