Chapter 1 Comments: - I don't think having kids figure out what a stem-and-leaf plot is increases comprehension of it. It will take half a lessen and will they really have learned it better? I think it'd be better to define it, and have students figure out under what situations this is good.
- students often have problems remembering that x^2 is x-squared rather than 2x.
- The comment on page 7, that students need experience solving problems and they will better understand the sign systems, is right on. However, this seems a bit like the chicken and egg to me. We have to teach our kids the math, and then focus heavily on the sign systems. We shouldn't put the cart before the horse, but many teachers do.
Chapter 2 Comments - - I think the dialog from Ms. Wade is amazaing. The question is this.... in an attentive, high-performing class, this ought to work great. But what about an inclusion class, with many students who are slower? Will this help them learn better, or will they get more frustrated and lost?
- I think that having students listen to each other's answers is very important. But as they say in the middle of p. 15, the teacher also has to be good at listening to students and understanding their possible mistakes. In a backwards designed lesson, we anticipate misunderstandings. This seems important in math. There is often more than one way to solve a problem, and a student may discover one!
- I like the 3 proposed modes of listening: evaluative (assess), interpretative (access) and hermeneutic (negotation).
- I think the most recent math texts are getting easier and easier to read, and they combine lots of pictures, definitions, etc. But I'm not sure students learn how to CONNECT concepts from different sections together unless the book or teacher show them. This is the challenge. Getting students to apply what they've learned in new ways. The book mentions that this is important on p. 17, but somehow believe that this is related to math "reading". I think this is more generally related to problem solving, and thinking of how to apply knowledge in new ways, and not giving up. I agree it is about making meaning. But believe that the techniques, like inferencing, need to be taught. It is more than just reading.
- I agree that writing is a window into assessing what students know. So many teachers dock points for minor syntactic errors, when I believe the students understand the concept. Is this the right thing to do?
Comments on Chapter 3 - - Right off the get go, I have a big issue with "Reading Mathematical Test" on p. 21. They say that math students need to interact with the text in 3 ways: within the text, beyond the text, and about the text. I don't disagree. But I disagree that students read math texts and really want to spend time thinking "beyond" and "about" the text. My kids read their texts and do their homework only to get done. In class, students ought to only be referring to the text as a resource. So really, are kids going to want to really read to learn, or read to get their H/W done? My kids are A students, and do the latter.
- Next paragraph: Students need to read with paper and pencil in hand in order to work problems and follow along with the authors. ... students need to attend to every singe word in mathematics. ARE YOU KIDDING ME? I don't disagree with the ideal situation... but am more pragmatic in what kids will and will not do. Most kids do home work with music on and chat screens in the background. How can you really expect them to focus on each word and work along with the authors. If this is required, then our students are doomed. We may need to find ways to teach WITHOUT textbooks if this is what is required to use a text successfully.
- I like what Mr. Howard did. Seems identical to what Dennis and Rob did in class.
- Not sure why the 3 types of sentences: words only, words and symbols, or symbols only, is relevant.
- It seems to me that speaking in the math classroom is probably more important than reading a math text. How do kids learn that "-3" is "negaive three" and not "minus three"? How do they learn that sin(x) is pronounced "sign" and not "sin"? Reading as a "math language learning" may not help with spoken communication. This is just like somebody who reads a word they don't know, and then later mispronounce it.
- On p. 28, the authors make an argument for using the correct terms. This is an ongoing debate in the math community. Teachers who belabor using correct terminology and pedantically correct every error, will cause students to clam up. If it is the understandings we care about, do we really care if a student refers to numerator and denominator as top and bottom of a fraction? I like how the authors treat this subject, and acknowledge that colloquial usage makes sense until we're sure the students have the concepts. We can then belabor the proper vocabulary w/o saturating the students.
- I like dictionaries like the ones shown or the one we started. But they have to be QUICK to access, for entering and looking up. Can this be made faster? I think our personal word dictionaries are too slow to use.... How can we make these faster?
- I never thought much about how hard it must be for a new student to understand when we read 5(3x+2) as 5 times the quantity 3x plus 2. Who taught them that "the quantity" means "(" with an implicit ")" at the end of the sentence? Tricky....
- After all the examples in this chapter, I guess the takeaway message is that the language of math is tricky, and we have to teach it consciously and creatively.
