Hypatia: mathematician, astronomer, and philosopher

“All in all we have a picture of a dedicated teacher, a versatile one whose interests embraced virtually the whole of the mathematics of the time and extended beyond this to speculative philosophy and to scientific endeavor. We see in her life little of the compartmentalization of knowledge that such a recitation of achievement imposes upon modem ears. Rather, geometry was a route to the One, just as was a celibate lifestyle. Arithmetic and even astronomy were similarly sacred. We may well imagine that the conservation and transmission of knowledge was a matter of passionate concern for her.”

Deakin, 2007, p113

More is known about Hypatia’s death than her life since there are multiple records of her death from a variety of sources. Her birth has been placed between 350 and 375 and she lived in the late fourth and early fifth century in Alexandria. During this period, Alexandria was part of the Roman Empire, but it was influenced by Greek culture. Hypatia was a pagan and a Neoplatonist philosopher in a city with people of many different backgrounds including Christians, Jewish people, pagans, and secular people. There was a great deal of political unrest at the time which led to the murder of Hypatia by Christian fanatics in March, 415.

Hypatia never married and was considered “exceedingly beautiful and fair of form” (Damascius). Socrates puts it a little differently: “[She had] self-possession of manner, which she had acquired in consequence of the cultivation of her mind . . . [she was admired] on account of her extraordinary dignity and virtue.” (Deakin, 2007, 55).

Hypatia’s father, Theon, was considered one of the leading mathematicians of the time and he provided her education in mathematics. “She is variously described as a philosopher (Hesychius, Damascius, Theophanes, Synesius, and Malalas), a teacher of philosophy (Synesius), a mathematician and astronomer (Philostorgius), an astronomer (Hesychius), a learned woman (Socrates), and a geometer (Damascius)”  (Deakin, 2007, 57). She was a famous and gifted speaker, and it is thought that the topic of her lectures was philosophy. However, her primary scholarly focus was mathematics.

None of Hypatia’s philosophical writing remains. However, there is discussion of her philosophy by several sources. Socrates situates her in the tradition of Plato and Plotinus. Deakin suggests that an understanding of her philosophy can be gained from examining the work of her pupil, Synesius. He also learned astronomy from her as well as different branches of mathematics. The Dion, written before Synesius’s conversion to Christianity, is founded on Hellenic culture including Greek language and literature, and religion: “his writings absolutely brim over with literary allusions, citations, and direct quotations (which, incidentally, he must have expected his teacher to recognize and appreciate: we deduce that Hypatia herself was widely read)” (Deakin, 2007, 79).

Regarding Hypatia’s work on mathematics there is a great deal of speculation about her writings. Deakin highlights a few works which can definitively be ascribed to Hypatia. According to the Suda Lexicon, Hypatia wrote three books which Paul Tannery says are “a Commentary on Diophantus, [one on] the astronomical Canon, and a Commentary on Apollonius’s Conics.” (in Deakin, 2007, 89). Letters from Synesius describe her mathematical and scientific work as well.

During much of Hypatia’s lifetime, Theophilus was the bishop of Alexandria. After his death in 1412, his nephew Cyril took over and began attacking the pagans. He demolished the temple of Serapis which simultaneously put an end to the Museum. He closed all synogogues in Alexandria and closed the churches of the Novatianists.

Orestes was outraged at Cyril and the two soon came into conflict. Deakin (2007, 73) writes that “Orestes ended up the clear winner in the dispute with Cyril. Those who had come to fight in Cyril’s cause must have felt the bitter rancor of defeat. Another attack was called for and this time against a somewhat easier target. That target became Hypatia.”

Some scholars suspect that on the orders of Cyril, Hypatia was murdered by a group of Christian zealots led by Peter the Lector. She was pulled from her carriage on the way home. She was brought into a church, stripped naked, and stoned to death with roof tiles. She was then dismembered and set on fire.

Hypatia was a charismatic speaker, a gifted teacher, and her interests were varied. Within the branch of mathematics, she focused on astronomy, geometry, algebra, and computational technique. Her writings seem to be connected with her teaching and she was renowned in her own time for her skills.

Deakin, M. A. B. (2007). Hypatia of Alexandria: Mathematician and Martyr. Prometheus Books.

Hypatia [Online image]. Encyclopædia Britannica. https://www.britannica.com/biography/Hypatia#/media/1/279463/17143

Exclusion in education: The South African context

According to UNESCO’s International Bureau of Education, exclusion in education has many forms including the following:

• Exclusion from having the life prospects needed for learning
• Exclusion from entry into a school or an educational programme
• Exclusion from regular and continuing participation in school or an educational programme
• Exclusion from meaningful learning experiences
• Exclusion from a recognition of the learning acquired
• Exclusion from contributing the learning acquired to the development of community and society

The Best Habit Tracking Apps

“Amateurs sit and wait for inspiration, the rest of us just get up and go to work”
(Stephen King, On Writing: A Memoir of the Craft).

What makes exceptional people exceptional? Are they different from ordinary people? Are ordinary people just lazy? Are exceptional people just lucky to be born with strong will power and self motivation?

Extraordinary people don’t wait for inspiration: they do things whether they feel like it or not. If you look at exceptional people, one thing they have in common is being consistent.

A successful writer will write X words every day. A successful athlete will exercise X amount every day. They have a schedule and they stick to it. They don’t wait to feel motivated. They act in spite of their feelings, not because of them.

Set Effective Goals

So you want to be successful and exceptional. Where do you begin? Phillippa Lally conducted a study to determine how long it takes to form a habit.

