Archives

26 Mar

Exploring the Apollo Moon Landings with Google Earth 5 & the ActivBoard

Author: Administrator  //  Category: Classroom

Image from http://earth.google.co.uk/Continuing our recent exploration of Google Earth 5 with the Activboard where we explored then blogged about ocean data and using Google Earth to plot  GPS coordinates , we then decided to explore the Apollo moon landings using Google Earth 5 ‘layers’ and ‘Moon Gallery’ feature.

Where Shall We Go Today, Class?

For this simple experiment we were using out ActivBoard 330 Pro and our Flip Video camera, a great way to capture instant moments of inspiration and ideas, with minimum fuss.

We started at the Kennedy Space Centre in Florida, to see where the beginnings of the moon landings took place. Then, using a new icon in Google Earth 5 on our toolbar, we toggled between views of Earth, Sky, Mars or Moon, and selected to visit the moon (see image below).

Selecting 'Moon'By holding down the right-click function of the ActivPen we were then able to zoom into the moon without losing our reference point and without crossing the page to use the zoom functions provided by Google Earth.

Using Google Earth Layers

The layers facility in Google Earth 5 provides us with an opportunity to investigate the moon further. From here, we selected the ‘Moon Gallery’ and drilled down to ‘Apollo Missions’, choosing the Apollo 11 landings. We were then able to exlpore the surface of the moon, looking at craters and learning more about the landings.

A Rich Mix of Media for the Classroom

Perhaps the best feature of Google Earth 5 (apart from being free!) is that it also gives you access to further materials for learning. When we visited the Apollo 11 landing site we were able to view a YouTube video of Neil Armstrong citing those famous words and look at other resources relating to the landing.

Overall, what we’ve illustrated is how easy it is to deliver a complete learning experience mixing different media (ActivBoard, Google Earth 5, YouTube) to deliver an engaging lesson…just watch the video to see how it’s done and try it for yourself!

Comments (0)  //  Add Comment
24 Mar

Understanding History to Make Sense of the Future

Author: Administrator  //  Category: Classroom

The National Underground Railroad Freedom CenterNot many people would look behind when going forward, but what if we all took a step back to revisit our history – could this make sense of a sometimes clouded future?

Over the past couple of months, Promethean Planet has been working with the National Underground Railroad Freedom Center (NURFC) in Ohio, to bring to the Planet community resources that focus on African- American heritage, in particular, the slave trade. All of these resources, flipcharts, podcasts and images, can be downloaded from Planet.

Mr Carl WestmorelandAs part of this series of thought-provoking resources, the Planet team are honored to be blogging with Mr Carl Westmoreland, Senior Advisor for Historic Preservation at the National Underground Railroad Freedom Center.

Mr Westmoreland talks about the importance of remembering our heritage, how the museum helps people understand our past and what messages teachers can pass on to their pupils.

How important is Heritage to the Freedom Center?

The documented and vetted history of the history of the Underground Railroad, the civil rights movement which lead to the Women Right’s  movement and today’s Human Rights movement, is vital to the need for people of dissimilar backgrounds in developing a positive  understanding of the multicultural world in which we live.

Objective research teaches us that the documented history of all ethnic groups in the world is varied and important, and understanding of the cultural heritage that is unique to the world’s population is needed to avoid global conflict, genocide, political and economic domination that has destabilized an ever shrinking world.

How does the museum help pupils to understand about African-American slavery?

Using objective research which, for example, we quote Dr. Ira Berlin, University of Maryland History professor, who in his book Many Thousands Gone (Harvard University Press, 1998), documents that the value of free enslaved labor in 1860 had a value of 3 billion dollars in 1860 money, we are able to build an outline that creates a base for the understanding of enslavement in America.

Dr. Berlin and other scholars openly quote John Calhoun, Senator from South Carolina in the 1850’s and 1860’s and the Vice President of the Confederacy Alexander Stevens, as well as Stephen F. Austin of Texas, all of whom publicly stated that slavery was the basis of the Southern agricultural economy in the 18th and 19th century.