Mark, I agree with your thoughts about textbook reading. It's far fetched to expect that students will learn from a text on their own. It's very time consuming and they have enough to do as it is. Such student centered learning would fare better in a classroom with cooperative strategies. I do think that students should be able to know how to read a mathematics text if they do want to use it as a resource. Not every child will be able to do their homework without difficulty and their textbook can provide them with the information they need to be able to complete it. However, a textbook will be of no use if they don't know how to actually use it. Chapter 3 addresses the idea of wanting students to be able to learn without relying on a teacher. If we do want them to try to learn on their own, assigning textbook reading may not be so far fetched. Consider the strategies used in Chapter 11. They do need to be modeled in class first, but once students have a grasp on how they are to be used, they should be able to apply them on their own. The assigned reading would cover what would be taught in the following day's lesson. Students would be reading ahead and applying a strategy or two described in Chapter 11. Then their understanding of what they read, or lack thereof, and questions they have, could be assessed and addressed in class. However, I think this type of assignment should only be assigned if students have a firm grasp on how to read a text and the prior material needed to understand the assigned section.
On page 139 of Chapter 11, it says, "students must become fluent with the vocabulary if they are to become successful mathematics...learners." Definitions are essential to understanding and doing math. I can't even begin count how many times I heard the maxim "know your definitions" when I was an undergrad. The idea behind this is that no matter what level of mathematics a students is studying, he or she can't even begin to learn math unless the definitions are mastered first. After reading Mark's comment on math vocabulary (the paragraph beginning with 'On page 28...'), I'm starting to second guess the 'know your definitions' notion. Now I'm left wonder what really is better: definitions first, concepts later or concepts first, definitions later. Or maybe it's one over the other depending on the topic, not mathematics as a whole. This is something I think would be better left to discussion. I'd like to address it on Thursday.
Also, I wonder how often it would be beneficial to use textbook reading strategies in mathematics. I think certain pre-reading strategies, such as brainstorming, can be utilized without reading; having students do pre-reading exercises can key them into what the lesson will be on, which will help them know what to listen for when the lesson is finally presented.
Chapter 1 On page 6 the author suggests that many students struggle in mathematics because they have not developed the ability to translate from words to symbols and vice versa. It’s fun to see a text implicitly relate math to a foreign language. We learn language by producing it. Thus, we need to have kids “speak” in math. In how many language classes are you allowed to speak in English? The teachers push and guide you as you struggle. In math, we should be pushing students to speak like mathematicians. Constantly improving on the language of math whether it be symbols or new words. Sparking off of Mark’s question if Ms. Wade’s class would succeed in an inclusive classroom, how long would it take a class to participate in this type of lesson if they have been spoon fed material the previous years? How do you break the cycle?
Chapter 3 I agree that math texts should be read at a slower pace and more attention to detail. However, when have you heard of a K-12 student independently reading and practicing along with a math textbook? I learned from the teacher in school and rarely relied on the text except for a formula here or there. So in essence, I learned from accessing my prior knowledge on the subject. On page 24 the text says that prior knowledge is the main determinant of understanding. It makes perfect sense that you cannot integrate a function without knowing how to add. Chapter 5 I agree that students do not know where to begin with word problems. They know what needs to happen in the end, but getting there is the issue. Children complete concrete problems with ease. As soon as the decision making process begins the effort ends. The Zoom-In Zoom-Out strategy may help students conceptualize the problem since it gives them smaller and more manageable steps to complete as opposed to being introduced to a large daunting problem. The text suggests that with time students will be able to implement this strategy to future questions and become more independent with their learning. Chapter 11 The pre-reading, reading, and post-reading is similar to the Zoom-in Zoom-out strategy where students find key information (i.e. titles, headings), reading for comprehension and flow (the text), then solving and explaining (postreading). This is probably a stretch, but there are similarities. I don’t agree at first thought with the idea that students must become fluent with vocabulary to become successful in mathematics. I agree that some must be learned, but the understanding for a person could be just that, but without the ability to convey the understanding using math vernacular. After reviewing the reading strategies I couldn’t remember of a time in a math class where one of these was implemented. These reading strategies were for “reading classes such as language courses and history.
Chapter 2: I do think it is better for students if a classroom has an interactive dialogue. When the teacher is solely doing the talking it is easy for students to lose interest and begin to daydream. In addition, when it is time for them to do the work on their own they are left to do it based on what they learned by watching the teacher. When a classroom has an interactive dialogue the students are figuring out what to do for themselves with guidance from their teacher. It also helps them clarify prior knowledge and it gives them a better understanding of the topic. In my observations I have seen how interactive dialogue can change a class for the better. In one class I have observed the teacher would only ask students about three or four questions throughout the lesson and the rest of the time he was talking. During the lesson I found myself losing interest, so I can only imagine how quickly the students were gone. However, in other class that used interactive dialogue the students were animated and eager to show off what they knew.
