Category Archives: TPCK

Financial Literacy for the Elementary Student – Coin Box Simulator Through Anchored Instruction

Background:

Financial literacy is highlighted throughout the elementary grade levels in the Content area of BC’s New Curriculum. Most paper-pencil curricula address money identification, counting coin and dollar amounts, and one or two step word problems connected to money. However, these paper-pencil activities minimally equip students for financial literacy skills and applications. While exploring the information visualization simulators during this past week, the elementary and middle school simulations from Illuminations were easy to understand and seemed quite plausible to implement into already developed curriculum.


Literature Support for Lesson Cornerstones: 

In a study conducted by Srinivasan, Pérez, Palmer, Brooks, Wilson and Fowler (2006), engineering freshman students who completed learning using MATLAB did not experience what they perceive as an authentic experience. The students felt that their experience was disconnected from real expert experience because they manipulated a simulated system rather than a real-life system. The researchers conclude that a probable reason for this disconnect is that the students “need/want authenticity to be able to make connections the experts make with the simulation” (Srinivasan, 2006, p.140).  This perception from the students leads educators to consider the value of real-life experiences in connection with simulated experiences.

Transferring simulated experiences to real-life experiences is supported through the study completed by Finkelstein, Adams, Keller, Kohl, Perkins, Podolefsky and Reid (2005). In their study, students in a second semester introductory physics course, who had used a simulation first to design a circuit system, were more successful later in designing real-life models. These same students also achieved greater success on related exam material that was completed two months after the simulated and real-life circuit building experience (Finkelstein, 2005). Due to these findings, authenticity of learning through the transferring of knowledge from simulation to real-life experience is a main cornerstone of the following lesson design.

In addition to authenticity, two lesser cornerstones, rich content and goal challenge motivation, are also incorporated into the lesson design as supported through the writings of Srinivasan et al. (2006). A pre-test assessment begins the lesson in order to determine prior knowledge and the optimal area of learning for the individual student. As well, this pre-test assessment can be used to determine pairings/groupings throughout the lesson activities. By providing rich content within the lesson plan, this affords opportunity for students with less prior knowledge to acquire new knowledge before exploring the simulated and real-life experiences. Building prior knowledge within students is critical for their success as Srinivasan et al. (2006) state, “Prior knowledge accounts for the largest amount of variance when predicting the likelihood of success with learning new material” (p.138). In regards to gaining knowledge of the student’s optimal area of learning, this connects closely to Vygotsky’s zone of proximal development, but is also supported by goal oriented motivation when learning goals are neither too steep, nor too simple: “If learning goals are too steep for a learner’s current context, learning is not successful. On the other hand, when learning is simple for the learner, the instruction can become over-designed and lead to diminished performance” (Srinivasan, 2006, p. 139).


Lesson Overview: 

The following lesson incorporates the instructional framework of anchored instruction. This has been accomplished through a narrative multi-step problem solving feature. The three cornerstones highlighted in the section above are evident within the lesson: goal challenge motivation {decided by pre-test assessment}, content-rich material, and authenticity through real-life application.


LESSON

Pre-test Assessment:

Provide paper-pencil assessment including photos of Canadian coins asking students to identify individual coins.

Addition questions for pre-test assessment may include:

  • How many quarters makes a dollar? How many dimes? How many nickels?
  • Show 3 different ways of making one dollar using a mix of coin types. Draw coins with labelled amounts to share learning.

 Include two ‘making change’ questions that require student to calculate amount of change from $1.

Content-rich Material: 

Read and discuss Dave Ramsay’s book entitled, My Fantastic Fieldtrip on saving money.

Provide pairs of students with real sets of Canadian coins with accompanying anchored money solving problems. Problems may require students to interact with other students in the class or with the teacher. An example of an anchored money problem solving scenario follows:

Macey has been saving her allowance for seven weeks. She has a saving goal of $20.00. Each week she receives $1.50. Three weeks ago, Macey decided to buy her sister a rubber ball for her birthday which cost $1.00.  She used a loony from her savings . After seven weeks, Macey wanted to exchange all of her quarters for loonies, but she also wanted to keep half a dozen quarters for when she visited the candy machine at the grocery store when she went shopping with her mom.  She knew that several of her classmates had loonies that they could exchange for her quarters. (At this time, go around to your classmates and exchange your quarters for loonies just like Macey wanted to.) Once Macey exchanged her quarters for loonies with her classmates, how many loonies does Macey have? How much money does Macey have all together? How much more money will Macey need to save to reach her saving goal?

Simulation  Activity:

Illuminations –  Coin Box {elementary level}: Initially, direct instruction is required to demonstrate how by clicking on the cent icon in the bottom right corner, the student can see the amount of each coin as they are  US coins and difficult to decipher visually. Direct instruction should also be provided to guide the student to the “Instructions” tab and show the subtitled areas “Modes”. Student can then have time exploring the “Activity” section using the dropdown menu in the top left corner. Student should have ample time to explore all five activities including: “Count”, “Collect”, “Exchange”, “Change from Coins”, and “Change from Value”.

