Chapter 9 Comments - - I thought this was a very interesting chapter. Most things I agreed with... and there were plenty of connections to other literacies, since "language" can be written, spoken, heard, or read. - I liked the square root lesson. Though quite honestly, this is how I would have run the lesson too. Though I might have still introduced the term "square root" first. I can see how it could work better to understand the concept before learning it has a name!
- I agree with the comments on p. 110 about the word wall. I also noticed the connections made between the suggestions on this page and the multi-rep charts of chapter 6 and the "these are/these are not" of chapter 8. But since this was about the meaning of a word, this was even closer to the CPR strategy modeled last Wednesday.
- I loved reading about the word etymology of the math terms. I think that kids won't be as geeky as me about the etymology, but I do believe this could be a fun "mid lesson" or "mid unit" hook. Definitely worth doing. I was so intrigued by these connections, I went ahead and ordered Schwartzman's book "The Words of Mathematics". I never understood how to explain numerator and denominator in a way that made sense. Now I do! I never thought I'd learn something about math in a literacy class!!!! Further proof to initial "skeptics" like me of the relevancy and urgency of content literacy.
- I thought the Venn Diagram's were cute, but really question whether they will lead to deeper understandings. That might clear up some misunderstandings though. But it seems like a lot of work just for that benefit, and there might be faster ways of doing this. Perhaps if the teacher creates these and hands them out, then the time is minimized and the gain maximized. It'd be hard for the students to fill these in. Heck, I would have had a hard time filling them in! So I think that handing them out and explaining them, and perhaps asking the students to give a sentence, equation, formula, etc to align to sections in the Venn diagram.
- I'm very skeptical about invented language. As the text pointed out... months after creating "midray", students created "midplane". How many times between the creation of "midray" and "midplane" did they continue to use "midplane" instead of bisector? Like a bad golf swing... hard to correct a bad habit. It is one thing to use invented language briefly, but it can't and shouldn't be propogated once the concepts are learned. If one allows the invented language to continue until this point, the teacher could seem hypocritical. Terms they allowed early on, then get "marked down" during assesments???? If you don't mark it down, what happens when they use "midray" on a standard assessment or some future math class with another teacher? Just like the author said, they learned "2" as a symbol for bisector, and it wasn't until college that they realized that this was an "invented" symbol. They were being too polite. This was an incorrect, imprecise, and irrelevant symbol, that would have shown their ignorance had they used it publicly. And they're encouraging this strategy????? While they did mention "transitioning" the students to the proper terms. But once again, that midplane example comes back. I will say that I liked the explanation, "somebody's gotta come up with a name, and this is what they came up with".
- Fortunately, they redeemed themselves with the literature section. Books on math are awesome, and appreciated. Even at high school, kids won't admit it, but they find stories fun. I read "Animal Farm", which I think was suggested by Jane Turk, to a class of Juniors! They feigned not liking it, but got the point.
Chapter 10 Comments - - Right off the bat, I loved the assertion that group projects need to be cognitively demanding, to encourage collaborative problem solving.
- I also liked the recommendation of using "think pair share" when you see puzzled faces. But rather than instituting this, I think students should be TRUSTED and ENCOURAGED to collaborate on their own, as long as it is about math. In a true learning environment, this should happen. Can students be mature enough to support this vision? Can a teacher create a culture of respect and a classroom Discourse to enable and nurture this?
- I've always loved the co-op strategy. The use of this for linear functions is very creative. Being able to see what the problems had in common was a great way for kids to discover the concept of a linear equation more or less on their own.
- Okay... after reading a few more strategies, which I won't comment on... I wonder. Why do we need to EXPLICITLY use a strategy to encourage students talking and listening? The teacher I observed during my literacy case study made it a habit of regularly asking questions, giving the students thinking time, and calling on many students to get their opinions. She also called on other students to rephrase what other students said. This gets students talking as part of the "teacher-taught" lesson. This isn't an explictly strategy, but rather a "classroom/teaching" priority. I think that a good teacher should get the students talking and listening at all times, and not have to reply on explicit strategies to do so. The strategies should be used as a way of increasing understandings or speeding the learning process, not for shoe-horning listing/speaking literacies into a classroom for the sake of listening/speaking.