Chapter 3: I agree that mathematics is just like learning a foreign language, as it has its own set of vocabulary words and symbols that students must know to understand it fluently. I agree with the reading principles on page 24. However, I don’t think just because students don’t have a fluent math vocabulary they can’t succeed in math, I think understanding the concepts is also key.
Chapter 11: I liked many of the strategies. However, I wonder how practical they really are and how many math teachers actually use them. From my experience and my observations I have never seen a math teacher have the students read the text first.
Chapter 5 - I like zoom-in zoom-out. I don't believe this is so much a reading strategy, as much as a good teaching approach in which the teacher is cognizant about letting the students solve the problem on their own. By remembering the metaphor of zooming, a teacher can guide without giving the answers away.
I also thought it was ironic that they mention Polya. If you remember, I brought in the Polya book to class! It is a great read for all math teachers!
Chapter 11 - This is just a great chapter, chalk full of interesting strategies. I think it would behoove a teacher to be comfortable with all these strategies, and possibly even differentiate specific strategies with different students.
The vignette about solving word problems really is the number one reading issue for our students. True, we hope they can read and learn from their textbooks, but the reality is that they probably won't. But being able to decode and understand word problems is critical for the high stakes tests. Using strategies like KWL or zoom-in-zoom-out, if taught to students as a way of determining a problem solving strategy, sounds like a great thing to do. This is not constrained to midde school!!!!
These are excellent comments. I've been following your individual comments through my email but want to say, more generally, that I appreciate the careful reading of this book and the thoughtful display of your ideas here. You go beyond just summarizing or listing strategies you like/don't like and really raise some interesting ideas worthy of in class discussion tonight in your group - issues like reading a math text (when and what's appropriate to expect), speaking like mathematicians and dialogue in math (again, what's appropriate to expect), the value of thinking about math learning in relation to language learning (what would that do to our thinking about how we would conceptualize class time?), the role of these "pre-reading" strategies (what does "pre-reading" really mean here? As R suggests, maybe we can thinking about them as pre-intake of information strategies). I'm sure there are others - these are just some that stand out for me as I reread your posts online. I really want to encourage your discussion about the use of the math text - when and how do you read a math text??? What's important about that in terms of not only the short term goal of getting kids to learn the material in this school year but also in supporting their development as independent learners in the long haul, especially in thinking about their continuation with math at higher or later levels of education. I thought Ann and Raphaella made some good points worth taking apart and exploring more. I also thought the discussion about speaking math was interesting, especially in reference to the Ms. Wade discussion. That example evoked for me the Dagmar case we read earlier. Is this kind of interactive dialogue that reveals both teacher and student metacognition important, indeed essential, for all students, not just the high end? We read a social studies case for tonight on discussion that starts with a statement, loosely paraphrased, that student learning is related to the kind of classroom talk that goes on. What do you think? Great, provocative posts. I look forward to the discussion tonight! As with dialogue journals, keep making powerful connections between what you read in this book and other readings, your experiences teaching, being students, and observing in the field.
During our discussion last Thursday we first discussed the parcticality of reading strategies inside of a math classroom. We agreed that it implementing daily reading strategies in math classrooms would require us to invest much time and energy. Following this we tried to fine tune. What is common in a math classroom to read? Word Problems!!! In Dagmar's article we saw an entire class period devoted to one word problem. The text brought up the instructional approach of "Zoom-In Zoom-Out" found on page 62.
Secondly, we discussed if students need vocabulary to be successful in math and if vocabulary or concepts appear first. The text provided the number 30. This number represented the amount of times that a student would need to use a word to understand it. We're sure that this didn't mean copying the word 30 times down the side fo a page. Anyway, in math classrooms, we agreed that math concepts is what math teachers should be looking for. If a student can describe a piece of mathematics in their own words, then God bless them. Not to say vocabulry is not important, we believe that new vernacular should be scaffolded in.
Where we ended was thinking about the brilliant person who doesn't know the vocabulary. Or perhaps a person who is a literate thinker but lacks physical/verbal literacy. This topic may deserve some more attention.
"If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them." ~Phil Pastoret
Looks good. Thanks for the model.
ReplyDeleteWill do! Ditto on the easy read.
