Shape Sorter (Grades 6-8)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=34
The shape sorter was created for students in sixth through eighth grade. Students need to sort all the shapes in the Venn diagram. The Venn diagram is where the individual compares two things using two circles that overlap each other. The section where they overlap is where the put the characteristics that are the same for the two things that you are comparing. In this case, the student can choose two rules when working with shapes and then sort the shapes based upon the rules. This activity was very easy to understand because the directions were very clear and there was an example of how the program worked. This is an effective program because the students can choose the rules they want to sort the shapes. Overall, I thought this was an amazing Math Applet. I really liked it, and thought that it was very creative how the students choose what they work on. It was easy to understand and used visual presentation well.
I thought this was a great program because it can be used during any part of the unit when learning about shapes and different characteristics of shapes. This could be an introductory lesson or a lesson used at the end of the unit. This would also be great if there is a class where students are at different levels of understanding. The reason behind this is the fact that the students get to choose the rule they want to work on and sort the shapes. Due to this, it allows a lot of growth for students. Students can have a variety, so students won't feel like they are doing the same activity over and over.
Saturday, September 18, 2010
Math Applet Review One
Cubes (Grades 3-5)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=6
This applet is mainly aimed for third to fifth graders learning about geometry and how to calculate volume of a cube, using mathematical terms such as width, depth, and height. The students first start off by having a five 2-D squares that are different colors and three different size cubes, these 2-D squares are 5x3. There is a single cube, a rod of five cubes, and a flat that covers the surface of the 5x3 squares. At the bottom of the screen there is a chart that lists the measurements whenever you add a cube, rod, or a flat. Using these three cube sizes the students would need to determine what the volume is using these cubes. Once the students finish this box, they can click, "change box" and begin working on another box pattern. I don't think this applet was that effective, and I also thought it was more confusing. The directions given were somewhat vague, and didn't really express how to figure out what the volume was. If a student didn't know how to calculate volume, I can see students becoming frustrated with not exactly knowing how to do this problem.
Something I do like while using this applet, is that each side of the square is color coded, and when you add the cubes, they are automatically match the colors alike. This distinction helps students realize how tall each layer is, and how it matches up to a one of the 2-D sides. I also like how there is a chart that is keeping track of how many cubes are the student has added. Another pro, is that there are many different examples to work on, so this can reinforce the idea of finding volume in a third to fifth grade classroom.
Overall, I believe this is a good start to a nice program, but the directions need to be clarified, because they are unclear of what the student needs to do. Once the directions are written more clear with possibly an example or two, I believe students will get more out of this activity because they will be able to understand the purpose of it.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=6
This applet is mainly aimed for third to fifth graders learning about geometry and how to calculate volume of a cube, using mathematical terms such as width, depth, and height. The students first start off by having a five 2-D squares that are different colors and three different size cubes, these 2-D squares are 5x3. There is a single cube, a rod of five cubes, and a flat that covers the surface of the 5x3 squares. At the bottom of the screen there is a chart that lists the measurements whenever you add a cube, rod, or a flat. Using these three cube sizes the students would need to determine what the volume is using these cubes. Once the students finish this box, they can click, "change box" and begin working on another box pattern. I don't think this applet was that effective, and I also thought it was more confusing. The directions given were somewhat vague, and didn't really express how to figure out what the volume was. If a student didn't know how to calculate volume, I can see students becoming frustrated with not exactly knowing how to do this problem.
Something I do like while using this applet, is that each side of the square is color coded, and when you add the cubes, they are automatically match the colors alike. This distinction helps students realize how tall each layer is, and how it matches up to a one of the 2-D sides. I also like how there is a chart that is keeping track of how many cubes are the student has added. Another pro, is that there are many different examples to work on, so this can reinforce the idea of finding volume in a third to fifth grade classroom.
Overall, I believe this is a good start to a nice program, but the directions need to be clarified, because they are unclear of what the student needs to do. Once the directions are written more clear with possibly an example or two, I believe students will get more out of this activity because they will be able to understand the purpose of it.
Wednesday, September 15, 2010
Mathematics Teaching in the Middle School Journal Article
Moyer, T.O. (2010). Keeping all the trains on the tracks. Mathematics Teaching in the Middle School, (16)2, 116-121.
