Tag Archives: technology

“Paper Models of Polyhedra” – Resource Sharing and Rationale

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“Paper Models of Polyhedra”

One of my favourite parts of mathematics is 3-Dimensional solids. 25 years ago, in my first few years of teaching and well before computers in the class, I had students make Platonic Solid mobiles to hang in the class. The many different sizes, colours and variations made it a really neat project. I spent years building all the Archimedean solids, prisms, anti-prisms, and various other polyhedra. They were great to take off the shelf, pass around, and then have students discuss formulae or approaches to calculating surface area and volume. And the names are fun to say too! “Great Stellated Rhombicosidodecahedron”

Question: why is visualization necessary (or not) for student understanding of math or science?

I have not included the study of polyhedra in my math classroom for years, as I have had a hard time reconciling this study to the time constraints of the curriculum. However; numerous studies have shown that spatial ability is positively related to achievement in mathematics (Battista et al., 1982). It is now becoming possible to model situations visually and geometrically with quite astonishing sophistication (Jones & Mooney, 2003). It is for the benefits to cognitive development that this study should be incorporated into the classroom. Without the ability to engage these visualizations “ the concepts …are often seen as abstractions” (Stieff and Wilensky, 2003, p.285). The ability for students to visualize, and in this case even hold a construct is a valuable one. It is more immediate and less theoretical to actually trace angles and vertices with your fingers, measure side length with a ruler and feel the weight and size of the object in your hands. Cognitive connections can be more strongly afforded by these 3-dimensional polyhedrons.

The website “Paper Models of Polyhedra” features a huge amount of 3-D solids in photographs and nets, and is a great resource for both Elementary and Secondary Math teachers.

References

Battista, M.T., Wheatley, G.H., & Talsma, G. (1982). The importance of spatial visualization and cognitive development for geometry learning in preservice elementary teachers. Journal for Research in Mathematics Education 13 (5) (Nov., 1982), pp. 332-340
Jones, K. and Mooney, C. (2003). Making space for geometry in primary mathematics. In: I. Thompson (Ed), Enhancing Primary Mathematics Teaching. London: Open University Press. pp 3-15.

Stieff, M., & Wilensky, U. (2003). Connected chemistry – Incorporating interactive simulations into the chemistry classroom. Journal of Science Education and Technology, 12(3), 285-302

Focus on Edelson and Technology-Supported Inquiry Activities

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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.

Based on the reading, what broader educational challenges have provoked the author to do this research?

Edelson recognizes that the traditional approach to education in general and science in particular is an emphasis on memorization and repeating back facts and figures. This, however, leads t a shallow understanding. Edelson feels that in an inquiry learning model, students develop deep, content knowledge and inquiry skills through activities that incorporate authentic forms of scientific inquiry. This inquiry-based pedagogy is embodied by the. Also, there is a need for connection between science and computers/technology which can assist in many of the inquiry-based activities including data collection, data analysis, modeling, and the communication of results in scientifc research. Recent National Science Standards invite teachers to focus o inquiry learning to foster deeper and more robust conceptual understandings through firsthand use of authentic scientific practice (p.355).

What is the author’s theory of learning?

Edelson focuses on multiple theories of learning in his article. Inquiry-based constructivism seems to be at the core of much of his approach. The authentic practice of actual scientific observations, and creating a desire or motivation to learn further are based in situated theories of Cognition. Edelson indicates that “motivation must precede construction, and to insure accessibility and applicability, refinement must follow construction” (Edelson, 2000, p.359).

4 principles

(Edelson, 2000, p.357).
1. Learning takes place through the construction and modifcation of knowledge structures.
2. Knowledge construction is a goal-directed process that is guided by a combination of
conscious and unconscious understanding goals.
3. The circumstances in which knowledge is constructed and subsequently used determine
its accessibility for future use.
4. Knowledge must be constructed in a form that supports use before it can be applied.

3 steps

(Edelson, 2000, p.358-359).
Motivation: Experiencing the Need for New Knowledge. (create demand and elicit curiosity)
Knowledge Construction: Building New Knowledge Structures. (observe and communication)
Knowledge Refinement: Organizing and Connecting Knowledge Structures.(reflect and apply)

An ideal pedagogical design of a TELE for the Science classroom.

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  • Question—–>What do you think designers of learning experiences should do?
    If the goal of a technology-enhanced-learning experience (TELE) is to incorporate technology into the process of education, we should be very careful that it is both relevant and feasible. Technology for the sake of technology is not a reason to cast aside previous methods (see my previous post “A Working Definition of Technology” ). If the technology replaces a prior process well and effectively, and has the potential to afford a deeper connection to the knowledge, then it is worth incorporating into the classroom.

  • Question—–>How would you design a technology-enhanced learning experience?
    The dreaded “lab” process in Science class is seen by some students as a painful exercise and laborious process. Many schools have class sets of iPads. I would like to see the process of conducting an experiment as completely digital – i.e. paperless. In student lab pairings or groups, one person could record all data, in text, photos, videos, interviews, and graphs; and the group could seamlessly incorporate the lab report, results, web content, extensions, etc… into a final product that relies heavily on technology, but also on the imagination and vision of the students. The product could be handed in to the teacher’s network “inbox”, but really, the process itself is more educationally valid than the product. I recognize that this process may be currently used in some schools, but not in ours or any that I know about!

A Working Definition of Technology

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I think my own definition of technology is perhaps closest to Muffoletto (1994), who observes that technology is not just about the latest gadgets, but more a way of acting. He suggests that technology is applying the latest tools to address needs and problems. I do think; however, that technology is more pervasive than this. It has infiltrated virtually every aspect of our lives in both work AND play. Perhaps most especially play!
My iPhone is permanently attached to my hand or in my pocket. I use Siri for the most ridiculous things…just because I can, and I am currently battling a terrible addiction to Temple Run 2. Our “First-World” use of technology has progressed past addressing needs and problems and into a more dangerous realm. It has created a class of technology-junkies, who are not satisfied with what they have; with their eyes on the horizon, they are desperate for their next score. Who will be the next person to scoop a new piece of technology and show it off to envious friends? This dependence on technology has hampered social gatherings, dinners out, and yes, Education.
Just because something is new and guaranteed to be fabulous does not mean it should automatically be implemented in to our instruction! Muffoletto’s (1994) use of a way of acting. is important because he stresses not just the tools, but the process of applying the tools to situations. In a classroom, technology is a wonderful tool and attractant for the students, but taking notes on paper still has its role! Certainly technology is helpful, time-saving (mostly!) and “cool” but there are still things we do without modern technology that need not be cast aside.

Muffoletto, R. (1994). Technology and restructuring education: Constructing a context. Educational Technology, 34(2), 24-28.

Getting this Blog Started!

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This e-folio blog is for the course ETEC 533 (65A) Technology in the Mathematics and Science Classroom. This is my 7th course in UBC’s Masters of Education Technology (MET) program.

In this blog I will record required e-folio content, as well as other content that I explore during this semester, as well as my changing perspectives, and insights into this area.

Other blogs will reflect different ways that technology can be included, as well as interesting and educational points from colleagues in this class. Readings from the required list will be commented on, and at the end of the course a final analysis of the e-folio will be posted.


Enjoy my journey…I intend to!