ReplyDeleteChapter 1 Comments:
ReplyDelete- I don't think having kids figure out what a stem-and-leaf plot is increases comprehension of it. It will take half a lessen and will they really have learned it better? I think it'd be better to define it, and have students figure out under what situations this is good.
- students often have problems remembering that x^2 is x-squared rather than 2x.
- The comment on page 7, that students need experience solving problems and they will better understand the sign systems, is right on. However, this seems a bit like the chicken and egg to me. We have to teach our kids the math, and then focus heavily on the sign systems. We shouldn't put the cart before the horse, but many teachers do.
Chapter 2 Comments -
ReplyDelete- I think the dialog from Ms. Wade is amazaing. The question is this.... in an attentive, high-performing class, this ought to work great. But what about an inclusion class, with many students who are slower? Will this help them learn better, or will they get more frustrated and lost?
- I think that having students listen to each other's answers is very important. But as they say in the middle of p. 15, the teacher also has to be good at listening to students and understanding their possible mistakes. In a backwards designed lesson, we anticipate misunderstandings. This seems important in math. There is often more than one way to solve a problem, and a student may discover one!
- I like the 3 proposed modes of listening: evaluative (assess), interpretative (access) and hermeneutic (negotation).
- I think the most recent math texts are getting easier and easier to read, and they combine lots of pictures, definitions, etc. But I'm not sure students learn how to CONNECT concepts from different sections together unless the book or teacher show them. This is the challenge. Getting students to apply what they've learned in new ways. The book mentions that this is important on p. 17, but somehow believe that this is related to math "reading". I think this is more generally related to problem solving, and thinking of how to apply knowledge in new ways, and not giving up. I agree it is about making meaning. But believe that the techniques, like inferencing, need to be taught. It is more than just reading.
- I agree that writing is a window into assessing what students know. So many teachers dock points for minor syntactic errors, when I believe the students understand the concept. Is this the right thing to do?
Comments on Chapter 3 -
ReplyDelete- Right off the get go, I have a big issue with "Reading Mathematical Test" on p. 21. They say that math students need to interact with the text in 3 ways: within the text, beyond the text, and about the text. I don't disagree. But I disagree that students read math texts and really want to spend time thinking "beyond" and "about" the text. My kids read their texts and do their homework only to get done. In class, students ought to only be referring to the text as a resource. So really, are kids going to want to really read to learn, or read to get their H/W done? My kids are A students, and do the latter.
- Next paragraph: Students need to read with paper and pencil in hand in order to work problems and follow along with the authors. ... students need to attend to every singe word in mathematics. ARE YOU KIDDING ME? I don't disagree with the ideal situation... but am more pragmatic in what kids will and will not do. Most kids do home work with music on and chat screens in the background. How can you really expect them to focus on each word and work along with the authors. If this is required, then our students are doomed. We may need to find ways to teach WITHOUT textbooks if this is what is required to use a text successfully.
- I like what Mr. Howard did. Seems identical to what Dennis and Rob did in class.
- Not sure why the 3 types of sentences: words only, words and symbols, or symbols only, is relevant.
- It seems to me that speaking in the math classroom is probably more important than reading a math text. How do kids learn that "-3" is "negaive three" and not "minus three"? How do they learn that sin(x) is pronounced "sign" and not "sin"? Reading as a "math language learning" may not help with spoken communication. This is just like somebody who reads a word they don't know, and then later mispronounce it.
- On p. 28, the authors make an argument for using the correct terms. This is an ongoing debate in the math community. Teachers who belabor using correct terminology and pedantically correct every error, will cause students to clam up. If it is the understandings we care about, do we really care if a student refers to numerator and denominator as top and bottom of a fraction? I like how the authors treat this subject, and acknowledge that colloquial usage makes sense until we're sure the students have the concepts. We can then belabor the proper vocabulary w/o saturating the students.
- I like dictionaries like the ones shown or the one we started. But they have to be QUICK to access, for entering and looking up. Can this be made faster? I think our personal word dictionaries are too slow to use.... How can we make these faster?
- I never thought much about how hard it must be for a new student to understand when we read 5(3x+2) as 5 times the quantity 3x plus 2. Who taught them that "the quantity" means "(" with an implicit ")" at the end of the sentence? Tricky....
- After all the examples in this chapter, I guess the takeaway message is that the language of math is tricky, and we have to teach it consciously and creatively.