Keeping All the Trains on the Tracks
This article begins by explaining how a popular formula, distance=rate x time is commonly taught (and hopefully learned) in an eighth grade mathematics classroom. The author, a teacher explains how the approaches from the textbook typically do not "hook" or get the students attention right away, which there for is a struggle throughout the whole unit. The teacher then explains to the students how this works and gives students "real life" examples. She then sets up the equations and as a class they solve the problems. At this point, the teacher is still explaining the purpose of this and how the equation works. The article continues explaining how having a visual helps many students, and a way to adapt this into a math classroom is to design a chart, or program the equation into a graphing calculator, plug in the data, and then see the line graph that is created from the data. This is a great tool to adopt into a math classroom because it benefits the "visual," "listening," and "do-er" learning. The student has to listen to hear the instructions from the teacher, the students are physically putting in the data, and then the visual of the chart quickly appears on the screen.
I really like this article because it was so "user friendly." The author gave out very clear directions of how to teach this lesson. I also liked how the author included two activities directly related to this topic. This definitely helps teachers, especially new ones to get ideas of how to teach this in a creative and fun way. One thing I know I need to be cautious about if I ever do teach mathematics is to not rely too much on the calculator. It is an excellent tool to have and students should become familiar with a graphing calculator, the only issue is that I would not want students to become so dependent on the calculator that they can only complete math problems using a calculator.
Keeping All the Trains on the Tracks
This article begins by explaining how a popular formula, distance=rate x time is commonly taught (and hopefully learned) in an eighth grade mathematics classroom. The author, a teacher explains how the approaches from the textbook typically do not "hook" or get the students attention right away, which there for is a struggle throughout the whole unit. The teacher then explains to the students how this works and gives students "real life" examples. She then sets up the equations and as a class they solve the problems. At this point, the teacher is still explaining the purpose of this and how the equation works. The article continues explaining how having a visual helps many students, and a way to adapt this into a math classroom is to design a chart, or program the equation into a graphing calculator, plug in the data, and then see the line graph that is created from the data. This is a great tool to adopt into a math classroom because it benefits the "visual," "listening," and "do-er" learning. The student has to listen to hear the instructions from the teacher, the students are physically putting in the data, and then the visual of the chart quickly appears on the screen.
I really like this article because it was so "user friendly." The author gave out very clear directions of how to teach this lesson. I also liked how the author included two activities directly related to this topic. This definitely helps teachers, especially new ones to get ideas of how to teach this in a creative and fun way. One thing I know I need to be cautious about if I ever do teach mathematics is to not rely too much on the calculator. It is an excellent tool to have and students should become familiar with a graphing calculator, the only issue is that I would not want students to become so dependent on the calculator that they can only complete math problems using a calculator.
Tuesday, September 14, 2010
Teaching Children Mathematics Journal Article
Young, E. (2010). Probability: a whale of a tale. Teaching Children Mathematics, 17(2), 106-112.
Probablilty: A Whale of a Tale
This article was a breeze to read due to the creative lessons described in this article. This study took place in two Title I third grade classrooms. The study consisted of introducing probability in both classrooms in a very nontraditional way, and seeing if it was more effective than the a more traditional way of practicing with endless amount of problems. The article first began by explaining that both classrooms introduced the topic of probability by reading a novel typically used in an English class. The title of the book is "Dear Mr. Blueberry." The reason this book was chosen was because of the vocabulary that was introduced and how it led to such a great discussion on how likely it was; based on the terms: likely, highly likely, not very likely, or impossible. The teacher then made a line chart where the students would have to put their term deciding if having a whale in the backyard would be likely or impossible. After a discussion, students were given new sentences and had to place their probability sentences next to the words that best described them. Students also had to draw pictures and write one sentence that were likely, certian, unlikely or impossible. Teachers would then display the pictures around the classroom after the group discussion. Another activity is having students match the sentences and the pictures together. Having creative activities help students learn the material in a fun and non stressful environment. The author concluded the article with another lesson plan with dice and having students roll the dice and predicting the sum of the dice.
I really enjoyed this article a lot because I thought the lesson plans were very orginial and authentic. Learning probability can be an intimidating topic because it can be difficult judging if something is likely or highly likely to happen. Having many ways of introducing this article will help students realize what the vocabulary terms mean and become more comfortable with using the terms. I also really enjoyed how the math classroom integrated a novel into the classroom. As a student, I always wanted to know how something applies to my life, and bringing in a book and having the teacher explain that todays lesson will directly correlate with this novel would be such a neat way to introduce a new math topic.
