30
Nov 10

Misconceptions, Coherence, and oh yeah, Learning Progressions

The readings this week around Learning Progressions brought up some discussions we had earlier in the semester for me, and I’d like to use this post to try and sort out some of these disconnected thoughts.  The specific concepts that came up for me were misconceptions, coherence, and the idea from Vygotsky that we shouldn’t just focus on the outcome, but on the process toward getting to the outcome.  I’ll talk through these one at a time:

Misconceptions

This one is probably the hardest to tie to a specific reading, but there was a sense of deja vu as I read through the Stevens et al article (developing an LP for the structure of matter) and the Steedle et al article — it seemed like there was a motivation that if we can just map out all the learning progressions, and figure out the paths from one place to the other (the learning trajectories that are mentioned in Steedle et al), we’d be done with educational research.  In the margins of the conclusion to the Stevens et al article, I wrote: “catalog the full collection of LP’s, determine appropriate LT’s, build robot teachers, and take over the world!”.

That takes the whole thing too far, but this sense of collection reminded me of some of the earlier research we heard about around misconceptions, where there were goals of cataloging the full set of misconceptions a student could have around a topic and ways to undo those misconceptions, and bingo — you’re done.  Learning progressions seem to offer more than misconceptions as a concept did, however, since they offer a specific structure to student concepts, and the notion of movement from one set of concepts to a different set of concepts.  That seems more useful as a notion of learning than the idea that you either have one of a ton of possible misconceptions, or you have the right answer, which was the sense I had from the misconceptions discussions we had in class.

 Coherence

diSessa brought up the whole idea of coherence when looking at different conceptual change theories of learning, and the Steedle et al reading made me think about this as well.  Part of my concern around developing hypothetical learning progressions is that they will be biased toward coherent sets of beliefs — for example, the whole set of physics around the assumption that a constant force is required for an object to move with a constant velocity.  From Steedle et al: “…exploratory model results provided no evidence of systematic reasoning beyond that which was identified by the confirmatory model.”  I’m interpreting this to say that learners aren’t building an entire physics around a misconception — they can pretty effectively separate that notion from the rest of their ideas about how things move if it gets in the way.  This gets to their next point, which is that students don’t always fit within one of the available learning progressions.

Studying the Learning Process

I don’t remember if there was a nifty single word for this, but the last idea that this brought up for me was Vygotsky’s comment that it seems pointless to study the way that someone reacts after they have already learned the behavior — instead we should be looking at how they are learning the behavior.    What I like about Learning Progressions after these readings is that they dive into that place and try to open up discussions about exactly what it is that students are thinking when they’re having trouble with a concept.  This was certainly available in the misconception research as well, but here it seems like we’re thinking of these models cumulatively moving toward the upper anchor of the learning progression, rather than being a stumbling block on the way to the concept.  That way of looking at it seems like it is likely to be more fruitful, since teachers are usually working with students who don’t already know the concept they’re teaching — so ignoring anything outside of mastery seems counterproductive.


30
Nov 10

LP

So I’m a little confused by the Steedle et al article. I guess I’m just confused about how they went about getting their data and where this facet class came from. It also would have been helpful if they would have included the test questions that they used. Oh well. What I got from their article was that their proposed “novice to expert learning progression” did not predict all of the students’ conceptions about force and motion.  Their conclusion that a “novice to expert learning progression” cannot describe every students’ understanding of constant speed probably can be carried over to other subjects. Even though this type of learning progression might not capture every student’s level of understanding, I think they are still helpful to the teacher to have an idea of what kind of conceptions their students may have.

I found Wilson’s paper to be quite helpful. It showed the different types of construct maps that you can create for a learning progression that I didn’t know existed. I always thought construct maps were likes those presented by project 2061 that have arrows pointing to each related concept.

Our previous readings would suggest that learning progressions fall into the conceptual change and constructing knowledge category. You are identififying students’ misconceptions and trying to change them at the same time building on previous knowledge.


02
Nov 10

Blumenfeld et al.

I feel that I must warn you that this post is not my best because it’s late and the election results are on. So, sorry.

Scott was right when he said that the Blumenfeld piece is a summary of all the theories that we have learned. I found the paper helpful in that it refreshed my memory of all the theories that we went over in class. It shined some light on how they build off of each other and how they are related. It also provided us with examples of how to apply the theories in a classroom setting.

