CCSSM Standards Project Reflection

I found this project to be overwhelming in the beginning. Once we started working on it and breaking the project into smaller chunks it was less stressful. I liked how we were able to look up articles with teaching activities that coordinated with our standard. This helped me understand what the standard was really getting at. I also liked how we presented the standards in a jigsaw style. This way everyone in the class was able to gain from the research each group did.

Classroom Based Formative Assessments Article Reflection

The authors of this article discussed five base assessments that should be mixed in to math classrooms. The five formative assessments are: Observation, interview, show me, hinge question, and exit tasks. The first three, observation, interview and show me are assessments that are done during the day or lesson, whereas the last two, hinge question and exit tasks are done at the end of the lesson to assess the daily knowledge. I really like this idea of mixing up the assessments in math with using these five assessment tools. I think the show me is a great assessment. This is basically an assessment where students have to demonstrate how they are able to arrive at the answer to the problem. With math, teachers sometimes think that the only forms of assessment comes though quizzes and tests. This short article is a nice reminder that there are many ways to assess mathematics.

Video 1 Reflection

Planning:

I liked how the teachers, principal, and the math coach all sat down together to discuss how they were going to take notes from the lesson Ms. Lewis was about to teach. This meeting allowed everyone to be on the same page so they knew the expectations on how they are supposed to interact with the students and what the key ideas they want to take note of. Ms. Lewis and the math coach had planned out a lesson that re-teaches problem solving with the use of addition and subtraction. I liked their plan of going over poster examples as a whole class and then letting the students reflect on their work they had previously done and make any corrections or additions to their work after discussing the example problems.

 
Lesson:

Ms. Lewis started with the example posters with the students sitting up front on the rug. I thought this was good information and instruction, however it did not follow their plan of action and not many of the posters were covered since too much time was spent on the first one. Some of the same students kept participating, which is good. However, it would have been nice to see more overall participation from the whole class during the whole group poster activity. Ms. Lewis strayed from the plan when students got their work back. They had planned to only have the students work on 3 and 4 individually or to verbally say what they were doing. Teachers and observers were not supposed to interact in a way to aid or give answers. The small clip shown of the math coach showed her interacting with the student to understand their thought process, but she did not help the student or say whether their process was right or wrong. Ms. Lewis was helping a student through one of the problems, which wasn't part of the lesson plan.


Debrief:

I thought Ms. Lewis's reflection was spot on. She recognized that she took too much time in the beginning and was only able to get to a few of the posters. She also recognized that the lesson as a whole was not as she had planned. I like how they explained the rest of the posters that were not shown during the lesson so that the observers were then aware of what additional resources the intended lesson was supposed to be.
 

Overall:

I thought this video provided a nice example of how teachers collaborate and how they continually try to improve their teaching methods to help their students. I have already done my novice teaching experience and I can definitely relate to how the plan and actual lesson were different! No matter how much you plan and prepare for a lesson, you never know what may throw off the pace of the lesson. Students were struggling with the first poster, so Ms. Lewis spent more time on this than she had intended. I thought she did a great job adapting the lesson on the go. When teachers realize their students are not getting a topic, they need to step back and adjust the lesson plan from what they had initially planned. Same with if students are easily getting the topic, teachers can adjust the speed so that students move through the material at an appropriate rate.

Preserving Pelicans Article Reflection

The teacher in this article had discovered something many math teachers find out. She realized her students lacked the connection of mathematics to the 'real' world. She discovered there was a U.S. Fish and Wildlife organization that let students help them receive data. The teacher used this opportunity to teach an MEA or model-eliciting activity. These activities align with the common core for mathematics when it comes to problem solving. By connecting this math common core activity with a pelican colony research students were interested and engaged in this new math project. Students had to calculate the amount of pelicans in an area of nesting located on a map. Students were allowed time to brainstorm as a large class group and then as individuals. Students decided to use a square grid to calculate the area. When squares were only partially filled, they would cut out that area and move it to fill up a whole square. By using the modeling activity students were able to successfully show their understanding for the common core math standard that requires students to solve math problems related to realistic contexts.

I thought this was a great way to engage the students and get them excited about mathematics. Connecting the animal aspect would make the students want to solve the math problem even more because they can see how math can apply to real world ideas.

Articles that Relate to CCSSM Standards of Mathematical Practice 1 & 2

The first article I found corresponds with the first standard: Make sense of problems and persevere in solving them. The article is Quick Reads: Problem Solving with Laser Precision by Scott A. Goldthrop, published in Mathematics Teaching in the Middle School.

