Content Standards

The two main areas that were not covered in the textbooks that I found was solving inequalities at a 6^th grade level and graphing systems of equations at an 8^th grade level. Both of these concepts would be on the more difficult end of the curriculum for the grade level but should be included in the textbooks so that the teachers can correlate their units to the Common Core Standards while using the textbook. It is also important that the teachers challenge their students with new or more demanding material, specifically those students that may be above grade level in mathematics.

From kindergarten through 5th grade, it seems that most areas were covered in the textbooks that my peers located. Also, the curriculum seems to build from year to year quite well. Review is incorporated but the material also becomes more difficult as the student advances, as it should. The textbooks seem to mirror this growth and include information covering most of the Common Core Standards in these younger grade levels. However, one area that some of the textbooks seemed to fall short was including real world applications and a large amount of word problems compared to mostly straight computational problems.

Problem/Project Reflection

This assignment was very enjoyable to me and I think that I gained some valuable practice in planning and developing a great student project. After my group and I came up with our initial idea, we were able to make a five day plan that encompassed all of the material that would be needed to complete the project. I think that having the students do a project is an awesome way to have them apply material over many different math topics. Any time that math can be applied to a real life situation brings more excitement and appeal to the students so they will be more likely to remember what they have learned and take that information onto their next grade or even in their own lives. It was fun for me to work with my group to expand our idea and add details to make it like a real project that I could use someday!  

Error Analysis Reflection

Our work with decoding student work and deciphering what errors they were making in their work was a surprisingly difficult yet constructive task. Sometimes it was very challenging to figure out what mistake the student was making or the misconception they had, so it was good practice for us future teachers to analyze the various student work. However, that is only the first step. Next we will need to know what we can do to help the student to correct these errors and understand the topic. In class, we discussed how to accomplish this which I thought was a very beneficial conversation, It got me thinking about how in mathematics it is important for the teacher to allow room for multiple ways of solving a problem so that each student has a method in which the information clicks and so that they can be successful.

Assessments in Math Reflection

This class truly opened my eyes to a multitude of ways to assess mathematics that I had not previously experienced. One main facet in the math classroom that can be used as a form of informal assessment that I had not thought would be an important part of learning math is discussion. Whether it contains the whole class, small groups, or student pairs, allowing the students to communicate their ideas and listen to the suggestions of their peers is an important step in helping them to fully understand a concept. When it comes to more of a formal assessment, I think that mathematics tends to fall in the routine of paper and pencil testing. However, this class let me see that students can be even more thoroughly assessed through completing a project or solving a question that has multiple parts where the student is required to justify their answers as part of their evaluation. In class, we were even assessed in many ways such as through blogging, individual and group projects, as well as an interview. I am confident that I now have the knowledge and ability to continue to create authentic assessments for my future students as I have been doing throughout this class.  

Technology in Math Class Reflection

Technology is clearly an enormous aspect in today's classroom and will continue to expand and evolve as time goes by so it is important to continually integrate the use of various technologies in the classroom. In this class, I think that sharing Smart Board skills was a beneficial task for everyone. I not only learned more by presenting an ability of the board but learned many new skills from my peers as well. Also, the video aspects required for a couple of our group projects as well as my portfolio challenged me to broaden my normal skill set for presenting material and I specifically became more familiar with Jing. Lastly, our assignment that focused on finding and experimenting with math apps and applets was very useful to me. I found many programs that would have a strong purpose in my future classroom. due to their content and the fact that students enjoy working with technology.

Manipulative Reflection

Allowing students to work hands-on while learning gives them use of another sense that will be geared toward the learning experience besides just listening and watching the teacher. It will make the material they are learning more memorable as well as give them a visualization that they can refer back to when solving a problem. If the students are able to use manipulatives to obtain an answer to a question, it usually means that they have grasped the entire concept, not simply memorized an algorithm. The students will then also be able to apply their ability to draw representations to solve other problems which relates directly back to them practicing with the manipulatives.

Always requiring students to justify their work will allow the teacher to see if the use of manipulatives was helpful or influenced the student's reasoning behind solving a particular problem. Also, when students work in groups, it is important for each student to individually turn in a completed task so that they get practice writing down the steps or creating justifications for the answer that the group reached. The teacher needs to make sure to observe the students during group work to ensure that all members are participating and gaining valuable knowledge while working with their peers.

Curriculum Plan Reflection

I think that this assignment required me to apply many skills that I will be needed in my future career. Planning one lesson or even a unit is a task that I have completed numerous times but compiling a whole plan for one year, let alone three years was a whole other challenge. It forced us to work as a group to come up with creative ways to meet all the math standards from grades 6 to 8. I was proud of my group and I for our ability to use our resources and previous knowledge to come up with some great ideas for quarter and semester long projects for our students. Being able to work with a group and cooperate is an important life skill and will definitely apply to my teaching career as well so I was glad that we were able to collaborate throughout the whole process. Also, since these were standards that we had previously worked with for our Lesson Segment Assignment, all of our work fit together nicely and we were sort of experts in each of our designated math topics. Creating the video presentation was the aspect that I was most worried about, however I felt that it was an effective way to deliver our plan and our video ended up working out just fine. This assignment was a valuable experience and gave me a taste for how much work I can look forward to when I have a class of my own!