Category Archives: Inquiry

Making Sense of the Chaos – Thoughts on Role Play in Mathematics and Sciences

I have been the facilitator of gathering students together to represent the unseen phenomena of molecular movement in states of matter. Students who are “solid” stand very close together and jiggle on the spot, while the “liquid” students stand further apart and move a bit more freely. The students who represent gas find their own space and move around in comparable bliss. I have had students dramatize the story of Archimedes and the king’s golden crown, and have seen a line of students model each part of the ear as sound moves through it. These students are taking on the roles of scientific phenomena, but their role play, as Resnick and Wilensky (1998) would suggest, is merely representing the results rather than “the processes and interactions that give rise to the results” (p.168).

Traditionally role play has found itself in the arts and humanities, helping students view themselves and society through varied lenses, making connections and altering perspectives. Winn (2003) quotes Reyes and Zarama suggesting that in the sciences, too, perspectives of self can be changed. The learned distinctions can often “tell us more about ourselves than about the world we are describing” (Winn, 2003, p.19). As well, Resnick and Wilensky (1998) have found that “role-playing activities provide a framework in which learners can start to make … distinctions – learning to project only the specific parts of their own experiences that are useful for understanding other creatures and objects” (pp.168-9). Can role play in the sciences and mathematics classroom aid in growing these distinctions? In subject areas where traditionally there is one correct answer, can seemingly random and indeterminate role play help bring order and understanding to complex ideas?

Resnick and Wilensky (1998) would affirmatively attest that role play is not intended for simply representing a result, but for “developing new relations with the knowledge underlying the phenomena” (p.167). In fact, they assert that for complex and system sciences, role play is ideal for providing “a natural path for helping learners develop an understanding of the causal mechanisms at work in complex systems. By acting out the role of an individual within a system…, participants can gain an appreciation for the perspective of the individual while also gaining insights into how interactions among individuals give rise to larger patterns of behavior” (p.167). Gaining insights into how localized patterns influence larger-scale, or globalized activity, is essential in understanding the intricacies of a complex system.

The enactivism theory of cognition supports Resnick and Wilensky’s affinity for role play within the sciences and mathematics. As described by Proulx (2013): “[e]nactivism is an encompassing term given to a theory of cognition that views human knowledge and meaning-making as processes understood and theorized from a biological and evolutionary standpoint. By adopting a biological point of view on knowing, enactivism considers the organism as interacting with/in an environment” (p.313). As the organism and environment interact, both change and adapt in response to the interaction, making them even more compatible. This evolution of structure is referred to as coupling (Proulx, 2013). Learning through enactivism is neither simple nor linear, but rather complex and undetermined. Using role play to understand mathematics and complex and science systems takes the student through an evolutionary process of change. The student takes on a role, interacting with the problems (environment) presented, and through this interaction poses new problems and pathways of solution. Along the way, the student finds their initial role is changing too, in order to adapt to the changing environment. 

Interestingly, the chaos theory of instructional design also recognizes the value of instruction and learning that is evolutionary in nature (You, 1993). Similarly to Resnick and Wilensky, the chaos theory allows for patterns and order to emerge from seemingly randomness and chaos. You (1993) states that central to the chaos theory is “[t]he discovery that hidden within the unpredictability of disorderly phenomena are deep structures of order” (p.18). Quoting from Hayles (1990, 1991), the characteristics of the chaos theory are described with such phrases as a pattern of order within disorder; chaos is the precursor and partner to order rather than the opposite; and chaos is paradoxically locally random, but stable within a global pattern (You, 1993).

