Muslim Mathematicians

1. Al-Khwarizmi

The terms Algebra and Algorithm are familiar to all of us but how many have heard of their originator Muhammad al-Khwarizmi. In Geography he revised and corrected Ptolemy's view and produced the first map of the known world in 830 CE. He worked on measuring the volume and circumference of the earth, and contributed to work related to clocks, sundials and astrolabes.

His full name is Abu Abdallah Muhammad ibn Musa Al-Khwarizmi. The last-mentioned name (his nisba) refers to his birthplace, Khwarizm, modern Khiva, south of the Aral Sea. He was born around 780 in the town of Kath part of Khwarizm. Kath is now buried in the sand. He died around 850. He was summoned to Baghdad by Caliph Al-Ma’mun and appointed court astronomer. From the title of his work, Hisab Al-Jabr wal Muqabalah (Book of Calculations, Restoration and Reduction), Algebra (Al-Jabr) derived its name.

Algebra symbolises the debt of Western culture to Muslim mathematics. Ironically, when it first entered the English language it was used as a term for the setting of broken bones, and even sometimes for the fractures themselves. This reflects the original literal meaning of the Arabic word “Jabr,” 'reuniting of broken bones,' from the verb jabara (to reunite). The anatomical connotations of this meaning were adopted when the word was borrowed, as algebra, into Spanish, Italian and Medieval Latin from one or other of which English acquired it. In Arabic, however, it had long been applied to the solving of algebraic equations (the full Arabic expression was 'Ilm al-jabr wa'-l-muqabalah', literally 'the science of reunion and equations,' and the mathematician Al-Khwarizmi used al-jabr as the title of his treatise on algebra.

In the twelfth century Gerard of Cremona and Robert of Chester translated the algebra of Al-Khwarizmi into Latin. Mathematicians used it all over the world until the sixteenth century.

A Latin translation of a Muslim arithmetic text was discovered in 1857 CE at the University of Cambridge library. Entitled 'Algoritimi de Numero Indorum', the work opens with the words: 'Spoken has Algoritimi. Let us give deserved praise to God, our Leader and Defender'.

It is believed that this is a copy of Al-Khwarizmi's arithmetic text, which was translated into Latin in the twelfth century by Adelard of Bath, an English scholar. Al-Khwarizmi gave his name to the history of mathematics in the form of Algorism (the old name for arithmetic).

2. Al-Kindi

Al-Kindi was born and brought up in Kufa, which was a centre for Arab culture and learning in the 9th century. This was certainly the right place for al-Kindi to get the best education possible at this time. Although quite a few details (and legends) of al-Kindi's life are given in various sources, these are not all consistent. We shall try to give below details which are fairly well substantiated.

According to [3], al-Kindi's father was the governor of Kufah, as his grandfather had been before him. Certainly all agree that al-Kindi was descended from the Royal Kindah tribe which had originated in southern Arabia. This tribe had united a number of tribes and reached a position of prominence in the 5th and 6th centuries but then lost power from the middle of the 6th century. However, descendants of the Royal Kindah continued to hold prominent court positions in Muslim times. 

After beginning his education in Kufah, al-Kindi moved to Baghdad to complete his studies and there he quickly achieved fame for his scholarship. He came to the attention of the Caliph al-Ma'mun who was at that time setting up the "House of Wisdom" in Baghdad. Al-Ma'mun had won an armed struggle against his brother in 813 and became Caliph in that year. He ruled his empire, first from Merv then, after 818, he ruled from Baghdad where he had to go to put down an attempted coup. 

Al-Ma'mun was a patron of learning and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. Al-Kindi was appointed by al-Ma'mun to the House of Wisdom together with al-Khwarizmi and the Banu Musa brothers. The main task that al-Kindi and his colleagues undertook in the House of Wisdom involved the translation of Greek scientific manuscripts. Al-Ma'mun had built up a library of manuscripts, the first major library to be set up since that at Alexandria, collecting important works from Byzantium. In addition to the House of Wisdom, al-Ma'mun set up observatories in which Muslim astronomers could build on the knowledge acquired by earlier peoples. 

Al-Kindi wrote many works on arithmetic which included manuscripts on Indian numbers, the harmony of numbers, lines and multiplication with numbers, relative quantities, measuring proportion and time, and numerical procedures and cancellation. He also wrote on space and time, both of which he believed were finite, 'proving' his assertion with a paradox of the infinite. Garro gives al-Kindi's 'proof' that the existence of an actual infinite body or magnitude leads to a contradiction in [7]. In his more recent paper [8], Garro formulates the informal axiomatics of al-Kindi's paradox of the infinite in modern terms and discusses the paradox both from a mathematical and philosophical point of view. 