We put a human face on the numbers that quantify the value to the United States’ economy of enslavement and the use of visual images throughout the museum, such as the image in the Tom Feelings mural in the Slave Pen gallery which depicts the tragedy of an infant being separated from its mother, communicates directly to children that during enslavement, the Black family had no legal standing and no social legitimacy in America.

Children are exposed to the truth that it was against the law in the North (Ohio), as well as in the South, that it was against the law to educate children in the 19th century.  The Black Codes of Ohio (1802) were derived from the Virginia Slave Codes a fact that demonstrates to contemporary children that slavery impacted the lives of all Africans in America, enslaved or free.

[See post to watch Flash video]

What are the most important messages for teachers to remember when teaching about slave history in the classroom?

Slavery could be compared in the classroom to the life of a child that is traumatized in infancy by the onset of asthma.  This narrative, if examined in depth with sensitivity, would explore the dark side of an infant being challenged for every breath.  It would also explore the parental response of seeking medical assistance that would enable the infant to run free.  A student would need to understand that no miracle drug will bring instant relief to the asthmatic, that there is no permanent cure, but with medication, parental supervision and the pain of exercise, many asthmatics have emerged as Olympic champions in a wide range of sports and tens of millions of asthmatics live relatively normal lives.

Enslavement, like most chronic diseases, foreclosed the free movement of the Black body, forbade the development of the Black mind, and was designed to eliminate any thought of a future that included freedom.  The physical act of escaping on the part of the enslaved was combined with the desire of the enslaved to become educated and employed is inspiring.

The National Underground railroad Freedom Center staff works constantly to open young minds to the opportunities available to them that will permit them to achieve an expanded reality and personal freedom.

What strategies may be suggested for teachers to inspire their students to take courageous steps for freedom today?

Mr Westmoreland by the Slave Pen exhibitAt the National Underground Railroad Freedom Center, there is a constant effort to draw parallels between the history of enslavement  and the deprivation of human rights of people who represent  the landless, the powerless, the other based on race, gender, religion, sexuality.  We attempt to make our visitors aware that depending on locality, nationality, etc., all races are a despised minority somewhere, and quite often their basic human rights are ignored.

In Africa, inter-tribal conflict still exists on a daily basis at the cost of lost arms and limbs, sexual and military exploitation of children, and ethnic cleansing based on religion (the Sudan, Dafur, Ethiopia, Ghana).  In Europe the religious conflict,  between Irish Catholics and Protestants still simmers, and the multi-century conflicts between those two groups have claimed hundreds of thousands of lives.

It will take an abundance of courage, a small army of informed social activists, business and political leaders to open the wounds of America’s past transgressions, and to listen to the airing of the pain caused by our callous expansion. It is our belief that with such a protracted enterprise, healing can begin and a more perfect union will be the result.

How do we go about keeping the stories, the memories, and the understanding of the Underground Railroad alive?

The first challenge of keeping the stories of the Underground Railroad alive is to use the historical icons, Frederick Douglas, Harriet Tubman, etc. as a launching point to explore the thousands of slave narratives that were developed in 1937 by the WPA (Works Progress Administration).

There are millions of unopened letters, Bibles, and archival materials in the Courthouses of the South, the storage rooms of African churches in The RagGonNon TextileAmerica, plantation records and the trunks of Black America.  These documents contain narratives that chronicle and celebrate the day to day miracles of ordinary people who through their own efforts and the efforts of people who looked like them began a physical journey from slavery to a lifelong pursuit of education, employment in an effort to retain respect.

The acquisition of Wilberforce University by Bishop Daniel A. Payne and other leaders of the A.M.E. Church in 1866 in Wilberforce, Ohio, is a perfect example of a journey from enslavement and powerlessness to freedom that extended beyond the artificial date of the Emancipation Proclamation.  It also establishes the reality that physical freedom is only a beginning.

The joy and the challenge of continuing the effort can be fed by the knowledge that ordinary people were the heroes of the Underground Railroad, that in fact they were the great grandparents of the thousands of anonymous African Americans who in the summer of 1963 filled the jails of the South.  They rode buses into fire, and beatings in Birmingham, and they climbed the bridge at Selma showing the world the mettle, and the perseverance that had come down to them from those who had walked the same roads in chains.

