Chapter 8: For me, this chapter touched on several important things covered in my classes this semester: strategies for building meaning involving different literacies such as visual, kinesthetic and oral, the benefit of graphic organizers, and understanding concepts. The last one is really the main focus of the chapter, which the meaning making strategies mentioned above seek to facilitate. I definitely think that conceptual understanding, as the author asserts, should come before teaching skills. Throughout middle and high school, I often found math frustrating because I was taught a formula without any explanation of why it worked. I always wanted to know 'why' and felt lost knowing only 'how.' I also had trouble applying math skills because I didn't understand the concepts behind them. This changed in college when concepts and understanding were emphasized more than skills. Skills were important, but they didn't come first. This didn't erase my frustration with math entirely (the higher level stuff is extremely difficult), but I certainly developed more of an understanding of and appreciation for it. This is why I agree with the author on teaching towards concepts first. It not only allows students to make meaning of the material, it also gives meaning to the math they are learning. What I mean by this is that concept development allows students to make mathematical connections, between other concepts and real life, which then lets students see and determine how math can be meaningful for them. This is especially important for motivation. If a subject has no meaning for students, often they see no reason why they should bother learning it (other than to pass a test, etc). I'd like to further discuss the importance and implications of concept development, or lack thereof for anyone who disagrees with me, this Thursday.
A few final comments on Chapter 8: I liked most of the strategies presented in this chapter. I even saw one in action during recent field observations: the teacher used visual modeling to introduce and help students understand division with fractions (before teaching the keep-change-flip algorithm). The multi-rep chart from last meeting's chapters could also have fit in nicely with this chapter, not only because it just helps with making connections, but it requires students to make connections between the different ways of communicating a concept. The only strategy I had doubts about was the semantic grid. The smaller example seemed OK, but the larger one appears cumbersome and may prove difficult for middle school students to create and understand. Any thoughts on this?
Chapter 4: Chapter 4 raised a number of questions and concerns for me. I understand, after reading the chapter and recalling lessons from other classes, that discourse is important in the classroom. However, Chapter 4 briefly describes a method for achieving a specific discourse environment which does not appear at all easy to use. How long does one or can expect stay in each stage of the method? Does this differ drastically from class to class or is there more common length of time with a standard deviation? To add to this, what type of class work can we assign to aid in the transition from one stage to another? Should the assignments vary by level of possible discourse or should they allow for discourse in each stage and the teacher be in control of the level depending on the current stage of the class? Further, classes will most likely vary in ability as will students in each class. So despite any common or varied lengths of times for implementing the stages of the method, students will always be at different levels both within a class and from class to class. While it may not be impossible, I foresee molding instruction in order to implement these stages as difficult based on this variance alone. (Never mind everything else we'll have to keep track of.)
On a final note, I was intrigued by the seating arrangement in the vignette (something I've never heard of or seen before). The explanation in the vignette implies it works well. I am curious to see it put to use in a classroom in the future, either one I will observe or my own.
Raphaella - When I was a teacher, I too used the seating arrangement. If the desks are disconnected from the seats, it is easy for students to turn and face forwards. But nearly all math lessons involve seat work or group work, so having desks in pods is just amazing. It saves time and works well. It is up to the teacher to establish norms, like the vignette says... students work in pairs unless instructed otherwise.
My comments on chapter 4 - I agree a discourse community, in which students are thinking and sharing, is an amazing way to enhance learning. However, I disagree HEAVILY with a comment on page 40: ... Fourth, Ms. Ross asks many questions. She rarely if ever tells students. She constantly expects that they supply the mathematical thinking.
OMG - I hope this is an exaggeration! It is okay to pose questions and have students suggest solution approaches. But this is problematic for many reasons: 1) the same students are likely to always volunteer info, 2) the approaches may not be comprehensive or may have fallacies when generalized to other problems, 3) students can't "divine" mathematical notation, this has to be taught. There definitely needs to be a balance between student-volunteered creativity vs. teacher led instruction.
But I agree in princicple with the main theme of this chapter... getting students to think for themselves and elaborate, before giving them the answer, helps strengthen math knowledge and teachs students how to problem solve for themselves.
My comments on Chapter 8 - I agree that concepts are more important than skills. But concepts vs skills are likely to be acquired at different rates. For example, for somebody like me, very left brain, who's also good at math, I learn by concepts and prefer to discover the skills. But I've seen students who are math phobic, and trying to teach them concepts, increases their anxiety. Teaching them the skills how to solve the problem, in the hope that this leads to deeper conceptual understanding, is likely to be more successful. I agree both are important. But the implication, at least in the intro to this chapter, is that there is only one right way, and this right way is to focus on concepts.