I agree with the general idea that a concept should be discovered before leaning the proper definition. Of course we as teacher need to have some common sense adn not wait for the day beofre the test to introduce students to the math words they have been learning over the past two weeks. I too, along with Mark, enjoy the square root lesson. Students are discovering on their own without much guidance from the teacher. And as the investigation continues they begin to see the similarities and differencies between the properties of the numbers. At this point the class should be brought back together and the students should present their findings. I think this could be done in a compare and contrast format with the aid of a diagram. I once again agree that terms used in the classroom should be spoken aloud and written down in a meaningful way. During this section I thought about the Multi-Rep chart and the example that Ariel's group used last class.
Mark, I agree 100% that etymology must be taught and learned by students. I think back when I began learning words for the SAT and there were many common prefixes to words and other similarities between them. Never before in any of my math classes were the math terms truly broken down and investigated. Figure 9.3 on page 112 I believe would help.
A Venn Diagram is the prime (cute, right?) example that many texts show as a way to compare and contrast. I agree that this would take a lot of time in class but I could see it as a homework assignment. Perhaps having the students venture out in dictionaries, newspapers, and other medias that use these words. Students can create a meaning of a word by seeing how it's used in various areas. But I still ahve some questions. Do students posses the precise language necesary to complete the Venn? Or would this assignment rely heavily on the teacher to perform a majority of the work? I think it would take a lot of time exhausting the possibilities of various definitions.
Yes I agree that students need to make mathematics their own, but they MUST posses a mathematicians vocabulary. It's important for students to know that "midray" will not be accepted on exams. My inition thought is that you can't find a midray. We'll discuss this in the book club session I suppose.
Student must read, write, speak and listen in math. How else would we determine minunderstanding or misconceptions? The Cooperative Learning Strategies shed light on ways we can get kids moving around in an organized way. I agree that much conversation can be produced with Mark's description of what he saw. Yet, I do think that groups force all students at once to engage in an activity and the learning process. Cooperative Learning Strategies will be useful with activities that are more cognitively demanding.
During the Give and Take, I though about students using their Personal Language as Discussed in the previous chapter. Personal Language WON'T WORK!!! If one student uses their personal language to describe a shape and that's not the language the the listening knows, then the students will get nowhere... They won't understant what their partner is saying unless there is a common language. After some further thought on Give and Take, I think a neat spin off could be Math Taboo. This would force students to use various kinds of descriptive words. The obvious just doesn't cut it here if any of you have played Taboo before. Don't bother trying to steal Math Taboo, I've already copyrighted and patented it :)
For the Make My Day, I first thought about a Math Simon Says. I see some parallels (Woah, math word!) between the two. I'm not sure if an elimination factor to the game will make students days, but it could certainly be fun.
I think the strategies are useful, but once again we see that it is not the "cure" to make every lesson work.
The beginning of this chapter expounds upon the idea of concepts before vocabulary. Teaching for conceptual understanding before specific content knowledge such as skills and vocabulary seems to be a recurring theme in this book. The 'concepts first' notion was also presented in chapters 3 and 8. Once again I found myself pausing to reflect on this idea. The authors present a good argument for 'concepts first.' I think their reasoning of teaching math vocabulary after students explore math concepts and ideas is sound. This is how math was explored throughout history and continues today. New ideas branched out from puzzling observations and prior math knowledge. Vocabulary terms were created after sufficient exploration of those ideas. No mathematician ever said, "I just thought of a new word. What math concept can I put with it?" Of course students shouldn't be expected to rediscover math from scratch; but a teacher guiding student exploration of concepts then attaching the proper term to those concepts does seem like a more natural approach. I can see teaching this way being a challenge for me given that I've been exposed to the other way my entire education career. Similar to the challenge of backward design lesson planning. Actually, the 'concepts first, skills/vocab later' theme resembles backward design in a way.
The word origin section was my favorite of the chapter. Mark does have a point in saying that students probably won't be all that excited about learning math etymology but that it's worth teaching anyway. Excited or not, I can see teaching etymology of math terms helping students understand words that most likely appear alien to them.
I also agree with Mark about the Venn diagrams. They look like a good idea but would most likely be too time consuming. Students would probably benefit more from a classroom discussion about contextual differences with vocabulary. Handing out pre-made diagrams and discussing them makes more sense than having students create the diagrams from scratch.
I was not a fan of the invented language section. Having or letting students invent their own terms then correcting them later seems like it would take more work and would only end up with students being frustrated and more confused. I like the idea of teaching unnamed concepts then adding proper terms better. Even using informal language at first (proposed in chapter 3), like top and bottom for numerator and denominator, makes more sense than using made up words.
