Monthly Archives: March 2017

Authentic Learning with Nature

Through the readings from this past week, I have explored a seemingly disjointed array of ideas. Following is a brief overview:

Carraher, Carraher and Schliemann (1985) present the effect of contextualized learning on mental math computation processes with street vendor children in Brazil; Falk and Storksdieck (2010) share results from their study on adult leisure science learning at the California Science Center in Los Angeles; Butler and MacGregor (2003) provide an in-depth explanatory overview of the GLOBE program designed to enable “authentic science learning, student-scientist partnership, and inquiry-based pedagogy into practice on an unprecedented scale” (p.17)! Although these three readings are diverse in study and purpose, one significant theme pronounced itself throughout: the theme of contextualized learning. Regardless of the age of learner, socio-economical position, or location on this great planet, contextualized learning offers authenticity of learning and effective growth in both content areas and competencies.

When considering authentic learning, I like to refer to Herrington and Kervin’s (2007) definition:

      The nine characteristics of authentic learning include:

  1.     Authentic context that reflects the way knowledge will be used in real life.
  2.     Authentic activities that reflect types of activities that are done in the real world over a sustained period of time.
  3.     Expert performance to observe tasks and access modelling.
  4.     Multiple Roles and Perspectives to provide an array of opinions and points of view.
  5.     Reflection to require students to reflect upon knowledge to help lead to solving problems, making predictions, hypothesizing and experimenting.
  6.     Collaboration to allow opportunities for students to work in pairs or in small groups.
  7.     Articulation to ensure that tasks are completed within a social context.
  8.     Coaching and Scaffolding by the teacher in the form of observing, modelling and providing resources, hints, reminders and feedback.
  9.     Integrated Authentic Assessment throughout learning experiences on a task that the student performs i.e. project rather than on separate task i.e. test.

     (Herrington & Kervin, 2007)

Although all of these characteristics of learning are not prominently practiced in the networked communities explored during this past week, many, if not all, can be emphasized through teacher design by incorporating a combination of non-technology based and network community activities.

The follow learning outline is designed using the network community called Journey North along with other on-going non-technology nature study activities. As an individual and an educator who advocates for regular nature study as a part of one’s life, the Journey North community peeked my interest as a very viable resource to integrate with already implemented nature study practices with students from grades K-4. I have chosen two projects at Journey North that could be easily implemented with my younger distance learning students. Following is a chart with resources and activities aligned with the authentic characteristics of learning as described by Herrington et al. (2007).





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. 
Falk, J. & Storksdieck, M. (2010). Science learning in a leisure setting. Journal of Research in Science Teaching, 47(2), 194-212.
Herrington, J. & Kervin, L. (2007). Authentic Learning Supported by Technology: Ten suggestions and cases of integration in classrooms.  Educational Media International, 44 (3), 219-236. doi: 10.1080/09523980701491666

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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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Filed under Embodied Learning, Inquiry, TPCK

Individualism, Immersion and Evolution

Embodied learning acknowledges the individualism of the learner. The individual’s cognitive behaviour connects to past cognitive experiences and present interpretations in ways that are unpredictable and dependent on the the learner’s Umwelt. Umwelt is described as “the environment as the student sees and knows it – a limited view of the real world, ever changing as the student explores it and comes to understand it” (Winn, 2003, p.12). The learner’s interaction with the surrounding environment can be viewed as a biological interaction and a way of knowing. Metaphorically, the learner is an organism interacting with and within its environment. In effect, both the organism (the learner) and the environment evolve and are changed through the interaction (Proulx, 2013). Proulx refers to this interaction as enactivism and suggests that enactivism is the necessary cognitive theory behind problem solving, or more succinctly “problem posing”, in mental mathematics. Through problem posing, “the solver does not choose from a group of predetermined strategies to solve the task, but engages with the problem in a certain way and develops a strategy tailored to the task (both of which also evolve and are co-defined in the posing). Strategies are thus not predetermined, but continually generated for solving tasks” (Proulx, 2013, p.316).

