Khan Academy

 

The Khan Academy is a non-profit educational website created in 2006 by educator Salman Khan, a graduate of MIT and Harvard Business School. The stated mission is “providing a high quality education for anyone, anywhere”.

The website supplies a free online collection of more than 4,000 micro lectures via video tutorials stored on YouTube teachingmathematics, history, healthcare, medicine, finance, physics, chemistry, biology, astronomy, economics, cosmology, organic chemistry, American civics, art history, macroeconomics, microeconomics, and computer science. Khan Academy has delivered over 240 million lessons.

Khan Academy has eclipsed MIT’s OpenCourseWare (OCW) in terms of videos viewed. Its YouTube channel has more than 268 million total views, compared to MIT’s 50 million. It also has more than twice as many subscribers, with 1,000,000.

Khan Academy currently provides various levels of mathematics courses, and Salman Khan has stated that (with the help of volunteers) soon they will begin to have topics beyond just math such as physics, chemistry, finance, computer science, logic, and grammar.

for more information: https://www.khanacademy.org/

TeacherTube

TeacherTube is a video sharing website similar to, and based on, YouTube. It is designed to allow those in the educational industry, particularly teachers, to share educational resources such as video, audio, documents, photos, groups and blogs. The site contains a mixture of classroom teaching resources and others designed to aid teacher training. A number of students have also uploaded videos that they have made as part of K-12 and college courses. As of July 2008, the website contained over 26,000 videos and now as of October 2010, TeacherTube has over One Million+ educational members and over 400,000 educational videos. It has found favor with educators for whom YouTube content is blocked by content filtering systems.

 

 

 

for more information, you can visit:  http://teachertube.com/

What are the Disadvantages of using SMART Boards in the Classroom?

Like any other technology, Smart Boards also have disadvantages. First, Smart Boards are very expensive. The cost of the actual board, the software, projector, and installation fees are very high; approximately $1000, but can vary depending on model and year. For school districts, such a rural school and smaller schools that already have low funding, this can be a problem as they do not have as much access to such technology. Because of the high cost, if a school district is able to purchase this technology, the school may only be able to afford one or two. That means that not every teacher will have access to the Smart Board. Even if a portable Smart Board on wheels is purchased, teachers still would have to check out the Smart Board for use in their classroom. Not all students would have access to this technology. Also, teachers need to be trained to use this new technology. The software can be challenging to learn and practice is often needed to become an expert. A lot of time and money needs to be invested into the training process. Another downfall of Smart Board technology is that most Smart Board specialist come from outside the school district. Teachers do not have easy access to someone with the knowledge and questions cannot be answered right away. Also, some teachers may pick up the information quickly, whereas others may need additional training or support before they feel comfortable incorporating the Smart Board into their classroom. For these teachers, the new technology may be too overwhelming and cause disruptions and frustrations in the classroom due to lack of proper training. The technology would then be only a hindrance rather than a help in the classroom.

Another disadvantage of Smart Boards is that they require maintenance. Like other electronic equipment, Smart Boards also need to be kept working properly and installed with the proper updates. Most of the time teachers are the ones that need to find the time and download these updates, which may cause a problem. This may require additional technology assistants to be hired to help with problems that arise with the Smart Board and also keep the Smart Board updated.

Smart Boards can also be a problem if they are not working correctly on a given day. A teacher would always need to have a back-up lesson plan or activity in case the technology crashes. Additional time would need to be put into planning each day for the teacher.

One other issue dealing with smart boards is the cost. This new technology cost a significant amount of money.

for more information: http://www.ehow.co.uk/list_7435216_disadvantages-smart-board.html

The Advantages of a Smart Board in Education

 

Interactive presentation tools are in demand for educators and others who want to involve their classes or audiences in learning alongside technology. A Smart Board is an interactive electronic whiteboard that gives educators an additional presentation device for the classroom. A Smart Board can interface with a computer, displaying images through a digital projector, and its users can control the software from either the computer or the board, where they can manipulate images or text. Students or audience members can participate by adding their annotations or pointing out material using a pen or highlighter.

therefore, there are so many advantages of smart board:

