CCSSM Project Reflection

At first, upon looking at the directions and talking about the project briefly in class I was very confused and somewhat worried about the amount of work. However, once we began to work on it, I felt much better and was relieved by how simple it was once broken down. I found this project to be very useful. I was completely unfamiliar with the standards for mathematical practice, so it was a great opportunity to learn something completely new.  The standards we focused on were standards six and seven. I now feel very comfortable with those two standards. I think that our group did a good job and we worked well together.

I thought that it was a great idea for each of the groups to share their projects with each other. However, I think that there may have been a better way to go about it in order to help the audience to retain the information. I think that even just having the individuals go through the presentations verbally rather than watching the videos would have helped. However, I do think that I have a much better idea of what the standards are than I had previously.

Journal Reflection- Constructing Meaning

Constructing Meaning: Standards for Mathematical Practice

D. Christopher Stephens, and Angela T. Barlow 

 

Stephens, Christopher D. & Barlow, Angela, T. (2015). Constructing meaning: standards for mathematical practice. Teaching Children Mathematics. (21,6).

 

The main idea of this article was to clarify the standards for mathematical practice. During a conference focused upon the common core math standards, it become evident that there was a lot of misunderstandings and confusion about the standards for mathematical practice amongst teachers. The article discusses the practice standards 2, 4, 7, and 8 and how they should be used. The article gave examples of problems and what teachers should look for in the student responses. 

This article is important for teachers of all grade levels to read. The standards for mathematical practice are overwhelming and confusing at first, and this article helps to alleviate some of that confusion. Teachers who are unsure of how to evaluate whether the standards are being reached will benefit from reading this article. This shows many examples of problems and what to look for within the problems.

Journal Summary- Going with the Flow

Going with the Flow: Challenging Students to Make Assumptions

Mathew D. Felton, Cynthia O. Anhalt, and Ricardo Cortez 

 

Felton, Mathew D., Anhalt, Cynthia O., Cortez, Ricardo. (2015).  Going with the flow: challenging students to make assumptions. Mathematics Teaching in the Middle School. (20, 6).

 

This  article mainly focuses on the concept of modeling mathematics problems. The article talks about a unit which was made for pre-service teachers to discuss using modeling.  Many students think that modeling just means drawing pictures, using manipulatives, making graphs, etc. This is not exactly true, modeling is a process which includes many steps. According to the CCSSM, these steps inclue; making sense of the problem, determining what information is needed, coming up with a solution, interpreting results, determining if the solution makes sense, and reporting the solution. The example given in the article is about water conservation. The problem is to determine whether baths or showers conserve more water. In order to solve this problem, the student would have to work through the whole process of modeling. 

I think that this article is helpful for teachers. Prior to reading it, I also shared the assumption that modeling could be as simple as just drawing a picture under your work. This is something important that teachers need to have an understanding of. Mathematics teachers will be able to include real-world type problems and examples of how to model them. This will help their students to understand and follow the process.

Video Blog #1- 2nd Grade Word Problems

I found these video to be very interesting. I thought it was really impressive that a group of educators were putting so much time and thought into just one math lesson. It was clear to me that the teacher would do almost anything to help the students succeed. She had a clear desire to understand the way the students were thinking and to understand how to help them improve. I think that the basis for the lesson was well planned and useful. It is important for teachers to be able to pinpoint the places where students are struggling so that they can adjust their teaching to fit the needs of the students.

I really enjoyed the way the lesson was set up. I think that it was beneficial for the students to discuss the various ways of solving problems 1 & 2 together as a whole class. I think that it may have been helpful to only have one problem on each poster page. I noticed that during the discussion, students were kind of going back and forth between the two problems on each page, which may have caused slight confusion.Giving the students the opportunity to see different ways in which their peers have solved the problems was a great idea. I think this opened the students' eyes as to how to clearly explain their own work so that others can understand it.

My favorite part of the lesson was when the students had the opportunity to change their previous work. It was a good idea for the teacher to make copies of the work so that nothing could be erased. It was very smart of the teacher to also not discuss problems 3 & 4 as a class, but still have the students adjust their answers if they thought they needed to. This will allow the teacher to see how much the students have gained from the lesson and whether they fully understand how to improve their work.

Overall, I thought the video was interesting and eye opening. It is interesting to see how much thought and work goes into planning what from the outside may seem like just a simple lesson.

Journal Article: Reason Why When You Invert and Multiply

In the article "Reason Why When You Invert and Multiply", Tina Cardone discusses the importance of children understanding why inverting and multiplying is used when dividing fractions. This relates to the mathematical practice #7 about making use of structure. Students must understand the structure division and fractions separately first, before applying them together. The author discusses various way to go about dividing fractions. Her examples include both dividing whole numbers by fractions as well as dividing fractions by fractions. After one example Cardone (2015) says,  "In this case, students discover that multiplying by the reciprocal is the equivalent of getting the common denominator and dividing the numerators." This clearly relates to mathematical practice #7 because it shows the need for students to use and understand math structures. Students tend to just memorize rules and strategies, but that is not always helpful to their learning. Many rules are forgotten or misinterpreted as students move through their math career. Understanding structure will help them to achieve higher.

Cardone, Tina. (2015). Reason why when you invert and multiply. Mathematics Teaching in the Middle School. 

Important Notes about the Standards

The standards in mathematical practice are the eight important skills that math teachers are working to help their students develop. These are not the standards themselves, but through using the standards, these practices will be developed. Mathematical practice #6 is to attend to precision. This means that students must work carefully and be able to communicate findings with correct detail. Students must develop the skills to know what degree of precision is needed and when. For example, when talking about the number of chips in a bag, that can be a rough estimate. However, talking about the amount of weight a bridge can hold must be relatively precise. Mathematical practice #7 is to look for and make use of structure. This is very important because students must be able to make connections between different topics and ideas. When they are able to make these connections, they will gain a deeper understanding of the concepts.