Category Archives: B. Knowledge Diffusion

How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities?

According to Rosalind Driver, “The objects of science are not the phenomena of nature but constructs that are advanced by the scientific community to interpret nature.”

Knowledge relevant to science and math is constructed as part of socially accepted ideas that have permeated and prevailed into scientific communities through symbolic representation of empirical research. The role of the teachers, therefore, is to initiate students into the scientific ways of knowing (Driver et al., 1994), by introducing them to scientific concepts, as well as intervening and negotiating their conceptual understanding. Educators are mediators that guide students in differentiating between the everyday world of perceived science and the accepted world of science developed by the scientific community, as emphasized by Driver.

With the advances in science informational technologies (IT) provide, scientific and mathematical knowledge construction is heavily influenced by social processes and context. Carraher’s study of ‘Mathematics in the Streets and in Schools’ compared computational strategy effectiveness, given a context (such as completing transactions in the streets of Brazil) to routine learned computations strategies in school, without context. The study found that the knowledge construction was more powerful and effective if it was learned within a context, making fewer computational mistakes since the learning was being meaningfully applied for that student (Carraher et al., 1985). This implies that learning using an IT context needs to include opportunities for students to make meaning for themselves of the scientific knowledge they are delving into. As educators wanting to use networked communities such as Exploratorium and Virtual Field Trips like Discovery Ed, we need to negotiate differences between common sense science and the scientific symbolic representations of actual science.

Digital Libraries and Museums can offer excellent scientific reasoning opportunities for students to engage in. Interactive installations and activities allow for physical observations of scientific phenomena for students, while enhancing the scientific community of young learners by enabling choice and interest through a variety of topics (Hsi, S., 2008). These virtual museums can allow for students to access true scientific material from remote areas, rather than relying on student collected empirical data to make informed scientific research. In my own practice, I have found citizen science projects, such as Zooniverse.org, to be effective ways to engage young learners in scientific discovery and dataset research and interpretation. The distributed data collection using IT allows for a broadening of the scientific community that can enhance interest and learning far greater than what was available to the average student in the past.

However, as Spicer points out, there is still no truly effective replacement for real field trips and scientific knowledge building through hands-on and socially constructed learning opportunities. Staff and student interaction during real field trips facilitates deeper “emergent” issues through discussions that allows for more profound learning to occur (Spicer et al., 2001). Therefore, with any IT enhanced science or math engagement opportunity, the learning should be enhanced not replaced with virtual learning environments. Virtual field trips, for examples, should be used as a ‘before and after’ routine that can further a student’s thinking towards a particular scientific principle, rather than relying solely on the guided or open tours available through a virtual museum’s website.
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.

Driver, R., Asoko, H., Leach, J., Scott, P., & Mortimer, E. (1994). Constructing scientific knowledge in the classroom. Educational researcher, 23(7), 5-12.

Hsi, S. (2008). Information technologies for informal learning in museums and out-of-school settings. International handbook of information technology in primary and secondary education, 20(9), 891-899.

Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.

This week, I chose to focus my attention on the Carraher, Carraher & Schliemann (1985), Spicer & Stratford (2001), and Yoon, Elinich, Wang & Steinmeier (2012) articles.

When I started reading the Carraher et al (1985) article I wondered the relevance it would have to my Grade 1 students who come from a fairly privileged neighborhood. I quickly realized that the young children in the study who were able to determine the price of ten coconuts without the use of paper and pencil and little to no education were a great example of how to teach mathematics. More than ever, educators are starting to veer away from the traditional math worksheets and teach using a variety of hands-on activities with a wide variety of manipulatives. Had these Brazilian students been sitting in a classroom listening to a teacher speak at the front of a classroom about multiplication, would they have understood the concept as clearly? It is evident that hands-on, applicable learning is key in students understanding mathematic concepts as well as being able to apply them to different situations in their lives.