Using literature to teach math seems like it would be fun. I really want to read the books on the list at the end of the chapter. I imagine getting some funny looks from people as I raid the children's section of my library.
I was already familiar with the first four cooperative learning strategies presented. Still, I liked reading another point of view about the benefits of these strategies. I was not familiar with the last four strategies. I like the idea behind Silent Teacher. Students do need to chance to practice using what they are taught. (A term needs to be used 20 times before it's committed to memory?) Understanding a concept is only part of math literacy. Students also need to be able to communicate their knowledge and ideas. I thought the Symbol-Language Glossary was an interesting idea. It could certainly make a useful study guide and help students organize what they learn. However, will students actually use it? I really like Give and Take. It not only gives students practice with math communication, it teaches general oral communication and listening skills, which are important for jobs and social relationships. Make My Day is cute. I think it makes a good formative assessment. It also reinforces listening skills. I can see myself having fun with this one.
Chapter 9: As it is said over and over again math is a language onto itself, and this chapter helps provide some great strategies to help students related their everyday English to math, which can help them expand their knowledge and understanding. I thought the chart on page 112 was a really good idea. I think it can help serve two purposes. One, by introducing students to the origins of a math term can help them gain a deeper understanding about the concept it relates to. Second, by listing words that are related can help expand the vocabulary of the students, not only in math but in English as well. Who knows maybe this will get them thinking about math when they are in English class. How often does that happen? I thought the idea about having students pronounce, spell, and write in a sentence for a term that is introduced to avoid misinterpretation was very fascinating. The idea of writing sentences in math really stood out to me because I never did nor have I seen it done in any of my observations. I do think it can be helpful in avoiding misinterpretation, but I wonder how it would really play out in a classroom where the focus is always on building skills and concepts and very little focus on building vocabulary. Like Raphaella, I am interested in reading some of the literature books that were listed. I wonder how many kids, whose parents aren’t math teachers, read them for fun.
Chapter 10: Students need to be able to have a fluency in math not only in the written form, but orally as well and this chapter provided some great strategies to help students achieve that. I liked the Symbol-Language Glossary strategy. It is very easy for students to misinterpret symbols in math when they have to verbally express them, and I think creating the glossary will help students avoid such mistakes. The example of 13 - 5 expressed incorrectly as 13 less than 5 is a mistake that I constantly see students make. By having the glossary will help students reinforce the correct interpretation. I agree with the book that the Give and Take strategy would be an excellent formative assessment to use in both the beginning and the end of a unit to assess a student’s knowledge. I really liked the Make My Day strategy, even though I had images of Clint Eastwood stuck in my head while reading the section. It gives students a chance to get up and move around. I think this would be great and fun way to have students review for a test. You could break the class into teams and have them compete against each other or turn it into a version of Simon Says as Kenny mentioned. Also, it gives students a chance to use different types of literacy such as oral, auditory, and visual. I disagree with Raphaella on the Silent Teacher strategy. This is something that has been discussed before and I am still not convinced that the teacher not talking is helpful to students. Since I have seen it being done in my observations, I agree students reading aloud can be extremely helpful to them understanding a concept, but to have students read the lessons and not the teacher seems too much. Yes, to get a deeper understanding students need to figure things out for themselves, but they still need the teacher to guide them in the right direction.
Kenny did a great job as Discussion Director. He found 4 general areas of interest to us, synthesized the information, then gave some pretty deep questions. We actually felt rushed to get through the topics and probably could have spent another hour discussing them.
The first interesting topic was Etympology. Kenny asked us whether or not it had to be fun and if so, how could we make it fun. The general group concensus was that "fun" is subjective, and the fact that it might light a spark with some of the students. One idea we had to make it fun was to put it in as part of a word search. Ways of integrating it into the lessons, without necessarily making it fun, would be to make etymology part of a word wall or other strategies.
The second area of interest was Venn Diagrams. We all still felt, even after discussion, that students wouldn't know how to fill in sections, even with scaffolding. We did discussed that this could be part of a "do now", where a successful answer is not necessarily mandatory, and the teacher could guide filling it in. This is in contrast to Mark's suggestion of just handing it out filled in, and having the students give examples of each section, either in math symbols or sentences.
