Illuminating Illuminations

In their investigation into the effectiveness of computer simulations, Finkelstein et al. (2005) concluded that “the conventional wisdom that students learn more via hands-on experience is not borne out by measures of student performance on assessment of conceptual understanding” due to their findings that “properly designed simulations used in the right contexts can be more effective educational tools than real laboratory equipment, both in developing student facility with real equipment and at fostering student conceptual understanding”. Providing students with opportunities to explore concepts in a variety of contexts enriches the learning environment and diversifies instruction to better meet student needs. In the mathematics lesson below, the concept of fractions is embedded in inquiry-based activities to help students visualize this concept while exploring selected interactive applets. Reflection plays a key role in the intended abstraction as a means of guiding students through a process of self-assessment to better understand their conceptual understanding.

Illuminations Lesson for Fractions
(click link above for lesson)

Rationale

By Grade 7, students are expected to have a basic, but solid, understanding of fractions so that they can proceed with more in depth explorations of relationship comparisons and eventually addition and subtraction operations. Unfortunately, this is often not the case and measures need to be taken to assist students’ conceptualization of fractions in preparation of their extensive use in math strands in successive grades. Much of the problem seems to lay with students’ misconception and simplification of fractions down to sets of rules to be committed to memory creating inaccurate mental models. It’s not surprising then that they are frequently unable to adapt strategies they have used in one context to fit a new situation. Their knowledge of fractions remains superficial and does not lead them to a deeper understanding of what fraction symbols communicate as a representation of a whole. When learning abstract concepts, such as fractions, students must understand the fallacy of focusing on memorization as it “leads to ‘inert knowledge’ that cannot be called upon when it’s useful” (as cited in Edelson, 2001) resulting in a poor or non-existent transfer of skills.

Using Illuminations activities provides students with a “variety of visual cues in the computer simulations [to] make concepts visible that are otherwise invisible” (Finkelstein et al., 2005) or at least more difficult to visualize. When integrated into an inquiry-based framework, they can be used to enhance students’ abstraction of fraction concepts while promoting the acquisition of adaptive expertise and thinking skills.

Intertwining the constructivist principles of the Learning for Use framework and T-GEM instructional model provides and impressive foundation for math explorations. The GEM cycle stages of Generate – Evaluate – Modify are complemented by the 6 tenets of LfU, motivate, elicit curiosity, observations, knowledge construction, refine and apply. While collecting information and generating ideas, curiosity and motivation are provoked as students realize what they do not yet know, but need to in order to be able to complete the task. Through key observations, students construct knowledge as they begin to evaluate their assumptions around relationships between variables. As students work to modify their original theories, they need to refine and apply new understandings that have arisen from their investigation. Applications of the LfU and T-GEM frameworks to instructional design presume that overlaps in each of the stages will occur as they both involve a cyclical process of exploration and inquiry. In fact, several cycles may be needed due to the incremental nature of learning; however, the order of the stages remains a critical factor. In the lesson outlined above, two complete cycles of T-GEM and LfU can be observed.

 


British Columbia Grade 7 Math Learning Outcome (Number – A7)

  • compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using
    • benchmarks
    • place value
    • equivalent fractions and/or decimals

Comparing percent to fractions and decimals is a Grade 6 outcome, but by Grade 7 this is consistently not understood well so it needs to be re-taught in preparation for Grade 8 expectations with percent (greater than 100% and fractions of percent between 0 and 1) providing students with a more substantive opportunity to understand the overriding relationships between all three values; therefore, in this activity, this Grade 6 learning outcome will be reinforced as an integral component of the task.

Grade 6 Math Learning Outcome (A6): demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially, and symbolically.


Before beginning lessons involving self-directed exploration of Illuminations activities, students must possess sufficient background knowledge to prepare them for success with the simulation activity. If the expectations for student learning are high given their current context, they will have difficulty navigating the activity (Kalyuga in Srinivasan, S. et al, 2006) and finding the necessary motivation to learn what they need to know to be successful. In this scenario, essential prior knowledge includes an understanding of:

  • numerator, denominator, common/proper fraction, improper fraction, mixed number, whole number, simplest form, equivalent fractions, multiple, factor, benchmark fractions/decimals/percents, addition equations equaling 1 whole, decimal place value (tenths, hundredths), parts of one, relating fractions to decimal place value, percent

Along with having prior knowledge, students must be able to access and activate it; therefore, the initial introductory task is intended as a revision of fraction concepts and relationships, which become essential elements, within the subsequent scaffolded activities.

