Learn STEM with MIT

http://k12videos.mit.edu/content/the-colorful-chemistry-of-acids-and-bases
http://k12videos.mit.edu/

Sample Video on Acids and Bases click the links

THE COLORFUL CHEMISTRY
OF ACIDS
AND BASES   

http://k12videos.mit.edu/content/the-colorful-chemistry-of-acids-and-bases

One divided by Zero = Infinity; Reflecting on Infinitely Large and Infinitely Small Numbers

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"The concept started for me at an early age when my father explained to me that 1 divided by zero was infinity.  Most typically, this isn’t how we approach the understanding, but the logic makes sense, which goes as follows:

1 divided by 0.5 is 2.

1 divided by 0.25 is 4.

1 divided by 0.125 is 8.

1 divided by 0.01 is 100.

1 divided by 0.0001 is 10 000." Michael Rosmer

Source:  http://www.michaelrosmer.com/zero-notation-infinitely-large-small-numbers/  Accessed:  June 16, 2012.

At the above referenced web page is an essay on infinitely large and infinitely small numbers.  I enjoyed how the concepts were presented and perhaps you will, too.


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Here is a related article on division by zero which may be of interest to readers of this post. It is from the following search:  http://onlinelibrary. wiley.com/advanced/search/resultsarticleDoi=10.1002/tea.20287&scope=allContent&start=1&resultsPerPage=20

Challenging Preservice Teachers' Mathematical Understanding: The Case of Division by Zero.  SCHOOL SCIENCE AND MATHEMATICS.  Volume 106, Issue 2, February 2006, Pages: 84–97, Sandra Crespo and Cynthia Nicol.  Article first published online : 17 MAR 2010, DOI: 10.1111/j.1949-8594.2006.tb18138.x

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A reminder that this blog links to other parts of the web that are not under my control, so, be sure to use safety precautions and check the links out as you would for any other web site.  Use them at your own risk.
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Infinity Hotel: All Sets Welcome
Vacancy

Here is an excerpt:

The new marketing manager at Infinity Hotel was thrilled that his new marketing campaign was working. Although the previous manager had had an infinite number of vacant rooms, the new manager, George O. Set-Theory, was sure if he directed his advertising to sets, he could fill all the rooms.

Mr. Set-Theory was certainly ambitious and began his advertising in Cantor Village

He expanded his advertising in infinite directions from its heart at Cantor.

No matter how large nor how small, every set was invited to infinity hotel. Lately he’s received a lot of attention from infinite sets. Already, the set of positive rational numbers was lining up at the hotel desk, ready for check-in. Fortunately, they had books they were reading, had knitting or other needlework, or palm-held electronic games. Really, they had an infinite number of ways to keep busy while they waited in line.

Mr. Set-Theory knew he’d better quickly review. He also had to think if there were more members in one set than in another. Counting the rooms and the sets wouldn’t work. It would take too long. Even with an infinite number of things to do, the set of positive rational numbers might soon grow weary.

Mr. Set-Theory thought he could use one-to-one correspondence, so he got his recreation managers to devise a game whereby all the sets of the hotel could pair up to see if each member of the first set corresponded or matched up to a number of the next set with no leftovers. Well, this might work, but, Mr. Set-Theory thought he’d hold off on that game for a while. He really did have to get the rooms assigned. That pairing game could go on ad infinitum. He’d better wait on that!

“Infinity plus 1 is infinity!” exclaimed Mr. Set-Theory. “yes,yes!” he cried. And, infinity times 2 is infinity. What a joy working at Infinity Hotel.

He called on his accountant, Ms. Transfinite A. Rithmetic, to help him. Ms. Transfinite Rithmetic had a sign in her office that was her motto, “Transfinite Rules.” She looked at her sign and quickly hurried to help Mr. Set-Theory. She suggested, “What about infinity times infinity?”

