Archive for March, 2010

I love the term ‘mashup‘ which is defined in Wikipedia as: “[an] application that uses or combines data or functionality from two or many more external sources to create a new service.” I think when Gardner was writing about “the synthesizing mind” (Gardner, p.45)  he was describing a mind capable of seeing that when you put ideas and information together in an innovative way, the whole will become greater that the sum of the parts.

Gardner makes the point that mastery of two disciplines (one requirement of a synthesizing mind) is unlikely to occur by the end of high school, but I don’t think giving students practice in synthesis should wait. Within a single subject such as math, learning activities can be designed that require students to synthesize information and skills from different topics or units in order to solve problems that are new and useful to them (so they can enjoy aha! moments of discovery). Strategies such as RAFT which challenge learners to broaden their perspectives by considering an issue or problem from several roles help students develop skills in “multperspectivalism” (pp. 71-73).

It is also possible to cross traditional boundaries and create projects and activities that blend learning outcomes from more than one discipine. In this case, the students have to research and integrate information and skills from different fields. The idea is to embed the learning into the process of grappling with an essential or driving question about an issue, concern, or event in the world at large, rather than preparing students for tests by simply covering the content. Technology tools and digital media can be used either by the teacher to develop instructional resources for the students or by the students themselves as they research, analyse, compile, and present their syntheses and conclusions.

The most extraordinary interdisciplinary, collaborative learning projects that I’ve come across in my travels through Web 2.0 are those of Thomas Cooper. When Cooper goes on extended canoe trips in the wilderness during the summer, he sometimes takes a pile of novels with him. Out of the relaxed reading and reflection in his non-paddling moments have come several wonderful learning projects. Thomas follows the Wiggins and McTighe model of instructional development known as Understanding by Design (UbD) and builds projects that have depth and breadth. Cooper covers this model in some detail in the Slideshare presentation at tcooper66. The original is has over 80 slides, so I’ve mashed up about 40 of them with my own perspective and some references to Gardner to create the synthesis embedded below.

View more presentations or Upload your own.

A quick look at the Project Objectives for Thomas Cooper’s Land of Hope project reveals the numerous perspectives he’s asking students to take on the issue of immigration when developing their syntheses: historical and contemporary, economic, cultural, geographic, environmental, local, global, and ethical. In his list of Basic Steps, Thomas sets out the activities in which the students will engage. I have highlighted the technologies he has incorporated.

“Basic Steps for Land of Hope

1. Have students join our community of learners. [This is a global project].

2. Choose a book on migration and have students read and discuss it regularly in order to identify the push and pull factors in migration.

3. Have students post their thoughts about what they read on the wiki every few days and respond to other members’ posts to promote discussion about the issue between students from different schools in different cultures.

4. Create a short video to introduce your research topic to other participating schools. You might think about focusing the video on the history of the issue, economics, labor, environmental problems, or other push / pull factors that affect migration.

5. While creating the video, task the Walker School’s graphics, film and video, and web design students to do any tech work for your video. This helps the students to get experience with out sourcing, as expressed in the book The World is Flat by Thomas Friedman.

6. Peer review each student video and make changes. This will be done on the discussion tab of the wiki and a conference call on Skype between student groups. [They also use Elluminate for meetings.]

7. Research detailed information on the issue and construct your wiki page, include your video. Each page will have a different push or pull factors as its focus.

8. Task Walker’s graphics, film and video, and web design students to do any tech work for your wiki page.

9. Create a layer in Google Earth that shows what push and pull factors influenced a particular migration. This will be a collaborative effort among student groups doing a specific book. Post your data on the School Data page.

10. Write a paper identifying common themes in migrations throughout history and use this information to make predictions on migrations that are occurring today.”

Cooper has thought deeply about how to get his students to wrap their minds around important issues of the day. He has created some truly innovative projects that involve students in the best of what Gardner would call “multiperspectivalism” (p. 71). Not only do the novels (each student selects one) explore a common theme from many different perspectives, but as the project progresses, the participants communicate with people in the US and around the world to test out their ideas as they explore the big picture through the lenses of many different disciplines. At the end the students have to express their findings and conclusions in a paper and use the theme/theory to make predictions for the future.

