- How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities? Provide examples to illustrate your points.
Morally Scientific
Lampert (1990) sought to change “the meaning of knowing and learning” in school by initiating and supporting social interactions appropriate to making mathematical arguments in response to students’ conjectures. Her aim was to give up conventional academic interaction, instead while seeking to help students act with “the moral qualities of a scientist” (p. 58). She compared the process, quite elegantly, to dancing, stating that it ““required some telling, some showing, some doing it with them along with regular rehearsals” (p. 58).
Perhaps the crux of her approach was an emphasis on avoidance of silence, and of a traditionally top-down approach to mathematics “learning”. She noted the importance of not keeping thinking implicit or private, suggesting that mathematics often involves “arguing, defending, challenging, and providing one’s own ideas” (p. 56).
The Great Divide
I really appreciated how Lampert described the inconsistency of how math is approached in and out of the classroom. In “real life” mathematical and scientific ideas are questioned almost constantly, and often hotly debated, and uncertainty on all sides is expected as a natural component of the process. Sometimes, the “right answer” may not even exist, or if it does it could be nearly impossible to prove. Unfortunately, “classroom” mathematics is too often entirely void of this essential process of questioning, these heated debates, and this exciting layer of uncertainty hovering over the proceedings. Instead, mathematics teaching encourages a flow of knowledge from top-to-bottom, with the “best” teachers often considered the ones who help students achieve the highest marks in the most efficient number of steps. What a wasted opportunity for learning.
Lampart took several approaches to counteract this stagnant learning environment:
- Providing students with open-ended problems to solve
- Collecting student responses and having them explain why another student’s answer is incorrect, or explain why they believe those answers to be correct
- Engaging in “cross-country” mathematics
This last point, “cross-country” mathematics, suggests that the problem-solving terrain” is “jagged and uncertain” (p. 41), and that watching someone traverse it (be it a teacher or even another student) is a key to learning how to traverse that terrain themselves. To be more specific, if it is only the teacher clearly demonstrating the rules, students will only see a limited picture of what’s necessary for expertise in the area, and will not learn how to solve anything but the most straightforward problems, and only in one standard way (p. 42).
The Right Stuff
Lampert found that by essentially refusing to give “the right answer”, students were forced to search for solutions to their problems in more creative and collaborative ways, often leading them to discuss with each other. Over time, students assumed the role of more experienced “knowers”, and became more comfortable and competent in mathematical discourse and, better embodying “the moral qualities of a scientist”.
Knowledge Construction
Lampert’s work, although probably not as extensive or rigorous as some of the other papers I’ve encountered, does point to the importance of students being co-constructors of knowledge. Her report suggests that knowledge relevant to math (and science) is perhaps best constructed constant questioning and debate. This approach allows all aspects of a problem to be explored, for all students to be involved in the generating of an answer (even in the absence of an all-knowing sage-like answer-distributing teacher) while ensuring that the answer to any given problem is the result of a collaborative effort from “all” students. Note: I say “all” because, without some help and encouragement from teachers, some students may be extremely unwilling to “put themselves out there” in a classroom debate.
A GLOBE-al Network
This week, I explored GLOBE.
Aside: I was impressed that a program that was first formed in 1995 has had continuous development work done on it, which is clear in its modern website’s presentation. I also had a literal “LOL” at David Dykstra’s comment about WhaleNet, which acts as a nice reminder that websites from the 90’s don’t get modernized by themselves.
Networked communities like GLOBE are not dissimilar from the above approach to math and science learning: GLOBE takes a “cross country” approach in its lack of a well-marked path, and its emphasis on exploration and discussion without a clear “right answer”. Students are literally acting not just with the “moral qualities” of scientists, but literal scientists, as they collect a variety of data in a standardized way. Sure, the structure of the program is slightly constricting, but the rigidly-structured data collection allows for their results to be compared, discussed, and debated with an online community without the fear of having their data thrown out due to invalid collection technique. Plus, standardized approaches to data collection does not negate opportunity for scientific discovery or discourse. I enjoy how GLOBE invites students (and their teachers) to take a trek into the unknown as they collect real-life data based on their own contexts, then get to compare said data with thousands of other students worldwide.
Clear Direction… to a Fault?