To bring this back to role play in mathematics and sciences, there is a need to recognize that complex ideas can be defined and understood through role play scenarios and interactions whether technology-based or non-technology-based. Through role play, localized complexities can be more clearly defined through continual problem solving and problem posing that allow the learner to begin to see and interpret patterns that emerge. As Proulx (2013) states, “The problems that we encounter and the questions that we undertake are thus as much a part of us as they are part of the environment; they emerge from our interaction with it” (p.315).  Perhaps by opening the world of role play to mathematics and science students, we will see more students acting like Barbara McClintock, a Nobel-winning biologist who attributes “her greatest discoveries to the fact that she had a “feeling for the organism” and was able to imagine herself as one of the genes within the corn (Keller, 1983)” (Resnick & Wilensky, 1998, p.168). Perhaps McClintock’s experience is a call for educators to consider further the possibilities for when students are handed permission to relate and interact through imagination, and hence are given opportunity to experience phenomena.

The possible’s slow fuse is lit by the imagination. ~ Emily Dickinson



Resnick, M. & Wilensky, U. (1998) Diving into complexity: Developing probabilistic decentralized thinking through role-playing activities, Journal of the Learning Sciences, 7(2), 153-172. DOI: 10.1207/s15327809jls0702_1

Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics, 84, 309-328.

Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114.

You, Y. (1993). What can we learn from the chaos theory: An alternative approach to instructional system design. Educational Technology Research and Development 41(3), 17-32. Retrieved from http://www.jstor.org/stable/30218385

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Wise Instruction – Inquiry, WISE and Model-Based Learning

The following posting is guided by the the following process questions:
  • What broader questions about learning and technology have provoked WISE research and the development of SKI?
  • Describe the authors’ pedagogical design considerations that shaped the development of “What’s on your Plate?” How and where was WISE integrated into a larger sequence of activities?
  • Analyze the evidence and author’s conclusions. Are the conclusions justified? In what ways does WISE support the processes commonly associated with “inquiry” in science? How might these processes be used to support math instruction?
  • What might be the cognitive and social affordances of the WISE TELE for students? Use “What’s on your Plate?” as an example to support your hypotheses.

 

Inquiry is the newest trend in pedagogical design and curriculum and infiltrates BCs New Curriculum established for K-9 students. As described in the following video on the BC Ministry of Education website, inquiry requires students to ask questions, hypothesize, investigate, experiment, create, reflect and revise. These actions are intended to help students to learn the processes of science, and not solely the content, while building skills in communication, collaboration, critical thinking, vocabulary building and analysis.

Linn, Clark and Slotta (2003) offer a deeper definition of inquiry and describe it as “engaging students in the intentional process of diagnosing problems, critiquing experiments, distinguishing alternatives, planning investigations, revising views, researching conjectures, searching for information, constructing models, debating with peers, communicating to diverse audiences, and forming coherent arguments (p.518). The designers of WISE (Web-based Inquiry Science Environment) have taken this latter definition, placed it into the Scaffolded Knowledge Integration network (SKI), while asking questions of how to design a technology-based learning environment that “scaffold[s] designers in creating inquiry curriculum projects and designing patterns of activities to promote knowledge integration for students and teachers” (Linn et al., 2003, p.518). The designing of WISE is an evolving inquiry as the design team, including science teachers, pedagogical specialists, scientists and technology designers, engage in inquiry processes through its continuous designing and revising. The designers of WISE are not simply interested in inquiry, but in the intersection of inquiry and technology and the enhancement of learning as a result. A considerable statistic cited by Linn et al. (2003) describing the participation level of students through asynchronous communication in comparison to face-to-face discussion is convincing: “Online asynchronous discussions enable students to make their ideas visible and inspectable by their teachers and peers and give students sufficient time to reflect before making contributions. Hsi (1997) reports that under these circumstances, students warrant their assertions with two or more pieces of evidence and over ninety percent of the students participate. In contrast, Hsi observed that only about 15% of the students participate in a typical class discussion, and that few statements are warranted by evidence” (p.530). Other WISE related studies also reveal enhanced learning as a result of students learning through a technology-based environment. One such design study is conducted by Gobert, Snyder and Houghton (2002) using a WISE project entitled, “What’s on your Plate” – a geology focussed project.