I was happy to see the paper addressed one of the problems I have with “situated” (as Greeno puts it), that knowledge is not transferable from one situation to another. I still think that knowledge is transferable otherwise I don’t think we would be reading or writing outside of school. I think this quote says what I’m trying to say a lot better than I can,

In addition, proponents claim that knowledge itself is a reflection of social setting and social interactions; knowledge is interpretation, rather than something that is objective and fixed. (pg. 831)”

The last part that says that knowledge is not objective or fixed tells me that contrary to Lave and Wegner, knowledge is transferable and not limited to the situation.

I liked how the authors said that the programs that were developed to help teach science were programs that teach for understanding.


02
Nov 10

Who’s in charge of the class?

I’m just picking out a few small issues to talk about in reaction to the readings — the Blumenfeld et. al. piece, for example, had enough to write a lot more about, but I wouldn’t be able to do it any justice at this point…
1. Teacher control vs. student control of the class
The biggest question that came up for me in these readings was around teacher control of the class versus student control of the class.  In Greeno, I saw it around the discussion of “conceptual agency” (page 88):
Conceptual agency is involved when an individual or group interacts with the subject-matter constructively — interpreting meanings, formulating questions, choosing and adapting a method, designing an apparatus, and so on… School activities often position students with little conceptual agency, teaching them instead how to perform algorithms correctly (disciplinary agency) or to set up apparatus to obtain known experimental results (material agency).
Reading this, I realized that I place a high value on the amount of conceptual agency I’d offer in a class — I want students to get involved in the process of designing their own experiments, thinking up their own explanations for what they see, and critiquing each others’ work.  But I get conflicted about this, for at least two reasons:
  1. It seems like it places a lot of control in students’ hands, and that makes me a little nervous (because I like to be able to predict what’s going to happen in the day).
  2. I’m not sure how honest it is.  To what degree can I really put the class in students’ hands when I am the one grading them and when I’m the one who is judged on including the state/federal/local standards in the classroom?
The Blumenfeld et. al piece also talks over this issue, but it mostly shows up in discussions around technology use.  I’ll talk about technology specifically below, but I just recognized that the examples provided where the process was very “canned”, or where the teacher had a very clear idea of exactly how the class would proceed before it even started, seemed less engaging to me.  I’m recognizing that there’s a specific way of thinking about science that I value and want to communicate which conceptual agency speaks to, and these approaches do not.  
2. Coherence
I’ve been thinking of evaluating theories based on splits: individual vs. group, holistic vs. reductionist, abstract/general vs. concrete/specific.  diSessa brings up a new way to evaluate theories: coherent vs. fragmented, and applies that split within the cognitive camp to contrast her views with the prevailing views within the cognitive camp: to paraphrase, she sees us as holding many ideas that can all be in conflict with each other, and suggests that effective teaching could involve building up the ideas that line up with the concept that we’re trying to teach, rather than trying to get students to reject an existing concept that is out of line with the new one.  In the discussion on misconceptions around force when looking at a ball thrown upward that rises and then falls, she notes (p 266): “Finally, the upward “force” in the incorrect explanation is not absent, but it is what physicists call momentum.”  
While I found the analysis around the work done on misconceptions useful, I didn’t find the idea of “coherence” as useful in thinking about other theories as it was in splitting these two versions of cognitive theory up.  As a result, it seemed like a bit less central question than some of the others seem to be.
3. Technology
All of the examples discussed in the Blumenfeld et al piece involved extensive use of technology, and I got a clear sense of technology being seen as good all by itself.  In Table 1 on page 837, under the “Tools” column, we see “Pencil, paper” and “Low bandwidth telecom” under the “Then” column, while the “Now” column shows “interactive, integrated computer-based” and “High-bandwidth telecom”.  This bugs me, and I’m trying to decide if I’m just in a “get off my lawn” space, or if I have a reasonable beef.  So I’ll provide two examples of why I think tech for tech’s sake is a bad idea.
  • The “Scientists in Action” program outlined on page 846 seems really limited — students analyze a series of scenes from a videodisc and go through a canned set of questions and interactions to work on their scientific reasoning and problem-solving.  It seemed like it would be extremely rigid to use, and goes against the whole “cognitive agency” thing I was talking about above.
  • The “Project-Based Science” program outlined on page 848 has students from different locations work together on teams using telecommunication, videoconferencing, and online access to data across locations.  Having worked on a project requiring this type of interaction in my prior job, I have to say that it’s tremendously hard to do well, and that the benefit would have to be extremely big to justify the effort (for me).  It’s hard for me not to see it as a way to add extra technology to make the project look more interesting.  
I don’t feel anti-technology, but I feel like technology often gets thrown around as a solution instead of a tool.  I’m extremely opposed to this type of view, because I feel like it sets the technology up for a pretty bad failure.

