Curriculum Plan Reflection

Even though this project was quite intense, I really enjoyed it. This is something I have to get used to doing because I will some day be teaching middle school math. It was amazing to have the opportunity to work with two other math concentrations to work on yearly plans for 6-8th grade because we all have had more math training and we were able to share and hear about different ideas. For me, the most difficult part of this project was getting the video to work. I was having technology troubles with my video program so that added unnecessary stress to the project. I thought all three of us worked really well together throughout the entire project of planning, creating projects, and filming the video. I liked the opportunity we had to watch all three groups' videos. I thought it was interesting on how different each of the groups interpreted the assignment, as all three were very different. Again, as a math concentration, I was interested in seeing the other groups' papers so that I could gain ideas of math activities so that if I end up teaching at a lower level in elementary I will still have a variety of activities I could use that are age appropriate in my classroom. Out of all the projects, this was the most beneficial because once we begin teaching, we have to know how to create a yearly, quarterly, and then more detailed plan for our curriculum.

Classroom

There have been many changes to a math classroom in Illinois lately. With the recent introduction of the Common Core Standards, to also having Common Core SMP standards, and NCTM standards it can be intimidating how many standards teachers need to be aware of when teaching math. The Common Core State Standard - Standard Math Practice or SMPs are eight different standards that teachers should be aware of and have included into their math activities. These 8 standards are: Make sense of problems and persevere through solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model in mathematics, use tools strategically, attend to precision, look for and make use of structure, and lastly, look for and express regularity in reasoning.
There are 4 NCTM standards for math. When I was in middle school, it didn't matter how we came to the answer, as long as we got to the correct answer. The NCTM standards as well as the SMPs want the students to explain their thinking and reasoning and justify as to why their solution is correct. These standards make students who are more aware of their math abilities and know how to problem solve. Even if students get an incorrect solution, they can look back at their work and reasoning to see where they ran into a problem. The NCTM standards are: Reasoning and proof, communication, connections, and representation.
Even though I can see people having difficulty in changing the structure of their class to meet all of these standards, I am glad that when I began my education at Bradley that the common core standards were already created. This way my whole teacher education training has been done using the same sets of standards. Now I have been given the time to really become familiar with these standards before I have to be responsible in teaching them to my students. This will prepare me best when going into my own classroom once I graduate with my teaching license.

Technology

Technology in the classroom is always changing. I remember having chalkboards in the classroom when I was in early elementary. Then we switched to whiteboards. I also remember having the giant carts with overhead projectors and the clear transparencies teachers used to write on. Now classrooms are equipped with electronic white boards, regular whiteboards, ELMO projectors (digital version of the overhead projectors), tablets, smart response remotes, and computers. There are so many ways teachers can use technology to engage their students and to make learning fun. Even if schools don't have the funds to have all of the technology styles out there for their classrooms, I think the most useful are computers, smart boards, and the ELMO projector. The ELMO projector is a digital camera that displays whatever is placed in the view of the camera onto the smart board. This is very useful when demonstrating how to complete a task on a recording sheet, or when reading a word problem passage together. There are many different ways to utilize the smart board. Students love coming up to the front of the room to get a chance to use the board. This is definitely a great tool to use in any classroom. I would definitely use as many technology tools as I can for my math class. There are amazing apps and applets teachers can use in the classroom on the smart board, computers, or tablets. These provide new and fun ways for students to learn the math curriculum.

Manipulative Reflection

How do you know students deepen their understanding while using manipulatives?

• Students can deepen their understanding using manipulatives because the students are hands on and involved in the process of learning. When students are actually able to create and represent objects using manipulatives, they are able to visually see the process and are better able to understand the math concept.

How do you know if the students can transfer their understanding from manipulatives to other situations?

• I will know if a student is able to transfer their understanding by having open class discussions. Students will discuss and compare and contrast different ideas that came up during the manipulative session. Listening to the student led discussion will allow me to see if the students were able to take away information from the activity. I could then have the students split up into groups and see if they could solve a real world problem utilizing their knowledge from the manipulative activity.

 

How can you assess that understanding or growth?