As for invented language, we still agree that invented language is a bad idea. However, we also made the distinction to giving something a "natural" name, until the mathematical name is learned. For example, we all felt calling the numerator and denominator of a fraction as the top/bottom numbers were not really "invented names". Dr. Clayton made a great suggestion of using the term "apprentice discourse" as a new unit and words are being taught, and eventually the class graduates to "math discourse".
We also discussed the "go to" stragegy as the one we'd likely turn to. We all seemed to like symbol/language and multi-rep charts. It was brought up that the multi-rep is similar to CPR.
What was most interesting was the discussion we had on literacy as it assists understanding. Should we force a literacy strategy in if it doesn't make sense? We all thought that it had to make sense for a lesson. But then towards the end, as we were running out of time, we discussed the other argument that literacy increases comprehension by changing how we think about problems. So that it probably does make sense to use it often, but by using strategies that are easy to implement. That is why Raphaelle suggested the symbol/language and Annie (I think) the textbook glossary.
Lastly, we discussed the discussion points suggested by Dr. Clayton. These were so brief though, I don't want to assume that they were fully discussed. We liked the number of strategies suggested in the book and their strong promotion of a math discouse community in the classroom. The most memorable stragtegy was the multi-rep chart. We would recommend the book to math teachers only. We had a brief discussion about how discourse and literacy relate, but didn't come to any real conclusions.
Thanks for the summary - Great one, Douglas. I'm glad you engaged so thoughtfully and critically with this book - both online and in class. The result is that one of you learned something about math and the rest of you seemed to really engage with some meaningful ways to think about literacy. I'm always intrigued by the ideas of integrating some literature content in math. I've heard students who don't see themselves as math folks feel more engaged with this content if they can see the "story" in math. I guess my point is that if we don't engage with some of these other ways in to the content, we continue to lose students. You folks likely didn't need these other ways in (although it may have enhanced your experience of math teaching) but if you just teach to student who were like you, then you are likely not teaching to the students who struggle in math, right? Again, thanks for your thougthful engagement with this text that also benefitted our larger class dialogue.
Chapter 9 Comments -
ReplyDelete- I thought this was a very interesting chapter. Most things I agreed with... and there were plenty of connections to other literacies, since "language" can be written, spoken, heard, or read.
- I liked the square root lesson. Though quite honestly, this is how I would have run the lesson too. Though I might have still introduced the term "square root" first. I can see how it could work better to understand the concept before learning it has a name!
- I agree with the comments on p. 110 about the word wall. I also noticed the connections made between the suggestions on this page and the multi-rep charts of chapter 6 and the "these are/these are not" of chapter 8. But since this was about the meaning of a word, this was even closer to the CPR strategy modeled last Wednesday.
- I loved reading about the word etymology of the math terms. I think that kids won't be as geeky as me about the etymology, but I do believe this could be a fun "mid lesson" or "mid unit" hook. Definitely worth doing. I was so intrigued by these connections, I went ahead and ordered Schwartzman's book "The Words of Mathematics". I never understood how to explain numerator and denominator in a way that made sense. Now I do! I never thought I'd learn something about math in a literacy class!!!! Further proof to initial "skeptics" like me of the relevancy and urgency of content literacy.
- I thought the Venn Diagram's were cute, but really question whether they will lead to deeper understandings. That might clear up some misunderstandings though. But it seems like a lot of work just for that benefit, and there might be faster ways of doing this. Perhaps if the teacher creates these and hands them out, then the time is minimized and the gain maximized. It'd be hard for the students to fill these in. Heck, I would have had a hard time filling them in! So I think that handing them out and explaining them, and perhaps asking the students to give a sentence, equation, formula, etc to align to sections in the Venn diagram.
- I'm very skeptical about invented language. As the text pointed out... months after creating "midray", students created "midplane". How many times between the creation of "midray" and "midplane" did they continue to use "midplane" instead of bisector? Like a bad golf swing... hard to correct a bad habit. It is one thing to use invented language briefly, but it can't and shouldn't be propogated once the concepts are learned. If one allows the invented language to continue until this point, the teacher could seem hypocritical. Terms they allowed early on, then get "marked down" during assesments???? If you don't mark it down, what happens when they use "midray" on a standard assessment or some future math class with another teacher? Just like the author said, they learned "2" as a symbol for bisector, and it wasn't until college that they realized that this was an "invented" symbol. They were being too polite. This was an incorrect, imprecise, and irrelevant symbol, that would have shown their ignorance had they used it publicly. And they're encouraging this strategy????? While they did mention "transitioning" the students to the proper terms. But once again, that midplane example comes back. I will say that I liked the explanation, "somebody's gotta come up with a name, and this is what they came up with".