“Yes, yes! That’s the idea,” said Mr. Set-Theory. “Now, what about the set of positive rational numbers, the positive numbers we can express as fractions, {1/2, 1/3, ¾,5/6,…}. Oh, goodness! There are an infinite number of sets within this set. For every number in the set of counting numbers can match a set of rational numbers with that number as a numerator--- Goodness! Fortunately, Infinity Hotel can keep up. We do keep getting more floors, don’t we?”

Mr. Set-Theory had the recreation directors keep the sets busy so he could arrange the rooms.

Ms. Rithmetic started thinking about the sizes of infinity. She remembered reading a book in Cantor’s town library once that talked about hierarchies of ever-larger infinities. The largest one, she recalled, was called, “The Continuum.” “Oh, Mr. Set-Theory,” she stated matter-of-factly, “Your advertising campaign is working so well we may one day become, ‘The Continuum Hotel,’ ---- Imagine!

©2004 J. S. Shipman
[for more...e-mail Dr. J: shipmanjs at g mail dot com

Science, Technology, Engineering and Math Education--Thank you, World Leaders,

In a story by Chloe Albanesius you'll find, "President Obama on Monday unveiled a campaign intended to promote science, technology, engineering, and math (STEM) education among children – an effort that includes about $260 million in financial support from companies like Time Warner Cable, Discovery Communications, Sony, and the Bill and Melinda Gates Foundation"
Source: http://www.pcmag.com/article2/0,2817,2356254,00.asp
Accessed November 22, 2009.

Thank you, President Obama.

All other World leaders encouraging, "STEM," are thanked, too.

Readers, please submit what your leaders are doing regarding science literacy and science education (e-mail me and I will post your message).

Dr. J

Fun and Learning: Google Games---Seeking Top Performers for work...relating that to science and math education.

Here is a story about Google Games, a day of engineering- and math-heavy challenges. This particular story, by Wade Rousch, is about challenges that took place in 2008. It is about a recruiting method that can be adapted to science and math education. It is about the joy of learning. It is about being surrounded by others who want to learn and who learn recreationally.

Read the article here, then, think about what you can carry away from it to apply to science education situations.

Math team, chess teams, science fairs, bridge-building competitions and other venues blending learning and fun may foreshadow this type of recruiting. Do you feel joy from participants at these events? Do you feel joy from students in your science and math classes? Are your top students challenged? Are all students challenged at appropriate levels?

Do you remember finishing all the math exercises and science problems in the text books within the first two weeks of school because they were fun to do, and then being bored in class? Today, as a student, one can go to the internet and use Google (or other search engine) and find math and science challenges (For example, the MIT courses in the left hand column of this blog...). Neither work, nor, education, should hold people back from reaching their full potential, and being happy. Maybe we need a "Google Games," open to the whole public...pre-K through age 160+. Hmmm!

An algebra tutorial on sets

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut2_sets.htm

Remember, math provides an important tool for science. Science literacy needs scientists that can read mathematical equations and use them to analyze data and solve global problems. While the above tutorial is geared to older students, I want to share my own experience as a 9 year old studying the same material. Perhaps your students would like to learn this math.

As an elementary school child, my classmates and I had set theory in 4th grade (age 9). Here, the tutorial is a preparation for graduate students. The fourth graders in my class understood set theory enough to do related set theory problems. That elementary school preparation was a big help in writing technical manuals for an engineering company that made wave and tide recorders that helped prevent deaths from tsunamis. When I studied this math as a nine year old in, "modern math," I didn't know it would save so many lives. When I hear people knocking, "Modern Math," I think they don't know what they mean. When I compare myself to others my age that did not have, "Modern Math," it sometimes appears they just don't keep up as well on computers and other new technologies. (That hypothesis might warrant a research study.)