Perhaps one can even do both concepts and skills simultaneously. As Raphaella pointed out, focusing on just skills will not help lead to deep understandings, and could even lead to frustration. Though I posit that there's another level: Concepts - skills - facts. Skills require that the applier know certain facts, like you can add or subtract the same amount from each side. SKills at least imply "doing something", and this can lead to successful problem solving, even if the student is lacking the deep conceptual understanding. A student who uses their calculator to multiply something by 10 may still be an okay problem solver, but they haven't grasped based 10 math at a deep level.
I also challenge a bit the assertion that peer interaction is essential to concept development. I think exposure to multiple approaches to a problem enhances conceptual development a la constructivism. Peers provide another approach and hence enhance constructivism. But couldn't a math teacher totally take charge of the multiple exposures? It might be more taxing and take more time, but it could be done. In particular, what if peers do NOT suggest a valid problem solving approach, should the teacher just ignore this approach?
I like the various strategies in the chapter. I think the "these are/these are not" is a way of clearning up misunderstanings, which is part of understanding by design.
I think concept maps are a bit far fetched for deeper understandings. It might help explain things, but once a student "gets it", then I think they'll never be used again. So I wonder if they are the best strategy to use to teach the concepts shown (power, equation).
I actually like the semantic feature analysis, but am concerned that students will use it to get a "quick answer", rather than thinking about the properties/displays to get a deeper understanding. WOuldn't it be nicer if a student could think about a display method, and recreate the properties on their own? This requires conceptual knowledge of how displays are used and the various types of statistics one can show graphically. This is not shown in the semantic feature analysis. I view this more as a "reference" card, to help recall things. But it should by no means be a substitute!
I love kinesthetic activities, especially early in the morning to wake students up, or after lunch, to keep them from falling asleep!
Student "mathematical" discourse in a classroom, I believe to not be up for debate. Students need to talk math in a classroom which will eventually lead them towards a better understanding. I agree with Mark that some significant math can't be produced in classroom. If it was, I couldn't imagine how much time it would take. And if a student did, they should not be in this classroom for sure. As far as students supplying the mathematical thinking, I believe they can do so if they have previously been given the pieces. In the Vignette, the students appear to have been given similar information numerous times and now it is the time that they do it themselves. On page 44 they say that students should participate as the questioners. I believe the importance is that the students are the responders. I believe this part of the text isn't specific on who answers. I believe that teachers should answer wuestions they believe that the students can answer on their own. I struggle with accepting that students lead the lesson. I would think that if students have all the control, less will occur. However, if you give students the perception that they are in control, while the teacher actually has it, good things may happen.
Stand and Deliver should be seen by all students!
Groups! I think these are a big plus especially if your room is preset in this fashion. Yes I see the difficulty in moving desks and chairs around if you share a classroom, but the benefits are worth it in my opinion.
I believe in asking students understand what one of their classmates said, of course. However, Instead of looking for nodding heads (anyone can nod their head) I would ask a student in the room to repeat what another student said in their own words or different ones alltogether. Elaborate without becomming redundant and boring I would think is key.
Chapter 4: Like Raphaella, I was fascinated about the seating arrangement. I’ve never seen a classroom set-up like this and it would be interesting to observe in a class that is. I wonder how it affects the students facing the center rather than the board. I do like the idea of working in groups. Group work in math is extremely beneficial to the students. Many students will never admit in front of a class that they don’t understand something, but they will when in a small group. I agree with Mark that the teacher’s remark that she asks the students many questions, but rarely tells them anything is rather odd. I understand what the teacher is trying to do by posing questions to the students, but she is still the teacher. Math is really not something students can learn on their own, they need to be taught it.
Chapter 8: What I found most fascinating about this chapter was how focused it was on the many types of literacies that we have studied earlier in the semester. I do think using these types of literacies is a great way for students to develop a deep understanding of the concepts. However, I think whether to teach concepts or skills first depends on the student. Some students like to understand why they are doing something and seeing where it will lead rather than just simply know how to do a problem. However, for many students the reverse is true, especially for students who are not good in math. They first like to learn how to do something and master it before learning the concepts behind it. It is important for the teacher to understand that every student learns differently and they are more likely to get a deep understanding of a topic based on if they are taught skills or concepts first. And a teacher when possible should try to accommodate the different learning styles of the students.