Probablilty: A Whale of a Tale
This article was a breeze to read due to the creative lessons described in this article. This study took place in two Title I third grade classrooms. The study consisted of introducing probability in both classrooms in a very nontraditional way, and seeing if it was more effective than the a more traditional way of practicing with endless amount of problems. The article first began by explaining that both classrooms introduced the topic of probability by reading a novel typically used in an English class. The title of the book is "Dear Mr. Blueberry." The reason this book was chosen was because of the vocabulary that was introduced and how it led to such a great discussion on how likely it was; based on the terms: likely, highly likely, not very likely, or impossible. The teacher then made a line chart where the students would have to put their term deciding if having a whale in the backyard would be likely or impossible. After a discussion, students were given new sentences and had to place their probability sentences next to the words that best described them. Students also had to draw pictures and write one sentence that were likely, certian, unlikely or impossible. Teachers would then display the pictures around the classroom after the group discussion. Another activity is having students match the sentences and the pictures together. Having creative activities help students learn the material in a fun and non stressful environment. The author concluded the article with another lesson plan with dice and having students roll the dice and predicting the sum of the dice.
I really enjoyed this article a lot because I thought the lesson plans were very orginial and authentic. Learning probability can be an intimidating topic because it can be difficult judging if something is likely or highly likely to happen. Having many ways of introducing this article will help students realize what the vocabulary terms mean and become more comfortable with using the terms. I also really enjoyed how the math classroom integrated a novel into the classroom. As a student, I always wanted to know how something applies to my life, and bringing in a book and having the teacher explain that todays lesson will directly correlate with this novel would be such a neat way to introduce a new math topic.
Tuesday, September 7, 2010
Sample PBL Reviews
1. Lounging Around: A PBL Unit for Students in Grades 7-8
This PBL unit was mainly focused on working on geometry, algebra, measurement, data analysis and probability, numbers and operations. The scenario was that, at West Wood Middle School the principal wants to create a lounge for the 7th and 8th graders. The principal has allowed all the students to make a layout, and he will choose one of the designs. The principal has given limitations to what needs to the lounge, the only thing the students need to be conscientious about is staying within the budget. Some of the strengths for this PBL is that it is very organized and the standards are grade appropriate and match up to the objectives. I also thought the mini lessons were detailed and were easy to follow. Something I thought that could have been improved was having a few of the activities relate to the general idea of creating a lounge or something that is important to 7th and 8th graders. A specific example of this is Exploring Proportions Activity with the beans. It was a pretty general activity so I thought they group could have done something more interesting to middle school students, such as the ratio between different brands of shoes. Overall, I thought this was a fabulous PBL because of the creative lessons with clear directions and how this lesson was based upon the math standards and objectives.
2.Operation "Redo the Zoo" A PBL Unit for Students in Grades 5th-6th
This PBL unit was directed for students in the 5th and 6th grade. The students were going to take a field trip to the zoo, and observe the strengths and weaknesses of the zoo and things they wanted to change or add onto the zoo. They are then suppose to design a floor plan of different exhibits they wanted at the newly modified zoo. Something I really enjoyed about this PBL is that they within the groups of four students they are assigned a job role. This is a nice benefit because this way each student feels needed and a vital part of the group. During the adolescent years it is an important job for teachers to ensure that all of the students feel needed. Something that I thought this group could have improved on was having more detailed explanations. For example when it was the Higher Order Thinking portion, the group could have given specific examples of how students were going to improve their skills of analysis, synthesis, evaluation, and reflection. Overall, I thought this was a creative concept and if I was assigned this activity as a 5th or 6th grader I would have stayed intrigued in the topic.
3. Compare and Contrast the two PBLs
Both of the PBLs were interesting and it was evident that both groups spent lots of time completing this assignment. I personally liked the first PBL I reviewed because I thought the directions were more clear and there were more examples. Having said this I think the first PBL I reviewed is a better representation of what a PBL is suppose to look like. However, it was great how both PBLs incorporated technology into their unit plans, and being a Special Education major I really enjoyed reading the creative accommodations both PBLs had.