Over 12 weeks, they looked at 96 people who each chose a new habit and gave daily reports about whether or not they completed their task and how automatic it felt to do so. Everyone chose different tasks from drinking water to running. The researchers analysed the data, and found that it took anywhere from 18 to 254 days to form a new habit. It depends on lots of different factors, but the average time it took to form a habit was 66 days.

It was also found that messing up didn’t really effect the formation of the habit. So don’t worry! It will take time to form a habit. And if you miss a couple of times, it won’t have a devastating impact on your habit. 

The best place to start is by working out what you want to achieve. Check out SMART Goals to find out how to set effective goals.

Is e-learning in South Africa even possible?

I am trying to do a course about teaching with technology. We’re supposed to be talking about implementing technology.  My attempts to discuss how we can implement these technologies when we don’t have adequate internet infrastructure, access to technology, e-learning is literally taxed to line some politicians pockets, etc. etc. have been politely shut down. Again.

“Hi Vicki, internet connectivity is a critical issue, and it must be addressed.  Unfortunately, this is something that is outside of our control at present … so, in order to move forward with the learning on this course, I suggest that we focus on the things we can do given the current restricted situation!   I hope this makes sense to you!”

Here’s the reality.

I am house-sitting at my brother-in-law’s house. I don’t have data on my phone, he doesn’t have uncapped internet, and I just used almost all his data watching videos and Prezzis for this course that won’t load and then reload and mess up because of a poor connection. So I’m leaving this thought here and coming back when I can.

This is a useless conversation unless we acknowledge that it is impossible to talk about any of these technologies when our data is so expensive and we can’t afford devices. 

I am a white, middle class women with four degrees, six years of full time teaching experience. By South African standards, the only people more privileged and advantaged than me are the white men. I can’t afford the cost of this course. I literally can’t pay for the data. I can’t get a job with my qualifications. I spent all my savings in an unexpected operation, I’m living with my mother-in-law, my parents are paying for my medication. I’m forced to take a job in the Middle East in August because the money and resources I’ve spent on becoming a lecturer in South Africa have all been a waste.

Let’s talk about implementing technology into our teaching practices. If I’m struggling with my resources, how can those with even less access to resources cope?

Should we have an honest discussion or stick a band aid on a bullet wound?

Assessment, evaluation, and the learning process

Nitko and Brookhart (2011) examine how assessment can aid teachers and students to make decisions about the learning process. Assessment procedures can be used to give feedback to students and teachers, to motivate students to study, and to give guidance about what students should focus on learning. It is necessary to bear in mind the context of the decision making process when using assessment information.

Nitko and Brookhart provide clear definitions of four terms:
assessment, tests, measurement, evaluation.

• Assessment is the “process for obtaining information that is used for making decisions about students; curricula, programs, and schools; and educational policy” (3).
• Tests are narrower than assessment and can be defined as the instruments or procedures for “observing and describing one or more characteristics of a student using either a numerical scale or a classification scheme” (5).
• Measurement is the procedure in which numbers or scores are assigned to a “specified attribute or characteristic of a person in such a way that the numbers describe the degree to which the person possesses the attribute” (6).
• Evaluation is a more subjective term that involves “making a value judgment about the worth of a student’s product or performance” (6).

Although it is important to remember the distinction between these four terms, they are interrelated terms that can be used effectively to evaluate students, lesson material, policies, and educational institutions.

There are a number of ways assessment procedures can aid teachers and students. They are a primary way to gather information that can be used to make decisions before, during, and after teaching. Decisions need to be made regarding

• selection

• placement

• counselling and guidance

• credentialing and certification

Finally, assessment procedures can be used to

• give feedback to students and teachers

• motivate students to study

• give guidance about what students should focus on learning

 

Reference

Nitko, A.J. and Brookhart S.M. (2011). Educational assessment of students (Kindle version). Available from Amazon.com.

 

Techno-nursingeries.

I watched this:

and I read this: The Preschool Inside a Nursing Home

and I thought: We need to do this in South Africa right now!

Imagine the potential of combining kindergarten and old age homes in SA?

Saves on staffing if you have caregivers who can look after kids and grandparents.  The grandparents have so much wisdom and knowledge and love to offer the kids. Add technology to the mix and we have a real game changer!

Life-long learning centres

A place to start might be with life-long learning centres in areas that have the least developed facilities. A centre where people can come to get some food, get some medicine, but also just spend time together learning and playing with technology.

What needs to be done to get such a project started?

Who has the knowledge and resources to get a project like this going? Or perhaps update existing projects with technology instead of getting resources for a completely new one?

So much potential for new growth and development in SA, it really is interesting times.

Ako

The Maori word for learning, ako, does not “differentiate between those who dispense knowledge and those who acquire it. Knowledge is always a collective entity”[1]. Why do we not have a word just like this? Education is a reciprocal process in which the teacher and student embark on a quest together to find out something new about themselves, each other, the subject matter, the journey itself…

Study Buddies

I recently wrote the final exam for my Postgraduate Diploma in Tertiary Education, a journey that took two years across three countries (Oman, Cambodia, and South Africa).

It is with heavy sigh of relief that I would like to thank the pets that have supported me throughout my studies.

I’m going to start with Deya, who first began assisting me when I was writing my MA about Olive Schreiner (also pictur many years ago. Here she is in 2010.

Technologically Illiterate is Functionally Illiterate

It really concerns (terrifies) me that particularly in a module about Instructional Techniques and Media, my fellow students (teachers themselves) are not only technologically illiterate, but resistant to technology. There have been endless complaints about the use of technology in the modules we are completing as part of the Postgraduate Diploma in Tertiary Education (PDTE) at the University of South Africa (Unisa). I cannot understand how anyone could possibly prefer an old textbook and an outdated study guide, when there are so many more options available out there. Technology has transformed the education industry.

It is not a luxury to use technology in education; it is a necessity.