I agree that graphic organizers will help student comprehesnion especially if the students do not know how to take notes. They're something that students can look back on in their notes or perhaps create a mental picture in their head of the organizer. On the down side, if a student is given a prefab sheet they can just follow along and put down answers where they don't belong or place them in unmeaningful ways. in classes I have observed, some students just wait for someone else to say where information is supposed to go. I do not believe that you need to be an active note-taker in a classroom. Accountability needs to be in place.
As I was reading the Body Motion section all I could think about was Simon Says! Woah! I think this would be an awesome games that a teacher could challenge the students with or simply have students challenge themselves. "Simon says parallel lines!"
Touching and manipulating! I learn through a bit of self-discovery. I don't like having other people tell me what happens, or what would happen if you did A, B, or C. I like how the teacher gave students a question and they needed to investigate to come up with a solution. The students could have been nicer to each other when pointing out faults, but students talking about math isn't a bad thing as long as it's true!
Operations undoing each other! Enormous concept that I believe students don't know. Addition is opposite subtraction, multiplication and division, exponents and logs. Students don't know that they are inverse operations. The see them individual pieces with not too much connect. Or as Mark says, just facts and skills. There's no conceptualization to it.
Fractions and manipulatives, never thought about it before. I think it's a great idea if you can get a hold of some manipulatives that are really manipulative (i.e. break apart, bend,) Maybe magnets?
At this past Thursday's meeting, we agreed upon the general sentiments of the chapters we read: classroom discourse is important and teaching concepts is important. Most of the controversy lay in the specific strategies or methods described in the chapters. We were skeptical or questioning of several ideas. One was a particular seating arrangement from chapter 4. After discussing it, we agreed it was a strange setup and some thought there was no way it could work while other were simply confused by it. We did end up agreeing on group seating arrangements in general. Also, while we agreed that discourse is important, we thought the method for increasingly promoting discourse in chapter 4 was not only too rigid, but that there's no way students can learn some things in math on their own with minimal teacher input - there are some concepts and specific knowledge that teachers need to explain. A third source of controversy was the graphic organizer. Kenny wondered if kids would actually use it to clarify understanding or just fill it out to finish it. This led us to discuss how it would be appropriate to fit a graphic organizer students complete into a lesson or unit. Finally, we questioned the order of teaching skills and concepts. Mark proposed differentiating instruction with groups separated by skill and concept preference. However, at the end of the discussion the rest of us were still unsure when it's best to teach skill versus concepts.
I'm glad that there were a lot of sources of consensus. As usual, I enjoy reading your posts as they are written and deposited in my email. I agree that the emphasis on concept development is key and certainly is an underlying assumption in this course and backwards design (and, incidentally, just about everything I do here) but I was intrigued about your discussion of the dichotomy of concept and skills. I do totally agree that in most subjects, but perhaps even math moreso, the marriage of those two are critical. I'm not sure how I can demonstrate a deep understanding of concepts without utilizing skills to do so. And I do believe that skill building, done well and within a framework like understanding by design, leads to the potential (at least) for conceptual understanding. Perhaps, this author emphasizes conceptual development (and, to my read, does not discuss the interaction of conceptual and skill development as thoroughly) because practices in school often drill the mechanics (the how) of math to the detriment of developing the big ideas (the why). In reality - in practice - I think the relationship is less dichotomous and a lot more interactive.
The idea of social interaction as key to conceptual development rings true for me and is the basis of a sociocultural theoretical approach that underpins this book and current literacy research. Vygotsky's ideas of zpd and mentoring by a knowledgeable peer, the development of thought vis a vis language are critical ideas here it seems to me. How that practically plays out in the classroom is not only through peer interaction (although that's one possibility) but I believe that social interaction can also happen at least two others ways - guided practice with the teacher modeling thinking (think about the case of the math teacher helping students with reading) and encouraging students self-talk. Vygotsky even calls this "social." When students become aware of metacognition (when they are thinking about thinking in math), they are engaging in the necessary interaction to solidify understanding. That's how I (kindly) interpret the author's discussion of the role of social interaction in conceptual development. Thanks for the great summary, Raphaella.