This PBL unit was mainly focused on working on geometry, algebra, measurement, data analysis and probability, numbers and operations. The scenario was that, at West Wood Middle School the principal wants to create a lounge for the 7th and 8th graders. The principal has allowed all the students to make a layout, and he will choose one of the designs. The principal has given limitations to what needs to the lounge, the only thing the students need to be conscientious about is staying within the budget. Some of the strengths for this PBL is that it is very organized and the standards are grade appropriate and match up to the objectives. I also thought the mini lessons were detailed and were easy to follow. Something I thought that could have been improved was having a few of the activities relate to the general idea of creating a lounge or something that is important to 7th and 8th graders. A specific example of this is Exploring Proportions Activity with the beans. It was a pretty general activity so I thought they group could have done something more interesting to middle school students, such as the ratio between different brands of shoes. Overall, I thought this was a fabulous PBL because of the creative lessons with clear directions and how this lesson was based upon the math standards and objectives.
2.Operation "Redo the Zoo" A PBL Unit for Students in Grades 5th-6th
This PBL unit was directed for students in the 5th and 6th grade. The students were going to take a field trip to the zoo, and observe the strengths and weaknesses of the zoo and things they wanted to change or add onto the zoo. They are then suppose to design a floor plan of different exhibits they wanted at the newly modified zoo. Something I really enjoyed about this PBL is that they within the groups of four students they are assigned a job role. This is a nice benefit because this way each student feels needed and a vital part of the group. During the adolescent years it is an important job for teachers to ensure that all of the students feel needed. Something that I thought this group could have improved on was having more detailed explanations. For example when it was the Higher Order Thinking portion, the group could have given specific examples of how students were going to improve their skills of analysis, synthesis, evaluation, and reflection. Overall, I thought this was a creative concept and if I was assigned this activity as a 5th or 6th grader I would have stayed intrigued in the topic.
3. Compare and Contrast the two PBLs
Both of the PBLs were interesting and it was evident that both groups spent lots of time completing this assignment. I personally liked the first PBL I reviewed because I thought the directions were more clear and there were more examples. Having said this I think the first PBL I reviewed is a better representation of what a PBL is suppose to look like. However, it was great how both PBLs incorporated technology into their unit plans, and being a Special Education major I really enjoyed reading the creative accommodations both PBLs had.
PBL Journal Review
This article was introducing what a Problem Based Learning assignment is, and the benefits of such an assignment. The author stressed that these types of problems are important because they improve students problem solving skills and challenges their higher order thinking, while combining previous knowledge while working on a long term project. The author believes that the teacher needs to teach the material in the PBL beforehand, and the PBL should then be a creative approach to ensure that the students know the material and can apply it to real world situations or challenges. The author then continued on to say that PBL assignments improve test grades because while completing a PBL, the teacher should be more focused on the process of getting the answer and how the students came to find the answer. While completing a more typical assignment;such as an exam, students are more focused on finding the correct answer, and may not know exactly how to do that. Studies show that students educated in the traditional content-based learning environments exhibit lower achievement both on standardized tests and on project tests dealing with realistic situations than students who learn through a project-based approach. (Roh, 2003) The article concludes by explaining the teachers role, and how the teacher needs to guide students in their knowledge and need to encourage students to use their problem solving skills to discover the answer.
I thought this was a very beneficial article; because the author explained what the expectations are of a PBL and backed up their main points with specific results from previous studies. My favorite part of the journal is how the author connected the PBL experience with the NCTM Process Standards. This helps the reader justify why this is an important teaching strategy and why they should implement this into their classroom. The author believed the main point or lesson that should be learned through completing a PBL in a mathematics classroom is giving students a new challenge, while connecting the real world to the mathematics classroom. One of the weaknesses that I picked up from introducing the PBL into your classroom is the change of character the role is of the teacher. Instead of introducing or teaching, the teacher now needs to play more of encouraging role in the classroom. The author recommends that the teacher does not give out any knowledge while completing the PBL, instead the teacher needs to keep the students encouraged and focused. This new job in the classroom can be very difficult for some teachers, and may be the reason some teachers may not try this in their classroom.
Roh, K.H. (2003). Problem-based learning in mathematics. (Eric's Digest).
http://www.ericdigests.org/2004-3/math.html
*There wasn't a volume number or issue number for this journal article.
