Blog 3: Situated Cognition, and Principle 3
Blog 3: Situated
Cognition and the Culture of Learning, and the third design principle
The Knowledge Principle
Good learning designs
recognize concepts as tools, situate those concepts in the
context of their use reflecting authentic activity, conceptual
tool, and culture, and analyze content for generalizable knowledge.
As teacher designers we need to think:
> In the context the students are in (whether it be math or music), what conceptual tools do students need?
> In order to understand and use a concept, what do they need to know?
> What authentic activity may be done for student to learn/reinforce their understanding?
> Would these activity be authentic to the culture of that subject? (Would a musician do this? A mathematician?)
> What knowledge can be generalized, to go beyond that specific situation?
As a math teacher, I’m struggling with authentic activities. In
Algebra 1, we are presently studying how to solve equations. I know that there are real-life situations
where people need to find a value that, at the moment, is unknown to them. We continue to discuss this idea in class
but, once we go beyond the basic structure where, perhaps, 2.25x + 5 = 25.00,
to reflect an issue with money, can we come up with authentic situations for
problems where 3(2x – 1) + 5x = 4x + 7?
Students need to be able to solve problems where the variable is on both
sides of the equation, or they won’t have learned all they need to know. Is this now generalizing the initial concept
(with the money problem)?
I loved a clock activity that was shared with me, where each number on the clock is represented by an equation (in one variable) that students create. This is a fun activity. I’m still not connecting it to “authentic activity”, in terms of one that a true practitioner of math would be doing. My students don’t yet have the skills that someone who uses math for their career might be using…
I loved a clock activity that was shared with me, where each number on the clock is represented by an equation (in one variable) that students create. This is a fun activity. I’m still not connecting it to “authentic activity”, in terms of one that a true practitioner of math would be doing. My students don’t yet have the skills that someone who uses math for their career might be using…
Looking at the reading from Situated
Cognition, I see the links between Activity à Concept à Culture à Activity (as a triangle).
Culture being defined as, for me, the culture of mathematics. The concepts being the tools we use to explain/understand the world (within the culture of mathematics), and the Activities… I know I want them to be authentic experiences but, again, I reach questions. I want authentic activities, not just problems from a textbook.
As statisticians, students can certainly gather data to study. As accountants they can solve questions of credit and debt. As pharmacists or nurses they may study percentages or, again, statistics. Business uses linear equations. But I can’t find ties for everything we need to know in class. Some of what we do are stepping stones; learning ways of thinking about numbers and situations. What kind I find that would be authentic? I still need to reflect to make that connection. The knowing ßà doing connection is powerful. I am challenged in finding the activities that are not just arbitrarily constructed, as with textbook activities. What authentic activities can I find?
Culture being defined as, for me, the culture of mathematics. The concepts being the tools we use to explain/understand the world (within the culture of mathematics), and the Activities… I know I want them to be authentic experiences but, again, I reach questions. I want authentic activities, not just problems from a textbook.
As statisticians, students can certainly gather data to study. As accountants they can solve questions of credit and debt. As pharmacists or nurses they may study percentages or, again, statistics. Business uses linear equations. But I can’t find ties for everything we need to know in class. Some of what we do are stepping stones; learning ways of thinking about numbers and situations. What kind I find that would be authentic? I still need to reflect to make that connection. The knowing ßà doing connection is powerful. I am challenged in finding the activities that are not just arbitrarily constructed, as with textbook activities. What authentic activities can I find?
I go back to my question in class, how do we (as teachers) know what the math community/culture needs from our students? I wonder about this often. I can do the math work but how do I make the math work for them, if that makes sense.
ReplyDeleteYou present a great question about finding authentic activities for all of the mathematical concepts. I have some of the same concerns for activities in my language arts class as I agree it is difficult to tie in all of the mandated objectives. The class activity using the design process of structure, process, and discourse has broadened my thinking on the topic of authentic activities, however. Although breaking down the objectives to find the necessary knowledge and what can be done with this knowledge is quite doable, it is the discourse that can be difficult, which answers the question of “how do I use this in society.” It is certainly a creative process that requires a shift of thought towards the bridge between mandated objectives and societal need. In my class, I often package objectives with the more advanced objectives when assigning a project. Being a language arts teacher, I’m not sure if that would relate to math, but that is my best suggestion.
ReplyDeleteI'm cheating here, but I'm copying/pasting the comment I wrote on Mickey's blog. It seems like we're all wondering the same things, so.... here's my thought (not that it's an easy fix): I feel like we teachers are all struggling with how to teach our subjects to our students in authentic ways, and we are hitting our heads against brick walls because we are thinking of our SUBJECTS, rather than the real (authentic) SITUATIONS people would be in that promote learning. The situations incorporate many facets... many topics, many SUBJECTS (!) into one overall situation. PBL (Problem-based/Project-based Learning) seems to be the answer. We ought not to think of our content area specialties as magical. We need each other to do right by our students, and collaborate across the subject areas to truly engage them in authentic experiences.
ReplyDeleteJane, you posed very pertinent questions. I must admit that also struggle sometimes with the idea of coming up with ‘real’ situations which would require my students to use content as a tool to solve an authentic problem. To make things more complicated, my students’ command of Spanish language is still rudimentary and would only allow them to do basic tasks. At this point I feel that I’m transitioning my thinking. I think that I am starting to envision a new array of activities, but it will definitely take time and plenty of trial and error. Because of the nature of my subject area, there are some activities, such as pronunciation drills or conjugation practice, which will never be ‘authentic’. But I am happy if I can start revamping and redesigning some of my old routines. As Sharon said in her reply to one of your earlier posts, baby steps. I am sure that when we see some of the new activities that we design in action, more ideas will come.
ReplyDeleteI commented something similar on Mickey's post...for me, teaching 7th grade Math I am able to find lots of real world ties to connections, for example, fractions/decimals/percents, I tie in shopping activities for sales tax/tip/discount. Thinking back to my first year teaching Algebra I...you're certainly right, it can be quite the struggle finding real world challenges there. An activity I would do quite a bit that would really get them talking, though, is give them a big multi-step equation, have one person in their group solve one step, the next person does the next step, and so on. This ensures that they understand the concepts, and makes them look closely at the questions. Another thing I would do was an "I Have, Where is?" scavenger hunt. This worked well with 7th grade Algebra 1 students. I would post various questions and answers around them room and they had to find them. I'd group them up still giving them chances to discuss the concepts with each other. But as for real life ties, I understand your struggle. But as others have noted too, baby steps and the desire to change are the start!
ReplyDelete