  1. The interactive electronic whiteboard is great for demonstrations….
  2. The interactive electronic whiteboard is a colorful tool. Research indicates that students respond to displays where color is employed…
  3. The board can accommodate different learning styles…
  4. All ages of students respond favorably to board use…
  5. Distance learning is an excellent setting for interactive whiteboard use…
  6. One-computer classrooms can maximize the use of limited computer access…
  7. The interactive whiteboard is an excellent tool for the constructivist educator…
  8. The boards are clean and attractive tools…
  9. Students with limited motor skills can enjoy board use…
  10. It is interactive…
  11. It can interface well with other peripherals….
  12. The board is great for meetings are lessons where the participants need printed copies…
  13. It is a kid magnet! …

moreover:

  • Learners show increased motivation and enjoy the interaction the technology offers
  • It makes the subject come alive
  • It captures the attention of learners
  • It encourages the involvement of learners in the subject
  • It enables tutors to use multimedia resources and the internet with a whole class

therefore, smart boards are very helpful educational tools and are used to all scholls and classes.

for more information about smart boards, you can visit:

http://en.wikibooks.org/wiki/Integrating_Technology_In_K12/SmartBoards_in_a_Classroom  &  https://k12teacherstaffdevelopment.com/tlb/using-smart-boards-in-the-classroom/

 

‘Using Technology to Foster Mathematical Meaning through Problem Solving’

icon-MathTech

 

          In the article “Using Technology to Foster Mathematical Meaning through Problem Solving” by Rose Mary Zbiek, it is mentioned that using mathematics technology how encourage to students’ learning and interest. Thanks to using technology, students learn clearer and quicker. Moreover, it also has a lot of instructional opportunities such as the capability of storing, sharing and changed the problems and solutions. As technological sources, there are a lot of devices, tools and programs such as; several types of calculators, Cabri Geometry, The Geometer’s Sketchpad, PowerPoint, word processors and so on.

In the article, two examples which consist of a sequence of two or more related problems are also mentioned. In first example, it is wanted from students that image of given triangle under a reflection must be found between given other triangles. This example related with Euclidean transformations especially reflections. By this problem, students consider about preimage and image of triangles under transformations. After students identify triangle as the image under reflection, they discuss the other triangles. Then, they find image under rotation and they begin to think about relation between images under reflection and rotation. They realize that rotation equivalent to a composition of two reflections. By using technology, such as the Geometer’s Sketchpad or Cabri Geometry, we provide students to think about reflections line and rotation points more deeply and they also see clearer this relationship by visually thanks to technological programs. After these steps, composition of other types of transformations might be given with geometry construction program.

In second example, it is wanted that students find relations between parameters of function and its perspective on coordinate system. For example, on the equations such as f(x) = ax+b or f(x) = ax2 +bx +c, changing the value of “c” results in moving up /down of graph. Moreover, students find vertical intercept by storing 0 in “x” (on the equation f(x) = ax+b). In addition, on the function f(x) = C abx , students investigate the sign of equation by checking signs of “C”, “a” and “b”.  Thanks to the Geometer’s Sketchpad, students realize relations quicker and clearer since they have opportunity to see directly and a lot of examples and equations visually.

All in all, it is mentioned that technological devices and programs provide a lot of advantages to students when they learn mathematics and geometry. I totally agree with the writer because of three main reasons. First of all, thanks to using technology in mathematics, students see their mistakes, reasons and results visually by trying. Therefore, they learn permanently since they learn not only by doing but also by seeing. I think, if a student learns by discovering on your own, reasons/results are catchier. Secondly, dynamic tools provide a lot of examples, new problems and different ways to solve problems. Hence, students learn to solutions by not only one way but also a lot of ways and concepts. When, one way is not appropriate for one problem, students use another way they learned by using technological programs. This is very good because when a student cannot solve one way to question, s/he sees and applies other ways directly. Finally, thanks to technology, students see relationships between geometry and algebra visually by sliding points, lines in dynamic geometry. I think, realizing relations in geometry is the most important thing when understanding and solving a problem. Since, if a student cannot realize relations between points, lines or something else, s/he cannot put forward an idea in any way. Because of all these reasons, I think, using technology encourages students to mathematical meaning through problem solving.

http://www.jstor.org/discover/10.2307/27969542?uid=44902&uid=3739192&uid=5909400&uid=2&uid=3&uid=67&uid=29476&uid=62&sid=21102093905141

What is the Potential Impact of the iPad, Kindle, and other Tablet Computers in Education?

 

With the rise of the iPad, Kindle, and similar eReaders and touchscreen devices, tablet-shaped form factor computing power has become much more portable and yet sizable. This holds great promise for educators on par with the introduction of slates, which swept across classrooms at the turn of the century before last. Back then, the personal transcription device of chalk and stone slate tablets was seen as revolutionary.