(This post serves as further reflection on the application of knowledge representation and information visualization as it applies to my future personal practice and includes the alternate activity requested in lieu of directly related papers on the use of Illuminations)


References

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. http://onlinelibrary.wiley.com/doi/10.1002/1098-2736%28200103%2938:3%3C355::AID-TEA1010%3E3.0.CO;2-M/abstract

Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (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. Retrieved April 02, 2006, from: http://phet.colorado.edu/web-pages/research.html

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

Srinivasan, S., Perez, L., Palmer, R., Brooks, D., Wilson, K. & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 1-5

Walking the Talk …

The most prevalent obstacle that impedes inquiry-based learning in educational settings is the instructor’s understanding of inquiry and pedagogical approaches as well as the ability to implement these successfully. This was shared through the expressed frustrations of the Jasper Series designers when teachers did not seem to recognize the value in exposing students to analog problems that were conceived for the purpose of improving transfer and abstraction of concepts and strategies, opting instead for adventures that introduced the need to use different skills overlooking the opportunity to increase adaptive expertise (Hatano, 1984). Within the WISE environment, customizing the platform for successful inquiry-based learning requires a level of competence that designers cannot necessarily assume teachers possess. The inquiry map alone, which directs students through the process, can present a significant challenge in that even Linn, Clark & Slotta (2003) caution that its level of detail affects student engagement. The prescriptive nature of WISE projects provide students with the necessary information to proceed independently, but also provide opportunities for teachers to misinterpret the structure of the investigation. Manipulating the available scaffolding steps along with the limited opportunities for socially constructing knowledge embedded within WISE provide a potential recipe for reinforcing the transmission model, albeit with animations and the technological affordances of accessing past progress. While the Jasper Series was founded on stronger pedagogical principles that provide valuable insight into TELEs and continue to describe essential qualities of powerful and effective learning environments, both it and WISE promote more of a packaged approach to inquiry that does not require teachers to explicitly understand the theory and pedagogy behind them before integrating them. As potent as they could be in bringing inquiry-based learning to the classroom, they could also be used to further entrench traditional instructional approaches that reinforce inert knowledge. It cannot be assumed that teachers possess the aptitude to integrate these TELEs. Just as students require explicit instruction to develop inquiry skills, teachers need to be “explicitly taught about interactions among pedagogy, content, technology, and learners” to develop their Technological Pedagogical Content Knowledge, or TPCK. This conceptualization is critical.

The Learning for Use design framework and T-GEM cycle of instruction, originally attached to My World and Chemland TELEs, offer the greatest potential for reform in the mathematics and science classroom. With a primary emphasis on the inquiry process rather than prescribed activity steps, it requires teachers and students to adopt an inquiry mind-set that becomes the foundation for implementing them. They are not distinctly tied to one particular curricular area or TELE, offering transportability to any number of educational contexts, within the classroom or outside of it. Their cyclical nature and use of abductive reasoning puts greater emphasis on the relationships between students and between students and the teacher highlighting the role social collaboration and collective understanding plays in the development of robust mental models that can help students conceptualize content and repair misconceptions. Understanding this pedagogy requires teachers to pursue a pedagogical model that exemplifies the development and refinement of useful and adaptive pedagogical knowledge because inert knowledge or memorization of a set of activities in an effort to apply either of these methods will not suffice. The broad scope of these two approaches compel educators to seek knowledge for understanding.

Integrating constructivist pedagogy into classroom practice is not a simple process. “The constructivist theories of learning apply to teachers and designers” as well as students (Edelson, 2001, p. 381). If teachers are going to be successful implement the Learning for Use framework or T-GEM instructional cycles, it is imperative that have parallel experiences with this learning process themselves to model best practice and become co-learners with students in a continued process of reflection and refinement.

image: Walking the line by Kalexanderson released under a CC Attribution – Noncommercial – Share Alike license


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.