10
Oct 10

Individuals or Groups?

As this discussion unfolded, it helped me develop my understanding of both the cognitive and situated theories.  To save space, I’ll skip the discussion of each article and jump to the new ways of thinking about these theories that seemed to come up out of these articles.
One of the frames used to differentiate the two theories is introduced in Greeno’s piece: “factoring” done by cognitive theory versus the holistic view taken in situative theory.  Cognitive theory here is described as explicitly reductionist: we can get someone to learn something by breaking it down into pieces and getting them to learn each of the pieces.  In contrast, situated learning is presented as a theory where the total (the culture or community) is greater than the sum of the parts (the individuals).  Using this understanding of the two theories, he presents the situated understanding of transfer, where you always must evaluate knowing or learning in the context of a system or situation.  If I try to translate it to the language used in Lave and Wenger, does being a full participant in one community make it easier to become a full participant in another?  
We also got the chance to look at how to understand individual tasks in the social situated theory and how to understand social tasks in the individual cognitive theory.  For an example of the understanding of individual tasks in situated learning, Greeno discusses problem based learning in medicine (p 10):
…students working in groups, led by a tutor, analyze realistic cases in which they discuss alternative diagnostic hypotheses as well as general properties of the biological systems that physicians need to understand.  Their activities do not exclude individual study… The individual work, however, is meaningfully related to activities that make more sense, medically, than taking exams to show that text information has been absorbed.
In the situated view, we can see here how the importance of the “situated”-ness of this material encourages individual study.  So there is individual work, but it is individual work that gets grounded in a specific context.  The conceptual theory has an idea of the social world as well (Anderson et al. 1996, p20):
…the cognitive perspective provides us with ways of making progress (in advancing the cause of education).  The first step is to analyze the complex social situation into relations among a number of individuals and study the mind of each individual and how it contributes to the interaction.  This inevitably involves understanding the great deal of social knowledge that resides in the mind and how the person has learned to interact with the social and physical environment.  It does not ignore the social but it does try to understand the social through its residence in the mind of the individual.  (emphasis mine)
Here the difference in factoring between the two theories is quite explicit — Anderson et al. propose dealing with social situations in a way analogous to the way we’d approach a physics problem — show the relationships between the elements, sketch out what’s going on within the elements, and put it all together.  But the element I emphasized highlights the important point to me: we can have concepts about people (or systems, or communities, or cultures)!  
Since this is getting to be long, I’ll just mention one additional point.  The discussion from both camps around abstraction left me missing Vygotsky.  Anderson et al. seem to push for abstractions to avoid work done in a specific context, while Greeno argues that abstraction might be useful, but it might not be (and this is where the final article ends with abstraction).  The thought of a social theory that incorporates abstraction (this is how I tend to think of internalization in Vygotsky’s theory) was pretty appealing at this point.

10
Oct 10

Christina Week 8

The first Anderson et al. article pointed out a lot of holes in the situated learning theory. This article argues against Lave and Wegner’s article about situated cognition and that learning is dependent on the situation. Anderson et al say with Lave and Wegner’s situated learning, learning is contextual and cannot be transferred. However, there is a large body of research out there that supports the transfer of knowledge. I feel that knowledge is transferable from one situation to the next; however, it probably doesn’t occur with all knowledge. If our knowledge wasn’t transferable, then how would engineers be able to design cars, planes, or anything else that improves society? Without the transfer of knowledge they wouldn’t have been able to invent the cars or planes that we rely on everyday. According to Lave and Wegner, engineers shouldn’t have been able to do this since they weren’t in a learning situation that taught them how to invent something new like a car.

 

Though the first Anderson et al. article does point out a lot of problems with the situated learning theory, I think there is still some validity to it. I still do not think that it is the end all and be all of learning theory. The Anderson et al. paper helped to point out some of the problems with it and helped me to further justify my thinking that even though some learning can occur the way the theory points out, I still think that learning can occur without being situational all the time.