In the Spicer & Stratford (2001) article, they discussed a VR program called Tidepool and polled students on whether or not they believed VR programs such as this could replace actual field trips. In this particular VR program, students could copy and paste, add hyperlinks, pictures and text from the ‘field notebook’ to their own electronic notebook. This allowed students to gather information that they thought was most informative or valuable to them in an easy and accessible manner. This use of technology reminded me of how inquiry based learning can encourage deep and meaningful learning to occur as students are creating their own understandings based on the information that they deem to be useful. While the consensus of the study demonstrated that VR is not as immersive as actual field trips, it is clear that there is some merit to such experiences, especially when actual field trips are not possible. Utilizing programs like National Geographic’s live cams and Discovery Educations virtual field trips allows me to plan my science and mathematics program to ensure that my students are immersed in as much live content as possible. Being able to follow the life of a bald eagle and see its nesting patterns, etc. versus reading about it in a textbook or even on the web is not the same. Being able to view, in real time, live experiences through virtual realty programs is incredibly intriguing to students.

It is clear that with the inclusion of VR/AR activities, scaffolding and collaboration is key in the successful learning and understanding of students. As Yoon et al (2012) pointed out, “scaffolds would promote collaboration within the peer groups by encouraging students to discuss their observations and reflections of their experience”. This statement clearly demonstrates the importance of discussions when utilizing technology. Without collaborative discussions to outline what the students are examining through virtual realties, connections are not being made and the usefulness of these programs declines. Therefore, it is important for educators to purposefully utilize these programs in conjunction with collaborative activities for learning to occur.

All in all, after reading these article and taking time to explore the different websites/activities provided, it is clear that in order for such programs to be successful in the classroom, they must be utilized in conjunction with a clear plan outlined by the educator. Additional activities that delve into the deeper meaning of these programs and what is being viewed are necessary for deep learning to occur.

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.

Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.

Yoon, S. A., Elinich, K., Wang, J., Steinmeier, C., & Tucker, S. (2012). Using augmented reality and knowledge-building scaffolds to improve learning in a science museum. International Journal of Computer-Supported Collaborative Learning, 7(4), 519-541.

• Speculate on how such networked communities could be embedded in the design of authentic learning experiences in a math or science classroom setting or at home. Elaborate with an illustrative example of an activity, taking care to consider the off-line activities as well.

I found this week’s readings to be informative and applicable, especially when viewed through the lens of an inner-city school. I am specifically interested in Exploratorium, a museum in San Francisco. Their intention is to diffuse knowledge through their exhibits through an on-line option, that provides an extension of what you would experience in the museum. I like the fact that students can experience the museum from home or school. One of the apps listed on their website is called ‘Science Journal’. This app simulates a laboratory, which supports students as they document their observations through an experiment, however it is only available for android phones. Students can gather data, measure light, sound, and acceleration. The Exploratorium created companion activities for the app.

The Exploratorium websites shares that for “most students, science is still defined by textbook chapter assignments on Monday and vocabulary quizzes on Friday. Regrettably, students experience science in an interactive way in perhaps less than 10 percent of science classrooms. The Exploratorium is working to change that” (Exploratorium). In the design of an authentic learning experience in a science classroom, Exploratorium could be used to support inquiry. The website hosts many experiments, multimedia videos, and resources for students. “Inquiry is central to science learning. When engaging in inquiry, students describe objects and events, ask questions, construct explanations, test those explanations against current scientific knowledge, and communicate their ideas to others” (National Research Council, 1996, p. 2). In a school where field trip funds are minimal, teachers could use this website to support inquiry by creating an environment that supports construction of knowledge through hands-on experiments and activities. “Museums provide ideal environments for learning and practicing inquiry skills. While playing with exhibits, students on field trips can try various experiments, make observations, and have memorable experiences” Gutwill, J. P., & Allen, S. (2011). This can be mirrored in the classroom by giving students opportunities to experiment, document their observations, and provide stations for rotation with social interaction. “The role of the authority figure has two important components. The first is to introduce new ideas or cultural tools where necessary and to provide the support and guidance for students to make sense of these for themselves” (Driver et al., 1994).  Technology can be incorporated to access the appropriate apps, and then share their learning through ePortfolios. I believe that there is significant value in authentic field trips that provide students with new opportunities to make connections, build communication competencies, and experience new learning environments with resources (Gutwill & Allen, 2012). However, if classes are unable to attend more than one or two per school year because of lack of funds, I think virtual field trips are a great alternative. Spicer & Stratford (2001) support this statement and explain that virtual field trips should not replace authentic fieldtrips. What Exploritorium can do is provide scaffolding prior to a field trip, which could be an example of LfU, supporting motivation, knowledge construction, and refinement for both pre and post trip.