- Fortunately, they redeemed themselves with the literature section. Books on math are awesome, and appreciated. Even at high school, kids won't admit it, but they find stories fun. I read "Animal Farm", which I think was suggested by Jane Turk, to a class of Juniors! They feigned not liking it, but got the point.
Mark
Chapter 10 Comments -
ReplyDelete- Right off the bat, I loved the assertion that group projects need to be cognitively demanding, to encourage collaborative problem solving.
- I also liked the recommendation of using "think pair share" when you see puzzled faces. But rather than instituting this, I think students should be TRUSTED and ENCOURAGED to collaborate on their own, as long as it is about math. In a true learning environment, this should happen. Can students be mature enough to support this vision? Can a teacher create a culture of respect and a classroom Discourse to enable and nurture this?
- I've always loved the co-op strategy. The use of this for linear functions is very creative. Being able to see what the problems had in common was a great way for kids to discover the concept of a linear equation more or less on their own.
- Okay... after reading a few more strategies, which I won't comment on... I wonder. Why do we need to EXPLICITLY use a strategy to encourage students talking and listening? The teacher I observed during my literacy case study made it a habit of regularly asking questions, giving the students thinking time, and calling on many students to get their opinions. She also called on other students to rephrase what other students said. This gets students talking as part of the "teacher-taught" lesson. This isn't an explictly strategy, but rather a "classroom/teaching" priority. I think that a good teacher should get the students talking and listening at all times, and not have to reply on explicit strategies to do so. The strategies should be used as a way of increasing understandings or speeding the learning process, not for shoe-horning listing/speaking literacies into a classroom for the sake of listening/speaking.
I agree with the general idea that a concept should be discovered before leaning the proper definition. Of course we as teacher need to have some common sense adn not wait for the day beofre the test to introduce students to the math words they have been learning over the past two weeks. I too, along with Mark, enjoy the square root lesson. Students are discovering on their own without much guidance from the teacher. And as the investigation continues they begin to see the similarities and differencies between the properties of the numbers. At this point the class should be brought back together and the students should present their findings. I think this could be done in a compare and contrast format with the aid of a diagram. I once again agree that terms used in the classroom should be spoken aloud and written down in a meaningful way. During this section I thought about the Multi-Rep chart and the example that Ariel's group used last class.
ReplyDeleteMark, I agree 100% that etymology must be taught and learned by students. I think back when I began learning words for the SAT and there were many common prefixes to words and other similarities between them. Never before in any of my math classes were the math terms truly broken down and investigated. Figure 9.3 on page 112 I believe would help.
A Venn Diagram is the prime (cute, right?) example that many texts show as a way to compare and contrast. I agree that this would take a lot of time in class but I could see it as a homework assignment. Perhaps having the students venture out in dictionaries, newspapers, and other medias that use these words. Students can create a meaning of a word by seeing how it's used in various areas. But I still ahve some questions.
Do students posses the precise language necesary to complete the Venn? Or would this assignment rely heavily on the teacher to perform a majority of the work? I think it would take a lot of time exhausting the possibilities of various definitions.
Yes I agree that students need to make mathematics their own, but they MUST posses a mathematicians vocabulary. It's important for students to know that "midray" will not be accepted on exams. My inition thought is that you can't find a midray. We'll discuss this in the book club session I suppose.
Student must read, write, speak and listen in math. How else would we determine minunderstanding or misconceptions? The Cooperative Learning Strategies shed light on ways we can get kids moving around in an organized way. I agree that much conversation can be produced with Mark's description of what he saw. Yet, I do think that groups force all students at once to engage in an activity and the learning process. Cooperative Learning Strategies will be useful with activities that are more cognitively demanding.
ReplyDeleteDuring the Give and Take, I though about students using their Personal Language as Discussed in the previous chapter. Personal Language WON'T WORK!!! If one student uses their personal language to describe a shape and that's not the language the the listening knows, then the students will get nowhere... They won't understant what their partner is saying unless there is a common language. After some further thought on Give and Take, I think a neat spin off could be Math Taboo. This would force students to use various kinds of descriptive words. The obvious just doesn't cut it here if any of you have played Taboo before.