Edelson, D., Salierno, C., Matese, G., Pitts, V. & Sherin, B. (2002). Learning-for-use in Earth Science: Kids as climate modelers. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, New Orleans, LA.

Hatano, G. & Inagaki, K. (1984). Two courses of expertise. Research and Clinical Center for Child Development Annual Report, 6, 27-36. Retrieved from http://eprints2008.lib.hokudai.ac.jp/dspace/bitstream/2115/25206/1/6_P27-36.pdfbe

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

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

Linn, M. Clark, D. & Slotta, J. (2003). WISE design for Knowledge Integration. Science Education, 87(4), 517-538.

Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303.

Assessing the Affordances of TELEs

Anchored instruction in the Jasper Series, WISE’s scaffolded knowledge integration framework (SKI), the Learning for Use model when applied to My World, and applying the T-GEM cycle to Chemland explorations showcase the application of pedagogical design in response to ongoing research regarding effective technology-enhanced learning experiences (TELE) in mathematics and science classrooms. All four TELEs are driven by documented discrepancies between theoretical best practice and actual instructional approaches in all levels of education. Although varied in their application, each design is grounded in constructivist principles that focus on inquiry-based learning, mental models, socially constructed knowledge, and reflective conceptualization aimed at integrating both content and process outcomes of science or mathematics education. Reasons for pursuing this common pedagogical design are rooted in substantive conclusions of researchers who assert that “inquiry is associated with an array of positive student outcomes, such as growth in conceptual understanding, increased understanding of the nature of science, and development of research skills” (Khan, 2007, p.877). To achieve this authenticity within TELEs the design must be nourished by activities that “provide the opportunity to ground abstract understanding in concrete experience” (Edelson, 2001, p. 378). Reforming science and mathematics requires a pedagogical shift away from the passive “transmission approach [which] does not acknowledge the importance of the motivation and refinement stages of learning and relies too strongly on communication to support knowledge construction” (Edelson, 2001, p. 377).

While the tenets of How People Learn are most prominently applied to the Jasper Series and the development of anchored instruction, emphasis on pedagogically sound learning environments that embrace knowledge, learner, assessment, and community-centered principles is also woven into the pedagogical approaches attached to WISE, My World and Chemland. The degree to which each of these aspects are incorporated into the design structure of these TELEs varies, although all demonstrate a more concerted effort towards being knowledge and learner-centered beyond assessment and community-centered. The perceived authenticity of the inquiry plays a significant role in developing science process skills, conceptualization of content skills, and students’ connection with relevance of math and science outside of the classroom. All four TELEs strive to create an environment that promotes and nurtures learning from inquiry, as well as underscoring the importance of the facilitator’s role from a pedagogical perspective as technology is unable to independently and meaningfully guide students through this process.

Authenticity of the inquiry process is best illustrated in the Learning for Use framework and T-GEM cycle – each having potential in educational settings well beyond My World and Chemland. Investigating these two pedagogical approaches reveal a process-based structure that is emergent and tailored to students in a specific setting. Both offer cognitive and social affordances in learner-centered environments that move beyond the pre-packaged options of the Jasper Series or WISE projects. The depth of conceptualization possible in TELEs designed using these pedagogies provide students and teachers with an inquiry process that develops authentic problem solving skills, robust thinking skills and reflective practice. Every stage of the inquiry process is integral and must unfold explicitly for students if they are expected to develop effective knowledge organization indices that can be accessed in the future. Understanding the principles behind Learning for Use and T-GEM requires a broader comprehension of constructivism, situated cognition, abductive reasoning and inquiry-based learning. Implementing these approaches in a classroom involves the application of a holistic process that encompasses more than specific activity guidelines or steps, providing students with greater opportunities for skill transfer and improving teacher heuristics within technology supported inquiry learning (TSIL). The cyclical nature of Learning for Use and T-GEM parallels authentic inquiry in the scientific community and strengthens students’ abilities to evaluate and refine mental models as part of the process of abstraction. For successful integration, teachers must possess in-depth knowledge of their students and the ability to promote students’ gradual construction of knowledge individually and collectively.