I thought this was a very beneficial article; because the author explained what the expectations are of a PBL and backed up their main points with specific results from previous studies. My favorite part of the journal is how the author connected the PBL experience with the NCTM Process Standards. This helps the reader justify why this is an important teaching strategy and why they should implement this into their classroom. The author believed the main point or lesson that should be learned through completing a PBL in a mathematics classroom is giving students a new challenge, while connecting the real world to the mathematics classroom. One of the weaknesses that I picked up from introducing the PBL into your classroom is the change of character the role is of the teacher. Instead of introducing or teaching, the teacher now needs to play more of encouraging role in the classroom. The author recommends that the teacher does not give out any knowledge while completing the PBL, instead the teacher needs to keep the students encouraged and focused. This new job in the classroom can be very difficult for some teachers, and may be the reason some teachers may not try this in their classroom.
Roh, K.H. (2003). Problem-based learning in mathematics. (Eric's Digest).
http://www.ericdigests.org/2004-3/math.html
*There wasn't a volume number or issue number for this journal article.
Problem Based Learning (PBL) Readings
According to the readings, a Problem Based Learning experience, or commonly referred as a PBL is a hands on, in depth group project where students are given a challenging question that has many parts to solve. The question requires students to use past knowledge and use resources to solve the question, and the answer doesn't align just an equation. The question needs to be based on the real world, developmentally appropriate, and needs to be able to relate to the students interests. The teacher needs to give students time to work on the PBL collaboratively, but parts of the PBL need to be split up so students work independently. While students are working on a PBL, the teacher is suppose to have more of a mentor or coach role. The teacher is there to answer questions students may have, but not lead a group. The teacher needs to remember to give students time to work on this project and suppose to take this project very seriously and present the assignment as a document. Giving the students this much freedom sends the message that they are controlling their learning, while providing them of higher order thinking problems. With a PBL students can use a variety of resources (books, internet, interviews, going out in the community, etc.) to find their answers. At the end of this assignment, teachers should use a typical rubric to assess the assignment. The criteria should be clearly explained in the beginning of the assignment, so there aren't any mix ups. The criteria should include how smoothly and effectively the group worked together, how each individual worked on the assignment and how much the contributed, the solution of the problem, and how the group came to the solution.
Saturday, September 4, 2010
Enhancing Think-Pair-Share Journal Article
Dubon, L.P. and Shafer, K.G. (2010). Enhanciing think-pair-share. Teaching children mathematics 16(8), 451-455.
The article I read was called Enhancing Think-Pair-Share. The article was based on a study done in a kindergarten classroom. Three researchers (Tyminski, Richardson, and Winarski) developed and decided to test their more detailed "think-pair-share" teaching strategy in a kindergarten math classroom. One of the reasons these three scientists decided to complete their study in such a young classroom was because of the high energy and the passion for learning was so evident. Having so much energy brings a new level of communication in a classroom, and having a classroom based upon the standards is so much more effective than having a classroom based on the information that is being taught. At such a young age, teachers need to teach students how to think at a deeper level, by "conjecturing, reasoning, representing, and communicating mathematics." (NCTM).
The authors and researchers really encouraged student-to-student verbal interaction. They liked the think-pair-share teaching theory, but they added a few more steps to make it more effective. They also added a protocol, to help students organize their thinking and to improve on their listening skills. When this occurs it strengthens their problem solving skills. (NCTM). The protocol begins by expressing the problem by stating, "My problem is.." then responding with, "I heard you say...is that right?" The first person then responds by saying, "My suggestion is..." and then finishing the conversation with, "I can agree to.." (NCTM). Having students practicing this will help them solve problems more effectively and listen to their classmates. For the modified think-pair-share teaching strategy there are five phases. The phases are: orientation, play-investigate, share-reorient, pair-play pair-listening, and whole group share. Having these phases breaks down what exactly needs to happen when practicing the think-pair-share strategy. Students need to know what is expected out of them and what the directions are. Then they need to investigate/play the lesson. Once they become familiar with the task they can then share knowledge with their peers during the share-reorient phase. Afterwards, students can play and explain to each other what they have noticed. At this time the researchers went around and asked students questions, when they phrased the questions differently some students had a difficult time answering them. To conclude the lesson, the whole class should have a class discussion where all the students where they discuss their discoveries and different ways of completing the assignment. Overall, this modified teaching strategy really flourishes when students use each other to help develop new ideas and concepts. The researches new method helps the students discover these new ideas through communication and having students practicing how to listen to each other. This strategy is not only great for a math classroom, but any classroom.