Yes, the iPad is intuitive, the Kindle and Nook are cheap, and Android is Open Source, yet is the tablet form factor really all that? There is the immediate e-reader usage model, but what other roles can tablets play? And are those roles most cost-effective with digital devices vs. analog or even paper technologies?

First of all, Students using a tablet, can take notes with the stylus and highlight or circle especially important material. Students can combine written notes and drawings into one document and move text and images around a page with a click of the stylus.

Also, Tablets can assist teachers with recording attendance, calculating grades, presenting lessons, answering emails, calendaring events and playing audio and video files. The tablet computer will replace old paper lesson plan books, attendance rolls and dry erase boards.

According to Visualspatial.org, 60 percent of students in regular classrooms learn best with visual-spatial presentations. Tablet computers allow teachers and students to view, create, and manipulate charts, graphs and images.
I think, all these reasons explain the advantages and ımpacts of the tablet computers in education.
For more information, you can visit:

http://learnpad.co/support/features/tablets-in-education.cfm  &   http://visualspatial.org/

learning geometry in a dynamic computer environment

In the article ‘’Learning Geometry in a Dynamic Computer Environment’’, software programs in geometry can encourage the development of students’ understanding and reasoning about two-dimensional shapes. In traditional elementary and middle school geometry curricula, students must learn list of rules, definitions, theorems and properties of shapes. But in Interactive Geometry Microworld, first of all, students develop personally logical geometric concepts. Moreover, they analyze carefully spatial geometric problems by using this program, instead of memorizing. In a word, this system help to students identify the geometric shapes and understand reasons analytically about them.

In order to understand theories describing mathematics and geometry, first of all students must personally envision these theories by using their current knowledge. According to The Van Hiele Levels, when students’ knowledge increases, they move through several levels of geometric thinking. The first level is Level0 (prerecognition). In this level, students do not know completely and adequately to properties of a shape’s. Then, in Level1 (visual), by thinking visual characteristics of shapes, students can identify and recognize the shapes. But in this level, students do not think any formal geometric concepts. In Level2 (descriptive/analytic), in order to identify and describe spatial relationships between parts of shapes and other shapes, students use formal geometric concepts. Moreover, in this level, students know all properties of all shapes. Then, in Level3 (abstract/relational), for groups and classes of shapes, students know necessary characteristics and properties. In this level, the most important thing is students understand and form abstract definitions. In level4 (formal axiomatic), students logically understand theorems and prove them.

The Shape Makers is also mentioned in the article. Thanks to the Shape Makers, students not only make shapes, but also they changed shapes’ sizes, orientation by dragging its vertices with Mouse. In initial activities, students use shape makers in order to make their own pictures. But now, students make more careful analysis and also formulate and describe geometric properties of shapes. Additionally finding lengths and measuring angles, students can also test parallelism and symmetry.  Moreover, in the article, some examples are mentioned. They are related with some students using the shape makers. In episode1, three students were investigating the square maker at the beginning of their work with the Shape Makers. In episode2, students claim that all shapes made by the rhombus maker. Then, in episode3, students try to make some shapes by using rhombus maker. And in episode4, students try to make parallelogram, square, and rhombus by using rectangular in The Shape Maker. Finally in episode5, they realize that they can make only given shape by using shape maker. For example, by using parallelogram maker, they can make only parallelogram.

I think the interactive geometry instructional environment help students to realize that logic behind the shapes. When students do this, the Shape Maker help to student understand reasons about shapes by visually transforming them. Moreover, it encourages students to think about shapes and their properties. I think, because this model fosters the creativity, students learn permanently, not memorizingly. Therefore, that is the point, i think. Hence, I think, because of all these reasons, it is the best way of the learning geometry. But, in order to use this program by all students, all schools should have appropriate tools and technology. For this, government should provide schools to necessary budget.

http://www.questia.com/library/1G1-83032531/learning-geometry-in-a-dynamic-computer-environment

advantages of software programs for geometry

 

iterate

Technological devices and programs provide a lot of advantages to students when they learn mathematics and geometry  because of three main reasons. First of all, thanks to using technology in mathematics, students see their mistakes, reasons and results visually by trying. Therefore, they learn permanently since they learn not only by doing but also by seeing. I think, if a student learns by discovering on your own, reasons/results are catchier. Secondly, dynamic tools provide a lot of examples, new problems and different ways to solve problems. Hence, students learn to solutions by not only one way but also a lot of ways and concepts. When, one way is not appropriate for one problem, students use another way they learned by using technological programs. This is very good because when a student cannot solve one way to question, s/he sees and applies other ways directly. Finally, thanks to technology, students see relationships between geometry and algebra visually by sliding points, lines in dynamic geometry. I think, realizing relations in geometry is the most important thing when understanding and solving a problem. Since, if a student cannot realize relations between points, lines or something else, s/he cannot put forward an idea in any way. Because of all these reasons, I think, using technology encourages students to mathematical meaning through problem solving.

