- How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities? Provide examples to illustrate your points.
Mathematical knowledge is constructed by reason of use in relevant circumstances which may or may not occur within a formal classroom setting as shown by Carraher, Carraher, and Schliemann (1985). They found that the Brazilian children working as street vendors were able to perform mathematical computations, always without the use of paper and pencil and often above their equivalent formal “grade level”. This learning was anchored directly to their authentic contexts and not easily transferred into a school mathematics environment, however. These same children were not able to perform similar computations when presented with “formal mathematical problems without context and…word problems referring to imaginary situations” (p.24) that nevertheless used the same numbers or items they were able to compute in the informal setting. The mitigating factor appears to be that formal mathematics requires students to take contextualized situations (ie. the real life “word problems” of a customer asking them about the price of a certain quantity of coconuts) and translate them into algebraic expressions. The perceived deficit in mathematical knowledge found in the formal assessment is not about the child’s ability to compute values correctly at all, but is, in fact, about her “expertise in manipulating symbols” (p.25).
Networked communities, whether formal school classrooms, interactive museum exhibits, or virtual field trips can aid in this generation of knowledge by contextualizing concepts in authentic and relevant phenomena. Carraher, Carraher, and Schliemann (1985) suggest “seek[ing] ways of introducing these systems [of thinking] in contexts which allow them to be sustained by human daily sense” (p.28). Such a thing does not happen by accident, as Moss (2003) points out in his critique of one implementation of the JASON project. Even when professional development and classroom implementation is available, truly connective communities of practice that result in long-term retention of scientific concepts and reforming student understanding of the nature of science through formal settings is not guaranteed. Moss’s (2003) observations of science learning supports the previous authors observations of mathematical learning when he states that “students’ conception often can develop in the home and community, and do not necessarily develop in classrooms. It is essential that we recognize that learning science occurs beyond the science classroom throughout many aspects of students’ lives, and it is critical that we facilitate learning opportunities in class which take these prior experiences into account” (p.24). These networks, when leveraged properly, have the potential to provide authentic science and math experiences that may help bridge the gap between informal, generative knowledge that’s grounded in relevant contexts and is retained, and the formal algorithms and facts that must be translated into symbol-systems and manipulated in the short-term to demonstrate “learning” at school.
Discussion:
Moss (2003) suggests that Student Scientist Partnerships “must be viewed as complementary, and even beneficial, to testing initiatives which are driving the choice of curricular programs” (p.29) but that the way teacher training was handled and the constraint of time contributed to an ineffective implementation of the JASON project to that end. How might teachers or schools ensure that time invested in interactive and virtual learning has longer-lasting, richer effects than simply getting students to feel excited for the duration of the project?
References
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British journal of developmental psychology, 3(1), 21-29.
Moss, D.M. (2003). A window on science: Exploring the JASON Project and student conceptions of science. Journal of Science Education and Technology, 12(1), 21-30.
Hi Jan,
You bring up some excellent points for discussion. It is fascinating about what you say about the children in Brazil and how they were able to figure out the Math in real-life contexts but when given similar problem in a formal setting could not. I think that this reinforces the idea that we need to provide our students with real-life experiences for them gain conceptual understanding and transfer their knowledge through real-life application. One way we can do this is through careful and creative planning. My teaching team and I sometimes it can be difficult though because the outcomes that we have in our curriculum are ones that students our age would never use outside of school. For instance, one of our outcomes is for students to recognize and identify prime and composite numbers. OUr students are eight and would never use need this outcome in their real-life. Because we have to report on this particular outcome, it was taught and assessed in isolation. For outcomes that students use outside of school like addition and subtraction, we try and think of ways were able to bring in real-life scenarios so they can practice and apply their understanding. This year we had students plan a class party. They were given a budget and brought to a few stores to buy items for the party. They had to calculate how much money they were spending and keep track of how much they had left. This was a lot more meaningful because they were using their skills in a way that was real. This experience is one they still talk about but as one would predict, they never speak of when we learned about prime numbers 😉
Thanks for your post!
Sarah
Hi Sarah,
Perhaps you will not see this reply because I am behind and just reading it now but thanks for engaging! 🙂 I love the idea of the class party as a way to incorporate real world math. Did they actually have a party after this or was it just an exercise?
I was thinking about the prime and composite number situation too. I think topics such as this one need to be creatively embedded in order to be remembered. Using games may be one way to make this topic more memorable. I’m not sure if there is already a game about prime and composite numbers but one could be created either by the teacher or better yet given to the students as a projects – create a game that uses the identification of prime and composite in a meaningful way. You actually gave me an idea! I think some of the students would love to use the programming platform Scratch (scratch.mit.edu) to code a game that allowed players to select prime and composite numbers as they fell from the sky or only catch the primes with a pong-like paddle at the bottom of the screen or something, hmm…. now the wheels are turning. Thanks! 🙂
Hi Jan,
Great food for thought! Many of the technology applications that we choose as teachers and technology professionals are often self-contained and unusable outside of the context of the school and the particular learning task that we assign. I believe that teachers should not be afraid to use interactive real-world learning tools that have communities of practice outside the virtual walls of the school. Interacting with experts and experienced users gives students unique opportunities to learn more organically and engage at the zone of proximal development. Naturally, a risk assessment needs to be made so that precautions can be taken and students are trained properly on social interactions in public environments.
Vygotsky, L. (1987). Zone of proximal development. Mind in society: The development of higher psychological processes, 5291, 157.
Hi
I like the fact that you brought up the “Brazilian children working…without the use of paper and pencil”. A few years ago, I was at a gas station and the power went out and the attendant could not calculate the change. The attendant replied on the cash machine to tell him how much change to give the customers and without power — he was lost/confused.
Do they teach how to give change at the elementary level? In this video (https://www.wikihow.com/Count-Out-Change), it says to count the bills first. I was taught to give the coins first.
Christopher
Hello Christopher,
I have had similar experiences in retail with power outages. I know that elementary math teaches the concepts of money and change but from what I recall it does not stress the ability to do it efficiently the way I had to learn it when I worked at Burger King LOL i.e. taking the coins and counting up to the nearest dollar and then counting on to the total amount given. In the textbooks a question is something like someone wants to buy items that cost $21.32 and she pays with $40, how much will she get back? Normally students line up the place value columns and manually subtract with their pencil and paper. I actually wondered if the grade 9 and 10 math teachers would teach the “counting back” the change method now that the students were of the age to apply for part-time jobs!
Hi Jan,
Great question,
I think that using authentic, real-world problems and issues as part of virtual learning would create longer-lasting effects for students. Students need to be able to connect issues to themselves and see how it would affect them and the people around them. Teachers need to be explicitly aware and have intent behind their thinking of incorporating different uses of designs for teaching. If we want our students to feel enthusiastic about what they are learning, they need to be able to connect with it which will help them to feel more passionately about it thus encouraging and enhancing their learning.
Hi Sabrina,
I agree with your observation that by locating learning within the world and people around our students it allows them to connect with it and this connection can encourage and enhance their learning. This reminded me of the notion that learning does not take place without the choice of the learner to understand, whether via conscious or unconscious “understanding goals”, as artiulated in LfU’s second principle — “knowledge construction is a goal-directed process that is guided by a combination of conscious and unconscious understanding goals” (Edelson, 2001, p.357). By framing STEM explorations in the real world narrative we can create curiosity- or frustration-inducing circumstances that promote our students development and pursuit of these “understanding goals”.