In the brief article by Barab and Dede (2007), there is evidence of the cognitive theory of enactivism as the science learner is immersed in “narratively driven, experientially immersive, and multi-rich media” (p.1). The learner, as the organism, interacts with the immersive game-based simulated environment, bringing individualized input and then coupling {embedded interaction} with the environment. Problem posing exists as the learner poses solutions and generates strategies as interaction occurs with/in the simulated environment. In contrast to Proulx’s (2013) writing on enactivism and mental math problem posing through which students interact with an unprogrammed environment, Barab and Dede (2007) share studies of learners interacting with a programmed simulated environment. Can learner interaction with a programmed environment, even when programmed to be an adaptable environment, allow for enactivism to truly emerge? Or in other words, is the environment truly evolved by the learner, or is it an illusion? Also, what would be the best practices for teacher assessment and feedback when learners and environments are continually evolving and adapting?

In my own practice, I appreciate Proulx’s view on the individual learner and how this individualism aids the approach and walk through learning. I particularly appreciate that his focus is on mental mathematics, an area that seems to be neglected as students interact largely with workbook based curriculum and predetermined strategies. Continuing to engage students in number talks, breaks the misconception that there is one right way to find a solution, and opens the mindset to evolving possibilities. Immersive simulations that allow students to problem pose and structure solutions through interaction with the environment, and then use the adaptations to further generate strategies for solutions is ideal. I look forward to discovering simulations that encompass enactivism through the remainder of this module.



Barab, S., & Dede, C. (2007). Games and immersive participatory simulations for science education: an emerging type of curricula. Journal of Science Education and Technology, 16(1), 1-3.
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.

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TPCK and Learner Activity – A Synthesis of Four Foundational TELEs

Following is a collection of visual syntheses comparing and contrasting T-GEM/Chemland with the following technology-enhanced learning environments: Learning for Use (LfU)/My World, Scaffolded Knowledge Integration (SKI)/WISE, and Anchored Instruction/Jasper. The visual syntheses contain a focus on TPCK and learner activity with the guiding TELE being T-GEM/Chemland, and all other TELEs being compared and contrasted through alignment with the T-GEM/Chemland framework.

Each one of these TELEs is developed on inquiry instruction and learning, with T-GEM/Chemland consisting of specifically model-based inquiry. Each one of these TELEs promotes a community of inquiry with purposeful teacher-student and student-student interactions. To emphasize the non-linear processes of inquiry, each visual synthesis is designed in a circular format.

Unique to T-GEM is the cyclical progress that the learner takes moving through the steps of the learning theory. Arrows are placed in each TELE’s visual representation to elicit the learner’s movement in comparison to the T-GEM’s model.


As a general mathematics and science teacher for elementary grade levels, the process of exploring, analyzing and synthesizing  the four foundational TELEs presented in this course has been transformational in my development of TPCK. Initially, the importance of CK (Schulman, 1986), and my self-diagnosed lack of CK, was convicting as I tend towards growing in pedagogical ideas and creative ways of implementing them. To further this conviction, my understanding of inquiry processes and the intricate role that the teacher facilitates in conducting a community of inquiry began to become clearer throughout the readings and discussions of Module B. Skillful inquiry instruction requires a facilitator who is saturated in CK, being equipped to prepare, respond, question, prompt, and guide with carefully considered PK. At this time, I am challenged as an educator to begin with one brave adventure in mathematics using an anchored instructional approach, and another brave lesson in physical science using a T-GEM approach. I am certain that I will be generating, evaluating and modifying all along the way.  

 



Cognition and Technology Group at Vanderbilt (1992). The jasper experiment: An exploration of issues in learning and instructional design. Educational Technology Research and Development, (40), 1, pp.65-80

Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385.

Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.

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

Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14.

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Filed under Anchored Instruction, SKI, T-GEM, TELE, TPCK, WISE

Staying Afloat – Sink and Float Density T-GEM

When considering a challenging science concept, I recalled struggling with explaining the concept of floatation, or “sink or float”, when teaching kindergarten. Although exploring objects that sink and float in water is highly intriguing for young students, the reasoning behind which objects sink and float can get complicated and too abstract for a student at that age to fully understand. Why does a tiny popcorn kernel sink and a large watermelon float?

In the BC’s New Science Curriculum, density is not specifically addressed until grade six when students investigate heterogenous mixtures. In Suat Unal’s (2008) research, he recognizes that elementary students possess significant misconceptions relating to floatation as evidenced through other research by Biddulph and Osborne (1984) and Gürdal and Macaroglu (1997). This other research finds that “students offered many unrelated factors such as mass and weight” to explain floatation activity, and that even after sink and float investigations and learning of Archimedes had been completed, students “were unable to construct scientific understanding” about sink and float relations (p.135).