Chapter 8: For me, this chapter touched on several important things covered in my classes this semester: strategies for building meaning involving different literacies such as visual, kinesthetic and oral, the benefit of graphic organizers, and understanding concepts. The last one is really the main focus of the chapter, which the meaning making strategies mentioned above seek to facilitate. I definitely think that conceptual understanding, as the author asserts, should come before teaching skills. Throughout middle and high school, I often found math frustrating because I was taught a formula without any explanation of why it worked. I always wanted to know 'why' and felt lost knowing only 'how.' I also had trouble applying math skills because I didn't understand the concepts behind them. This changed in college when concepts and understanding were emphasized more than skills. Skills were important, but they didn't come first. This didn't erase my frustration with math entirely (the higher level stuff is extremely difficult), but I certainly developed more of an understanding of and appreciation for it. This is why I agree with the author on teaching towards concepts first. It not only allows students to make meaning of the material, it also gives meaning to the math they are learning. What I mean by this is that concept development allows students to make mathematical connections, between other concepts and real life, which then lets students see and determine how math can be meaningful for them. This is especially important for motivation. If a subject has no meaning for students, often they see no reason why they should bother learning it (other than to pass a test, etc). I'd like to further discuss the importance and implications of concept development, or lack thereof for anyone who disagrees with me, this Thursday.
ReplyDeleteA few final comments on Chapter 8: I liked most of the strategies presented in this chapter. I even saw one in action during recent field observations: the teacher used visual modeling to introduce and help students understand division with fractions (before teaching the keep-change-flip algorithm). The multi-rep chart from last meeting's chapters could also have fit in nicely with this chapter, not only because it just helps with making connections, but it requires students to make connections between the different ways of communicating a concept. The only strategy I had doubts about was the semantic grid. The smaller example seemed OK, but the larger one appears cumbersome and may prove difficult for middle school students to create and understand. Any thoughts on this?
Chapter 4: Chapter 4 raised a number of questions and concerns for me. I understand, after reading the chapter and recalling lessons from other classes, that discourse is important in the classroom. However, Chapter 4 briefly describes a method for achieving a specific discourse environment which does not appear at all easy to use. How long does one or can expect stay in each stage of the method? Does this differ drastically from class to class or is there more common length of time with a standard deviation? To add to this, what type of class work can we assign to aid in the transition from one stage to another? Should the assignments vary by level of possible discourse or should they allow for discourse in each stage and the teacher be in control of the level depending on the current stage of the class? Further, classes will most likely vary in ability as will students in each class. So despite any common or varied lengths of times for implementing the stages of the method, students will always be at different levels both within a class and from class to class. While it may not be impossible, I foresee molding instruction in order to implement these stages as difficult based on this variance alone. (Never mind everything else we'll have to keep track of.)
ReplyDeleteOn a final note, I was intrigued by the seating arrangement in the vignette (something I've never heard of or seen before). The explanation in the vignette implies it works well. I am curious to see it put to use in a classroom in the future, either one I will observe or my own.
Raphaella - When I was a teacher, I too used the seating arrangement. If the desks are disconnected from the seats, it is easy for students to turn and face forwards. But nearly all math lessons involve seat work or group work, so having desks in pods is just amazing. It saves time and works well. It is up to the teacher to establish norms, like the vignette says... students work in pairs unless instructed otherwise.
ReplyDeleteMy comments on chapter 4 -
ReplyDeleteI agree a discourse community, in which students are thinking and sharing, is an amazing way to enhance learning. However, I disagree HEAVILY with a comment on page 40: ... Fourth, Ms. Ross asks many questions. She rarely if ever tells students. She constantly expects that they supply the mathematical thinking.
OMG - I hope this is an exaggeration! It is okay to pose questions and have students suggest solution approaches. But this is problematic for many reasons: 1) the same students are likely to always volunteer info, 2) the approaches may not be comprehensive or may have fallacies when generalized to other problems, 3) students can't "divine" mathematical notation, this has to be taught. There definitely needs to be a balance between student-volunteered creativity vs. teacher led instruction.
But I agree in princicple with the main theme of this chapter... getting students to think for themselves and elaborate, before giving them the answer, helps strengthen math knowledge and teachs students how to problem solve for themselves.
My comments on Chapter 8 -
ReplyDeleteI agree that concepts are more important than skills. But concepts vs skills are likely to be acquired at different rates. For example, for somebody like me, very left brain, who's also good at math, I learn by concepts and prefer to discover the skills. But I've seen students who are math phobic, and trying to teach them concepts, increases their anxiety. Teaching them the skills how to solve the problem, in the hope that this leads to deeper conceptual understanding, is likely to be more successful. I agree both are important. But the implication, at least in the intro to this chapter, is that there is only one right way, and this right way is to focus on concepts.
