Mathematics and the World around Us: Helping Students See Connections

Helmer AslaksenDept. of Mathematics

National University of Singaporehelmer.aslaksen@gmail.com

www.math.nus.edu.sg/aslaksen/

I’m happy to talk to teachers!

• I am always very happy to talk to Singaporean teachers

• In the past I used to give a lot of talks to students, but these days I prefer to talk to teachers

• I believe that Singaporean teachers are overworked, underpaid and undersupported!

I’m happy to talk to teachers! 2

• MOE has a lot of good ideas, but is there enough support for the people who actually have to implement those new ideas?

How can I contribute?

• Singaporean teachers don’t need my help when it comes to teaching basic math

• I believe that Singaporean teachers are among the best in the world at teaching content

How can I contribute? 2• Singaporean students are good at math,

but they don’t necessarily like it• Many students fail to see its beauty and

relevance• The challenge is to make the students

excited about and appreciate math

What’s the goal of this talk? • I would like to share of my knowledge and

experience about this• I teach two General Education Modules at

the National University of Singapore• Heavenly Mathematics & Cultural

Astronomy• Mathematics in Art and Architecture

What’s the goal of this talk? 2

• I learned a lot of fascinating stuff, both mathematics and general knowledge that I’d love to share with you

• I hope to inspire you to develop exciting material for your own teaching

• In particular, I hope that it may inspire you to propose and supervise projects

What’s the goal of this talk? 3

• Mathematics is often taught as an isolated subject

• I want you to start reflecting on how mathematics is all around us, and see new ways to show your students the joy and relevance of mathematics

Goal of my courses

• I have three main goals for my courses

Appreciate and question

• Help the students appreciate the world around them and start looking at their surroundings with different eyes

• I want them to notice and question things they used to take for granted

Connections

• Show them connections between mathematics and culture

• I want them to stop thinking about knowledge in terms of school subjects, but as part of mankind’s struggle to understand the world

Relevance

• Demonstrate the relevance and importance of mathematics by showing how it solves problem of general interest

• I want them to see the beauty and centrality of mathematics

Content of astronomy course

• Basic astronomy from a hemispherically-correct view point

• Astronomy for latitudinally-challenged people

• Calendars, with an emphasis on the four calendars in use in Singapore: Gregorian, Chinese, Muslim and Indian

• Navigation

The theory of hanging clothes to dry

• Date: Wed, 18 Dec 2002 12:44:51 From: Liew Wen HweeSubject: The theory of hanging clothes to dry

• Hi Sir,Ohh my... I just discovered the theory behind my mum's "theory of hanging clothes to dry"...

Mum’s theory

• My mum have been telling me since I was a kid that for half of the year that she will have to hang the clothes out in the kitchen and the other half of the year in the corridor for them to dry...

• I was perplexed by her "theory" for a long time...

• I thought "wasn't the sun suppose to rise East always"??

MY MUM IS AN ASTRONOMER!!!

• And your lesson cleared my doubts!!! My flat lies exactly (ermmm maybe not that exact...didn't notice tat until I used the compass) in the East- west plane...

• And so for half of the year, the sun be in the South-east and the other half in the North-east...

• MY MUM IS AN ASTRONOMER !!!(ha...)...

What u have taught is of practical purpose!!!

• Sir, what u have taught is of practical purpose!!!

• (Maybe u could tell the next batch of students abt tat and they could advise their mum on how to better dry their clothes.. =))

• Thanks a lot, Sir!!!Warmest regards,Wen Hwee

Motion of the Sun and the Moon

Where does the Sun set?

The mathematics of the Singapore flag

The Motion of the Earth and the Moon

• The Earth revolves around the Sun during one tropical year, which is 365.2422 days, or just under 365 ¼ days

• The synodic month is the time from one new Moon to the next, and the average length is 29.53 days, just over 29 ½ days

The Lunar Year

• Since 365-12 x 29.5 = 11, a lunar year consisting of 12 lunar months is about 11 days short of a solar year

• After 2 years, the error is about 22 days, and after 3 years about 33 days

• Solution: Add a leap month

Leap months

• In order to prevent Chinese New Year from moving backwards through the calendar (like the Muslim holidays do), a leap month is inserted about every third year

• Any month can be followed by a leap month

Lunisolar Calendars

• A lunisolar calendar is a calendar that tries to follow both the Moon and the Sun

• The Muslim calendar is a lunar calendar that only follows the Moon

• The Chinese calendar is a lunisolar calendar because it adds leap months to keep in tune with the seasons

• Happy Lunisolar New Year!

Chinese vs. Muslim calendar

• The Chinese months start on the day of the new Moon

• The Muslim calendar starts with the first visibility of the lunar crescent

• The Muslim calendar will be 1 to 3 (usually 2) days after the Chinese calendar

Beginning of Spring

• Lìchūn ( 立春 ) marks the beginning of spring and falls on February 4 (or 5)

• It is halfway between the spring equinox and the winter solstice

• Chinese New Year is the new Moon closest to lìchūn

• It falls between Jan. 21 and Feb. 21

When is Chinese New Year?

• Chinese New Year moves backwards by 11 days (or 10 or 12) once or twice, but if a step would take it before January 21, it jumps forward by 19 (or 18 or 20) days

The Date of Chinese New Year

2005 Feb 92006 Jan 29 -112007 Feb 18 +202008 Feb 7 -112009 Jan 26 -122010 Feb 14 +192011 Feb 3 -112012 Jan 23 -112013 Feb 10 +182014 Jan 31 -10

Mid-Autumn Festival

• If spring starts on the first day of the 1st month, summer should start on the first day of the 4th month and autumn on the first day of the 7th month

• Mid-Autumn will then be in the middle of the 8th month

• It will fall between Aug. 8 and Sep. 8

立春 lìchūn Feb 4 start of spring

雨水 yǔshuǐ Feb 19 rain water

驚蟄 jīngzhé Mar 5 awakening of insects

春分 chūnfēn Mar 21 vernal equinox

清明 qīngmíng Apr 5 clear and bright

穀雨 gǔyǔ Apr 20 grain rain

立夏 lìxià May 6 start of summer

小滿 xiǎmǎn May 21 grain full

芒種 mángzhòng Jun 6 grain in ear

夏至 xiàzhì June 21 summer solstice

小暑 xiǎoshǔ July 7 minor heat

大暑 dàshǔ July 23 major heat

立秋 lìqiū Aug 7 start of autumn

處暑 chùshǔ Aug 23 limit of heat

白露 báilù Sep 8 white dew

秋分 qiūfēn Sep 23 autumnal equinox

寒露 hánlù Oct 8 cold dew

霜降 shuāngjiàng Oct 23 frost descent

立冬 lìdōng Nov 7 start of winter

小雪 xiǎoxuě Nov 22 minor snow

大雪 dàxuě Dec 7 major snow

冬至 dōngzhì Dec 22 winter solstice

小寒 xiǎohán Jan 6 minor cold

大寒 dàhán Jan 20 major cold

Joint ANU-NUS Msc in Science Communication

• There are good MSc programs in Math/Science and Math/Science Ed

• We are looking for something in between• Feel free to talk to me or go to the NUS

web page http://www.science.nus.edu.sg/graduates/coursewkprog/scicomprog.html

Final words

• We all have strengths and weaknesses as teachers

• We must not be afraid of trying out new ways to communicate with our students

• I hope to inspire you to push your own boundaries and grow as a teacher