Transfer to ‘Real-Life’ Context: Students should have opportunity to transfer the simulated learning to a real-life context. An example of a real-life context is provided below, however adapting this to uniqueness of the learning community is recommended:

Cookie Sale –  Each student bakes one dozen cookies to sell to classmates and other students at the school. Pricing: 1 cookie = $0.40, 2 cookies = $0.75, 3 cookies = $1.00, 4 cookies = $1.25, 5 cookies = $1.45, 6 cookies = $1.70. This activity allows for assessment by the teacher through observation. Student’s accuracy and ease of providing change could be assessed using a simple checklist. Students should work in pairs  or small groups to help ensure that change to buyer is accurate.

Self Assessment/Reflection: A reflection activity is to be completed by each student. This activity requires the student to reflect on and share about growth and relevancy of learning. A self assessment printable is here:

Self Assessment


Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., Podolefsky, N., & Reid, S. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physics Education Research,1(1), 1-8.

Srinivasan, S., Pérez, L.C., Palmer, R.D., Brooks, D.W., Wilson, K., & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology15(2), 137-141. doi: 10.1007/sl0956-006-9007-5

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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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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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Transforming Teaching and Learning Through Pro-D

During Module A discussion, the need for educational technology related professional development for teachers was highlighted as necessary in equipping teachers for technology use in their classroom. The specifications of professional development were not thoroughly described in the discussions, which welcomes Mishra and Koehler’s (2006) detailed explanation of effective professional development using a “learning-technology-by-approach design” (p.1035). This approach incorporates TPCK and focuses “on learning by doing, and less so on overt lecturing and traditional teaching. Design is learned by becoming a practitioner, albeit for the duration of the course, not merely by learning about practice (Mishra & Koehler, 2006, p.1035). TPCK encourages professional development in an alternative process than is typical through workshops; professional development needs to be an integration of learning about the technology (content) and learning to use the technology in an authentic learning context (pedagogy). “Standard techniques of teacher professional development or faculty development, such as workshops or stand-alone technology courses, are based on the view that technology is self-contained and emphasize this divide between how and where skills are learned (e.g., workshops) and where they are to be applied (e.g., class- rooms)” (Mishra & Koehler, 2006, p. 31). Also key to TPCK, is the learning not of specific programs – software or hardware, but of the underlying principles of technology use. This is essential as “newer technologies often disrupt the status quo, requiring teachers to reconfigure not just their understanding of technology but of all three components [i.e. content, knowledge, pedagogy]” (Mishra & Koehler, 2016, p.1030). Developing a repertoire as described by Wasley, Hampel and Clark (1997) and quoted by Mishra and Koehler (2006) as ‘‘a variety of techniques, skills, and approaches in all dimensions of education that teachers have at their fingertips’’ (p. 45) helps to equip teachers to move from a professional development experience into their classrooms and choose the technology tools that will best meet the needs of their students. This supports Petrie’s (1986) extension of Schulman’s aphorism, “those who can, do; those who understand, teach” (Shulman, 1986b, p. 14) as he describes understanding as needing to be “linked to judgment and action, to the proper uses of understanding in the forg­ing of wise pedagogical decisions” (as quoted in Schulman, 1987, p.14).

The term “transformation” that Schulman (1987) uses to refer to the experience that occurs as content knowledge is passed from teacher to student provides an effective visual image. He describes this transformation as “the capacity of a teacher to transform the content knowledge he or she possesses into forms that are pedagogically power­ful and yet adaptive to the variations in ability and background presented by the students (p.15). This transformation offers opportunity for individualized learning, teaching for the student rather than at the student, and aligns well with my teaching experience at present:

One example of incorporating PCK in my own teaching is in constructing individualized student learning plans for each of my students. As a distance learning teacher, I work with each student individually rather than offering a standard course or program. Conversations are held prior to the start of the learning year to design a student learning plan that consists of curriculum, resources, activities, etc. that cover the content area prescribed for the student’s grade level, but also adheres to the student’s interests, abilities, learning environment and effective ways of learning. Throughout the year, the student learning plan evolves as necessary, but again with the individual student’s needs guiding the changes. As students share their learning with me throughout the year, I provide specific feedback often suggesting areas that they can grow in their representation of ideas, as well as designing or recommending specific assignments to further their learning experiences. Although the forms of transformation may look different in a distance learning context, the process of moving from “personal comprehension to preparing for the comprehension of others” (Schulman, 1987, p.16) still occurs through preparation, representation, instructional selections, adaptations and tailoring (Schulman, 1987).

 

Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054.
Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14.
Shulman, L.S. (1987). Knowledge and teaching. The foundations of a new reform. Harvard Educational Review, 57(1)1-23.

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