CCSM Reflection

I really liked this project. Starting I was nervous and overwhelmed, since I have not really worked with the standards in-depth. After completing this it has made me more comfortable and intrigued with the standards. We worked with attend to precision and look for and make use of structures. I am a lot more comfortable with attend to precision since that is the one I focused on more but I am also comfortable with make use of structures. By working closely with certain standards it makes them more real and usable. It also encourages a calmness about looking into the other standards more in-depth.

It should be expected at this time since we have done group work so often in this major but it never ceases to amaze me to see the different ideas and viewpoints of other people. It was nice sitting with the other students to hear their perspectives, ideas and how they chose to set up their presentation. Through this process we got to see what everyone thought as important and how they interpreted the standards. 

Journal Summary: Constructing Meaning: Standards for Mathematical Practice

Teachers at an institute discussed the Standards for Mathematical Practice (SMP). At the institute they talked about what they liked, didn't like, understood and needed more clarification. Stephens and Barlow look into SMP 2, 4, 7, and 8. For SMP 2 teachers noted this to be the one to make the least amount of sense. They wanted clarification. This standard is "reason abstractly and quantitatively." Teachers wanted a better interpretation for abstract. The teacher came up with the words contextualize and decontextualize when discussing reasoning abstractly. The meaning for SMP 4, "model with mathematics," can be taken and used in two different ways. The first is modeling mathematics, which is using manipulatives, graphs, and pictures to help represent the problems being done. The next is modeling with mathematics, the way I had not really thought about the standard, using mathematics to solve the problems of everyday lives, society, and the environment. Finally, at the institute teachers mention having a hard time distinguishing between SMP 7 and SMP 8. SMP 7 is "look of and make use of structure" while SMP 8 is "look for and express regularity in repeated reasoning." I can see where it is hard to distinguish the two or not understand why we have two SMPs for the same idea. A teacher at the institute says SMP 7 is "exploitation of structure within a problem" while SMP 8 is "exploitation of structure across problems." When I first read this I was so confused but now it makes sense. In one problem the student can grasp the concept/pattern and then later in a more complicated problem they can use that concept in a different way.

I really enjoyed this article because it helps see the standards in a different way. This provided an opportunity to hear insight on the standards, issues, and explanations. I didn't think of some of these topics the way they were presented so it really helped me in that aspect.




http://www.nctm.org/Publications/teaching-children-mathematics/2015/Vol21/Issue6/Constructing-Meaning_-Standards-for-Mathematical-Practice/

Journal Summary: Fracking: Drilling into Math and Social Justice

Katie A. Hendrickson wanted to use a real-life example when teaching her class mathematics to go along with the focus of Common Core Standards for School Mathematics. This goes with using real-life examples. Where she teaches the issue of fracking is on the rise because land there has been found where fracking can be done. She goes on to explain tracking, extracting natural gas from the Earth. The biggest issue of using this topic is because it is a "hot topic" for where they live and controversial. Hendrickson's choice of fracking is an awesome idea because it gets the students thinking about a topic that is close to them and let's them form their own opinions and understand the process.

Next she talks about how she taught the subject. She starts with having the  students basically do a "plug and chug" sheet of formulas using percentages. Once she sees this is flawed she moved the work to be inquiry based. I absolutely loved this idea and seeing it used in real-life. I struggle with making inquiry based lessons so it's motivating to see an example. The students got to come up with ideas, research, and cut down their lists to having only math questions. The student got to modify their questions as they went and as needed.

I think this whole project would be so motivating for students because it is an issue that is something they know about, in their lives, they get to come up with their own math equations and questions, and present their findings to the class. I really loved this article and the ideas presented in it.


http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/2015/Vol20/Issue6/Fracking_-Drilling-into-Math-and-Social-Justice/

Word Problem Clues Video

The Word Problem Clues with Tracy Lewis was really insightful. I was not too sure about what to expect when starting the videos (and seeing that there were nine to watch)! As soon as I started finishing video after video I was intrigued with the meeting, lesson, classroom, and debriefing. I love that the teacher assigned the work and then evaluated it. Having the students sit down and discuss the work done in a positive environment is motivational. I think this makes them comfortable to answer questions and ask them. It also shows the students various ways to think about answer problems, maybe differently than they did, and it shows the common mistakes and how to fix them or think differently. I think they were on the carpet a long time but the students seemed to handle it well. In the debriefing she mentions running out of time. I almost wonder if it would have been better to do an addition example one day on the carpet and then a subtraction example the next day to really focus on the students getting the vocabulary. 

