Helping Students to Learn Mathematics (aka develop a mathematical mind )

Barbara Oakley wrote about her life of learning and how she overcame problems learning mathematics.
http://nautil.us/issue/40/learning/how-i-rewired-my-brain-to-become-fluent-in-math-rp

What an interesting read.

(She and Professor Terrence Sejnowski run the online course at https://www.coursera.org/learn/learning-how-to-learn)


Key points of the article:
Conceptual understanding during learning process - balance it with developing mastery and fluency.
This development of mastery and fluency must be involve active learning by the learner.

Repetition, memorization, and practice, and chunking of knowledge as in "....building well-ingrained chunks of expertise through practice and repetition was absolutely vital ...."
Experts were so because they were fluent, and had "....rote learning that emphasized the ability to think flexibly and quickly."

And her experiences in learning the Russian language very effectively were replicated in her own transformation from being a language person into a professor of engineering!
And she wrote this. "Language, math, and science, as with almost all areas of human expertise, draw on the same reservoir of brain mechanisms."


Some related articles about learning of mathematics

PBS : https://www.pbs.org/wgbh/misunderstoodminds/mathbasics.html
        : PBS Video on Misunderstood Minds
Montessori : https://www.montessoriservices.com/ideas-insights/building-the-mathematical-mind

Jump Math : https://jumpmath.org/jump/us,
                     AMS article by John Mighton http://www.ams.org/notices/201402/rnoti-p144.pdf
                   What barriers prevent students from paying attention and being engaged in math lessons?                      Research  https://jumpmath.org/jump/us/supporting_research

Mathematics- How Should We Teach or Learn it?

Some time ago I joined the MathFuture group, and it has been a wonderful personal learning journey as I discover fellow educators introduce cutting edge ideas in mathematics teaching pedagogy, use ICT to enhance teaching and learning, discuss many long standing problems in math education which I myself have been confused by at times. As I read the posts and see the various viewpoints and I begin to see a larger part of the "big elephant" which we are all trying to make sense of.

With due respect to all the distinguished members who are either renowned mathematicians or professors active in teaching and promoting quality mathematics education, do not come to the conclusion that my above analogy of the story of the "6 Blind Men and the Elephant" that the blind men are these members who posted their various viewpoints!


One very "heated" but very interesting discussion that brought out many aspects of Mathematics as a subject, and of the relevance of mathematics to society and to its practicality in life, and how and why we should or should not teach mathematics is at the post titled : 
"Seen This?" (<= click to view)


A very excellent book "The Number Sense: How the Mind Creates Mathematics" by author Stanislas Dehaene (1999, updated  2011), will make you really think about what mathematics really is and to realize how unique we human beings might be in the natural world because we created (and continue to evolve) language and mathematics in a special way that has no parallel in history in the evolution of any other living thing ! Do correct me if I am wrong. 


Dr Dehaene's work continues and he is the Director at 
INSERM-CEA Cognitive Neuroimaging Unit;  
where research continues on high-level human cognitive functions using experimental psychology, neuropsychology and neuroimaging approaches (functional magnetic resonance imaging, fMRI; magneto- and electro-encephalography, MEG & EEG). We can find research publications, and many leading edge discoveries shared at the site.


I needed to add on this :
The difference between teaching and instruction at the blog, Devlin's Angle which is maintained by mathematician Keith Devlin , who is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University, and is The Math Guy on NPR's Weekend Edition.

My Interest In Operations Simulation

Ha, ha.

Found my own MSc Dissertation on

"Simulation study of construction processes in repair and retrofitting of public housing." , available online at NTU's repository. at http://repository.ntu.edu.sg/handle/10356/13097 Hope it can be of use to others one day.

Productivity in the Work Place

To improve productivity in booking and managing school facilities & equipment such as meeting rooms, computer laboratories etc at your workplace, try MRBS (I guess it is the acronym for Meeting Room Booking System) at http://mrbs.sourceforge.net/

Or to create a booking system using Google Calendar, see the article at
http://articles.evolvedwebsites.com.au/google-calendar-a-simple-booking-system/313/

and the implemented system for a small business at
http://www.blacksheepfarm.com.au/nimbin/guesthouse/pricesbookings-calender/29

I am now trying to set up a simple site template for a booking system...
https://sites.google.com/site/bookingsytem/

Takes some effort but I think it is a good mental exercise and above all it is a free system by the courtesy of Google Inc.

......I really think Google Inc. is a cool company that allows the small businesses and people to tap on the internet technologies for free to learn to level up their 21st Century lifeskills before they move on to really use paid commercial software and systems for full scale commercial activities.

Technology Transformation

See Cisco's vision of the future and other videos! At CNN Money Fortune site.

Inking Directly Onto A Web Page

Well today I was thinking of surfing the web to find out any new tools which could be of educational purpose and enhance learning and communications.

So I found something on

1. Microsoft Silverlight
http://msdn.microsoft.com/en-us/magazine/cc721604.aspx#id0090133

2. Article on Microsoft Web Inking
http://www.codeproject.com/KB/mobile/webinkctrl.aspx

Hmmm... too heavy for me and still trying to understand how to implement it.