• I could lead a class discussion about the topic, then let the students work with the manipulatives, and then have a closing discussion. This way I can see what thoughts and ideas existed before and after the manipulative activity to see what growth was acquired from the manipulatives.

 

When students work in groups, how do you hold each youngster accountable for learning?

• I would assign roles to each student in a group (recorder, directions, and two people using the manipulatives). Then every few minutes I would rotate the roles. This way each student has the opportunity to be hands on with the manipulatives, give ideas and directions as to how to use the manipulatives, as well as listen and record the group member's ideas. By setting these roles, each student has a job to do within the group. This was each student is accountable to learning and participating within the activity.

 

When students work in groups, how do you assess each youngster’s depth of understanding?

• I could assess their depth of understanding informally by listening to each group as they work together. I could also assess more formally by having the students submit a reflection assessment as well as answer a few questions regarding the topic covered by the manipulative activity.

Assessments in Math Reflection

Assessments in math can come in all different varieties, just like assessment in any other subject. I remember in middle school we would have daily assessment grades on our homework. In high school we would have homework checks for completion, however homework was a learning tool so we weren't counted off if we had the problem wrong. We were supposed to learn from our mistakes so we could be successful on the tests and quizzes.

In math methods we have learned many more assessment styles and tools other than homework grades, quizzes, and tests. There is a big push for switching classrooms over to inquiry based learning. This learning style is best assessed by a rubric. In methods we have learned about the importance of a strong rubric that isn't biased and the level on the rubric should be clear. I think performance based assessments and portfolio assessments are a great way to assess students. Performance based allows students to take the knowledge of the topic and apply it to a real world situation. Portfolio assessments allow students to see the physical growth of their learning by collecting various assignments throughout the semester or year. These assignments are much more meaningful to students because they are applying what they have learned. The traditional tests and quizzes are also of value, however these mainly assess memorization and don't represent the depth of knowledge a student may have when compared to all the levels of Bloom's Taxonomy.

In my classroom I want to have a variety of assessments for mathematics. Many students get discouraged in a math class, and with allowing students to see the connections of math to the real world, they will have a much better appreciation for the subject.

Error Reflection

In class we explored different math problems done by students. Each student modeled a different error within solving the problem. Since I am a math concentration, I find this really interesting. I enjoyed looking at each student's work and analyzing it for where they made a mistake. This is something I will have to be comfortable with when I begin teaching math whether it is at the middle school level or at the elementary level.
I thought this assignment was very similar to the NAEP reteach assignment. The only difference was that the NAEP assignment all students were solving the same problem, whereas this assignment each student was solving a different problem.

Assessment Readings

Open-Ended: This article talks about using open-ended problems to assess math students' work. I like this idea, because with the many possible solutions to the problem, students may think outside the box to find a strategy to solve the problem. Open-ended problems allow teachers to see the students thinking process and allows them to help the students where they struggle.

Options: This article talks about the different ways math can be assessed. This is often referred to as the menu choice. This article mentions how even though multiple choice may be an okay assessment, performance assessments with accurate rubrics are a much better tool to assess whether or not a student is able to apply the information in a real life situation.

Reasoning: This article is about students' ability to problem solve in mathematics. The teacher in the article had students explain what area was in their own words. This allowed the teacher to see what each student was thinking and how they were able to think or reason throughout the problem based on what the student wrote.

 Conversation: This article discusses the importance of assessing student conversations. In the example used in the article, a teacher was able to understand that the students didn't know the properties of rectangles. Then the teacher was able to do an impromptu lesson on what is considered a rectangle before moving on with the area lesson. I think assessing conversations is a great way to assess vocabulary terms. This way teachers will know if students know the correct terms and the teachers are able to clarify to make the topic more clear.

Portfolio: This article is about a teacher implementing the use of portfolios in her classroom. Portfolios are an important tool that allow teachers as well as students and parents to see the mathematical growth of the child. I love this idea of having a folder where the student can reflect back on their work. I also liked how this teacher used a certain criteria to assess the portfolio so that this was a project that encouraged the students in mathematics, instead of discouraging them.