Tracy talks about different types of vocabulary the students are to use or "codes." This goes with the standard of precision I think..or maybe I am just focused on that because it is one my group is doing. BUT the students now knowing "how many more" is code of subtraction is an example of miscommunication or misunderstanding of their tools. This is a challenge for students especially at a younger age just starting word problems. The students learned tools to add and subtract, such as through pictures, number lines, or base 10 blocks, now they have to reach into their toolboxes to decide which is being asked for without being told. 

I like that in the faculty debriefing the teacher got to talk about what she would do differently and what she wished for and liked. I really liked the whole set up though of having the students do the work, working as a group to discuss and ask questions, then working in pairs. I think the teacher does an amazing job of switching the group sizes and going from guided practice to independent. Even having the students look at their work but not be able to erase it was awesome because the students get to reflect, write it down, and then assess themselves. Since I only worked with four and five year olds it is hard for me to imagine young students being able to self-correct. Even thinking about second graders doing it seems hard for me but this is proof that they can and the method used was wonderful. 

I loved the videos overall. I think it was a wonderful demonstration of lots of frameworks and models we are being taught now. We saw the discussions, the one-on-one, partner work, assessing the work and the teaching. It yeps motivate me to see these tactics we are being taught actually happen. 

Disappearing Act - Tina Cardone's Article

This article "Disappearing Act" demonstrates the use of precision in the classroom. In the article, the author stresses the importance of describing which operations to use when. The author is emphasizing the importance of teachers using the correct terminology when we are changing numbers and processes. When we switch up the terms "cancel" and "reduce" the students will be confused. Instead the students and teachers should use the operation necessary. The author talks about students using precise language when identifying what types of fractions. Cardone mainly focuses on fractions but I think it is important to remember with other functions in math using correct terms and making sure the students know what they mean.

Link to article: http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Disappearing-Act/ 

Mathematical Standards and Points of Importance

Mathematical Standards

1.     Make sense of problems and persevere in solving them

a.     Making sense and putting meaning to the problem

b.     Planning ways to come up with a way to start the problem

c.      Doing similar problems using the same strategy/plan

d.     Being able to explain/make sense of all the data and figures

e.     Can check the problem’s answer using a different method

2.     Reason abstractly and quantitatively

a.     Being able to demonstrate the problem with symbols, manipulate and rearrange them to get the answer needed

b.     Creating the representation

                                               i.     Quantities for each symbol

                                              ii.     Understanding what means what

3.     Construct viable arguments and critique reasoning of others

a.     Being able to see which arguments are correct and which are flawed

b.     Using manipulates to support their argument

                                               i.     Drawings, objects, charts, etc.

c.      Making sense of others arguments and knowing if they make sense

d.     Being able to ask questions

4.     Model with mathematics

a.     Using real life examples to solve the problem or applying the problem to real life examples

                                               i.     Knowing what type of equations/mathematical domain can be used where

b.     Making situations practical and applying quantities

c.      Making sense of the problem and improving models when needed

5.     Use appropriate tools strategically

a.     Being able to select the proper tools needed to solve the problem

                                               i.     Knowing what to use when

b.     Being able to research to figure out what is needed to solve the problem

                                               i.     Technology tools

6.     Attend to precision

a.     Communicating their reasoning clearly and able to explain definitions of symbols and definitions

b.     Units of measurement is written or expressed

7.     Look for and make use of structure

a.     Recognizing patterns

b.     Using the various properties appropriately

c.      Change perspective being used to view/work on the problem

8.     Look for and express regularity in repeated reasoning

a.     Noting repetition

                                               i.     Looking for shortcuts

b.     Noticing patterns and applying those findings on the reset of the problem