“computer simulations are particularly valuable for science teachers because they help students visualize aspects of science that are either too large or too small to view, afford rapid testing of ideas, reveal trends in graphs or other representations, and provide extreme situations to support thought experiments and what if scenarios” (Khan, 2010, p.216)

Exploring these TELEs has created an increased impetus for reflecting on my own integration of computer simulations and technology enhanced learning experiences in my practice. Being able to better articulate my pedagogical approach in specific educational contexts and analyze how I am using technology to support students’ development of authentic inquiry processes has strengthened my TPCK, which in turn will strengthen my ability to design knowledge, learner, community, and assessment-centered learning environments that promote inquiry and conceptualization. T-GEM and Learning for Use pedagogy will be valuable resources in designing the inquiry-based classroom I envision. The scaffolded knowledge integration framework and anchored instruction principles have contributed to an increased understanding of inquiry-based learning and enriched my instructional design principles which will in turn positively impact my current and future practice. The limitations observed in the WISE project design have challenged my perception of how best to approach teaching inquiry using technology because a one-size fits all model, transmitting incremental procedural steps, is inadequate. I believe teachers need to carefully gauge students’ inquiry skills to determine authenticity or if they are merely witnessing the appearance of authenticity in the wake of poorly designed or poorly implemented pedagogy. First and foremost though, this necessitates a depth of understanding involving inquiry-based learning from an educator’s perspective that cannot be underestimated.

 image: Thinking by heyjudegallery released under a CC Attribution – Share Alike license

 


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.

Edelson, D., Salierno, C., Matese, G., Pitts, V. & Sherin, B. (2002). Learning-for-use in Earth Science: Kids as climate modelers. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, New Orleans, LA.

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

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

Linn, M. Clark, D. & Slotta, J. (2003). WISE design for Knowledge Integration. Science Education, 87(4), 517-538.

Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303.

 

T-GEM Possibilities …

After reading the articles this week, I find myself contemplating GEM in my planning … a lot. I am excited to try and implement this model of inquiry as it seems to be what I’ve been looking for. While I think I have been incorporating aspects of it already, it has given me a better foundation to reflect on my efforts to help my students develop key processes of inquiry, not just in science and math either … everywhere. I realize I need to put more effort into using “modeling and inquiry [to] facilitate the development and revision of abstract concepts” (Kahn, 899) in my classroom.

In Grade 7, students are expected to understand properties of matter. It can be a difficult concept for some as the abstract notion of particles and molecules aren’t readily observable. Creating enough hands-on activities to demonstrate this is also a challenge because changes involve increases and decreases in temperature, which produce safety concerns and impinge on time factors. A computer simulation can help students understand this concept beyond text-book facts and static images.

To begin with we would investigate quantitative and qualitative properties of matter, so students would be introduced to the concepts of solids, liquids, gases and particles as well as the rationale behind temperature being measured in kelvins. This would provide the appropriate background information before engaging in the PHET simulation – Properties of Matter.

GENERATE
Students are asked to collect data on neon and its particles in the 3 different states of matter. The first relationship they are asked to generate is how the particles compare to each other in each state.

EVALUATE
They need to test their hypothesis by investigating 2 other substances, argon and oxygen, in their different states of matter.

RE-GENERATE/RE-EVALUATE
Students collect further data by documenting temperature observed at each state with each substance. They are then asked to explain and test the relationship between temperature and the energy of the molecules, using the option of heating or cooling the substance.

EVALUATE/MODIFY
Finally, water is investigated to see if their theories of particle movement and interaction in relation to temperature continue to be valid. Students will be guided toward the solid model of water to investigate its particles further, its response to further cooling, and asked to evaluate/modify their assumptions about particles within solids – leading towards an understanding of the properties of ice compared to other solid substances.

Further investigations ~ this would extend into the next science class

Students use the temperature data they have collected to investigate what happens to different substances when they are heated or cooled to the same temperature observed by another substance in a particular state. E.g. Neon is observed in a gas state at 55 K … what does argon look at 55 K? What state of matter is most likely represented at this temperature?

Students are asked to comparatively investigate the substances and determine the impact variations of temperature would have on these substances according to a scale of temperature. E.g. Investigating boiling points, melting points and freezing points.

image: Beaded Molecules: preliminary tries by fdecomite released under a CC Attribution license


References

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

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.