 

I tend to disagree with Anderson et al. when they explain individual learning and side with Greeno that there always some social aspect involved in learning. Though the person may be engaged in the process of learning alone, I still think there is a social aspect to it. Such as with the example they give about a tax preparer learning the tax code on their own and not while a client is around. Though the tax preparer is sitting alone reading a book about tax code, he/she is still learning in a social atmosphere because a group of people decided what the tax code should be and published the book that the tax preparer is reading alone. The tax preparer is then learning about something that a group of people thought was relevant which then makes his/her learning of the tax code social and not individualistic.


04
Oct 10

Christina Week 7

A lot of the reading this week ties into what we have been reading the past few weeks and addresses some issues I had with Brown, Collins, and Duguid’s piece about apprenticeship and authentic activity.

The Ann Brown et al. paper addresses how schools fit into learning by saying that “schools should be communities where students learn to learn (pg 190).” It keeps up with our previous readings that learning is a social and cultural activity. They coin the term apprentice learners as a way to describe students. They say that the apprentice learners are learning how to think and reason in a variety of subject areas. This breaks away from the traditional apprenticeship roles that was used in the previous readings to explain how learning occurs. Our previous readings said that in order to learn we should be fully engrossed within that culture and engage in authentic activity. However, I don’t think this can always be applicable to the classroom. Students are not going to think like a scientist just because you have them engaged in an inquiry activity. I think that they need to be taught by a more informed peer to think and reason like a scientist. Ann Brown et al. states that this does not necessarily have to be a teacher but can also be a fellow student, which is also known as distributed expertise. Distributed expertise gives students a chance to teach each other about a topic in which they have become an expert. This relates back to Lave and Wegner’s article that learning can occur while engaging in discussion with other learners.

I have to agree with Ann Brown et al. when they say that it is impractical to think that all students must engage in authentic activity to learn and that it is not fair to the student. If we were to think that all students must engage in authentic activity like in a traditional apprenticeship as proposed by Brown, Collins, and Duguid, then each student would be a writer, mathematician, scientist, musician, artist, etc. all at once. I think we should view students as apprentice learners in that they are learning to learn and think about each subject and then be allowed to choose for themselves.    


03
Oct 10

Getting a little more real

The theme of the week’s readings for me was complexity: all of the sudden, we can actually imagine that there may simultaneously be thoughts in my head and that I might learn something from another person!  While the ideas of learning seem to get more complex when you try to incorporate multiple theories of learning at once, it really seems to allow a discussion of scenarios that are more realistic.  

Pintrich et al did a lot to help the conceptual change model find a way to connect with society.  By giving the learner motivation, we can then use the idea of motivation to introduce all sorts of social factors into the learning process.  This seems like a big help, since (as the authors mention) it is easy to imagine the student in a class completely ignoring all the discrepant demonstrations a teacher would want to make to highlight a misconception. 
Driver et al also seemed to draw from the conceptual change model, but looked at apprenticeship models with this when trying to extend the concept.  The article did a nice job of arguing for both learning science as both a social and individual process, which would not have seemed like such a big deal to me a month ago, but now seems like a breath of fresh air.
The final article I’ll discuss by Brown et al seemed to move away from the idea of getting students to enculturate or apprentice to the community or culture of practitioners: “We argue that schools should be communities where students learn to learn.” (p 190), “We aim to produce a breed of ‘intelligent novices’, students who, although they may not possess the background knowledge needed in a new field, know how to go about gaining that knowledge.”  This seems to offer a response to the critique that asking teachers to represent professional historians, writers, biologists, mathematicians, etc. was a bit unrealistic.  This idea of “learning to learn” is appealing to me — since we ask school to be the starting point for students who will go on to any number of varied practitioner cultures, how can we possibly choose between all the varied practices that students could end up in to decide which ones get represented in schools?  If instead we teach students how to learn, we can keep the idea of a school culture that feeds into all the various practitioner cultures that students will go to once they matriculate.  Even with this benefit, I’m still wondering about the following:
  • We’re back to considering “inauthentic activity” — kids learning (just) for the sake of learning.  So we lose whatever benefits come from learners doing “authentic activity”.
  • Is it really possible to “learn to learn”?  I can imagine some skills that are important in this — ideas about how to research, critical reading, formulating hypothesis and determining how to follow up on them — but I guess I’m somewhat uncertain about how well this would work if I imagine it separate from any content area.
The case study was very compelling to me, and imagining students developing their “majors”, as the article put it, was exciting.  The description of the email exchanges between one student and a graduate student regarding hibernation was particularly interesting, but left me uncertain about a big part of the endeavor: to what extent are the types of resources they used in the paper (experts, specifically) available?  Particularly now that email is so widespread?
For me, the most relevant part of the article was around the structure of their classes: the idea of the 10 week block of time for a subject, using the structures they outlined for the class (breaking the students into research groups by topic, having the groups split up the topics by student, and then coming back together in the “jigsaw” groups to peer teach) seemed like a good goal to move toward when I have my own classroom.