Here is a commentary on set theory as relates to my own experience with, "Modern Math," and a thank you to my teachers. Perhaps we don't convert among bases regularly, nor use set theory every day, as we learned in Modern Math (Thank you, Mrs. Degnan!!!), but our brains understand the underlying concepts of how computers, and, wave and tide recorders, among many other devices of today and of the future.

I, for one, was greatly helped by, "Modern Math." I will add that I had to teach myself to do the base 10 multiplication tables faster. When I took, "Teaching Algebra," at Harvard, Dr. Boller could follow exactly how my brain "thought math." (Thank you, Dr. John Boller. You also taught me how all the different types of math are interrelated.) The graduate student that graded papers, however, struggled to follow the kind of thinking that, Mrs Degnan taught us in, "Modern Math." I think he would have benefited from such study. He was excellent in math, though, and also taught us how he did the math.

I am happy that the wave and tide recorders, produced by Sea Data Corporation (now defunct) saved lives, and glad that I was able to write the manual to using the instruments from only the schematic because of my "Modern Math" classes. Thank you Mrs. Degnan, you saved lives and taught us well!

You and your student can decide if this math is for your student at this point in time. But, as for me, I loved it as a child.

More mathematics information for your benefit
Advanced notice for pi day March, 14th: How will you celebrate?

Magic Math link: http://library.thinkquest.org/27103/eng/home.htm

"Web site "Set Theory" offers educational tools and resources to help you learn fundaments of mathematics. You can take full advantage of the "Internet style of learning." http://library.thinkquest.org/C0126820/start.html


María J. Frápolli, 1991, "Is Cantorian set theory an iterative conception of set?". Modern Logic, v. 1 n. 4, 1991, 302–318.

Math supports science!!!

One reader brought this link to our attention...Strengthening math helps science...http://mathcollege.tripod.com/ Take a look by clicking the link and then hitting cancel. See if it is helpful to you.

Please post comments here. Thanks. J

Please add your comments on this program

http://edequity.org/?q=programs/science-and-math-programs#22

Click, "Comments," below to add your experience with this program.

Excel ^(TM) in Education

In math and entertainment:
A use of Excel to model Sudoku is presented in a paper available on-line at:
http://archive.ite.journal.informs.org/Vol7No2/WeissRasmussen/
Related papers of interest are found at:
http://www.maa.org/joma/Volume8/Bartlett/references.html

http://portal.acm.org/toc.cfm?id=1352383


In all subjects and in science:
Dr-J has found that student use of Excel^TM to create indexes of their notebooks (including class and lab notes, as well as homework and handout sheets), enables students to see what is important to both the teacher and to themselves. It enables students to prioritize study time while customizing their own learning toward their own interests and value systems. Indexing also helps students link concepts they are studying, teaches job skills (computer and organizational). Familiarity with a spreadsheet program in this way encourages students to see how the same spreadsheet can be used to create tables, analyze laboratory data, and see how skills in science class are transferable to other subjects.



Excel is a registered trademark of Microsoft.

[Under development]

Math Challenge

Try this:
http://nct.meeker.k12.co.us/highschool/Math/TierraS.htm

Hints from Bob Dorsett, MD

New Math ...Reflection...

Many people make fun of the, "new math," lots of baby boomers were taught in the USA. Here is an example:
http://www.youtube.com/watch?v=a81YvrV7Vv8 and another version of the same song:
http://www.youtube.com/watch?v=GAm3KWiDPKU&NR=1

I studied the New Math. It meant I did Boolean algebra in 4th grade (age 8 and 9). I loved it. It also helped me a great deal when I did my doctorate and when I used engineering skills at work. I get tired of hearing people bad-mouthing New Math because I believe it helped give me a basis for understanding all sorts of computerized lab equipment and also wave and tide recorders used in the field to predict tsunamis.