I do wonder, however, how effective GLOBE might be for developing critical/independent thinking skills. While the data collection and community aspects can allow for discovery and engagement, the GLOBE lessons provided for teachers seem highly scaffolded, including very specific instructions and assessment methods. What do you think… do specific instructions for teachers risk detracting from the exploratory essence of the program? Do you think greater teacher with GLOBE could result in a more genuine experience which expects more from students in terms of generative learning?
Thanks for reading 🙂
Scott
References
Butler, D. M., & MacGregor, I. D. (2003). GLOBE: Science and education. Journal of Geoscience Education, 51(1), 9-20.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63.
Hi Scott.
You made a couple of points that really resonated with me. The first was in your title – the importance of not keeping thinking private. So often with a new class, no one wants to say anything as they may be singled out as being wrong. How have we gone so wrong as society that ideas are discouraged, and students are negatively judged for creativity? The whole point of science is to be engaged in the process of learning which includes making educated guesses and seeing if they work. Students need practice in this to get better – but how can we encourage academic risk taking in our students? One idea I came across is an app called Creative Start where students are simply encourage to through out as many ideas as possible, and are judged on quantity not quality. One example my students had a lot of fun with was “how to peel a banana – without using your hands”. I used this as a brain stimulation exercise before an assignment requiring creative thinking.
The other thing that struck me was the use of open ended questions with no “right answer”. Over my years of teaching, I have noticed students becoming more and more dependent on the right answer, and ignoring the process of learning for the facts. I find this most prevalent with the strongest students as they are often marks rather than learning oriented. As teachers we need to work on our mental fortitude and learn to say no so that students can be independent learners. For example, in my robotics club, they have learned that I don’t know anything and generally sort out problems themselves. If unsure, they will come to me, and I will usually say something like “talk to Jacob and Austin, with the three of you come up with some options and give me a proposal of what you think the right one is”. At first they were resistant to this type of problem solving, but now it’s just met with a shrug and “OK”, before going off and doing it. Somehow I have to train myself (not them) to do this in class too!
Dave
Hey David,
I really appreciate your thoughts and feedback and I apologize for taking so long to respond!
The two points that resonated with you really seemed, to me, to be part of one whole: allowing students to express themselves and their thoughts safely and in a supportive environment. I have always tried from Day One of each of my courses to let students know that if they are wondering something they should question it; I will never judge a student in class for asking a question (some colleagues at my college absolutely do judge and discourage, and I hate that). Students are much less likely to be in an open state of mind, fit for learning, if they feel that their opinions or points of view are foolish or unwanted. I really enjoyed learning more about Creative Start (https://creativestartapp.com/) and I’ve added it to my “Neverending Learning List” for possible future use 🙂
I believe that your experience of students becoming increasingly dependent on the “right” answer is quite common across the board; and it’s our fault, as teachers, for we have conditioned them to expect this. Students simply adapt to the expectations we’ve set. They’re extremely perceptive; if we place heavy weight, and thereby future opportunities, on marks that are related to a specific answer, they’re dang well gonna regurgitate that answer whether they believe in it or not. Who wouldn’t? Why put one’s self on the line and explore new ideas if it will ultimately hurt one’s opportunities in the long run?
Of course, this system is totally backwards — the most special praise should perhaps be reserved for those who pour themselves into their learning — but it’s not the fault of the students. It’s the teachers and others “at the top” who lead that charge. Unfortunately, as I referenced above, not all of us are on board. Making a change here has to start with us, and it would be an uphill battle even if all teachers were on board.
BUT, that doesn’t mean I don’t try to make a change where I can. I hold out hope that keeping positive, and looking ahead to a better future, will eventually pay off, especially as “new blood” keeps rolling in!
Sorry for the ramble there…
Thanks for sharing your story about your robotics club. It’s so interesting to me how the less classroom-like an activity is, and the more seemingly-informal, the more students tend to engage in what they truly enjoy and the more meaningful the learning that can take place.
Let’s tie it to the previous chat about marks and the “right” answer: Robotics club rarely exist to provide some single “right” answer determined by a textbook or an instructor, and I would hazard to guess that students have a large amount of control over what they do in the club.
Do you think that the biggest reason for this extra engagement is because the robotics club is completely devoid of a marks-based system?
Thanks for your contribution David!!
Scott