Comments (0)  //  Add Comment
18 Mar

The Secret of Actions

Author: Administrator  //  Category: Classroom

The list of “Actions” in the “Action Browser” within Inspire is pretty extensive.

Action Browser

If you are like me, you use a few actions over and over, but never really explore many of the other actions.  By the way, my favorite is “Hidden” ( little x through eyeball icon).

Many of the actions are pretty self explanatory, such as a link to a website or switching to pen or magic ink. However, some actions come with an odd parameter field that may need an explanation.  Ever wonder what those parameters do?  Ever wonder what the difference between stretch top incrementally verses size top incrementally is? Me too!

Within the following link is a pdf attachment that answers many of your burning questions regarding actions!

Comments (0)  //  Add Comment
17 Mar

Book review: The missing manual – Living Green

Author: Administrator  //  Category: Science

Over the past few years “sustainable living” has suddenly grown in importance in the more developed and affluent countries of the world, and most people are at least curious about it. Yet it isn’t always easy for people to know if their lifestyles are green or not. An easily readable yet comprehensive and enjoyable resource for green living would be of great value to everyone, from the die hard eco-warrior to the gently curious citizen. Nancy Conner’s Living Green is just that much required reference to fill that void.

A well written book that can be read as a serious reference or a quick pointer for specific questions, this book (from O’reilly’s missing manual series) addresses most questions anyone could have about living green, and what all it involves. Living green isn’t just about replacing a few light bulbs or occasionally bicycling to work, but is about a comprehensive lifestyle change where the consequences of all our actions are considered from an earth perspective. The book also does well in suggesting that we do have choices, and by living green we do not have to abandon all the comforts we have become accustomed to.

This book is organized in chapters that deal with changes we can make in our homes, all the way through green business and getting involved towards sustaining a greener planet. If you are just starting with small changes in your life, and want to see what little things you can easily do around the house, the first section addresses these questions. You will easily be surprised by the number of toxins you are exposed to routinely, from harsh detergents to cleaners and solutions commonly used in bathrooms or kitchens. Importantly, the book provides low cost, simple alternatives that are far less harmful to our own health as well as the health of the planet. Taking just one example, it was most useful to hear that the ultimate all purpose natural cleaner is white vinegar and boric acid powder, which can be used to scour sinks, clean bathtubs, wipe countertops and clean floors. With a few modifications, it can also be used as a garden pesticide. The book then builds towards reducing unnecessary consumption (going for quality over inexpensive quantity is an easy first step), and reusing and recycling. It then goes a level higher, and provides outstanding resources and ideas towards building houses that are green as well as energy saving, talking about everything from simple design solutions to LEED certification for buildings.

The next section talks about a complete lifestyle change, from raising a green family (ever thought about how many landfills a baby’s diapers could fill up?), green eating and cooking, raising kids who are sensitive towards the environment, through responsible shopping, and another big cause of pollution to the earth, daily transportation. The book provides a handy reminder of the different transportation options (from walking and biking to car pooling) to the costs of air travel or hotel stay, and how easy it can be to offset these effects for little or no extra cost. There are excellent resources for example on hotels or automobiles that take their environmental costs seriously, and are trying hard to improve energy efficiency and environmental stewardship. So, given a choice between two hotels or two cars of similar quality, this book makes it easy to choose the one that does a better job in protecting the environment.

The final section goes in depth into green business, and how it is possible to actually make a profit or create substantial savings by actually being green. Much of it is just simple improvements in efficiency. Using less paper or office recycling programs are low cost efforts that result in big “green” savings. There are significant energy savings offices can obtain by simply allowing more natural light in, or opening windows (as opposed to cranking up the air conditioners all the time). There are choices that can be made for the source of energy (and the differences between renewable and non-renewable energy choices, as well as how one can buy and use more renewable energy resources). Finally, the book goes into different ways by which one can be involved, from activism to socially responsible investing.

There is little doubt that the book is comprehensive, and provides information to someone curious about green living at every level. Yet, there are some caveats or limitations in this book.