References:

Driver, R., Asoko, H., Leach, J., Mortimer, E., & Scott, P. (1994). Constructing scientific knowledge in the classroom. Reconsidering Science Learning,23(7), 5-12. doi:10.4324/9780203464021_chapter_2.2

Gutwill, J. P., and S. Allen. 2012. Deepening students’ scientific inquiry skills during a science museum field trip. The Journal of the Learning Sciences 21 (1): 130–181.

Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.

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.

Niemitz, M., Slough, S., Peart, L., Klaus, A., Leckie, R. M., & St John, K. (2008). Interactive virtual expeditions as a learning tool: the School of Rock Expedition case study. Journal of Educational Multimedia and Hypermedia, 17(4), 561-580

How can learning be distributed and accelerated with access to digital resources and specialized tools and what are several implications of learning of math and science just in time and on demand?

Knowledge is actively built and socially constructed upon prior conceptions and personal theories. Learning views do not require specific pedagogy necessarily, though invented constructs imposed on phenomena are socially negotiated, then validated as public knowledge. Technology enhances distributed learning, challenging ideas through discrepant events while introducing multiple ways of seeing. Learners form communities of practices through cultural apprenticeship co-constructing knowledge (Driver et al., 1994), though inquiry requires guidance being unlikely that inexperienced students learn through pure discovery. Teachers gradually withdraw support as students connect plausible mental representations towards symbolic convention, where intervention helps make sense of further action. Meaning is constructed in conversation resolving disequilibrium knowledge schemas, inducing cognitive conflict along with social interaction to provide multiple perspectives. Teachers recognize students hold plural conceptions given social context, structuring tasks to internalize and enculture experiential evidence. Students develop common sense reasoning using everyday language and pragmatic understanding rather than adopting coherent world picture, leveraging models for scope.

Globe provides universal access to employ natural curiosity, actively participating with distributed collaborators, researching spatial-temporal data. For accuracy, training the trainer ensures first line of defense against erroneous data (Butler and MacGregot, 2003). Systems provides integrated understanding with graphical, visual and technical tools, enabling international cooperation with multiple languages across isolated communities. Student interaction with adult professionals offers authenticity, enhancing commitment and quality assurance. Given uniform classification systems and protocols, sampling techniques perform over 80% accuracy, where ongoing collection allows for durable, low-cost, long-term stability, empowering students to do responsible science. Active research projects and learner involvement become valuable incentive to improve analytical interpretation, supplementing classroom activities to make informed inferences. Motivational factors like challenge, fantasy and curiosity sustain goal-directed behaviour, with challenge neither too steep or simple providing novelty, interest and importance (Srinivasan et al., 2006). Working memory allows for simultaneous processing and information preservation, providing various worked out examples as effective strategy. Challenges with time availability and systematic schedules need to be overcome, focusing on fundamental science content and method. Debugging breadboard components is time consuming, fraught with variables to address prior knowledge, ability and motivation. Curiously although simulations were less cost expensive, participants deemed software as fake unable to provide authentic experience, resulting in little quantitative difference between physical equipment (Srinivasan et al., 2006). Users described how not knowing background made practical training difficult let alone theoretical, where both real hardware and simulation laboratory provide incomplete solutions.