Mark, I agree with your thoughts about textbook reading. It's far fetched to expect that students will learn from a text on their own. It's very time consuming and they have enough to do as it is. Such student centered learning would fare better in a classroom with cooperative strategies. I do think that students should be able to know how to read a mathematics text if they do want to use it as a resource. Not every child will be able to do their homework without difficulty and their textbook can provide them with the information they need to be able to complete it. However, a textbook will be of no use if they don't know how to actually use it.
ReplyDeleteChapter 3 addresses the idea of wanting students to be able to learn without relying on a teacher. If we do want them to try to learn on their own, assigning textbook reading may not be so far fetched. Consider the strategies used in Chapter 11. They do need to be modeled in class first, but once students have a grasp on how they are to be used, they should be able to apply them on their own. The assigned reading would cover what would be taught in the following day's lesson. Students would be reading ahead and applying a strategy or two described in Chapter 11. Then their understanding of what they read, or lack thereof, and questions they have, could be assessed and addressed in class. However, I think this type of assignment should only be assigned if students have a firm grasp on how to read a text and the prior material needed to understand the assigned section.
On page 139 of Chapter 11, it says, "students must become fluent with the vocabulary if they are to become successful mathematics...learners." Definitions are essential to understanding and doing math. I can't even begin count how many times I heard the maxim "know your definitions" when I was an undergrad. The idea behind this is that no matter what level of mathematics a students is studying, he or she can't even begin to learn math unless the definitions are mastered first.
After reading Mark's comment on math vocabulary (the paragraph beginning with 'On page 28...'), I'm starting to second guess the 'know your definitions' notion. Now I'm left wonder what really is better: definitions first, concepts later or concepts first, definitions later. Or maybe it's one over the other depending on the topic, not mathematics as a whole. This is something I think would be better left to discussion. I'd like to address it on Thursday.
Also, I wonder how often it would be beneficial to use textbook reading strategies in mathematics. I think certain pre-reading strategies, such as brainstorming, can be utilized without reading; having students do pre-reading exercises can key them into what the lesson will be on, which will help them know what to listen for when the lesson is finally presented.
ReplyDeleteChapter 1
ReplyDeleteOn page 6 the author suggests that many students struggle in mathematics because they have not developed the ability to translate from words to symbols and vice versa. It’s fun to see a text implicitly relate math to a foreign language. We learn language by producing it. Thus, we need to have kids “speak” in math. In how many language classes are you allowed to speak in English? The teachers push and guide you as you struggle. In math, we should be pushing students to speak like mathematicians. Constantly improving on the language of math whether it be symbols or new words.
Sparking off of Mark’s question if Ms. Wade’s class would succeed in an inclusive classroom, how long would it take a class to participate in this type of lesson if they have been spoon fed material the previous years? How do you break the cycle?
Chapter 3
I agree that math texts should be read at a slower pace and more attention to detail. However, when have you heard of a K-12 student independently reading and practicing along with a math textbook? I learned from the teacher in school and rarely relied on the text except for a formula here or there. So in essence, I learned from accessing my prior knowledge on the subject. On page 24 the text says that prior knowledge is the main determinant of understanding. It makes perfect sense that you cannot integrate a function without knowing how to add.
Chapter 5
I agree that students do not know where to begin with word problems. They know what needs to happen in the end, but getting there is the issue. Children complete concrete problems with ease. As soon as the decision making process begins the effort ends. The Zoom-In Zoom-Out strategy may help students conceptualize the problem since it gives them smaller and more manageable steps to complete as opposed to being introduced to a large daunting problem. The text suggests that with time students will be able to implement this strategy to future questions and become more independent with their learning.
Chapter 11
The pre-reading, reading, and post-reading is similar to the Zoom-in Zoom-out strategy where students find key information (i.e. titles, headings), reading for comprehension and flow (the text), then solving and explaining (postreading). This is probably a stretch, but there are similarities.
I don’t agree at first thought with the idea that students must become fluent with vocabulary to become successful in mathematics. I agree that some must be learned, but the understanding for a person could be just that, but without the ability to convey the understanding using math vernacular.
After reviewing the reading strategies I couldn’t remember of a time in a math class where one of these was implemented. These reading strategies were for “reading classes such as language courses and history.
Chapter 2:
ReplyDeleteI do think it is better for students if a classroom has an interactive dialogue. When the teacher is solely doing the talking it is easy for students to lose interest and begin to daydream. In addition, when it is time for them to do the work on their own they are left to do it based on what they learned by watching the teacher. When a classroom has an interactive dialogue the students are figuring out what to do for themselves with guidance from their teacher. It also helps them clarify prior knowledge and it gives them a better understanding of the topic. In my observations I have seen how interactive dialogue can change a class for the better. In one class I have observed the teacher would only ask students about three or four questions throughout the lesson and the rest of the time he was talking. During the lesson I found myself losing interest, so I can only imagine how quickly the students were gone. However, in other class that used interactive dialogue the students were animated and eager to show off what they knew.