For one, it is certainly true that many people have tried various eco-friendly/green choices around the house, and it just didn’t “work as well” as the regular choice. This book, while providing excellent choices for green options around the house, does not acknowledge that there can be some limitations with green products. From my own personal example, we’ve tried just about every single green dishwashing solution out there. But none of them work as well as conventional dishwashing gels (which do have phosphates in them) while cleaning dishes that have been used for spicy, sometimes greasy, and often heavily cooked Indian or Thai food, though they do work satisfactorily for more standard “American” cooking. So, after much trial and error, we had to go back to conventional dishwasher detergents, after experimenting with a dozen natural ones that claimed to be just as “hard on dirt” but gentle on the environment. On the other hand, many other green products work satisfactorily (green laundry detergent with a little bit of hydrogen peroxide added to it works fine for lightly soiled clothes, but perhaps not as well for the rare, heavily soiled garment). Future editions of the book would do well to acknowledge some limitations of green products, and perhaps compare the two, saying where the green product is perfectly adequate, but where it might fall short. Acknowledging some limitations of green products is not necessarily a weakness, and makes it easier for the average person to make better choices while stepping towards green living.

Then, there is an extensive (and overall good) chapter on food, which oversimplifies the “organic is good” mantra, unequivocally casting all fertilizers, pesticides and genetically modified food as the great evil. However, the argument is far from that simple, since it is a very complex area that is grey and not black or white. Yes, pesticides can be harmful, and overuse of fertilizers has ruined land. But it is also true that careful and controlled use of fertilizer (along with suitable crop rotation and mixed cropping) can yield more food (at no nutritional disadvantage) than simple organic mono-cropping alone. Nor are all genetically modified foods dangerous. It remains a fact that every single food crop we eat today has been modified, over years of crossing and creating “hybrids”, except that the methods used have been different. There certainly are issues with proprietary seeds and over aggressive patents, but casting all genetically modified food as bad is simplistic at best and false at worst. There is no doubt that sustainable (including organic) food practices are excellent for the earth, but by avoiding nuance, this book might put away some people who aren’t blindly gung ho yet about everything green.

The book has been written from the perspective of a person living green. So, perhaps, the tone does not fully reach out to people across the aisle. Living in Texas has taught me that direct confrontation (about lifestyle) rarely works. In a place where say people often leave their lawn sprinklers on during three hour thunderstorms, or where cities still don’t have recycling programs (and where one has to collect and cart recyclables to a recycling center oneself), finding middle ground is a starting first step. Perhaps this book can do more to address that.

However, overall the book is superbly written, and provides a single stop for the reader to find out anything about living green. A more than useful manual, it should be the book of choice should one want any reference towards green living. It is a worthy addition to any household, and lets you start making those small steps towards green living.

Comments (0)  //  Add Comment
15 Mar

The Harmonic Series in Music and Mathematics

Author: Administrator  //  Category: Maths

For years I have wondered if there is a connection between the harmonic series in music theory and the harmonic series in mathematics. Here is what I know so far, music first, mathematics second.

The Harmonic Series in Music
Much of what I know about harmonic series in music comes from the many guitar lesson books I have read as well as from the information provided by Wikipedia at

http://en.wikipedia.org/wiki/Harmonic_series_(music)

Here is how I understand it. Strings on a guitar are fastened to two nodes, one called the nut, which is located at one end of the fretboard, and one called the bridge, which is located on the body of the guitar. A node is a fastening point at which little or no vibration takes place. See Figure 1.

Figure 1 Guitar nodesFigure 1 Guitar nodes

When a guitar string is plucked, it oscillates simultaneously at many different frequencies.

The Fundamental and its Overtones

The lowest of the frequencies at which a string vibrates is called the fundamental tone. The fundamental tone is the tone produced as the string vibrates over the full length of the guitar, from the bridge to the nut. See Figure 2.

Figure 2 The fundamental toneFigure 2 The fundamental tone

Each of the other frequencies is a whole number (the whole numbers are 0, 1, 2, 3, 4, 5, … ) multiples of the fundamental frequency. Symbolically, if we represent the frequency of the fundamental tone with the letter f, then the frequencies of the other overtones are represented by 2f, 3f, 4f, etc.

Check out Figures 3, 4, and 5 to see graphical representations of the first, second and third overtones.

Figure 3 The first overtoneFigure 3 The first overtone
Figure 4 The second overtoneFigure 4 The second overtone
Figure 5 The third overtoneFigure 5 The third overtone

Harmonics

The terms harmonics and overtones are often used interchangeably.