We did not memorize the (base ten) times tables, however we could multiply and divide in bases 2, 8, 10, and, 16. We could readily set up and solve problems. And, we could do all these things without a calculator and even without a slide rule. I do feel memorizing the times tables for base ten would have been useful and therefore, taught them to myself so I could do freshman chemistry problems quickly. That helped with rapid responses in physics, too. But, engineering courses and logic were much easier having had the bases and the Boolean algebra background in grade school.

So, based on my own experience, I suggest adding times tables and also radians to the, "New Math," but, I would not trade my, "New Math," experience. I loved it and found it very helpful toward my science career and to every day life in a computerized world. I understand the 1's and 0's so prevalent today.

I have come across a way of teaching math that I like that uses languages. More on that another day.

(c) 2008 J S Shipman

Publish Post

Sometimes we use math!!!

I thought you would enjoy this math video. It is well done and the lyrics are available. It is an excellent example of putting math standards into an audible form, very artistic. Smile.


Congratulations, Drew D'Amelia!

It is a wonderful example. Can you do a creative video on science standards that you are studying? Just trying will help to expand your mental brain capabilities. Whole brain development is encouraged by such creativity. Enjoy and share your results.

Dr. J

Pie Day, Oh, Pi Day.... Pi Day's coming!

Are you ready for Pi Day? ...Haven't heard of it? What?

pi = 3.14159265.....

Pi day is a day to celebrate pi and to encourage students in learning math. Now, math is important to scientists, among others, so I encourage you to get involved in Pi Day. When? March 14th of course (3/14).

Here's the official Pi Day site: http://www.piday.org/

Post under development.
Check back later.

From Tesselation and Fractals to Stretch Reading in Science

Here's a playful way to learn some advanced math that applies to science. Enjoy! http://wchow.home.znet.com/koch.htm

Here's a link to a pineapple fractal...Fractals are found in nature. This link goes to a photo taken by Dr. Ron Hurov who works in the botany of commercial pineapple production. http://www.geocities.com/wenjin92014/botany/pineapple.htm

One of Ron Hurov's papers is at this link. You can try reading scholarly works in botany and other fields as part of "stretch reading."

"Stretch Reading," invented by Dr. J, is needed in the sciences where vocabulary words are developed every day as we discover new things. First, just skim the paper and look at the graphs and pictures. Then, circle any words (on a photocopy) or list words in your notebook that you don't know. Now, just try to get the gist of the article in one sentence. This might be as simple as, "The article is about pineapples, whatever they are." As you look at more and more articles, you will find yourself more able to understand them. Do not worry about understanding when you first start. Even medical doctors and PhDs need to learn new words and especially if they switch their area of reading a bit. For example a biopsychologist may have to learn new jargon to read electrophysiology papers. So don't worry, even if every other word is one you don't know. You are getting yourself comfortable with the unknown. You are stretch reading. (More on that later.) When there is something that interests you enough, I have no doubt you will attack it to the point you understand it. And, you won't be afraid to tackle it. You might also like: Reading Science.

(c)2007 J. S. Shipman

Teeter-totter your way into math...

Algebra can be fun! Click on this link and see. Such math skills help you learn science, too. (Once you read the directions, hit the close button and you will see the teeter-totter in full.)

What can you learn from one plant?

Pick one plant, say potatoes, or chicory, or a tulip...or, any plant you like. What can you learn from that plant? Many subjects overlap with botany.

The selected plant: _______________________________________________________

Writing: Can you write an essay or a paper about your plant. Be sure to cite sources. Can you write a poem about your plant?

Art: Can you draw your plant? What colors are found in your plant? Is paper made from your plant?

History: Did the plant have an effect on human history? Does the plant have its own story?

Math? What is the growth rate of the plant? How big are the seeds? How big are the leaves? What is the range of sizes for leaves?

Classification and organization? How would you classify this plant? What characteristics would you use? How do other scientists classify it?

Geography: Where is the plant found in nature?

Biology: What lights affect the plant? Reds? Greens? Blues? White? Does day length affect the plant? What is the life cycle of the plant?