I want to finish this blog with a great list of questions from Chis Lehmann that can help us stand back from the push to infuse our currlicula with technology for a moment and assess whether it will really enhance students’ learning.

  • “How does the use of this tool contribute to a students’ understanding of the unit / project / class?
  • How does the use of the tool enhance a students’ ability to communicate their ideas / refine their presentation skills?
  • Does the tool change the frame or lens with with students can view their learning process?
  • Does the tool powerfully expand or change students’ learning network?
  • Is the tool more fun than useful? (Not that fun is bad, I like fun, but let’s also acknowledge that, in schools, our learning should be ‘serious fun.’)”
  • Cooper is using collaboration, communication, and publishing tools (I include video here), Google Earth, and Voicethread (in later projects) to involve students in global partnerships and in seeking feedback, getting a visual perspective on the issue, and sharing presentations with a real audience. If Cooper’s use of technology is ‘the guts’ of his projects, developing the “synthesizing mind” is the heart.


    Cooper, Thomas. (2009). Land of hope. Retrieved March 21, 2010 from The networked learner (website):

    Cooper Thomas. (2009). Understanding by design. Retrieved March 21, 2010 from Slideshare:

    Gardner, Howard. (2007). Five minds for the future. Boston: Harvard Business School Press.

    Lehmann, Chris. (2007, July) Curriculum design, reform, and technology infusion. Retrieved March 21, 2010 from Practical theory: A view from the classroom. (blog):,-Reform-and-Technology-Infusion.html

    Wikipedia, the free encyclopedia. (2010) Mashup (web application hybrid). Retrieved March 21, 2010 from Wikipedia (wiki):

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    An important topic to teach in math class is the Pythagorean Theorem. Students can generally memorize the formula and use it to solve problems with right triangles, but if they forget a step, the entire “house of cards” can collapse because the process was doable but not meaningful. This topic has plenty of applications in the real world, but tends often to be remembered as a set of discrete steps used to solve a specific type of question in the isolated setting of math class.

    When students’ answers are incorrect, they can become so anxious that to take them back to the concrete stage of using manipulatives to build a deeper understanding just frustrates them more. Especially in high school they can perceive having to relearn the concept as standing in the way of the real work — getting the questions done. My goal for these activities is to teach for understanding.  When the process has been forgotten, rather than simply supplying the missing steps, students can be asked to look back at their own visual and verbal representations of the theorem’s meaning and uses  to figure out for themselves what part of the process they missed. This should make for much stronger long term recall.

    My video selection, The Pythagorean Theorem, comes from The Assistant Professor series. It can be viewed in the full version (click the picture) but has also been divided into 3 short segments (listed and linked below).

    (Click image to view the full video.)

    This is a good selection for a number of reasons. Discovery has given permission to download and edit. It illustrates what the formula means, and it shows why it is necessary to square root the sum in order to get back to the length of the side you are trying to find. What follows are my suggested uses for this video in math class.

    I. Build general knowledge

    The full video is a good reference for introducing or reviewing how to solve right triangle questions. On my class website, I would have a collection of resources organized by topic and course unit. I would link to the video from there so students could refer to it in class or at home when they wanted to review.

    By downloading the video into an editing program, I could insert questions using the title function. Instead of having the students watch the video for the first time together in class, they could view it and answer the preliminary questions for homework. Students who were already familiar with the concepts could fast forward through it, and the others could rewind and repeat as needed.

    II. Organize information in a useful way; restate the theorem in new words

    The students could be asked to develop a mind map of the key content in the video using a tool such as Inspiration. After placing the full video at the centre hub (linked), they would develop their own way of organizing and prioritizing its content. Inspiration mind maps can be turned into traditional outlines for ‘scribeposting’ of notes into the student’s own blogs (from Dan Meyers; see especially paragraph 5).

    III. Ensure understanding of the underlying concept (i.e. that the areas of the 2 small squares on the short sides add to the area of the larger square on on the longest side)

    Segment 1 could be use with  a collection of similar videos or interactives (such as the selection below) to create a Voicethread.