The Harmonic Series in Music

Figure 6Figure 6

In stringed instruments, such as the guitar, the harmonic series in music theory is the set of integer multiples of the harmonic.

Symbolically, we have \{f,2f,3f,4f,5f,\ldots\}

A frequency is harmonic if it is an integer multiple of the fundamental frequency. See Figure 7

Figure 7Figure 7

For example, if the fundamental frequency of a plucked string is 100 Hz, then

Figure 8Figure 8

The Harmonic Series in Music

In music theory, a harmonic series is the set consisting of the fundamental tone (fundamental frequency) and all its overtones. See Figure 9.

Figure 9Figure 9

When taken all together, the human ear perceives the harmonic series as a single tone. I think of this as adding all the tones together produces a single tone.

The Wavelengths of the Harmonic Series
If you look back up to Figures 3, 4, and 5, you can see that

Figure 10Figure 10

So, the ear perceives the sum of the fundamental and all the overtones as one single tone. If we think in terms of wavelengths we generate the sum illustrated below.

1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots = {\rm one single tone}

The Harmonic Series in Mathematics

The harmonic series in mathematics is illustrated below

1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\cdots

This series diverges. That is, it does not sum to a finite value. As terms are added, the sum just gets bigger and bigger with no bound. Put another way, given any number at all, we can go far out enough in the series to obtain a number larger than the number we are given. Here is a nice proof that the harmonic series diverges. To believe the proof, you have to believe that

\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\cdots

gets bigger and bigger and bigger, and never adds to a finite value. The proof shows that the harmonic series is even larger than the ½ series.

Proof by ComparisonProof by Comparison

Because the sum of the infinitely many ½ terms diverges to infinity and the harmonic series is larger than the ½ series, the harmonic series must also diverge to infinity.

Relating the Harmonic Series in Music and the Harmonic Series in Mathematics

Now, finally we get to it. The harmonic series in mathematics diverges. If we think in terms of wavelengths, the harmonic series in music is the same as the mathematics harmonic series. This means that the harmonic series in music also diverges.

But we noted that the ear perceives the harmonic series as a single tone. That seems to indicate that the series adds to a finite value. What! But we know it does not. I think what happens is that once we are out far enough in the series, the wavelengths are so small (say like 1/500, 1/1,000,000), that we do not hear the sounds they generate. We hear only the sounds that correspond to maybe the first few wavelengths. Theoretically, there are infinitely many tones. We hear only some. But practically, there are probably not infinitely many tones. The string and the guitar are physical objects and as such there are likely only a finite number of overtones. It would be hard to believe there could be infinitely many nodes along a guitar fretboard.

I think, too, that part of the problem I was having in relating the two series was one of terminology. In English as a noun, the word series means a group of related or similar things arranged in some order or succession.. As a noun, a series is also defined as a sequence of related things. Thus, the set of harmonics \{f,2f,3f,4,5f,6f,\cdots\} can be viewed as a series. In mathematics, however, the set of harmonics \{f,2f,3f,4,5f,6f,\cdots\} is a sequence. It is a set in which the individual elements are listed in a particular order. A series in mathematics is the sum of the elements of a sequence. So as a noun, the words series and sequence are used interchangeably. In mathematics they are distinct terms. I was thinking of series in the mathematical sense, as a sum of terms.

When I started this article I really did not know how what the relationship between the harmonic series in music and the harmonic series in mathematics would be. But by writing about it and drawing the pictures, I had to think about it. I think I have my thoughts about a connection between the two resolved.

What’s more, I resolved it without once referring to my cousin, let’s call him “Dave,” and his fascination with white socks and sock heights. This week I will think hard about a connection between the harmonic series and white socks and the affect of sock height on series convergence.

"Dave" and his socks

I generated the pictures of the overtones using the free graphing calculator provided by the nice people at

http://rentcalculators.org/stheli.html

I captured the graphs with screen shots using Snapz Pro X by Ambrosia Software.

http://www.ambrosiasw.com/utilities/snapzprox/

Comments (0)  //  Add Comment
« Previous Entries

Categories

Blogroll