Wednesday, 25 July 2012

Math Cartoons (Just for Laughs)

Technology and Mathematics (Cartoon :)

Technology and Mathematics

Fact or fiction?: 

The greatest advantage of using technology in the math classroom is learning to apply it in real-life situations and to be able to interpret the answer.

Math teachers often use PowerPoint presentations and graphing calculators as useful tools to have a better understanding of movement problems in Calculus. The use of PowerPoint presentations and graphic calculators enriches the teaching-learning process of topics from Calculus (i.e. effects on the graph of exponential and logarithmic functions). Most teachers reveal that even though the use of these resources requires extra class prep time, there are important time savings during class and presentations are more organized.

The main disadvantage of using technology in the math teaching-learning process is that students seem to get caught in the mechanical part to get the results and not on the interpretation of the results. This means that students don’t learn to apply math to real-life situations and are not able to interpret the answer.
Testimonial of a high school level calculus teacher from Santa Catarina, Mexico:
They know how to find the derivative for the cost function, and they might remember that it’s called the marginal cost, and they could actually get the derivative using any software and even graph it, but they might not know that actually evaluating a value on the derivative represents the cost for an additional unit to be produced.

Helping Children Master the Basic Facts (Chapter 10)

Fact mastery relies significantly on how well students have constructed relationships about numbers and how well the understand the operations.

Fluency with basic facts allows for ease of computation, especially mental computation, and therefore aids in the ability to reason numerically in every number-related area. Although calculators and tedious counting are available for students who do not have command of the facts, reliance on these methods for simple number combinations is a serious handicap to mathematical growth.

Teaching basic facts well requires the essential understanding that students progress through stages that eventually result in "just knowing"that 
3 + 7 = 11 or that
5 x 6 = 30.

According to 
Arthur Baroody
a mathematics educator:

Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). 

I feel that this can help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes children's mathematical learning in an interesting, thought-provoking and comprehensible way. 
Eventually, as teachers, we appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics!

Monday, 16 July 2012

Interesting: To swap or not to swap?

The Monty Hall Problem

Testing out the Monty Hall Problem!

Systems of Equations

1st Day of Class

First day of class was interesting and very engaging. Dr Yeap prepared a lot of materials and did hands-on activities with us. Not what I had in mind, the usual boring Math lessons like in Primary and Secondary schools. He made learning and teaching Mathematics FUN!

We learned about how children learn MATH 
- Concrete, Pictorial, Abstract
- Variability

CPA Approach by Jerome Bruner

Theory of Variability by Zolten Dienes
- Every choice of number is purposeful.

We also learned that Mathematics and Language has to go hand-in-hand!

Mathematics is an excellent vehicle to develop and improve children's intellectual competence.

Dr Yeap quoted this,
"Anything that is important, cannot be measured. Anything that can be measured, is not important." ~Albert Einstein

Another quote to note,
"The important thing is to understand what you're doing, rather than getting the right answer."