My Weekly Report and Reflection 4

          This week's math class was a beneficial one for me as I learned about interleaving practice and creating rich performance tasks. It is very easy to get caught up in the idea that a math class must be organized into neatly packaged blocks that teach students a concept and then has them performing tasks related to said content. After that information has been ingrained into each student the teacher will give an assessment that relates to that idea. The issue with this approach is that it doesn't leave room for students to make decisions about the strategies they will use to solve the problem. They already know that they will be using a particular set of operations to find the solution. Interleaving practice helps teachers to overcome that stale form of instruction. Interleaving practice involves the instruction of more than one concept at a time and then requires students to decide what kind of strategies need to be used to solve the problem. They will already have all of the tools necessary to address both content areas but will need to take that learning one step further as they ask themselves questions about what is being asked of them and which operations are needed to find a solution. In class I discussed the idea of teaching students the content areas of perimeter and area and having them solve problems that relate to both concepts. Our instructor felt as though this would be an appropriate form of interleaving. As I left the class I continued to think about this issue and was reminded of my past experiences teaching these two concepts to grade 4 students. Perimeter was one that they grasped fairly well, however, area took a lot more finessing to achieve a deeper level of understanding. In this regard I think it is important for educators to perform lots of formative assessments as they teach these two concept areas so that they have enough evidence of learning to determine whether or not their students are ready for an interleaving assessment. Creating rich performance tasks for students in both content areas can give educators the information they need to make that judgment call.

           Rich performance tasks are ones that allow students to ask questions, leads to other problems and has many possibilities. Much like the decision making process involved in interleaving practice, rich performance tasks encourage students to ask themselves questions about what the problem is asking them to do. I experienced this in today's class as we were given two mixed fractions: 3 1/4 and 3 31/9. The question asked us to find three other mixed fractions that fit in-between these two given mixed fractions. Right away I was asking myself what needed to be done here and how was I going to determine which three mixed fractions fit in the middle. I immediately turned to decimals so that I could give myself a range. Once I had that I needed to fool around with some other fractions to find if their decimal equivalents fit within my range. It was interesting to see how this kind of question had other possibilities as well. Some students decided to make common denominators to figure out the improper fractions that would fit in-between the original mixed fractions. These improper fractions could then be turned into mixed fractions and I was again reminded about some of the operations that I had forgotten since high school.

(Dekker, 2016)

          Later we expanded on that idea by using various repeating decimals to figure out what fractions would be their equivalents (without using Google's search engine). These problems had me intrigued and I first struggled with figuring them out. After some trial and error I was able to figure out how to get the correct answer and I started to think about what kinds of real-world applications that could be used to create rich performance tasks that have students asking questions about this kind of content area. Fractions have always been a difficult subject area for me as I have mentioned in previous posts and I'm still wondering and interested about ways that I can incorporate these kinds of problems into my classroom to help students work with fraction problem solving.