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My Grade 11 Math Google Earth virtual field trip “Are We Using the Best Number Systems?” is directed towards the following instruction goal:

• Outcome 1 Demonstrate understanding of the mathematics involved in an historical event or an area of interest.

• Learning Concept : A well crafted driving question is essential to inquiry based learning.

It begins “at home” with an ordinary cash register receipt.  This typical receipt is the culmination of centuries of mathematical progress yet the number systems used are taken for granted while at the same time they are unexamined.  The tour moves to present day Pakistan to examine the origins of the decimal system using a Discovery Education (DE) video and writing prompt to encourage respect for Harappin and other Indian mathematicians and hopefully correct the mistaken belief that the Arabs alone invented the decimal system and zero.  The tour stop at the World Clock encourages students to consider the irregularities of our system of measuring time.  Stopping at the Googleplex in Silicon Valley gives students an appreciation of the binary system.  The YouTube video offered supplies a novel and effective introduction to 2 based math which the students can practice immediately using the Google Earth measuring tool.

Originally, the 20 based number system would have been explored in Nunavut, as the Inuit used it.  This honours our curriculum document as it explicitly states we must have a respectful approach to the wealth of mathematics in other cultures, particularly First Nations and Métis.  While gathering resources, I recognized that the DE Mayan math video was a serendipitous discovery for developing the ethical and respectful mind.  Not only is the Mayan math also First Nations, but because the Mayan had a system of writing it is more tangible than the Inuit who depended on oral traditions.  The Mayan calendar is also explored in the video.  (Students may already have an interest in the Mayan calendar as it ends in 2012.  This would provide a fascinating tangential discussion.)

As students compare the First Nations Mayan 20 based number system to the 2 and 10 based systems as well as the calendar systems, there is wonderful potential to develop respect for the Mayans, especially, as students have just seen the European 10 based system was first developed by minds in the Middle East and those minds developed ideas rooted in the Far East.  While the driving question chosen is “Are we using the best number systems?” another driving question is hinted at in the final picture of the tour, “Are mathematical discoveries inevitable?”

This is the video and script of my reflection about the ways I will continue to develop my five minds:

It would be unethical for me to pretend that I will continue to develop just Howard Gardner’s five minds in myself or my students.  While Gardner focused on the five minds; the disciplined, synthesizing , creative, respectful, and ethical, I was constantly seeing the virtues that supported these particular five minds.  He believes these five minds are for the future, but the virtues of these minds and hundreds of other virtues are for now and the future.  There is a complete set of innate virtues in all our students waiting to be developed.

To name just three for each, the disciplined mind requires commitment, diligence, and determination.  The synthesizing mind consideration, enthusiasm, flexibility.  The creative mind confidence, courage, perseverance.  The respectful mind compassion, humility, understanding.  The ethical mind honesty, integrity, responsibility.

To paraphrase William George Jordan “Into the hands of every individual is given a marvellous power for good or evil—the silent, unconscious, unseen influence of our life. This is simply the constant radiation of who we really are, not who we pretend to be.”  This is especially true for teachers.  By living and teaching the virtues, we can prepare ourselves and our students for whatever the future brings.

Julene Reed’s article “Global Collaboration and Learning” has the apt subtitle “How to create a world of success without leaving your classroom”.  Reed writes, “Knowledge of other cultures around the world leads students to understanding and compassion. That, in turn, creates students who take action to make a difference in resolving problems and changing the world to be a better place.”  For my Google Earth project, I am working on a math outcome that results in students demonstrating understanding of the mathematics involved in an historical event or an area of interest by doing inquiry based learning that requires data collection.  One of the locations will Nunavut, home of the Inuit, a First Nations group.

Using our Elluminate Live! virtual classroom, I can see connecting our students in Saskatchewan with those in Nunavut to respectfully and ethically collect demographic data together, evaluate it, use statistical methods to interpret it, and then draw conclusions.  As well as the virtual classroom and email, students might use a wiki for asynchronous collaboration and then a web site with photos and video to share out their findings.