In geometry al-Kindi wrote, among other works, on the theory of parallels. He gave a lemma investigating the possibility of exhibiting pairs of lines in the plane which are simultaneously non-parallel and non-intersecting. Also related to geometry was the two works he wrote on optics, although he followed the usual practice of the time and confused the theory of light and the theory of vision. 

Reference :
https://tiriztea.wordpress.com/2010/08/18/7-tokoh-ilmuwan-matematika-islam/
http://www.muslimheritage.com/article/al-kindi
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Al-Kindi.html

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7 Ways to Motivate The Unmotivated Student

A motivational problem is not always easy to define, although teachers usually have no trouble recognizing it: The unmotivated student is the one whose attitude toward schoolwork screams, "I don't care!"

The unmotivated student actually is highly motivated when it comes to schoolwork -- he's motivated to avoid it. He puts more work into avoiding academic challenges than he puts into tackling them. Although his test scores often convey high potential, his classroom performance suggests something else. When given an assignment, the unmotivated student will shrug his shoulders and complain, "Why do we have to do this?" He gives up at the first sign of a challenge. He is content with just getting by.

WHAT YOU CAN DO

Interrupt the cycle of failure. An unmotivated student often is a demoralized student. Try to alter his perceptions by orchestrating positive academic experiences. Assign work that gives him a feeling of accomplishment, but that he is capable of completing successfully. Structure the assignment so the beginning is relatively easy, hopefully giving him confidence to move on. If he struggles with a task, focus on what he has done well; gently correct his mistakes without criticizing. Help him understand that setbacks and mistakes are a normal part of the learning process. As he begins to enjoy more success, his confidence will grow and he will become more willing to take risks.

Give a choice of assignments. An unmotivated student often is more likely to put forth effort if he has a say in the assignment. For example, you might allow him to choose from among three assignments -- each of which meets your objective. In studying the Civil War, for example, he might choose to do a book report, an oral presentation, or an art project. (Of course, you reserve the right to require him to do certain essential assignments.) Keep an eye out for other ways to give the student some ownership over the learning process; by having him choose what book he will read or what topic he will write about or what reward or he will receive for reaching a goal.

Incorporate the student's interests into the lesson. Find out some of the student's interests. (You might have him complete an interest inventory.) and try to integrate those interests into your lessons or classroom activities. If the student has a paper route, for example, you might design math problems requiring him to calculate how much he would earn delivering papers under various conditions. If you are doing a transportation unit and the student builds model airplanes, have him bring in some models to show the class. If the student is artistic, invite him to help you design your bulletin boards. If he excels on the computer, have him become the class troubleshooter.

Relate lessons to real life. Students who are unmotivated often want to know "Why do I have to know this?" Help them see how classroom lessons can be applied to life outside the classroom. When teaching shapes, for example, have students point out shapes in the classroom. Show why being able to count is essential when buying things at the store. In a unit on plant life, have students make a leaf collection. Plan field trips that show how their lessons work in real life. For example, plan a trip to a recycling center as part of a unit on the environment.

Break tasks into manageable steps. Some students put forth little effort because they see the task as overwhelming. If that's the case with your student, present the task in small chunks. Give the student one step at a time, and don't move on until he has mastered that step. As the student gains skill and confidence, gradually expand the size of the task, give him more difficult problems, or move at a faster pace. Apply the same approach to homework. If the student struggles with math and rarely completes those homework assignments, consider giving him half the number of problems the other students do; select problems you are confident he can complete.

Expand your teaching style to spark interest. A student who appears to be in the dark when listening to classroom lectures can light up during hands-on activities. For example, you might have students participate in a debate about a controversial historical issue, conduct an experiment to demonstrate a science principle, or do a cooking project to learn about different units of measurement. Those kinds of activities stimulate students' interests and help them retain concepts.

Focus on the student's individual progress rather than on his performance in relation to his peers. A student who is compared to classmates who outperform him -- even if his poor performance is due to a lack of effort -- eventually can become discouraged and shut down completely. You can avoid that by focusing on the student's improvement rather than on his performance relative to his classmates. You might evaluate the student through a portfolio assessment in which you examine his work during the year and consider his progress a measure of his performance. The student might receive a confidence boost by seeing how his work has improved over the course of the year.

http://www.educationworld.com/a_curr/shore/shore060.shtml

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