This project really served to help me learn a lot more about the standards. Our group worked the closest with the standards of Attend to Precision and Look for and Make Use of Structure. Sure, doing the initial research on these standards was beneficial, but I think I learned the most about them in depth when we made our presentations and really got into discussing them together as a group. This also helped me to look at the standards as more of a usable structure instead of just reading through them without full understanding.
Since I was not in class on the day of presentations, I went back and listened to the Prezis and Jings from home. It was very interesting to see how the other groups went about presenting their particular standard, and especially interesting to see what individuals had to say about each one. This is why I love the idea of presenting our work whenever we do some in depth research; it gives us the opportunity to understand how others are interpreting our group work.
Sunday, May 31, 2015
Thursday, May 28, 2015
A Blizzard of Value
This article begins with the teacher talking about the background for why she decided to use this idea for problem/project. She had seen many of her students over a break at their local Dairy Queen, and she came up with the question: Which Blizzard size is the best value? Working with this problem, her students were given the opportunity to work on modeling with mathematics. NCTM also mentioned that this task "supports learning mathematics content, promotes engagement in mathematical practices, and fosters mathematical communication among students." To begin the problem, students in the class came to the conclusion that they think the large Blizzard would be the best value, based on prior experience. The class self-selected groups of 3 or 4, and the teacher distributed the problem:
Students went about the problem using different approaches. For example: some students used a graph to model the mathematical elements. Other students used pictures to show their calculations of the diameter of the bottoms of each sized cup. Lastly, other students created a "tabular" approach and made a table including each element of all sizes of Blizzards to compare and contrast. The teacher here was able to remind students, then, that there could be many different ways to go about figuring out the problem and problems similar to this.
I would love to use a problem like this in my classroom because it ties in so many good aspects together. For one, it would be great to use this problem or something similar because the students will be able to connect to it very well and realize that it is a real life situation that they might come across. Another great reason this would be useful in class is the fact that you can show many different ways to figure out the problem that all students will be able to try and find the best way for them.
I would love to use a problem like this in my classroom because it ties in so many good aspects together. For one, it would be great to use this problem or something similar because the students will be able to connect to it very well and realize that it is a real life situation that they might come across. Another great reason this would be useful in class is the fact that you can show many different ways to figure out the problem that all students will be able to try and find the best way for them.
Word Problem Clues Video
I loved the first clip of this video right from the start. I think it was great that they pulled together a group of so many educators to discuss a common issue this second grade teacher was seeing in her classroom. I thought this was a good process to go through to get more insight into what the teacher's thinking process was while coming up with this reengagement lesson, and it will also benefit everyone in the end because they will be able to give her more feedback after the lesson is completed.
What I really liked about how the beginning of the lesson was going was how she had larger examples on posters of some of the students' work to show the students as they sat down in front of them. This way, the students were able to see many different ways that other students figured out the word problems. The only thing that I didn't like about this part of the lesson was that I think Ms. Lewis did spend a little too much time on the previous examples and it was sometimes unorganized discussion with the students about each problem. If she would have organized this section a little more, there would have been more time at the end for the students to be correcting their papers and talking with their classmates.
Another thing that I really liked was how Ms. Lewis constantly encouraged the students to use correct vocabulary when speaking about the word problems. We can see this connect back to the standard of Attending to Precision, where the goal is to be able to use and understand correct mathematics vocabulary and be able to communicate your work clearly to others.
The final debriefing section was a wonderful way for Ms. Lewis to reflect on her lesson and talk with the group about what she thought went well, and what she would have liked to have done differently. The ending clip here also brought to my attention how affective only watching this series of video clips was. It brought to my attention the many ways that we can get students involved in learning math processes as an entire class in the way that they shared with partners and discussed different strategies. It also brought to my attention that even the younger students can learn to self-correct and are able to explain their thought process when given the opportunity.
What I really liked about how the beginning of the lesson was going was how she had larger examples on posters of some of the students' work to show the students as they sat down in front of them. This way, the students were able to see many different ways that other students figured out the word problems. The only thing that I didn't like about this part of the lesson was that I think Ms. Lewis did spend a little too much time on the previous examples and it was sometimes unorganized discussion with the students about each problem. If she would have organized this section a little more, there would have been more time at the end for the students to be correcting their papers and talking with their classmates.
Another thing that I really liked was how Ms. Lewis constantly encouraged the students to use correct vocabulary when speaking about the word problems. We can see this connect back to the standard of Attending to Precision, where the goal is to be able to use and understand correct mathematics vocabulary and be able to communicate your work clearly to others.