But I know it will be very interesting. If pupils can write directly onto a wiki page or web page or even Google Document, then it is like handing up paperless homework!

Wow...

Using Google Docs to Make Quiz with Images

I have found information on how to add images to Google Doc Quiz (Forms) by altering html code as suggested by author in http://winterfever.com/mwilliamsgooglequiz.html .

The video on how to create a Google Doc quiz is at http://www.youtube.com/watch?v=EFl3iw6Bp3g&feature=related

This means it is possible to actually prepare math quizzes with complex mathematical symbols and diagrams first in word document with equation editor, capturing the questions and choices as screen shots jpg with ScreenHunter http://wisdom-soft.com/products/screenhunter.htm.

Then use Google Docs Form to create the html file which generate the quiz and allow for collation of responses. Download the html file code and place these picture files with the quiz's html file (taken from Google Docs) in the same local directory. The pictures will appear in the file using the HTML "IMG SRC" tag before or after the question's caption and choice text tags. Test it as a local file.

The picture files and html file (the quiz) unfortunately cannot be deployed back to Google Docs or Sites as Google is not allowing user files with scripts to be uploaded.

I found that only PBWorks sites allow for this....!!! Great and I succeeded in doing one test quiz file. See http://dmn-math-lewws.pbworks.com/f/SurveywithImageTest2.html

Embedded here for you to try out




PBWorks allow for hosting the html file and the pics, and runs the scripts and once you click submit after doing the quiz, the Google spreadsheet which originally generated the quiz (without images) will receive the quiz response.

My next foray will be to do automatic grading of the responses for the survey!
You Tube video on this at Automatically Grade Your Google Docs Quiz
... cheers.


It was a tough but fulfilling day.

More Mathematics Software to Aid Learning of Math and Science

Just discovered other software beside Geogebra that are very helpful for learning of Math and Science















Modellus - graphing, modelling and animation of math functions. Help visualize and understand physical meaning of abstract math functions, formulae and concepts


SMath - Free mathematical program with "paper"-like interface and numerous computing features, and best of all can be run on smartphones !

Game Creation Software for Education

After our teachers' midyear ICT seminar on 4 May 2009, I was inspired by one of the exhibits, MissionMaker 7 for educational game creation, I decided to look for free stuff.

Adventure Games Studio looks like a good bet with a lot of tutorial videos on how to use it!

http://www.adventuregamestudio.co.uk/acres.shtml

You should go try it out too!

Another exciting possibility is the Adventure Game Maker which can make games for iPhones!
at http://www.adventuremaker.com/

2008 Sec 2H Class Photos

Check out and download the rest of the class photos at the link on the title, or below :
http://www.mediafire.com/?sharekey=1dcbb1b71d7e301991b20cc0d07ba4d2923c537574b9bf6c

Blogs on Mathematics

Check this out.
A Singapore Super Math Tutor's site.
Very interesting and well designed site.

Some Interesting Tools of Learning for the Future

Check these very powerful learning tools for yourself.
Empower your self with knowledge and skills ....and help others too.
Let me know your comments after you've seen the sites or tried the software..







Geogebra
Learn mathematics through visualization and dynamic manipulations of algebra and geometry.
http://www.geogebra.org/cms/







Pandora Bot (AIML Project by Dr Richard Wallace)
Create your own online thinking robot ( You train the robot to be intelligent)
http://www.pandorabots.com/








ALICE
Create your own 3D interactive animation story! Learn computer programming and artificial intelligence.
http://www.alice.org/









Lifenaut
Create, store your mind, images, and life story in motion (videos), connect with others....
If you think Facebook, myspace, Friendster are cool, Lifenaut's got to be the coolest!
Beats 'em all in terms of features, storage space, intelligence and easy usage!
http://www.lifenaut.com/

Nepal Trip 11 Dec to 20 Dec 07

This blog ain't dead. Was away on a trip.. and kinda busy clearing up my study in between CCA supervision.

Check out some photos of my trip to Nepal with my son.

It was a great trip. I recommend it for teenagers(endorsed by my son)! Exciting, fun, challenging -sightseeing the Himalayan ranges and rural life, trekking, whitewater rafting, paragliding, elephant riding in really cool weather and amidst very friendly people.

See some Nepal trip photos (will update when there's more time)
http://picasaweb.google.com/lewweisern/NepalTrip

Feedback on Teaching

Would appreciate if you all could give me feedback on my Math teaching at the following survey link. I value your feedback and hope to serve you and your schoolmates better next year.

http://dunmanite.mathteachingfeedback2007.sgizmo.com

Happy holidays

Cool things to try out : Google Sketchup

Learn about Google Sketchup, which you can use to draw all kinds of objects. Especially useful for those who like D&T

You won't regret it. Here are the links to video tutorials on how to use

1. http://sketchup.google.com/gsu5vtvideos.html
2. http://sketchup.google.com/gsu6vtvideos.html

The link to download the free version of Google Sketchup is at http://sketchup.google.com/download.html

When you have tried it, let me know what you think about it.
Would you recommend the school use this software for D&T ?

Last Day of School

Hm...
It's the last day of school.

Report books are out today...Clean up classroom and it's time to go home.

What will you all be doing after 9.30am?