Perhaps one can even do both concepts and skills simultaneously. As Raphaella pointed out, focusing on just skills will not help lead to deep understandings, and could even lead to frustration. Though I posit that there's another level: Concepts - skills - facts. Skills require that the applier know certain facts, like you can add or subtract the same amount from each side. SKills at least imply "doing something", and this can lead to successful problem solving, even if the student is lacking the deep conceptual understanding. A student who uses their calculator to multiply something by 10 may still be an okay problem solver, but they haven't grasped based 10 math at a deep level.
I also challenge a bit the assertion that peer interaction is essential to concept development. I think exposure to multiple approaches to a problem enhances conceptual development a la constructivism. Peers provide another approach and hence enhance constructivism. But couldn't a math teacher totally take charge of the multiple exposures? It might be more taxing and take more time, but it could be done. In particular, what if peers do NOT suggest a valid problem solving approach, should the teacher just ignore this approach?
I like the various strategies in the chapter. I think the "these are/these are not" is a way of clearning up misunderstanings, which is part of understanding by design.
I think concept maps are a bit far fetched for deeper understandings. It might help explain things, but once a student "gets it", then I think they'll never be used again. So I wonder if they are the best strategy to use to teach the concepts shown (power, equation).
I actually like the semantic feature analysis, but am concerned that students will use it to get a "quick answer", rather than thinking about the properties/displays to get a deeper understanding. WOuldn't it be nicer if a student could think about a display method, and recreate the properties on their own? This requires conceptual knowledge of how displays are used and the various types of statistics one can show graphically. This is not shown in the semantic feature analysis. I view this more as a "reference" card, to help recall things. But it should by no means be a substitute!
I love kinesthetic activities, especially early in the morning to wake students up, or after lunch, to keep them from falling asleep!
Chapter 4
ReplyDeleteStudent "mathematical" discourse in a classroom, I believe to not be up for debate. Students need to talk math in a classroom which will eventually lead them towards a better understanding. I agree with Mark that some significant math can't be produced in classroom. If it was, I couldn't imagine how much time it would take. And if a student did, they should not be in this classroom for sure. As far as students supplying the mathematical thinking, I believe they can do so if they have previously been given the pieces. In the Vignette, the students appear to have been given similar information numerous times and now it is the time that they do it themselves.
On page 44 they say that students should participate as the questioners. I believe the importance is that the students are the responders. I believe this part of the text isn't specific on who answers. I believe that teachers should answer wuestions they believe that the students can answer on their own.
I struggle with accepting that students lead the lesson. I would think that if students have all the control, less will occur. However, if you give students the perception that they are in control, while the teacher actually has it, good things may happen.
Stand and Deliver should be seen by all students!
Groups! I think these are a big plus especially if your room is preset in this fashion. Yes I see the difficulty in moving desks and chairs around if you share a classroom, but the benefits are worth it in my opinion.
I believe in asking students understand what one of their classmates said, of course. However, Instead of looking for nodding heads (anyone can nod their head) I would ask a student in the room to repeat what another student said in their own words or different ones alltogether. Elaborate without becomming redundant and boring I would think is key.
Chapter 4: Like Raphaella, I was fascinated about the seating arrangement. I’ve never seen a classroom set-up like this and it would be interesting to observe in a class that is. I wonder how it affects the students facing the center rather than the board. I do like the idea of working in groups. Group work in math is extremely beneficial to the students. Many students will never admit in front of a class that they don’t understand something, but they will when in a small group. I agree with Mark that the teacher’s remark that she asks the students many questions, but rarely tells them anything is rather odd. I understand what the teacher is trying to do by posing questions to the students, but she is still the teacher. Math is really not something students can learn on their own, they need to be taught it.
ReplyDeleteChapter 8: What I found most fascinating about this chapter was how focused it was on the many types of literacies that we have studied earlier in the semester. I do think using these types of literacies is a great way for students to develop a deep understanding of the concepts. However, I think whether to teach concepts or skills first depends on the student. Some students like to understand why they are doing something and seeing where it will lead rather than just simply know how to do a problem. However, for many students the reverse is true, especially for students who are not good in math. They first like to learn how to do something and master it before learning the concepts behind it. It is important for the teacher to understand that every student learns differently and they are more likely to get a deep understanding of a topic based on if they are taught skills or concepts first. And a teacher when possible should try to accommodate the different learning styles of the students.