Chemistry: What chemicals are found in the plant? Does pH affect the plants growth? Does salt?

Music: Is the plant used to make musical instruments? Can you write a song or a symphony about your plant? Can you do a spring concert based on songs your class wrote about flowers?

(c) 2007 J S Shipman.

College Undergraduate Female Science-Math-Engineering Scholarships...

The Clare Boothe Luce Program -- provides grants for undergraduate scholarships for women studying science, engineering, and mathematics. Colleges are invited to apply for a grant from the program. For a list of institutions receiving Clare Boothe Luce awards, click her linked name.

Graphics Resource

http://www.seb.cc/index.html

Poetry in Motion, I mean Mathematics...

Here is a post you don't want to miss. Poetry.
http://www.thisisby.us/index.php/content/mathematics

Fractals...Math found in Nature

Fractals are exciting and integrate math and science and art. The overlap of areas in the humanities and sciences appears to make fractals very popular. A movie follows which shows a well-known fractal and gives a link to more learning about fractals. Then, there is a portion of a research article showing one application of fractals in forestry. There are many more applications. This post is to give you an idea about fractals and encourage you to pursue the fractals in your own area of interest whether art or science or applied science. Enjoy the movie.



"Biologists have traditionally modelled nature using Euclidean representations of natural objects or series. Examples include the representation of heart rates as sine waves, conifer trees as cones, animal habitats as simple areas, and cell membranes as curves or simple surfaces. However, scientists have come to recognize that many natural constructs are better characterized using fractal geometry. Biological systems and processes are typically characterized by many levels of substructure, with the same general pattern being repeated in an ever-decreasing cascade. Relationships that depend on scale have profound implications in human physiology (West and Goldberger 1987), ecology (Loehle 1983; Wiens 1989), and many other sub-disciplines of biology. The importance of fractal scaling has been recognized at virtually every level of biological organization (Fig. 1; Section 5).

"Fractal geometry may prove to be a unifying theme in biology (Kenkel and Walker 1993), since it permits generalization of the fundamental concepts of dimension and length measurement. Most biological processes and structures are decidedly non-Euclidean, displaying discontinuities, jaggedness, and fragmentation. Classical measurement and scaling methods such as Euclidean geometry, calculus and the Fourier transform assume continuity and smoothness. However, it is important to recognize that while Euclidean geometry is not realized in nature, neither is strict mathematical fractal geometry. Specifically, there is a lower limit to self-similarity in most biological systems, and nature adds an element of randomness to its fractal structures. Nonetheless, fractal geometry is far closer to nature than is Euclidean geometry (Deering and West 1992).

"The relevance of fractal theory to biological problems is dependent on objectives. To the forester interested in estimating stand board-feet, a Euclidean representation of a tree trunk (as a cylinder or elongated cone) may be quite adequate. However, for an ecologist interested in modelling habitat availability on tree trunks (say, for small epiphytes or invertebrates), fractal geometry is more appropriate. Using a fractal approach, the complex surface of tree bark is readily quantified. A forester's diameter tape ignores the surface roughness of the bark, giving but a crude estimate of the circumference of the trunk. For an insect 10 mm in length, the 'distance' that it must travel to circumnavigate the trunk is much greater than the measured diameter value. For an insect of length 1 mm, the distance travelled is greater still. This has consequences on the way that the tree trunk is perceived by organisms of different sizes. If the bark has a fractal dimension of D = 1.4, an insect an order of magnitude smaller than another perceives a length increase of 10D-1 = 100.4 = 2.51, or a habitat surface area increase of 2.512 = 6.31. By contrast, for a smooth Euclidean surface, D = 1 and both insects perceive the same 'amount' of habitat. The higher the fractal dimension D, the greater the perceived rate of increase in length (or surface) with decreasing scale."
Source: http://www.umanitoba.ca/faculties/science/botany/LABS/ECOLOGY/FRACTALS/fractal.html