In this article, Scott explains how his students are given a problem and must find out a way to solve it. Students are divided up into small groups and are given a few tools to help them solve the problem. Two of the activities referenced in the article were to solve how high flags were in the gymnasium with the use of a mirror, ruler, and a laser pointer, and to determine the width of a soccer goal with only a paper towel roll, ruler, and trundle. These two activities definitely relate back to standard 1 because the students are having to plan out what they want to do and have to do some problem solving to get to their answer.

I thought these were great activities for a middle school classroom. In the beginning of the article the author discusses how with modern technology, students' attention spans are shrinking and students can readily gain information such as equations or formulas. He wanted his students to really grasp the concepts of mathematics, so he made his lessons more inquiry based and discussion based so students would be more likely to remember what they had learned.

I definitely agree with this. It will do students no good to just memorize formulas and to plug numbers into formulas to solve problem after problem on worksheets. With the use of technology, students would easily be able to look up a formula within seconds. I believe it is more valuable to teach students problem solving skills because these skills will be used every day for the rest of their lives. Using inquiry for students to learn concepts will allow students to become creative and discover on their own how to come to the solution. When classrooms are student centered, students are discovering about the topic on their own or in small groups by collaborating with others. When classrooms are more student centered, students will retain the information longer because they had discovered information on their own instead of just being given a formula. As a teacher, I want my students to retain as much information as possible as well as leave my classroom with various problem solving skills that they can use for the rest of their lives.

Goldthorp, S. A. (2013). Quick reads: Problem solving with laser precision.
     Mathematics Teaching in the Middle School, 19(2). Retrieved from
     http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/2013/
     Vol19/Issue2/Quick-Reads_-Problem-Solving-with-Laser-Precision/

The second article I found corresponds with the second standard: Reason abstractly and quantitatively. The article is Develop Reasoning Through Pictorial Representation by Wendy P. Ruchti and Cory A. Bennett, published in Mathematics Teaching in the Middle School.

In this article, the authors discuss the importance of using pictures to represent student work. They explain how it is much easier to follow a student's train of thought by looking at pictures of how they went about solving a problem. The pictures allow the teacher to see their students' problem solving techniques. This way teachers will be able to find where a student is struggling as well as see the different ways students approached the problem. Not only is this technique helpful for teachers, but it is also helpful for students. Drawing out pictures allows students to visually see the problem. If the problem is more of an abstract idea, the picture will allow the students to create a visual to help them understand what is going on in the problem.

I am a visual learner, so I find drawing pictures to be extremely helpful. I liked the problems presented within the article because they showed the student work examples of different ways to go about solving the problem. This is also a strategy that can be used at a wide range of grades. Teaching students as young as kindergarten students to draw when problem solving will only increase their ability and creativity in problem solving down the road.

Ruchti, W. P., & Bennett, C. A. (2013). Develop reasoning through pictorial
     representation. Mathematics teaching in the middle school, 19(1), 31-36.
     Retrieved from http://www.nctm.org/Publications/
     mathematics-teaching-in-middle-school/2013/Vol19/Issue1/
     Develop-Reasoning-through-Pictorial-Representations/

Important Points about CCSSM Standards for Mathematical Practice

The first standard I researched was: To make sense of problems and persevere in solving them.
Here are some main points:

• It is important for students to gain and implement problem solving skills when it comes to mathematics. Instead of getting a math problem and jumping right into trying to solve it, this standard works towards students learning to understand the problem and to choose an approach that logically makes sense.
• Once the student solves the problem, students are to choose a different approach to check their answer. This shows students that there are many different ways to approach a problem and to still come to the same conclusions.
• This kind of mathematic problem solving will really show whether the student knows the topics well because the students must understand the different topics and be able to implement them in different situations.
• In this checking process, students are able to take a step back and look at their work. Students are then able to see whether or not their work answers the question or whether or not their answer makes sense.

The second standard I looked into was: Research abstractly and quantitatively.
Here are some main points:

• Students often struggle when it comes to thinking about abstract mathematical problems. The problem often lies in their ability to visualize what they are trying to solve.
• To overcome this, the standard wants students to use manipulatives and pictures to help symbolize these abstract ideas so the students are able to understand the problem and what they need to do in order to solve.
• Students should also be able to think quantitatively, or with numbers. For this portion, students will learn and will be able to understand the various units used to label numbers, convert from one unit to another, and understand what the number value is telling the students about the problem.