The article I read was called Enhancing Think-Pair-Share. The article was based on a study done in a kindergarten classroom. Three researchers (Tyminski, Richardson, and Winarski) developed and decided to test their more detailed "think-pair-share" teaching strategy in a kindergarten math classroom. One of the reasons these three scientists decided to complete their study in such a young classroom was because of the high energy and the passion for learning was so evident. Having so much energy brings a new level of communication in a classroom, and having a classroom based upon the standards is so much more effective than having a classroom based on the information that is being taught. At such a young age, teachers need to teach students how to think at a deeper level, by "conjecturing, reasoning, representing, and communicating mathematics." (NCTM).
The authors and researchers really encouraged student-to-student verbal interaction. They liked the think-pair-share teaching theory, but they added a few more steps to make it more effective. They also added a protocol, to help students organize their thinking and to improve on their listening skills. When this occurs it strengthens their problem solving skills. (NCTM). The protocol begins by expressing the problem by stating, "My problem is.." then responding with, "I heard you say...is that right?" The first person then responds by saying, "My suggestion is..." and then finishing the conversation with, "I can agree to.." (NCTM). Having students practicing this will help them solve problems more effectively and listen to their classmates. For the modified think-pair-share teaching strategy there are five phases. The phases are: orientation, play-investigate, share-reorient, pair-play pair-listening, and whole group share. Having these phases breaks down what exactly needs to happen when practicing the think-pair-share strategy. Students need to know what is expected out of them and what the directions are. Then they need to investigate/play the lesson. Once they become familiar with the task they can then share knowledge with their peers during the share-reorient phase. Afterwards, students can play and explain to each other what they have noticed. At this time the researchers went around and asked students questions, when they phrased the questions differently some students had a difficult time answering them. To conclude the lesson, the whole class should have a class discussion where all the students where they discuss their discoveries and different ways of completing the assignment. Overall, this modified teaching strategy really flourishes when students use each other to help develop new ideas and concepts. The researches new method helps the students discover these new ideas through communication and having students practicing how to listen to each other. This strategy is not only great for a math classroom, but any classroom.
NCTM Process Standard: Communication
According to the NCTM article on Communication process standard in a grades 3-5 classroom, "students should be able to use communication as a tool for understanding and generating solution strategies." (NCTM). After reviewing the information about communication in a classroom, I realized that without communication, a classroom would not be able to run efficiently. Communication isn't just oral instructions from the teacher to the students, it also includes communication from students to students. According to NCTM, students learn best when they are involved in a hands on activity where they can discuss their observations and conclusions with their peers. (NCTM). Communication in a classroom is essential, because this is how teachers can evaluate where their students stand, and see if they can move on with new material.
For the Communication standard for grades 3-5, the students should be able to use math language more often and use this type of language correctly. When students write their writing should be well developed and explain thoroughly what they discovered and learned. Teachers need to remember to model the use and the importance of communication in the classroom. To begin a lesson the teacher needs to have a discussion with the class and go through what steps need to be taken when evaluating a new math problem. In the middle school years students feel satisfied when they come to the answer themselves, so knowing this teachers need to remember to guide students through communication to come to the solution.
When discussing how communication and the standards are related, you can connect communication with all of them. The one standard that took out more than any other standard was making sense of the problem and perceive when solving it. The reason why is in order for somebody to make sense of anything, communication is key. Understanding math terms is a challenge, so when students attempt to make sense of the problem, communication is used. Another example is when students use reasoning to solve math problems. When using constructable arguments and critique communicating is being used. In order to develop anything, communication is used. Overall, communication may not always be verbally discussing something, it could be in a written reflection or working on a problem and showing every step.
For the Communication standard for grades 3-5, the students should be able to use math language more often and use this type of language correctly. When students write their writing should be well developed and explain thoroughly what they discovered and learned. Teachers need to remember to model the use and the importance of communication in the classroom. To begin a lesson the teacher needs to have a discussion with the class and go through what steps need to be taken when evaluating a new math problem. In the middle school years students feel satisfied when they come to the answer themselves, so knowing this teachers need to remember to guide students through communication to come to the solution.
When discussing how communication and the standards are related, you can connect communication with all of them. The one standard that took out more than any other standard was making sense of the problem and perceive when solving it. The reason why is in order for somebody to make sense of anything, communication is key. Understanding math terms is a challenge, so when students attempt to make sense of the problem, communication is used. Another example is when students use reasoning to solve math problems. When using constructable arguments and critique communicating is being used. In order to develop anything, communication is used. Overall, communication may not always be verbally discussing something, it could be in a written reflection or working on a problem and showing every step.
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