a) name and write fractions and mixed numbers represented by a model 

b) represent fractions and mixed numbers, with models and symbols 

In the interview that I had with my CT, she said that he can identify improper fractions and mixed numbers with a picture, and another strength is identifying it in both forms on a number line. She says that he struggles actually changing the fraction from an improper fraction into a mixed number and vice versa.

2. Homework
After reviewing his homework assignment on changing improper fractions to mixed numbers and vice versa, and representing that fraction, I found that there is no specific error pattern. He received a 52% this homework assignment. It seems as if he has no conceptual knowledge of how to change improper fractions to mixed numbers and vice versa. There is no consistency in the errors. 

3. Student Interview
After I conducted my interview with PJ, I found that there is still no specific error pattern. To change an improper fraction into a mixed number he has no conceptual or procedural knowledge of changing the fraction. For changing and mixed number into an improper fraction, he has some sort of procedural knowledge with multiplying the whole number and denominator but doesn’t know what to do after that.

o  The student will use cut-out manipulatives to represent the improper fraction or mixed number

o  The student will use a white board to write out his thinking process, change between fractions, and draw representations of the fractions.

Student Engagement

o  Using fractions in everyday life. 

o  Making up his own improper fraction and mixed numbers

Expression of Understanding 

o  The student will use cut-out fraction circles to show their understanding of improper and mixed numbers.

o  The student will use a white board to show their procedural understanding.

 

There were a few things that worked really well in my lessons and I continued to use throughout. One thing that worked in my lessons was that I started each session reviewing what we learned in the last one, that way all of the information is being refreshed in his mind and he can build off of that information in the next lesson. I broke up the lessons in a scaffolding way so that each new lesson builds off of the last. I would also start teaching new content by asking him what he already knew about it. That way I could go off of whatever his prior knowledge was. By using cut-out fraction circles, he was able to work hands on and visually see the representations of the improper fractions or mixed number. Another thing that worked in my lessons was when I allowed him to come up with his own improper fraction or mixed numbers when doing example problems. He really liked it when I gave him that choice and I continued to use it throughout the lessons. Lastly, when I saw that he wasn’t understanding something, I would go back and re-explain and model again. I would ask him “how” or “why” questions throughout the learning process to get him to think on higher levels.

His overall progress shows that he did master the content taught in the tutoring sessions. On the pre-assessment homework sheet on improper and mixed numbers he received an 11/21, which is equal to a 52%. I gave him an exit ticket to complete individually each day to assess what he learned during that session. There were 4 questions each exit ticket and he got all of them right each day. My objective was for him to get 3 out of 4 correct, and he exceeded that getting 4 out of 4 correct each day. The post assessment was given on the 5^thday and was a cumulation of all the content that was taught over the 4 days of tutoring. He also got all of the questions correct on that assessment. The intervention with PJ was a smooth and successful experience, and I’m confident that he now has the conceptual and procedural knowledge of improper and mixed numbers and how to interchange them.