WIKIS and MATHEMATICS

I was watching  a short film on YouTube tonight. It explains what a wiki is and how to make one. It was a really helpful little movie. Anyway I then searched for some maths wikis and stumbled across the wikibooks website and found a lot of maths text resources online . Click on the link and check out the maths wikis on line . They might come in handy for you and your students.

Paul

Click below to take you right where you want to go.

HSC Extension 1 and 2 Mathematics A-level Mathematics Abstract algebra Algebra Applicable Mathematics Applied Math Basics Beginning Mathematics Calculus Complex Analysis Conic Sections Differential Geometry Discrete mathematics Introduction to Game Theory Finite Model TheoryGeometry Geometry for elementary school Handbook of Descriptive Statistics High-School Mathematics Extensions Linear algebra Mathematical Proof Numerical Methods Pre-Algebra Probability Real Analysis Set Theory Statistics Topology Trigonometry The Book of Mathematical Proofs

Digital Natives, Digital Immigrants, Part II:

I just read Prensky part 2.Digital natives, digital immigrants. He quotes some pretty amazing statistics. In 2001 the average teenager was spending between 4-5 hours per day on gaming,email,texting and television. When these statistics were evaluated there was no myspace or facebook and many more of the goodies on Web 2.0 .

So if the average teenager gets home roughly at 4pm has a snack to eat and gets into his average tech time then it will be somewhere around 8.30-9pm before he comes up for air! but I’ve forgotten about dinner with the family!! So when do they get a chance to do their homework and assessment?

Digital Natives, Digital Immigrants, Part II:
Do They Really Think Differently?
By Marc Prensky
From On the Horizon (MCB University Press, Vol. 9 No. 6, December 2001)
© 2001 Marc Prensky
Different

PODCAST – Education The Future

Here goes my first podcast on my dream for education. teach-pod-cast-1

I hope you enjoy.

Paul

P.S All the photos were taken by me and I wrote and produced the music – So Copyright is clear

Digital Racism??

In Prensky’s Brave New World (Digital natives, digital immigrants.)- The Digital Native is the Young restless Imperialist – a leader , waiting to assume his rightful role on the throne. He must be patient as he suffers in his interactions with his Digital immigrants subject/tutors- Let’s face it these immigrants will always have an “accent” and do things a little backwards like reading a manual or printing off a report instead of reading it online.

Have you ever had the pleasure of trying to teach the ‘twitch speed’ native a difficult skill such as playing piano. I have taught piano for the last 15 years and am yet to find a correlation between these highly prized multi-tasking ,hyper texting- native skills and the ability of natives to play a simple piano piece of their own choosing. Concentration is a demanding skill.

The most unfortunate thrust of this article is the divide it sets up between natives and immigrants. There never appears to be a place where one can learn from the other in respect and tolerance. There is a simple term for that-racism. If we have bullying and cyber bullying, why not digital racism?

Racism never leads to positive outcomes . Lets look for the things that unite. I hope you enjoy the photo.

CONSTRUCTIONIST -Constructionism- Here we go again

I thought it might be nice to open my first blog with a  few thoughts on Constructivist and Constructionist approaches as outlined in “Piaget’s Constructivism, Papert’s Constructionism:What’s the difference?
Edith Ackermann “
paper and also link back into where we are heading with Assessment 2

Assessment 2 -Criteria see below

Your discussion will explore ways of using learning technologies (relevant to your chosen specific topic) to support meaningful learning (definition to be discussed in classes), with an emphasis on your 7-12 curriculum area(s). Your discussion must go ‘beyond’ exploring didactic, instructional uses and when possible, emphasise constructionist approaches (definition to be discussed). Also, you are encouraged to think about opportunities for plearning (definition to be discussed), both on a local and global level.

Here we go again ,being asked to emphasize teaching approaches that after half a century have no body of research to support their techniques. Constructivist has moved on to Constuctionist and of course no research anywhere in the literature comparing it to direct instructional methods and showing why it is conclusively better – but we are expected to champion it.

1. Minimally guided instructional constructivist approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. Sweller, John, Kirschner, Paul A. and Clark, Richard E. (2007) ‘Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries’, Educational Psychologist, 42:2, 115 – 121 .

2.On the other hand “Direct instructional guidance is defined as providing information that fully explains the concepts and procedures that students are required to learn as well as learning strategy support that is compatible with human cognitive architecture. Learning, in turn, is defined as a change in long-term memory.”

“We have not evolved to effortlessly acquire the biologically secondary knowledge such as the use of algebra or scientific theories that are characteristically taught in educational institutions. That information passes through working memory and so requires conscious effort. It must be explicitly taught; indeed we invented educational institutions in order to teach such knowledge,and the manner in which it is taught needs to take into account the characteristics of working memory, long-term memory and the relations between them.” (Sweller2007)

And now we have Constructionism

“Papert has been a huge proponent of bringing IT to classrooms, as in his early uses of the Logo language to teach mathematics to children. Constructionist learning involves students drawing their own conclusions through creative experimentation and the making of social objects. The constructionist teacher takes on a mediational role rather than adopting an instructionist position. Teaching “at” students is replaced by assisting them to understand—and help one another to understand—problems in a hands-on way.” Wikipedia

We let children draw their own conclusions . I like that. And then we spend the rest of the lesson correcting faulty conclusions and assumptions .

Most learners of all ages know how to construct knowledge when given adequate information and there is no evidence that presenting them with partial information enhances their ability to construct knowledge. Actually, quite the reverse seems most often to be true. Learners must construct a mental representation or schema irrespective of whether they are given complete or partial information. Complete information will result in a more accurate representation that is also more easily acquired. Constructivism is based therefore, on an observation that, although descriptively accurate, does not lead to a prescriptive instructional design theory or to effective pedagogical techniques(Clark&Estes, 1998, 1999; Estes&Clark, 1999 ; Kirschner , Martens ,& Strijbos, 2004).

Can we have a balance between both modes of instruction.(Direct and Constructivist)?

Here endeth the rant.

Paul