Here you can find  some examples of these technological programs:
http://www.cabri.com/
http://www.dynamicgeometry.com/

teknoloji destekli matematik öğretimi

Teknolojinin eğitime girişi ile yeni yöntem ve tekniklerin kullanılması olanaklı
hale gelmiş ve bu sayede öğrenme ortamlarının düzenlenmesinde yenilikler yapılmıştır.
Çoğu eğitimci ve araştırmacılar etkin kullanılan öğretim teknolojilerinin eğitim
sistemini iyileştirecek potansiyele sahip olduğu kanısında birleşmişlerdir (Jonassen &
Reeves, 1996; Means, 1994; Çağıltay, Çakıroğlu, Çağıltay & Çakıroğlu, 2001). 2004
yılından beri yürürlükte olan yeni ilköğretim programı yapılandırmacı öğrenme ve
öğretme yaklaşımına dayalı olarak hazırlanmıştır. Öğretmen yetiştiren fakültelerde
kendi öğretim programlarını yeni ilköğretim programına uygun olarak yenilemek
durumunda kalmışlardır. Ancak, teknoloji eğitiminin öğretmenlere kazandırılması
konusu hala bir problem olarak devam etmektedir. Araştırmacıların teknolojinin
eğitimde bir amaç olmaktan ziyade bir araç olarak kullanılması gerektiği konusunda
birleşmektedirler (Strudler & Wetzel,1999; Loucks-Horsley, Hewson, Love, & Stiles,
1998). Buna rağmen genelde fakültelerimizde sunulan öğretmen eğitimi sırasında
teknoloji eğitimi sadece bilgi ve becerilerin kazandırıldığı ve diğer alanlarla ilişkisiz
olarak sunulan bir teknoloji dersiyle kazandırılmaya çalışılmaktadır. Bu durumda konu
alanlarına ilişkin modellemeler öğretmen adaylarına kazandırılamamakta ve
teknolojinin nerede ve nasıl kullanılacağı konusunda bir anlayış oluşamamaktadır.
Moursund ve Bielefeldt (1999) tarafından yapılan bir araştırmada öğretmenlerin
yalnızca teknoloji öğretimi amaçlı derslere katılımının teknolojiyi öğretimlerine entegre
edebilme yeterlikleri arasında anlamlı bir ilişki bulunamamıştır. Son zamanlarda birçok
araştırmacı teknolojinin özel konu alanlarının öğretiminde kullanılmasının, öğretmenler
tarafından anlaşılmasının gerek şartı olarak teknoloji, pedagoji ve içerik (Technology,
Pedagogy, and Content Knowledge, TPACK) bilgisine sahip olunmasını saymaktadırlar
(Koehler & Mishra, 2005, 2008; Niess, 2005, 2006; Suharwoto, 2006; Archambault &
Crippen, 2009)

 

Music and mathematics

maths-and-music

Music theorists sometimes use mathematics to understand music. Mathematics is “the basis of sound” and sound itself “in its musical aspects… exhibits a remarkable array of number properties”, simply because nature itself “is amazingly mathematical”.Though ancient Chinese, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, thePythagoreans of ancient Greece are the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers. Their central doctrine was that “all nature consists of harmony arising out of numbers”.

From the time of Plato, harmony was considered a fundamental branch of physics, now known as musical acoustics. Early Indianand Chinese theorists show similar approaches: all sought to show that the mathematical laws of harmonics and rhythms were fundamental not only to our understanding of the world but to human well-being. Confucius, like Pythagoras, regarded the small numbers 1,2,3,4 as the source of all perfection.

To this day mathematics has more to do with acoustics than with composition, and the use of mathematics in composition is historically limited to the simplest operations of counting and measuring.The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. Some composers have incorporated the golden ratio and Fibonacci numbers into their work.

You can find a video explaining relationship between music and mathematics below.