Science in visiting hands-on interactive centers allow free-choice learning guided by well-formed interests. Leisure settings provide brief, moderately structured activity while retaining considerable personal control. Visitors as active meaning seekers balance learning and entertainment categorized into five broad motivational categories: Explorers, Facilitators, Hobbyists, Experience seekers, Rechargers (Falk and Storksdieck, 2010). Recollections of exhibits highlight personal curiosity, excitement, allowing faster and better learning, motivated by personal curiosity. Instead of disliking school for reading without application and witness in real life, free-choice learning offers realistic expectations over compulsory. Fascinating objects help crystallize meaning to pursue learning satisfaction without external validation, where genuine openness to learn immersed within setting minimizes performance mentality.

References

Butler, D. M., & MacGregor, I. D. (2003). globe: Science and education. Journal of Geoscience Education, 51(1), 9-20. doi:10.5408/1089-9995-51.1.9

Driver, R., Asoko, H., Leach, J., Mortimer, E., & Scott, P. (1994). Constructing scientific knowledge in the classroom. Educational Researcher, 23(7), 5-12.

Falk, J. H., & Storksdieck, M. (2010). Science learning in a leisure setting. Journal of Research in Science Teaching, 47(2), 194-212.

Srinivasan, S., Pérez, L. C., Palmer, R. D., Brooks, D. W., Wilson, K., & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 137-141.

How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities?

Knowledge of math or science is constructed through a variety of experiences both personally and socially (Driver, Asoko, Leach, Scott, & Mortimer, 1994); experiences that we acquire from the beginning of our existence. While we might not label them or differentiate them as “math/science”, these interactions with our world become part of our knowledge. We want to expose our students to many different experiences, and these networked communities are one such avenue.

As we are all well aware, we each have different life experiences. My experiences with a family very comfortable with the outdoors gave me different experiences than my friends who never went hiking, camping or star gazing. I got to attend the “ultimate fieldtrip” to NASA to study science when I was in grade 11 and got to experience and construct knowledge in a much different way than others who did not attend. Fieldtrips and experiences such as these are not accessible for a number of reasons such as safety and expense. Even at my school in the Fraser Valley, going into Vancouver to go to Science World or the Vancouver Aquarium is too costly to take our students. Though not everyone will have these experiences, I believe that everyone deserves the opportunities to learn, and virtual fieldtrips allow educators, parents, and anyone else who wants to learn, that opportunity. As was shown in Spicer & Stratford (2001) students feel that these virtual fieldtrips should not replace fieldtrips, where possible, but could offer pre- or post-trip learning opportunities. As they also outlines, virtual fieldtrips (VFT) are “good but not a substitute”.

When these in-person opportunities are not available to our students, I think that many teachers get creative. While not a virtual field trip, Science World offers Scientists in Schools (https://www.scienceworld.ca/sis) where real scientists or professionals in STEM subjects come into your classroom and do hands-on activities with your students – free of charge. I’ve had some amazing experiences with these professionals and students get hands on inquiry learning. Students have the opportunity to construct math/science knowledge in a very different way than what many teachers are doing in their classrooms and via the guidance of experienced professionals.

Informal learning environments such as The Exploratorium (www.exploratorium.edu) are excellent digital resources. The variety of experiences that students can participate in, from apps to videos to activities, gives students the opportunity to involve themselves, either in the context of a lesson, or purely out of interest was phenomenal. The connectivity to real world happening (this summer’s Solar Eclipse for example) provides students with context and real-world application of knowledge.  These learning environments, extend “learning opportunities outside of formal school” and assimilate, ‘IT technologies transforming them into new practices and applications to support their curiosity and interests” (Hsi, 2008). They also allow students to bring home their learning and converse with parents, as they are also able to access the materials that their children are using. In school, the important social connections can still be made through careful planning by the teacher.

While I do not believe these virtual experiences should replace traditional field trips, they can afford students and others new, meaningful, and experiential science/math opportunities. With rapid advances in technology the possibilities are “endless”.

References

Driver, R., Asoko, H.,Leach, J., Scott, P., & Mortimer, E. (1994). Constructing scientific knowledge in the classroom. Educational researcher, 23(7), 5-12.

Hsi, S. (2008). Information technologies for informal learning in museums and out-of-school settings. International Handbook of Information Technology in Primary and Secondary Education, 20(9), 891-899.

Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.

How can learning be distributed and accelerated with access to digital resources and specialized tools and what are several implications of learning of math and science just in time and on demand?

I found the study by Carreher et al. very interesting.  I have travelled to many countries around the world and I am always impressed with the Math skill (English skills also) of children that have none or little formal schooling. The children used in this paper, “tended to be accomplished by strategies involving the mental manipulation of quantities while in the school-type situation the manipulation of symbols carried the burden of computation, thereby making the operations ‘in a very real sense divorced from reality’” (pg.28)  This proves that knowledge can be constructed in informal ways.

As for learning being distributed ad accelerated, access to digital resources and specialized tools allow students to explore regions of the world as well as phenomena that would never be accessible to them in real life. GLOBE allows students to interact with scientists as well as analyze data from various locations around the world.   All my students know are deserts, so to open teir minds to other regions of the world with other topographies would be great to accelerate and deepen their learning.

His’s paper explores informal learning institutions; such as, museums and zoos, that are creating freely available educational resources accessible over computer networks and the Web to create extended learning opportunities outside of formal schooling.  Once again, these networked communities allow students to explore areas and topics that may be limited by costs and/or geographic location.  They increase the possible ways that learning can be distributed and accelerate learning.

I remember taking my Grade 9 Biology class in Montreal to the Bodies exhibit many years ago.  I let the students walk around freely and explore the space.  I overheard conversations about anatomy and physiology that we had studied in class, I remember being full of pride and joy that my students could apply the items we had learned to the exhibits they were seeing.

Butler, D.M., & MacGregor, I.D. (2003). GLOBE: Science and education. Journal of Geoscience Education, 51(1), 9-20.

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.

Hsi, S. (2008). Information technologies for informal learning in museums and out-of-school settings. International handbook of information technology in primary and secondary education, 20(9), 891-899.

A theme is unquestionably emerging throughout this week’s readings, and linking ideas to previous weeks’ reading, as well. When learning is anchored in real life contexts, students are happier and their construction of knowledge is abundant.

When Third World street vending children are capable of performing complex mathematical processes mentally yet can not perform the same process in a decontextualized problem on paper, how can one not conclude the relevance of situated learning (Carraher & Dias, 1985)?  In another study, visitors to a free local museum were interviewed immediately after their trip and two years later.  Researchers determined that those visitors whose motivation to attend was curiosity driven, learned more and valued the experience more than those visitors who were merely socially motivated to attend (Falk & Storksdieck, 2009). And when researchers surveyed university biology students regarding their experience using a virtual field trip (VFT), as opposed to a traditional lecture, students overwhelmingly reported positively, 80% of the time, although they also reported that the VFT is best to enhance actual field trips, and not replace them (Spicer & Stratford, 2001).

Each of these readings funnel towards the importance of providing anchored instruction throughout educational practices. I think back to why I enjoyed physics more than any other science and it began with taking Dr. Matthews’ first year physics class where he utilized the entire theatre for his demonstrations and he took incredible measures to draw the most incredible, realistic diagrams. He was also incredibly funny, so I spent most lectures in an amused state! Although his teaching style would still be considered “traditional”, he wove realism into his lectures, every class.

Despite being bombarded with Inquiry Learning approaches in my Professional Development, and with Vygotskian Constructivist Theory in MET, I still believe that in my subject areas, senior physics and academic math, lecturing has its place. I do not have time to allow students to discover Every. Single. Concept. Nor can I allow them to choose what learning outcomes they wish to learn about.  My students are future engineers, doctors, and other intensively trained professionals and I am not prepared to sacrifice content for ease and happiness of the learning experience. To students who are not handling the rigour of my courses, I say, it is OK. It is OK to NOT become a doctor.  It is OK to NOT become an engineer. If you can’t take the heat, get out and find a training path that does not require you use math or physics at a high level. That still leaves a HEAP of other, very gratifying professions to follow!