03
Oct 10

Week Seven Readings

I find that I ramble all too easily so I’m going to try my best to keep this brief to spare Scott and my group mates.

Brown

 Brown says, “It is clearly romantic to suggest, as do J. S. Brown et al., that students in public schools be enculturated into the cultures of mathematicians, historians, and literary critics. For a start, practitioners of these callings do not as a rule populate schools; teachers of these subjects may be consumers of the outputs of these disciplines, but they are rarely practitioners. History teachers are seldom historians. Practicing mathematicians infrequently teach high school, let alone grade school. (p. 189)” 
This was something I brought up earlier in the semester. A problem I had was that some of my teachers didn’t even know the material they were teaching. Granted, Brown takes it a bit further than I was willing to take it, because I’m not sure exactly what sets apart a historian from a history teacher apart from the field research they conduct. But again, that same argument could probably be made about any teacher in any subject. I’m not necessarily claiming that instructors should be practicing experts, but I do believe that in my experiences my teachers could have been far more knowledgeable on their subjects.
It’s really tough for me to even make it past the first few pages because there are so many quotes that I’m really enthusiastic about. I’ll pick one more and move on to the next author.
“If it is not to apprentice children to the traditional academic disciplines, what is the purpose of schooling? (p. 189)” 
Again, I don’t know if I’m 100% on board with this, but it’s really got me thinking. For some reason I feel some sort of connection to this theory of apprenticeship, but I still feel like it’s too uninformed a decision. But I’ve felt this way about so many of the different learning theories we’ve gone over. This does contradict Lave and Wenger, because they would argue that the purpose of school is for students to view their educational society around them, and witness how the other students learn. Or perhaps L&W would argue that students should simply be out in the field, learning first-hand. Maybe they would recommend a combination of the two? It’s all so enticing!
Driver

“There is an important point at issue here…presenting is in conflict with learners’ prior knowledge schemes.(p. 7)”
This is a long paragraph and would take a while to type it all out. But basically, what I’m getting from this paragraph is that learning is, indeed, a social mechanism, and the role of the teacher is to act as an intervener, offering guidance along the way. I think so far, this may be my favorite “explanation” of the process. After reading all of the articles so far, I’m sold on the thought that learning is a societal mechanism. Learning can not be done solely on an individual basis. But I think this is so far my favorite distinction of the teachers’ roles. I’m very nervous that I will end up taking my role as teacher too far, and become more of a babysitter than a form of guidance. 
Pea

With Pea, I get what he’s trying to say. I just don’t think I agree with how he says it. Yes, I do think intelligence can be acquired. But I’m not sure one can necessarily quantify it, which is one reason why I have a problem with standardized exams. I understand that intelligence can be “distributed” in the sense that many people can share the same intelligence, or knowledge, or whatever. Again, I get what Pea is doing, just not sure if this is the way I would go about explaining the learning process.
I guess that was brief?

27
Sep 10

Lave and Wenger

As I was reading the first couple of pages of this article, I was reminded of the concept of Zone of Proximal Development. The writers’ term “legitimate peripheral participation” has some similarities to ZPD.  I think that they are both similar in that an already knowledgeable person is required for the student to learn.

A lot of this paper also reminds me of Vygotsky in that society teaches us (the student), we internalize, and then become the teacher.

“Learning itself is an improvised practice: A learning curriculum unfolds in opportunities for engagement in practice (pg 93).” I thought this sentence was interesting. Cause if you think about it, learning is improvised and not set in stone. You aren’t going to move onto a new thing until you have learned the material you are focusing on now. For example, you aren’t going to move onto learning multiplication until you have mastered addition.

“The effectiveness of the circulation of information among peers suggests, to the contrary, that engaging in practice, rather than being its object, may well be a condition for the effectiveness of learning (pg 93).” I also found this to be quite interesting because it suggests that being part of a society helps our learning and that discussing information with other learners helps aide learning. As a future teacher I will try to encourage my students to discuss the material with others. I believe talking about the material can help you make sense of it and talking with other learners can help you understand what you thought was confusing and to maybe see something that you didn’t.

 


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