Chapter 8
ReplyDeleteI agree that graphic organizers will help student comprehesnion especially if the students do not know how to take notes. They're something that students can look back on in their notes or perhaps create a mental picture in their head of the organizer. On the down side, if a student is given a prefab sheet they can just follow along and put down answers where they don't belong or place them in unmeaningful ways. in classes I have observed, some students just wait for someone else to say where information is supposed to go. I do not believe that you need to be an active note-taker in a classroom. Accountability needs to be in place.
As I was reading the Body Motion section all I could think about was Simon Says! Woah! I think this would be an awesome games that a teacher could challenge the students with or simply have students challenge themselves. "Simon says parallel lines!"
Touching and manipulating! I learn through a bit of self-discovery. I don't like having other people tell me what happens, or what would happen if you did A, B, or C. I like how the teacher gave students a question and they needed to investigate to come up with a solution. The students could have been nicer to each other when pointing out faults, but students talking about math isn't a bad thing as long as it's true!
Operations undoing each other! Enormous concept that I believe students don't know. Addition is opposite subtraction, multiplication and division, exponents and logs. Students don't know that they are inverse operations. The see them individual pieces with not too much connect. Or as Mark says, just facts and skills. There's no conceptualization to it.
Fractions and manipulatives, never thought about it before. I think it's a great idea if you can get a hold of some manipulatives that are really manipulative (i.e. break apart, bend,) Maybe magnets?
Sources of consensus and controversy:
ReplyDeleteAt this past Thursday's meeting, we agreed upon the general sentiments of the chapters we read: classroom discourse is important and teaching concepts is important. Most of the controversy lay in the specific strategies or methods described in the chapters. We were skeptical or questioning of several ideas. One was a particular seating arrangement from chapter 4. After discussing it, we agreed it was a strange setup and some thought there was no way it could work while other were simply confused by it. We did end up agreeing on group seating arrangements in general. Also, while we agreed that discourse is important, we thought the method for increasingly promoting discourse in chapter 4 was not only too rigid, but that there's no way students can learn some things in math on their own with minimal teacher input - there are some concepts and specific knowledge that teachers need to explain. A third source of controversy was the graphic organizer. Kenny wondered if kids would actually use it to clarify understanding or just fill it out to finish it. This led us to discuss how it would be appropriate to fit a graphic organizer students complete into a lesson or unit. Finally, we questioned the order of teaching skills and concepts. Mark proposed differentiating instruction with groups separated by skill and concept preference. However, at the end of the discussion the rest of us were still unsure when it's best to teach skill versus concepts.
I'm glad that there were a lot of sources of consensus. As usual, I enjoy reading your posts as they are written and deposited in my email. I agree that the emphasis on concept development is key and certainly is an underlying assumption in this course and backwards design (and, incidentally, just about everything I do here) but I was intrigued about your discussion of the dichotomy of concept and skills. I do totally agree that in most subjects, but perhaps even math moreso, the marriage of those two are critical. I'm not sure how I can demonstrate a deep understanding of concepts without utilizing skills to do so. And I do believe that skill building, done well and within a framework like understanding by design, leads to the potential (at least) for conceptual understanding. Perhaps, this author emphasizes conceptual development (and, to my read, does not discuss the interaction of conceptual and skill development as thoroughly) because practices in school often drill the mechanics (the how) of math to the detriment of developing the big ideas (the why). In reality - in practice - I think the relationship is less dichotomous and a lot more interactive.
ReplyDeleteThe idea of social interaction as key to conceptual development rings true for me and is the basis of a sociocultural theoretical approach that underpins this book and current literacy research. Vygotsky's ideas of zpd and mentoring by a knowledgeable peer, the development of thought vis a vis language are critical ideas here it seems to me. How that practically plays out in the classroom is not only through peer interaction (although that's one possibility) but I believe that social interaction can also happen at least two others ways - guided practice with the teacher modeling thinking (think about the case of the math teacher helping students with reading) and encouraging students self-talk. Vygotsky even calls this "social." When students become aware of metacognition (when they are thinking about thinking in math), they are engaging in the necessary interaction to solidify understanding. That's how I (kindly) interpret the author's discussion of the role of social interaction in conceptual development. Thanks for the great summary, Raphaella.
I agree - Raphaella's summary was incredibly accurate, especially considering I had an agenda of 6 questions that I brought up. Awesome job Raphaella.
ReplyDeleteI also loved the metacognition and Vygotsky connection made by Dr. Clayton.