Sources
Global Collaboration and Learning - EDTECH: Focus On K-12. (n.d.). Welcome To EDTECH™. Retrieved April 21, 2011, from http://www.edtechmag.com/k12/events/updates/global-collaboration-and-learning-2.html.
Image “Winter Shoreline” from Art Explosion Image Library.  Nova Development Corporation

I am a developer and have no students so I voluntold (an eminently expressive word from a Canadian-Ukrainian friend) my Grade 10 son as participant.  Before the discussion, he read the creativity card from a set of virtues.  As a starting point, I asked him to rank the core subject’s level of creativity.  He graded math and science as low, social as moderate, and language arts as high.  He mentioned that math and science in particular are mostly repetition and it is very easy to get high marks without being creative.

He values the level of creativity in his Computer Production Technology (CPT) course as he finds the assignments challenge his creativity.  He sees opportunities for other subjects to challenge his creativity the same way CPT does.

I agree with Sir Ken Robinson that schools can kill creativity and I would also argue that schools can kill the joy of learning. I would have used the word “threaten” though rather than kill because I don’t believe you can ever truly kill creativity and the joy of learning. These amazing human experiences are more resilient than perennial weeds and can survive even the strongest institutional herbicides as their roots are deep in the human mind.

Schools were designed to produce professors and factory workers who happily follow the step-by-step directions dictated to them and would never think to question authority. If you didn’t fit into one of these two shapes, you tuned out or dropped out except for the years you had an exceptional teacher who made learning a joy and encouraged your creativity.

Digital media has the potential to help more teachers become exceptional.When  guiding students through the learning process of planning, exploration, and expression, employing digital media levels the playing field and gives all students tools to create. Handwriting is no longer a barrier. Word processing spelling and grammar checks improve writing quality as does the limitless ability to edit ideas. Image editing gives students the ability to capture and share their unique visions that might otherwise be trapped permanently in their heads. Audio communicates tone, pitch, pauses, and rhythm in a way text alone cannot. Finally, video combines the best of images and audio and then adds body language and motion. By integrating digital media into learning, teachers support the highest order thinking skill– creating.

Media-infused presentations foster the development of both Howard Gardner’s disciplined and synthesizing minds.  Gardner says the disciplined mind has “mastered at least one way of thinking” and adds, the “disciplined mind also knows how to work steadily over time to improve skill and understanding” (2007).  Gardner’s synthesizing mind “takes information from disparate sources, understands and evaluates that information objectively, and puts it together in ways that make sense to the synthesizer and also to other persons” (2007).

In Brain Rules 12 Principles for Surviving and Thriving at Work, Home, and School, John Medina gives us some insights into how digital media can assist both the disciplined and synthesizing minds. The first rule that applies is “Rule #4: We don’t pay attention to boring things.” (2008).  Compare a text book to a multimedia presentation with the same content.  Which one is more interesting?  I believe the vast majority of brains prefer multimedia.  Interesting things engage us and engagement is the essential first step in the learning process.  Medina’s Rules #5 and #6 “Repeat to remember” deal with short and long term memory.  Digital media can be endlessly modified to support repetition as the same concept can be presented as text, image, audio, and/or video.  Digital media also aligns itself with Rule #9, “Stimulate more of the senses.”  This needs to be practiced in moderation to avoid sensory overload.

The biggest rule for the disciplined mind is possibly Rule #10 “Vision trumps all other senses” (2008).  Medina estimates recall is six times greater when a visual is included with text and writes “We learn and remember best through pictures, not through written or spoken words” (2008).  Video tops both text and images as our brains pay the most attention to movement.  Our primitive brain knows the wisdom of paying attention to moving things, particularly sabre toothed tigers.  The movement in video constantly attracts our attention and attention trains a disciplined mind.