The final debriefing section was a wonderful way for Ms. Lewis to reflect on her lesson and talk with the group about what she thought went well, and what she would have liked to have done differently. The ending clip here also brought to my attention how affective only watching this series of video clips was. It brought to my attention the many ways that we can get students involved in learning math processes as an entire class in the way that they shared with partners and discussed different strategies. It also brought to my attention that even the younger students can learn to self-correct and are able to explain their thought process when given the opportunity.
Thursday, May 21, 2015
CCSSM Article: Standards of Mathematical Practice 6 & 7
The article that I found in the NCTM Journals really helps to explain some of what our standard, Attend to Precision, is all about. The title of the article is The Language of Mathematics, and can be found here: http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol21/Issue9/The-Language-of-Mathematics/.
Bruun, F., Diaz, J., & Dykes, V. (2015). The Language of Mathematics. Teaching Children
Mathematics, 21(9). Retrieved from http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol21/Issue9/The-Language-of-Mathematics/
Right from the beginning, this article starts to explain the importance of learning how to communicate Mathematics, and the struggle it poses to learn how since the learning of this is largely limited to school. "Principles and Standards for School Mathematics (NCTM 2000, p. 60) states that students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in math classes benefit because 'they communicate to learn mathematics, and they learn to communicate mathematically,' which helps children be successful in math class" (Bruun, et al. 2015). This is the statement that really sparked my interest in following along with the rest of the article to see that it really goes hand in hand with the communication aspect of attending to precision.
We then get to see how two graduate students use two different methods to teach math vocabulary to their 4th grade students. Method 1 was all about using journal writing and peer discussion. The journals allow students to explain their thought processes and make connections. They could share their journals to check for accuracy as well as to provide an aid for working through meanings of words. Method 2 focused on the modified Frayer model. Putting graphic organizers to use, students have the opportunity here to employ the reading strategy of visualization and drawing pictures of the math vocabulary, which should ultimately help them to better understand and connect with the text/vocabulary.
After reading about these 2 different methods, the article gives us some examples of visuals we would see the students complete using the modified Frayer model. It is noted that the graphic organizers took students no more than 20 minutes to complete, and, in my opinion, this method has the opportunity to work wonders in the classroom. It gives all students a chance to learn the material in there own way since it connects visual, oral, and hands-on learning.
In the end, after research had been conducted, it was confirmed that both of the graduate students' methods had a positive effect in the classroom. Students had learned and developed a conceptual understanding of the math vocabulary.
Bruun, F., Diaz, J., & Dykes, V. (2015). The Language of Mathematics. Teaching Children
Mathematics, 21(9). Retrieved from http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol21/Issue9/The-Language-of-Mathematics/
Right from the beginning, this article starts to explain the importance of learning how to communicate Mathematics, and the struggle it poses to learn how since the learning of this is largely limited to school. "Principles and Standards for School Mathematics (NCTM 2000, p. 60) states that students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in math classes benefit because 'they communicate to learn mathematics, and they learn to communicate mathematically,' which helps children be successful in math class" (Bruun, et al. 2015). This is the statement that really sparked my interest in following along with the rest of the article to see that it really goes hand in hand with the communication aspect of attending to precision.
We then get to see how two graduate students use two different methods to teach math vocabulary to their 4th grade students. Method 1 was all about using journal writing and peer discussion. The journals allow students to explain their thought processes and make connections. They could share their journals to check for accuracy as well as to provide an aid for working through meanings of words. Method 2 focused on the modified Frayer model. Putting graphic organizers to use, students have the opportunity here to employ the reading strategy of visualization and drawing pictures of the math vocabulary, which should ultimately help them to better understand and connect with the text/vocabulary.
After reading about these 2 different methods, the article gives us some examples of visuals we would see the students complete using the modified Frayer model. It is noted that the graphic organizers took students no more than 20 minutes to complete, and, in my opinion, this method has the opportunity to work wonders in the classroom. It gives all students a chance to learn the material in there own way since it connects visual, oral, and hands-on learning.
In the end, after research had been conducted, it was confirmed that both of the graduate students' methods had a positive effect in the classroom. Students had learned and developed a conceptual understanding of the math vocabulary.
Standards
While reading through the CCSSM Standards, I mostly focused on Attend to Precision and Look for and Make Use of Structure, as those were the two main standards my group would be working with. There were two main points from Attend to Precision that really stuck out to me. One was how important it is for students to be able to communicate their work to other students/colleagues. The second most important part of this standard was seeing how communicating work should vary through grade levels. For example, younger students should be able to state clear definitions and meanings, while older students should then be able to examine these claims and use them explicitly. There were also two important factors that stuck out to me from Look for and Make Use of Structure. One was how even younger students can start to realize that their is structure in their mathematics. For example, if a student's flashcard had the problem 3+4=7, they can also realize that 7-4=3. Secondly, with older students, they can begin to visualize the structure in more advanced algebraic equations, making it ultimately easier for them to begin and end a problem with many different components.
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