Chapter 3:
I agree that mathematics is just like learning a foreign language, as it has its own set of vocabulary words and symbols that students must know to understand it fluently. I agree with the reading principles on page 24. However, I don’t think just because students don’t have a fluent math vocabulary they can’t succeed in math, I think understanding the concepts is also key.
Chapter 11:
I liked many of the strategies. However, I wonder how practical they really are and how many math teachers actually use them. From my experience and my observations I have never seen a math teacher have the students read the text first.
Chapter 5 -
ReplyDeleteI like zoom-in zoom-out. I don't believe this is so much a reading strategy, as much as a good teaching approach in which the teacher is cognizant about letting the students solve the problem on their own. By remembering the metaphor of zooming, a teacher can guide without giving the answers away.
I also thought it was ironic that they mention Polya. If you remember, I brought in the Polya book to class! It is a great read for all math teachers!
Chapter 11 - This is just a great chapter, chalk full of interesting strategies. I think it would behoove a teacher to be comfortable with all these strategies, and possibly even differentiate specific strategies with different students.
The vignette about solving word problems really is the number one reading issue for our students. True, we hope they can read and learn from their textbooks, but the reality is that they probably won't. But being able to decode and understand word problems is critical for the high stakes tests. Using strategies like KWL or zoom-in-zoom-out, if taught to students as a way of determining a problem solving strategy, sounds like a great thing to do. This is not constrained to midde school!!!!
These are excellent comments. I've been following your individual comments through my email but want to say, more generally, that I appreciate the careful reading of this book and the thoughtful display of your ideas here. You go beyond just summarizing or listing strategies you like/don't like and really raise some interesting ideas worthy of in class discussion tonight in your group - issues like reading a math text (when and what's appropriate to expect), speaking like mathematicians and dialogue in math (again, what's appropriate to expect), the value of thinking about math learning in relation to language learning (what would that do to our thinking about how we would conceptualize class time?), the role of these "pre-reading" strategies (what does "pre-reading" really mean here? As R suggests, maybe we can thinking about them as pre-intake of information strategies). I'm sure there are others - these are just some that stand out for me as I reread your posts online. I really want to encourage your discussion about the use of the math text - when and how do you read a math text??? What's important about that in terms of not only the short term goal of getting kids to learn the material in this school year but also in supporting their development as independent learners in the long haul, especially in thinking about their continuation with math at higher or later levels of education. I thought Ann and Raphaella made some good points worth taking apart and exploring more. I also thought the discussion about speaking math was interesting, especially in reference to the Ms. Wade discussion. That example evoked for me the Dagmar case we read earlier. Is this kind of interactive dialogue that reveals both teacher and student metacognition important, indeed essential, for all students, not just the high end? We read a social studies case for tonight on discussion that starts with a statement, loosely paraphrased, that student learning is related to the kind of classroom talk that goes on. What do you think?
ReplyDeleteGreat, provocative posts. I look forward to the discussion tonight! As with dialogue journals, keep making powerful connections between what you read in this book and other readings, your experiences teaching, being students, and observing in the field.
During our discussion last Thursday we first discussed the parcticality of reading strategies inside of a math classroom. We agreed that it implementing daily reading strategies in math classrooms would require us to invest much time and energy. Following this we tried to fine tune. What is common in a math classroom to read? Word Problems!!! In Dagmar's article we saw an entire class period devoted to one word problem. The text brought up the instructional approach of "Zoom-In Zoom-Out" found on page 62.
ReplyDeleteSecondly, we discussed if students need vocabulary to be successful in math and if vocabulary or concepts appear first. The text provided the number 30. This number represented the amount of times that a student would need to use a word to understand it. We're sure that this didn't mean copying the word 30 times down the side fo a page. Anyway, in math classrooms, we agreed that math concepts is what math teachers should be looking for. If a student can describe a piece of mathematics in their own words, then God bless them. Not to say vocabulry is not important, we believe that new vernacular should be scaffolded in.
Where we ended was thinking about the brilliant person who doesn't know the vocabulary. Or perhaps a person who is a literate thinker but lacks physical/verbal literacy. This topic may deserve some more attention.
"If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them." ~Phil Pastoret