    (Click image to go to the puzzle.)
    (Click image to go to the puzzle.)

    Pythagoras’ TheoremFunny home videos are a click away

    The students would view the collection and respond to the example they preferred by recording their own verbal versions of: “the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.” To do this they would have to clarify their understanding of the concept and then put that learning into their own words.

    IV. Restate problem-solving steps in new words

    It is possible with an editable Discovery video to strip off the audio file.The portions of Segments 2 and 3 which demonstrate solutions could be combined to make a new clip without sound. The students would then add their own narrations about how to use the formula to solve problems.

    They might also be required to add material of their own to illustrate an authentic application to replace the typical, textbook ladder example in Segment 3. In this case they would be encouraged to edit out what they did not want and to add their own shots, screen captures, and audio material as needed.

    V. Apply the formula in authentic situations

    The material on the ‘builders’ triangle” in Segment 1 could be isolated and combined with several shots of students in our district’s construction program squaring up a floor or a wall on a work site. I would record the construction students posing this problem to the class: “How do you think we use the Pythagoras theorem to ensure our buildings are square (with all right angles)?” The math students would  work in teams to answer to the question, and the construction students would be invited to provide feedback. It might even be possible for the two groups to meet on the work site. The math students could try their solutions and the construction crew could demonstrate  what did/not work and show the consequences of building a wonky house.

    I think this selection of activities meets Gardner’s litmus test for helping students achieve a “disciplined mind” at least with respect to learning and using the Pythagoras theorem. There is some emphasis on content mastery, but I have used a number of “different entry points” (p. 33) and moved beyond the mastery of the information for the sake of solving text book questions towards helping students achieve “better-informed practice” (p. 30).


    The assistant professor: The Pythagorean theorem. Retrieved March 17, 2010, from Discovery Education (website): (First image was screen-captured from the video.)
    Five minds for the future. Boston: Harvard Business School Press.
    The scribe post. Retrieved March 17, 2010, from A difference (blog):
    Darth Vader explains the Pythagoras theorem. (2008, November). Retrieved March 17, 2010, from YouTube:
    Pythagorean puzzles. Retrieved March 17, 2010, from NLVM geometry grades 6-8 (web page): (Second image was screen captured from this web page.)
    Water-proof of Pythagoras’ theorem. (2006, December). Retrieved March 17, 2010, from YouTube:

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    I’ve been thinking back to a year ago when I started my first course in the Instructional Media program. A group of EDIM students who were using Elluminate to meet regularly to discuss assignments, share ideas, and support each other invited me to listen in and become part of their conversation. They’d just finished Digital Storytelling and had moved as a group into 508 (Digital Media). They were struggling with how to embed videos, how to make the files the posted in the drop boxes a reasonable size, and how to use Google Earth.

    What seemed to them at the beginning of their program to be ‘Herculean’ tasks feel to me now to be quite manageable and inside my comfort zone — which I know is an indication of just how much I’ve learned since last March. Although every new course has it’s challenges, I feel over the past year that I’ve faced most of my fears about technology, blended the best of ‘old ‘and ‘new’ methods, and refreshed my ability to see ‘school’ and learning activities through the eyes of the kids. I’ve revisited all the old frustrations and some of the joys of being a learner again and it’s given me a new appreciation for the courage our students muster when they sit down to tackle an assignment or try to learn something new.

    I have just retired after 36 years of classroom teaching. It was time for me to take my work in a new direction and my long term goal is to be working at the university level as a teacher educator. Right now I’m with family on a working holiday in Australia. I will be doing a series of workshops at a conference here in early April and hope to be able to visit schools as well  and possibly even do little co-teaching. Interestingly, I’ve come half way round the world to find that friends of my family have their children in a small rural school here that is participating in Vicki Davies Flat Classroom project for which I was a judge last year. What a connected world I seem to be living in!

    What I hope to take from this course is a collection of new resources I can share with colleagues. Because I no longer have courses of my own to prep,  I hope to broaden the ways I can help other newcomers (like I was 3 years ago when I didn’t even know that PPT existed) try using digital media in their classrooms.

    Image source: Glasbergen, R. (2000). Retrieved March 15, 2010, from

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