Where I have been “converted” is within the lectures themselves.  I would not even call what I do, “lectures”, to be honest.  Students still write notes, however, the notes are interactively created. With peers, we do numerous reinforcement activities in a non-threatening, collaborative manner. We construct our knowledge at times, but not at others.   My goal is to prepare them for university and college, while providing as many hands on or virtual experiences as possible.

On the other hand, I can see that if I were a junior high or middle school teacher, how I would have a very different perspective.

Well, maybe not for math….

For math, foundational skills are critical and need to be automated at some point. This is not only important for senior high math, but for mathematical confidence and mathematical self-esteem.  When students don’t know their times tables, for example, it is like they are in my class underwater, using an oxygen tank (their calculator) to breathe. They know that if they don’t have access to their “oxygen”, they will die. Being THAT depend on a tool to survive is not conducive for a healthy learning environment.

However, in science, bring on the “fun” learning! Situate, anchor, inquire, Jasper, WISE, and network those communities every day, as far as I am concerned! What ever it takes to promote a lifelong curiosity in science should be the goal of every junior/middle science teacher out there. Moreover, the world is depending on us to make this come to fruition! We are systematically destroying our environment, becoming 40-year-old-still-living-at-home dependent on technology, and perhaps most shockingly, in astonishingly high numbers, receiving our baseline news from Facebook.

<Please prepare yourself to be “should” on. I don’t like to engage in this practice, but every once in awhile, it needs to be done.>

If we do one thing, as a collective of educators, it should be to teach our younger students how to research, and remain scientifically curious throughout their lives.

That’s it!

Easy peasy.

We’ve got this.

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.

Falk, J. & Storksdieck, M. (2010). Science learning in a leisure setting. Journal of Research in Science Teaching, 47(2), 194-212.

Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.

When looking all of the different options for websites that help students construct and communicate knowledge, I was blown away by the opportunities available to engage students with research that scientists are conducting around the world.  One of the websites that really interested me that I’m looking forward to trying with my class is the Expedition around the Canada (https://canadac3.ca/en/expedition/) for the 150th anniversary. This is an incredible opportunity for students to connect so many facets of science with Canada. I can see how this endeavor could be tied into multiple grade levels in the curriculum.  As the expedition travels through 6 ecozones, sciencitsts will conduct research to share with Canadians, talk to local communities, and discuss ways to protect the environment in live forums.

At schools we have environmental committees that allow students and staff to discuss ways to protect their environment.  This is also a topic that comes up in class discussions in social studies and science.  Involving a group of students in this kind of activity gives them the opportunity to discover what the regions are really like…at the present time. Rather than just reading about them in a textbook (that’s probably out of date) students can see the different ecosystems, ongoing methods of environmental protection.

According to Carraher (1985) the presence of physical items acts as a facilitating factor in allows students to understand a particular concept. There are ample opportunities through exploring the arctic that will allow students to connect and see first-hand how experiments are being conducted and how reconciliation is being undertaken in the Aboriginal communities.

In Yoon et al (2011) it was observed that digital augmentation resulted in increased levels of interest and engagement. Opportunities to provide experiences outside of the classroom environment through educational technologies can assist in the development of conceptual knowledge (Yoon et al, 2011). Students are then able to apply real world examples to their skillset in the areas of collecting data, making predictions, drawing conclusions, and theorizing about different phenomena. Sometimes just providing digital augmentation alone can provide huge gains even with no other scaffolds according to Yoon et al (2011). I wonder how educators can ensure that students challenge themselves when participating in digital augmentation? Would creating their own learning objectives translate into more engagement?

References:

• Yoon, S. A., Elinich, K., Wang, J., Steinmeier, C., & Tucker, S. (2012). Using augmented reality and knowledge-building scaffolds to improve learning in a science museum. International Journal of Computer-Supported Collaborative Learning, 7(4), 519-541. doi:10.1007/s11412-012-9156-x

• Carraher, T. N., Carraher, D. W., & Dias Schliemann, A. (1985). Mathematics in the streets and in schools. The British Journal of Developmental Psychology, 3(1), 21.