Gobert et al. (2002) pursue a design study “to investigate the impact of decisions about curricular materials with the express goal of redesigning them in accordance with the findings obtained” (p.7). More specifically, they ask, “[I]n what ways does model-building, learning with dynamic runnable visual models in WISE, and the process of critiquing peer’s models promote a deeper understanding of the nature of science as a dynamic process?” (p.7). The two areas of SKI that are focussed on in this study are: 1) making thinking visible and 2) learning from others. Gobert et al.(2002) are also interested in observing changes in students’ epistemologies as they work through the WISE project. Specifically, they asked these questions: “How can we use the technology effectively to promote deep learning in line with epistemic goals? and How can we identify change in students’ epistemic understanding?” (p.2). In order to measure these epistemic changes, pre and post tests are conducted indicating significant increases in student understanding and reasoning related to model-based learning. Student post test responses include significantly more detail, scientific vocabulary and accurate knowledge, while peer critiques include reasoning and communicative understanding. Gobert et al. (2002) state established research for integrating model-based learning within science education, both models to learn from and model construction assignments. Positive effects of model-based learning integration are described here: “It is believed that having students construct and work with their own models engages them in authentic scientific inquiry, and that such activities promote scientific literacy, understanding of the nature of science, and lifelong learning” (Gobert et al., 2002, p.3). These positive effects of model-based learning are evidenced in the conclusions of the design study by Gobert et al. (2002). While model-based learning through WISE indicates significant growth in the students’ understanding of the use of dynamic visual models and the nature of science,  can this model-based learning also be effective in the acquisition of mathematics?

WISE supports the processes of inquiry through the “What’s on Your Plate” project including diagnosing, planning, researching, constructing, critiquing, revising, communicating and reasoning. Through these inquiry processes, students successfully make their thinking visible through the construction of models which are then critiqued by peers, and then revised through reasoning. Model-based learning in mathematics could be structured similarly using inquiry processes that require students to diagnose a problem, research the information necessary to solve the problem, construct a model using software or hands-on materials, and share their model with an explanation for peer critique. {This process is evident in The Jasper Series.} Reasoning and further research follow the critique leading to a revised model construction. In essence, model-based learning affords the student to become a “teacher” through the construction of a teachable model. In mathematics, model-based learning could predictably enhance understanding in areas of geometry, patterning and problem solving. Models could include simulations, diagram representations, symbolic data, or three-dimensional constructions.

After brief research, this following resource seems valuable in inquiring further inquiry into model-based learning: Model-Based Approaches to Learning: Using Systems Models and Simulations to Improve Understanding and Problem Solving in Complex Domains by Patrick Blumschein, Woei Hung, David Jonassen, and Johannes Stroebel (2009).

 

References
Blumschein,P., Hung, W., Jonassen, D., & Stroebel, J. (2009). Model-based approaches to learning: Using systems models and simulations to improve understanding and problem solving in complex domains. Rotterdam, The Netherlands: Sense Publishers.
Gobert, J., Snyder, J., & Houghton, C. (2002, April). The influence of students’ understanding of models on model-based reasoning. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New Orleans, Louisiana. This is a conference paper. Retrieved conference paper Saturday, October 29, 2013 from: http://mtv.concord.org/publications/epistimology_paper.pdf
Linn, M. C., Clark, D. and Slotta, J. D. (2003), WISE design for knowledge integration . Sci. Ed., 87: 517–538. doi:10.1002/sce.10086
McAleer,N. (2005, June 21). Getting started with student inquiry in science. [Video file]. Retrieved from https://www.youtube.com/watch?v=KYGawWpiDOE

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Plate Tectonics: Reshaping the Ground Below Us

Web-based Science Inquiry Environment (WISE)

Project: Plate Tectonics – 

Renamed: Plate Tectonics: Reshaping the Ground Below Us – ID 19738

WISE is theoretically based on the Scaffolded Knowledge Integration network (SKI) which includes the following four tenets: 1) accessibility to science, 2) making knowledge visible, 3) learning from others and 4) promoting autonomy (Linn, Clark, & Slotta, 2003). In piecing together a unit study for middle school students (grade 6-8), incorporating these four tenets of SKI into the non-technology based areas of learning is intentional to enhance visibility of knowledge and opportunities for peer review and critique. The WISE Plate Tectonic project is being used as a final assignment within a geology unit based on the structure of the earth, the surface of the earth, plate tectonics, and earthquakes and volcanoes. A few authorship changes have been made to the Plate Tectonic project mainly to include a Canadian perspective. These changes include the addition of Canadian map images showing placement of volcanoes, earthquakes and mountain ranges, along with appropriate text. As well, small alterations have occurred in the subtitles of the lesson outline.

