Re-teach Reflection

     In previous classes we have talked a lot about how it is important to adjust your teaching methods to best fit your students. This assignment was the first time I have actually taken a student work sample and applied this concept. It was difficult, but after we finished it was easy to see how you can use what your students do and do not understand to better your ability to teach them. It is important to look at students individually and as a whole so you can see where certain students may be struggling vs. where there may be holes in your teaching methods. It is just as much of a learning experience for us to teach our students as it is for our students to learn what we are trying to teach them.

Error Reflection

     Throughout this course we have talked a lot about how making math more inquiry based we can learn more about what students know because the responses we expect leave room for more explanation. In fact, explanation is encouraged and essential in most if not all inquiry based assignments. We have talked about how we know what students are grasping by looking at their correct answers and explanations. However, after completing the NAEP assignment and the reteach assignment based on the 14 error problems I think that there is more to be learned about individual student knowledge based on what they are doing wrong. If a student grasps a concept and can maneuver their way through it that is great. When they can't, if we have them explain their reasoning we can better understand exactly where they are going wrong. We can better understand how they are processing what we are telling them. This gives us a starting point as to how we can begin to explain things in a way that each student will better understand. I think that the error analysis is more beneficial and useful to us and in the end to the students as well.

Curriculum Plan Reflection

     This was by far the most stressful and difficult assignment in this course. It was a challenge to consider how each and every content area for a grade band fits into one another and how you might choose to teach each one. When you are trying to write individual lesson plans on a specific topic it can sometimes be difficult to know what to include and what to leave out. However, after completing this assignment it gives me a better idea of how lesson planning will go when I have an actual teaching position. I think that it will be much easier, not only in math but in all content areas, to lesson plan when you have at least a general idea of how the entire year will play out. Not only knowing what students need to cover on a yearly basis, but knowing what they have covered and what you are leading them up to will aid in a better understanding of what you need to cover specifically. This project gave me a glimpse of what it takes to plan for students learning long term and how important it is to communicate with teachers at all grade levels to know what they are covering as well.

Assessment Reflection

     In this class we have talked about assessment a lot. What it means, different types, how to create quality assessments, and how to assess ourselves. Without assessment how would we really know what we are learning? Assessment is a very important part of the learning process. When we assess we can learn how to improve ourselves, what our students are grasping, and what we need to work harder at, as teachers,  to help our students improve. In order to achieve all of these we must create quality and useful assessments. The NAEP project really helped me to see how difficult it can be to assess all students equally if you are not using a quality rubric. All students think differently  and may arrive at an answer to a problem differently, but we have to have a way to score their understandings. I like rubrics, I think that you can assess just about anything with them, but they are very difficult to create.

Classroom Changes Reflection

     I have to say the the CCSS-M SMP's and the NCTM Process Standards were very intimidating at first. It was a lot of information to look at and digest all at the same time. Once we, as a class, really looked at what each of the standards meant and clarified any misunderstandings it made them all much less intimidating. I think that we have had ample opportunity in this class to work with the standards and actually apply them with assignments like our lesson segments. Just like with anything else the more practice you have working with something the easier it will become and the more comfortable you will get with it. I think that I still have a little bit of practice ahead of me before I am really good at working with these standards, but I have no doubt that one day I will know these standards backwards and forwards without batting an eye to think about it.
     Another big change I have seen in the math curriculum is the push for less traditional methods of teaching math. The CCSS-M and NCTM Process Standards most definitely lean in favor of this as well. Students are expected to answer more open-ended questions and be able to explain their reasoning behind things rather then simply being able to complete a process or plug numbers into a formula. They must know how and why they are doing things. With the NAEP project and reading various article throughout the semester I think that this is going to be a definite struggle for me to teach students math in this way. Creating an all encompassing rubric that works the same on all answers, which may be completely different,  for the open-ended problems that are called for now also seems to be an impossible task.

Technology Reflection

     If I didn't have my computer as a college student it would seem nearly impossible to complete anything. On top of that we always have our phones in our hands or the tv on or some sort of technology we are using for most of the day. It seems essential to our daily function now a days. Technology has been incorporated into many different subjects throughout my schooling days, but when I thought about math I always thought about using a pencil and paper. In this class not only are we learning about how to use technology to teach math with things like the smart board, apps, and  applets, but we are also using technology to learn about teaching math. We have watched various videos and used this blog to reflect on our ideas. I am seeing the use of technology as a more beneficial aid to student learning, even in math, than I ever did before. I think that it can enhance the learning experience and offers a variety of ways to assist students in learning math.

Manipulative Reflection

     I really liked the in class activity we did to help us brainstorm various different ways that we can use different manipulatives. As educators we often have to be creative and get kids involved without spending a lot or any money at all on resources. By having us switch stations and keep thinking about what each manipulative could be used for I think that it helped us to come up with some really useful ways to use the different manipulatives. It was about making the tools as versatile as we can. 

     I think that you can tell a student really grasps something when they can use the manipulatives to show you a concept and explain it to you thoroughly while they are doing so. When they use the manipulatives as a tool for explanation you know they are really benefitting the child and helping them understand a concept in a more concrete way. Because of their deeper understanding through the use of the manipulative I think that students can more easily transfer concepts into other situation or domains. I think that one of the most beneficial ways to assess students is through observation and conversation. If you can watch what a student is doing when they are trying to learn and also talk about their processes with them you gain more useful knowledge about what they know. I think that if you talk to students individually to assess them even when they are working in groups on various concepts you can more accurately assess what they know and understand. You are improving a students problem solving skills by using manipulatives because you are giving them another tool they can use to solve the problem they are working on or the concept they are trying to understand.