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Graphics Calculators.

My initial reaction to the graphics calculator was not really a positive one. It is a new piece of equipment that I am not familiar with. It seems that I needed a degree just on how to use the thing. To me it seemed to be an overly complex wigit.

Realistically my opinion of these calculators matters little. The question that needs to be asked is “Do they add value to a math student’s ability to learn?” If it does, then my nearly 40yo brain needs to get into gear and learn how to use this tool effectively.

It would be of benefit to visit a school that actually uses them to gain an informed opinion of their value. Unfortunately, I know of no school that uses them. Why would this be so? There would be many good reasons for schools to give as to why they do not have them; cost, students loosing them, waste of time, to complex, no BOS compulsory programming requirement. I would suggest that the old cycle of “I learnt it this way, so current students can too!” would be a factor here also. Until mathematic educators demand appropriate technology in their classrooms, teachers will be confined to using the old methods of direct instruction and boring textbook lessons with the occasional use of the good-old worn-out overhead projector.

The Federal Government is looking at putting a computer for each student in all schools. I see this as a real bonus as websites have easy-to-use programs which cover all the capabilities of the graphics calculator and more on them. Such websites include  http://www.expertmathtutoring.com/Plot-Graphs.php for plotting functions, http://www.quickmath.com/www02/pages/modules/equations/index.shtml for solving equations, http://www.internet4classrooms.com/skills_5th_original.htm for quick skills testing and  http://www.funtrivia.com/quizzes/sci__tech/math.html   for fun quizzes in specific topics. These tools can assist students to have a better intuition for math problems and how functions and other answers should look like. I would like to see greater technology used in classrooms, either graphic calculators or computers, as students need to be familiar with it in today’s world and can have their learning greatly enhanced by using them.

During my reading this week I found myself wondering what all the fuss was about, why all this quibbling about the meaning of a few words that people have slightly different meanings attached to them. It appeared that they were all pretty much saying the same thing anyway. As I read on it became clearer as to why it is important to distinguish between these meanings. It is desirable for research to be conducted to enhance the knowledge we have on how people learn, think about, understand and apply mathematical knowledge. Mathematical knowledge is built upon itself; further ideas and concepts built upon previously learnt knowledge. Similarly, research also is built upon previous learning’s. Research is conducted across the world and it is not until common word meanings are agreed upon can this research move forward with any significance.  From my readings I understand the following to be reasonably close to what is loosely the general understanding of these words:  

Literacy is having the skills to understand the ideas of others and have your ideas understood by way of written skills. Primarily “literacy” is English text based, but must also include the understanding of symbols in whatever sphere your communicating about (in the maths area this would be mathematical symbols). 

Mathematical Literacy is the ability of an individual to solve real life problems in his/her real life using their mathematical knowledge. This may include their knowledge and use of technology to solve mathematical problems. 

Numeracy is the same as Mathematical Literacy in that an individual can solve their own personal mathematical problems but it has an additional element in that, a person can communicate their mathematical ideas to others and understand others’ mathematical ideas by means of symbols and/or jargon. 

Quantitative Reasoning is the ability to be able know which mathematical method/s to use and in which combination to be able to solve real life problems where different situations arise in real life 

Quantitative Literacy includes Quantitative Reasoning in that it is the ability to understand mathematical concepts to apply correct methods to obtain the desired mathematical result. It has a further element in that a person is able to understand and interpret the results obtained, to scrutinize them for the purpose required, including flaws, robustness of useability, to predict further problems and further solutions. It is a deep understanding of the, who, what, how, when, where and why of all things pertaining the mathematical situation at hand.   

Another Question – Is learning to use technology to solve mathematical problems considered legitimate “learning maths”, or is obtaining the knowledge of how, why and the relationships between maths concepts to be considered learning maths? Are you good at maths if you can get a right answer from technology or are you good at maths if you know how and why the answer is what it is? Can we make up some new words to describe these? (Just to muddy the waters a bit more).

Record your own views about learning mathematics with technology. Do you think secondary students should be allowed to use scientific and graphics calculators when learning mathematics? Are computers a useful learning tool? What might be some of the benefits and disadvantages in teaching and learning mathematics with technology?  

Disadvantages firstly, would include an over-reliance on technology to do simple calculation and missing the significance of mathematical patterns and relationships. Deep understanding of mathematic concepts require student to make connections with similar ideas as learning progresses through each level of learning. (Theory’s learnt in 1^st year about scaffolding information to create new understanding). Students may miss basic understanding and learning skills that should become automatic as students progress, 2.5 x 4 =…  should not require any tech aid. Secondly, in the vast majority of classes, students know more about technology than the teacher and also students will have a vast difference in their technology ability. When this is the case the teacher needs to take precautions that all students are challenged at the right level for individual abilities, which is a difficult thing to do. 

Benefits of technology firstly would include not having students bogged down in tedious calculations (often getting these wrong) and missing the main idea of what you’re trying the students to learn. An example being, doing a table of values for a certain function, by the end of the table students may think that getting the right table is an end, but may miss the whole idea of plotting these values to create the graphed function. A scientific calculator may avoid this problem, provided that they still know how and why a table is useful. Secondly, technology is becoming normal in all aspects of daily life and students would benefit by utilising technology to learn mathematics as it is increasingly becoming expected that students will have a competence in using technology for any endeavour, both in and out of school. 

Undeniably the way of the future is technology and students need to be well versed in such tools, however, teachers need to make judgements as to wether a certain technologies are an aid to student learning or a hindrance to the student’s ability to make necessary cross-connected relationships and patterns. These judgements need to be made on individual topics throughout each course.