Episodes in the Mathematics of Medieval Islam
I will list 3 point of interests and explain how I could incorporate those into my teaching.
1) Naming Arabic Names
I was quite surprised with the process of coming up with Arabic names. The process involved using their names and after this, comes the phrase "son of so-and-so". This fact can be extended even further and the genealogy can be compounded for generations. For example, Ibraham ibn Sinan ibn Thabit ibn Qurra in the text. I find this particularly interesting because these names have special meanings associated to them like with names associated with Chinese characters.
In mathematics and English, we use a lot of prefixes. On the top of my hand, I remember during my practicum teaching about terminologies to grade 9's like monomial, binomial, and trinomial for the polynomial unit. I had to emphasize that prefixes are important in the English language and it gives some clues as to what the terminology is. I think by explaining what mono, bi, and tri are, the students are able to think more critically and makes the overall polynomial lesson more engaging. It is also in shapes, like triangles, quadrilaterals etc. By recognizing some of these prefixes, students have some idea of the context.
2) Al-Khwarizmi's Contributions|
I remember in class, we discussed about non-European contributions to Mathematics and how they weren't appreciated as much as their European counterpart. However, Al-Khwarizmi is one of the most influential mathematicians outside of Europe. He also influenced European mathematics with the derivation of the world algorithm that we still use today.
As I have reiterated before, in mathematics, we don't really question the source of mathematical theorems. I think in the classroom, it would be important to encourage students to think how theorems and formulas have been derived. This way, it will spark their curiosity and help them think do their own diligent research. At the same time, I hope that they will find how in different parts of the world, mathematicians may have used different approaches to solve problems. In regards to that, students will know there is no single "algorithm" to derive an answer but there could be many different ways.
3) Decimal Fractions of 2π
To use this in the classroom setting, I want to tell the students about the process of finding the digits of π. I want them to know that to find success in doing well math requires persistence just as how al-Kashi had to keep calculating over and over again just to be accurate. Also, I would like to tell my students that there is always help and online sources they can reference to if they are struggling.
References
1) Naming Arabic Names
I was quite surprised with the process of coming up with Arabic names. The process involved using their names and after this, comes the phrase "son of so-and-so". This fact can be extended even further and the genealogy can be compounded for generations. For example, Ibraham ibn Sinan ibn Thabit ibn Qurra in the text. I find this particularly interesting because these names have special meanings associated to them like with names associated with Chinese characters.
In mathematics and English, we use a lot of prefixes. On the top of my hand, I remember during my practicum teaching about terminologies to grade 9's like monomial, binomial, and trinomial for the polynomial unit. I had to emphasize that prefixes are important in the English language and it gives some clues as to what the terminology is. I think by explaining what mono, bi, and tri are, the students are able to think more critically and makes the overall polynomial lesson more engaging. It is also in shapes, like triangles, quadrilaterals etc. By recognizing some of these prefixes, students have some idea of the context.
2) Al-Khwarizmi's Contributions|
I remember in class, we discussed about non-European contributions to Mathematics and how they weren't appreciated as much as their European counterpart. However, Al-Khwarizmi is one of the most influential mathematicians outside of Europe. He also influenced European mathematics with the derivation of the world algorithm that we still use today.
As I have reiterated before, in mathematics, we don't really question the source of mathematical theorems. I think in the classroom, it would be important to encourage students to think how theorems and formulas have been derived. This way, it will spark their curiosity and help them think do their own diligent research. At the same time, I hope that they will find how in different parts of the world, mathematicians may have used different approaches to solve problems. In regards to that, students will know there is no single "algorithm" to derive an answer but there could be many different ways.
3) Decimal Fractions of 2π
The first day of class, you asked the class what about mathematics interested you and I replied finding the digits of π. I still can only recite the first 9 digits which I think is more than enough to give an accurate measurement. What surprised me the most is that to get 16 decimal places, al-Kashi calculated perimeters of inscribed and circumscribed polygons, in a given circle which had 805,306,368 sides. I would have never have imagined having to calculate that many sides.
To use this in the classroom setting, I want to tell the students about the process of finding the digits of π. I want them to know that to find success in doing well math requires persistence just as how al-Kashi had to keep calculating over and over again just to be accurate. Also, I would like to tell my students that there is always help and online sources they can reference to if they are struggling.
References
Berggren, J. L., et al. Episodes in the Mathematics of Medieval Islam. Springer New York, 2016
You've made an astute observation about prefixes in english math terms. Bringing in narratives of how mathematics developed and what work particular people did is sure to help your students have a broader, more interesting picture of mathematics.
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