Personal Learning Path

 Being that this week we were to take a look at the case studies, I realized that I still did not fully understand the difference between procedural and conceptual knowledge in the context of mathematics. I took the opportunity to learn more about procedural and conceptual knowledge and found some examples that helped me to better understand the difference so that I could complete the case studies to the best of my ability. Below is a resource that I found to help me to differentiate between the two.  Procedural refers to the series of steps used to solve the problem whereas conceptual refers to the reasoning as to why operations work the way that they do.  It is important that math is taught in both contexts. Without procedural knowledge, students will not know the series of steps needed to complete a problem. Without conceptual knowledge, they will not know why they are using those steps and how those steps are meant to help. This means that they will not be able to exp...

 As we all know, fractions, even in their simplest form, are difficult to understand. There are a lot of components that go into understanding fractions. Recently, my class has started to compare inequivalent fractions on a number line. My co-tecaher and I have tried showing it on 2 number lines on on top of the other since the students had a difficult time figuring out how to partition one number line 2 different ways. It was apparent that the students were still not comprehending what to do and how to do it so we had to try another way. Today we took a lot of time using colored pencils to help the students try and visualize how to partition one number line 2 ways with 2 different colors. Although this seemed to help some more students grasp the idea, I still feel that more practice needs to be done. We always take the time to annotate the directions and objectives in a way that supports the students learning. Below is an image of the worksheet we worked on today and how the color...

The math concept game I intended to create was a board game. The game includes three different board faces that indicate three different levels of concept understanding. The board with the most amount of spaces is intended for those students with a greater understanding of the math concept whereas the board with the least amount of spaces should be given to the students who do not have a great understanding of the concept yet/ still. What is great about the board is that it can be used to teach any mathematical concept as long as you create questions to coincide with it. I created the board game questions so that they reflect the current topic of fractions for my third grade class. Although I have not yet had a chance to implement the game in the classroom, I look forward to doing so in the near future. Instructions for a teacher: The game requires two or more players. Groups should be 2-3 students depending on how many students are present the day the game is played. These groups shou...

 After observing how fractions were introduced to the students this past week and a half, there are still some students who are struggling to understand the concept of unit fraction versus fractions of a whole. This made me wonder what can we do to scaffold these concepts so that it does not become repetitive and boring for those students who understand the concepts, but still allows for concept development for those who do not understand.  I feel as though it is important to find the balance between extending and scaffolding learning for all students. By ensuring that learning math is fun and easy, students are more likely tp stay engaged and learn the concepts.  I have found a game for the students who do not understand fractions as well as others. This can be done as a guided lesson for those students to further their understanding of equal parts as fractions.  https://www.education.com/game/seashell-look-a-book/ A way to differentiate this for the students have a...

 This week, we began to introduce fractions to the students. My initial thought when talking with the cooperating teacher before we began was to use the example of a pizza pie. I remember learning fractions in the concept of circles so that was the first thing that came to mind. Almost immediately, the teacher turned to me and said "Although that sounds fun in theory, my advice is that you never introduce fractions by using circles. When it comes to partitioning a circle, it is far more difficult to do and for the students to comprehend than using a rectangle/ square model." This was something that really resonated with me because I would have never thought about it that way if it weren't for her telling me. I liked the idea of the pizza because it is something that is relative to them and engaging. In order to keep it fun and engaging to the students, I decided to use the rectangle models in the context of candy bars. The cooperating teacher had them use manipulatives th...