Don't bother trying to steal Math Taboo, I've already copyrighted and patented it :)
For the Make My Day, I first thought about a Math Simon Says. I see some parallels (Woah, math word!) between the two. I'm not sure if an elimination factor to the game will make students days, but it could certainly be fun.
I think the strategies are useful, but once again we see that it is not the "cure" to make every lesson work.
Chapter 9:
ReplyDeleteThe beginning of this chapter expounds upon the idea of concepts before vocabulary. Teaching for conceptual understanding before specific content knowledge such as skills and vocabulary seems to be a recurring theme in this book. The 'concepts first' notion was also presented in chapters 3 and 8. Once again I found myself pausing to reflect on this idea. The authors present a good argument for 'concepts first.' I think their reasoning of teaching math vocabulary after students explore math concepts and ideas is sound. This is how math was explored throughout history and continues today. New ideas branched out from puzzling observations and prior math knowledge. Vocabulary terms were created after sufficient exploration of those ideas. No mathematician ever said, "I just thought of a new word. What math concept can I put with it?" Of course students shouldn't be expected to rediscover math from scratch; but a teacher guiding student exploration of concepts then attaching the proper term to those concepts does seem like a more natural approach. I can see teaching this way being a challenge for me given that I've been exposed to the other way my entire education career. Similar to the challenge of backward design lesson planning. Actually, the 'concepts first, skills/vocab later' theme resembles backward design in a way.
The word origin section was my favorite of the chapter. Mark does have a point in saying that students probably won't be all that excited about learning math etymology but that it's worth teaching anyway. Excited or not, I can see teaching etymology of math terms helping students understand words that most likely appear alien to them.
I also agree with Mark about the Venn diagrams. They look like a good idea but would most likely be too time consuming. Students would probably benefit more from a classroom discussion about contextual differences with vocabulary. Handing out pre-made diagrams and discussing them makes more sense than having students create the diagrams from scratch.
I was not a fan of the invented language section. Having or letting students invent their own terms then correcting them later seems like it would take more work and would only end up with students being frustrated and more confused. I like the idea of teaching unnamed concepts then adding proper terms better. Even using informal language at first (proposed in chapter 3), like top and bottom for numerator and denominator, makes more sense than using made up words.
Using literature to teach math seems like it would be fun. I really want to read the books on the list at the end of the chapter. I imagine getting some funny looks from people as I raid the children's section of my library.
Chapter 10:
ReplyDeleteI was already familiar with the first four cooperative learning strategies presented. Still, I liked reading another point of view about the benefits of these strategies. I was not familiar with the last four strategies. I like the idea behind Silent Teacher. Students do need to chance to practice using what they are taught. (A term needs to be used 20 times before it's committed to memory?) Understanding a concept is only part of math literacy. Students also need to be able to communicate their knowledge and ideas. I thought the Symbol-Language Glossary was an interesting idea. It could certainly make a useful study guide and help students organize what they learn. However, will students actually use it? I really like Give and Take. It not only gives students practice with math communication, it teaches general oral communication and listening skills, which are important for jobs and social relationships. Make My Day is cute. I think it makes a good formative assessment. It also reinforces listening skills. I can see myself having fun with this one.
Chapter 9: As it is said over and over again math is a language onto itself, and this chapter helps provide some great strategies to help students related their everyday English to math, which can help them expand their knowledge and understanding. I thought the chart on page 112 was a really good idea. I think it can help serve two purposes. One, by introducing students to the origins of a math term can help them gain a deeper understanding about the concept it relates to. Second, by listing words that are related can help expand the vocabulary of the students, not only in math but in English as well. Who knows maybe this will get them thinking about math when they are in English class. How often does that happen? I thought the idea about having students pronounce, spell, and write in a sentence for a term that is introduced to avoid misinterpretation was very fascinating. The idea of writing sentences in math really stood out to me because I never did nor have I seen it done in any of my observations. I do think it can be helpful in avoiding misinterpretation, but I wonder how it would really play out in a classroom where the focus is always on building skills and concepts and very little focus on building vocabulary. Like Raphaella, I am interested in reading some of the literature books that were listed. I wonder how many kids, whose parents aren’t math teachers, read them for fun.