The geology unit includes three resources, two non-technology based texts and one project from WISE. The two non-technology based resources that have been chosen are faith-based resources as the school that I work for is an independent religious school. The Geology Book by Dr. John D. Morris is a textbook, but includes detailed and colourful diagrams illustrating the inside of the earth and side views of how the earth’s surface is formed. A Child’s Geography: Volume 1 by Ann Voskamp includes conversational style writing, hands-on activities, real world extensions and a living book list of extension readings. Talking about thinking is incorporated into both of these resources through oral narrations, discussions and the sharing of written work for peer critique. Learning is made visible through notebooking and hands-on model making.The table below illustrates the order of the unit with how resources will be completed in conjunction with each other.

In designing this unit, the four tenets of SKI are intentionally incorporated in addition to, or through the use of each resource. These four tenets provide a framework for students to work through an inquiry process as described in Inquiry and the National Educational Standards with students thinking “about what we know, why we know, and how we have come to know” (Center for Science, Mathematics, and Engineering Education, 2000, p.6). Linn, Clark and Slotta (2013) more specifically define inquiry “as engaging students in the intentional process of diagnosing problems, critiquing experiments, distinguishing alternatives, planning investigations, revising views, researching conjectures, searching for information, constructing models, debating with peers, communicating to diverse audiences, and forming coherent arguments” (p.518). The following table analyses each of the three resources and aligns them with the four tenets of SKI as well as the inquiry processes described by Linn, Clark and Slotta in the above definition.

Scaffolded Integration Knowledge Network Processes of Inquiry Geology Unit Resource
Accessibility to Science – {content, relevancy, real-life application} Diagnosing problems

Planning investigations

Revising views

Researching conjectures

Searching for information

WISE Plate Tectonics
Researching conjectures

Searching for information

Revising views

The Geology Book
Revising views

Researching conjectures

Searching for information

A Child’s Geography
Making Thinking Visible Constructing models

Communicating to diverse audiences

Forming coherent arguments

WISE Plate Tectonics
Constructing models The Geology Book
Constructing models A Child’s Geography
Learning From Others Diagnosing problems

Critiquing experiments

Distinguishing alternatives

Revising views

Debating with peers

WISE Plate Tectonics
Critiquing by peers

Revising views

The Geology Book
Critiquing by peers

Revising views

A Child’s Geography
Promote Autonomy Diagnosing problems

Critiquing experiments

Distinguishing alternatives

Planning investigations

Revising views

Researching conjectures

Searching for information

WISE Plate Tectonics
Researching conjectures

Searching for information

Critiquing by peers

Revising views

The Geology Book
Researching conjectures

Searching for information

Critiquing by peers

Revising views

A Child’s Geography

Center for Science, Mathematics, and Engineering Education. (2000) Inquiry and the national science education standards. Washington, DC: Author.
Linn, M. C., Clark, D. and Slotta, J. D. (2003), WISE design for knowledge integration . Sci. Ed., 87: 517–538. doi:10.1002/sce.10086
Slotta, J. D. & Linn, M. C. (in press). WISE Science: Inquiry and the Internet in the Science Classroom. Teachers College Press. Retrieved from https://edx-lti.org/assets/courseware/v1/634b53c10b5a97e0c4c68e6c09f3f1b6/asset-v1:UBC+ETEC533+2016W2+type@asset+block/WISEBookCh1-30209.pdf
Web-based Inquiry Science Environment.(1996-2016). Retrieved from https://wise.berkeley.edu/

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