In preparing a T-GEM lesson, I wanted to include student investigation of objects that sink and float in water, as well as in other liquids, to help student understanding of the concept of density. Because of this specification, the Gizmos simulation that is included in the following lesson is ideal, whereas other simulations that I found online provide investigation solely with water. An image of the simulation follows:

T-GEM Lesson – Density – Grade 6 (BC Curriculum)

Teaching Strategies Student Activity
Read Aloud – Chapter 5, “Archimedes and King Hiero’s Crown” from Archimedes and the Door of Science by Jeanne Bendick. Class discussion narrating ideas presented through reading; teacher comments neutrally

GEM – Cycle 1

G – Generate Instruct students to investigate selected object in a sink and float investigation using water in a container. Students are to record observations on a T-chart as well as represent observations on a paper chart template using cut and paste images of the selected objects. Ask students to make a prediction about the types of objects that sink vs. float. With a partner, students test sink and float tendencies of selected objects in water and record on a T-chart; Students place cut out pictures of objects onto chart template; After recording data, student journal predictions about the types of objects that sink vs. float.
E – Evaluate Ask students to record anything that does not make sense about their observations and prediction – questions they may have or confusing patterns; Ask students to think of a way to conduct a sink and float investigation that could help clarify some of the observations and predictions that do not make sense. Prompt students with a change in variable – either the solid objects or the liquid. Teacher guides student through extension investigations using an alternate liquid. Students discuss with partner and record observations and predictions that don’t makes sense; Share questions and confusing patterns with class and plan a new investigation with changing one variable. Watch teacher directed demonstration and participate in class discussion.
M- Modify Ask students to determine what changes they need to add to their T-chart and paper pictorial chart to accommodate the new information accessed from the teacher-led investigation Student makes adjustments to representations of t-chart and paper pictorial chart by including results with  variable change.

T-GEM – Cycle 2

G- Generate Direct students to Gizmos online simulations: https://www.explorelearning.com {Teacher needs to previously set up an account and select simulation to add to their “class”.}

Lead students to the the elementary level lesson under Physics called “Density” Provide a short explanation of the activity, sharing that instructions are provided in text within the simulation. Remind students to record on a new chart the weight (g) of the object when measured on the scale, the volume displacement (mL)of the object within the graduated cylinder, and the the ability of the object to sink and float in each of the available liquids (water, oil, gasoline, sea water and corn syrup). After all objects have been tested, journal a relation statement based on the acquired data.   

In partners, students use the Density simulation measuring weight and volume displacement of the following objects: ping pong ball, golf ball, toy soldier, apple, chess piece, penny, egg, rock, gold nugget, crown 1 and crown 2. Students will test the floatation of each object in five different liquids and record their observations. Students will analyze their data and make a relation statement in their journal.
E-Evaluate Teacher provides students with the equation for density:

Density = Mass/Volume
And the density measurements for the 5 liquids within the simulation:

Water = 1.00 g/mL

Oil = 0.92 g/mL

Gasoline = 0.70 g/mL

Sea Water = 1.03 g/mL

Syrup = 1.33 g/mL
Ask student to evaluate their relation statement using this new information

Students compare the density of the measured objects using the density equation and with the density of the liquids and evaluate their relation statement making changes as necessary.
M-Modify Ask students to design a pictorial representation (model) of the data. Students can choose to represent objects that sink, or float, or both. The model should include density measurements of both the liquids and objects. The model should include a comparison of two or more liquids. Recommend using a chart or graph format with pictorial representations of objects. Students choose data to include in their model representation following criteria provided by teacher.


Bendick, J., (1995). Archimedes and the door of science. Bathgate ND: Bethlehem Books.
BC’s New Curriculum, (n.d.). Science 6. Retrieved from https://curriculum.gov.bc.ca/curriculum/science/6
ExploreLearning, (2017). Gizmos. Retrieved from https://www.explorelearning.com
Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905. Doi 10.1002/sce.2022
Unal, S.,(2008). Changing students misconceptions of floating and sinking using hands-on activities. Journal of Baltic Science Education, 7(3), 134-146. Retrieved from http://oaji.net/articles/2014/987-1404719938.pdf

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