For Gardner’s synthesizing mind, Medina has these two rules:  “Rule #7: Sleep well, think well” and “Rule #8: Stressed brains don’t learn the same way” (2008).  Sleep is critical to synthesis as brain researchers are finding evidence that it is during sleep that we consolidate learning.  As stressed brains do not learn the same way, it is probably true that stressed brains do not synthesize the same way.  While we apparently need stress to prevent death from boredom, we can learn how to manage stress so it doesn’t hijack our brain power.

While digital media can help both the disciplined and synthesizing minds, our lifestyle choices of things like exercise, sleep, and stress management will determine the effectiveness of any mind.

I prepared this Prezi to illustrate the use of digital media to train the disciplined and synthesizing mind: http://prezi.com/-pukikqo8gw_/cell-phone-plans-as-systems-of-linear-equations/.

Sources
Gardner, Howard. (2007). Five minds for the future. Boston: Harvard Business School Press.
Medina, J. (2008). Brain rules 12 principles for surviving and thriving at work, home, and school. New York: Pear Press.

The Credenda learning template Application provides meaningful opportunities to interact and synthesize the information from the Exploration. In a recent outcome focused on solving systems of linear equations for Grade 10 Math, I integrated a geothermal savings calculator into a learning concept that had the students discover how intersection points can provide valuable information for decision making. The first Application question using the calculator provide details on an fictional average house.

Geothermal Savings Calculator

The beauty of the calculator was for the first time the students would have the opportunity to recognize that the results were the rate of change or slope as previously they would have been given the rate explicitly or would have had to calculate the rate. The second question using the calculator asked them to collect information on a house near them, find the break even or intersection point, and then compare the two houses. Most importantly, as synthesis, the students were asked if they could have predicted the results of the comparison. Prediction would only be possible if the houses had the same current heating system and similar locations. As students could use graphing to solve the system of linear equations, they could use an online graphing calculator to answer either question.

Digital assets like Discovery Education’s “Multiplying Two Polynomials” video segment from Algebra: Multiplying Polynomials have high edutainment value. This video tells the simple story of a family garden plot. As the garden plot grows, the video shows the algebraic expansion and then confirms and reinforces the algebraic concepts using area calculations. Although a skateboard park might have been a stronger engagement hook for our students, the video luminously provides helpful concrete visual images of algebraic variables and polynomials that can be stored for reference in memory.

As I develop math outcomes, I strive to create and integrate digital assets that facilitate the four parts of our learning template; engagement, exploration, application, and connection. I know I’ve found one when I hear myself saying, “I wished I had had this when I was a student.” I look first to video (with the exclusion of talking head videos) and then static images. I also treasure virtual labs because they support us as we predict and test our predictions.  This makes our learning active rather than passive.

“Multiplying Two Polynomials” video segment excerpt from Algebra: Multiplying Polynomials. ModuMath, 2007. Full Video. 29 September 2010. <http://www.discoveryeducation.com/>.

Using the concise communication of Twitter’s 140 characters, here are my answers to our introductory questions:

Who are you and what do you do?
Nancy Carswell, eLearning Course Developer @ Credenda Virtual High School.
What is your primary goal for taking this course?
Exploit digital media tools to revolutionize learning.
What is your philosophy of education?
http://prezi.com/1lzeqtpp90u_/the-joy-of-learning/
What do you see as the greatest benefit of using technology and/or digital media in the classroom?
It facilitates the learning essentials of engagement, exploration, application, and connection.
What is your biggest concern or challenge with using technology and/or digital media in the classroom?
Resisting the temptation to co-opt technology to reinforce Industrial Age methods of teaching.
Provide an example of how you currently use technology and/or digital media in the classroom.
Creating Flash animations for learning concepts in Math 10 Foundations and Pre-Calculus.
How does your classroom today differ from when you were the same age as your students?
It is literally virtual and our content is accessible 24/7.