ReplyDeleteChapter 10: Students need to be able to have a fluency in math not only in the written form, but orally as well and this chapter provided some great strategies to help students achieve that. I liked the Symbol-Language Glossary strategy. It is very easy for students to misinterpret symbols in math when they have to verbally express them, and I think creating the glossary will help students avoid such mistakes. The example of 13 - 5 expressed incorrectly as 13 less than 5 is a mistake that I constantly see students make. By having the glossary will help students reinforce the correct interpretation. I agree with the book that the Give and Take strategy would be an excellent formative assessment to use in both the beginning and the end of a unit to assess a student’s knowledge. I really liked the Make My Day strategy, even though I had images of Clint Eastwood stuck in my head while reading the section. It gives students a chance to get up and move around. I think this would be great and fun way to have students review for a test. You could break the class into teams and have them compete against each other or turn it into a version of Simon Says as Kenny mentioned. Also, it gives students a chance to use different types of literacy such as oral, auditory, and visual. I disagree with Raphaella on the Silent Teacher strategy. This is something that has been discussed before and I am still not convinced that the teacher not talking is helpful to students. Since I have seen it being done in my observations, I agree students reading aloud can be extremely helpful to them understanding a concept, but to have students read the lessons and not the teacher seems too much. Yes, to get a deeper understanding students need to figure things out for themselves, but they still need the teacher to guide them in the right direction.
Notes from our group Discussion:
ReplyDeleteKenny did a great job as Discussion Director. He found 4 general areas of interest to us, synthesized the information, then gave some pretty deep questions. We actually felt rushed to get through the topics and probably could have spent another hour discussing them.
The first interesting topic was Etympology. Kenny asked us whether or not it had to be fun and if so, how could we make it fun. The general group concensus was that "fun" is subjective, and the fact that it might light a spark with some of the students. One idea we had to make it fun was to put it in as part of a word search. Ways of integrating it into the lessons, without necessarily making it fun, would be to make etymology part of a word wall or other strategies.
The second area of interest was Venn Diagrams. We all still felt, even after discussion, that students wouldn't know how to fill in sections, even with scaffolding. We did discussed that this could be part of a "do now", where a successful answer is not necessarily mandatory, and the teacher could guide filling it in. This is in contrast to Mark's suggestion of just handing it out filled in, and having the students give examples of each section, either in math symbols or sentences.
As for invented language, we still agree that invented language is a bad idea. However, we also made the distinction to giving something a "natural" name, until the mathematical name is learned. For example, we all felt calling the numerator and denominator of a fraction as the top/bottom numbers were not really "invented names". Dr. Clayton made a great suggestion of using the term "apprentice discourse" as a new unit and words are being taught, and eventually the class graduates to "math discourse".
We also discussed the "go to" stragegy as the one we'd likely turn to. We all seemed to like symbol/language and multi-rep charts. It was brought up that the multi-rep is similar to CPR.
What was most interesting was the discussion we had on literacy as it assists understanding. Should we force a literacy strategy in if it doesn't make sense? We all thought that it had to make sense for a lesson. But then towards the end, as we were running out of time, we discussed the other argument that literacy increases comprehension by changing how we think about problems. So that it probably does make sense to use it often, but by using strategies that are easy to implement. That is why Raphaelle suggested the symbol/language and Annie (I think) the textbook glossary.
Lastly, we discussed the discussion points suggested by Dr. Clayton. These were so brief though, I don't want to assume that they were fully discussed. We liked the number of strategies suggested in the book and their strong promotion of a math discouse community in the classroom. The most memorable stragtegy was the multi-rep chart. We would recommend the book to math teachers only. We had a brief discussion about how discourse and literacy relate, but didn't come to any real conclusions.
Faithfully submitted, Douglas C. Niedermeyer
Thanks for the summary - Great one, Douglas. I'm glad you engaged so thoughtfully and critically with this book - both online and in class. The result is that one of you learned something about math and the rest of you seemed to really engage with some meaningful ways to think about literacy. I'm always intrigued by the ideas of integrating some literature content in math. I've heard students who don't see themselves as math folks feel more engaged with this content if they can see the "story" in math. I guess my point is that if we don't engage with some of these other ways in to the content, we continue to lose students. You folks likely didn't need these other ways in (although it may have enhanced your experience of math teaching) but if you just teach to student who were like you, then you are likely not teaching to the students who struggle in math, right?
ReplyDeleteAgain, thanks for your thougthful engagement with this text that also benefitted our larger class dialogue.