digitalLEARNING-Aug-2010-[44-46]-Technology, ICT and Math Education

case study

Technology, ICT and Math Education

Prof. Inder K Rana Department of Mathematics Indian Institute of Technology Bombay e-mail: ikrana@iitb.ac.in

Indian education system The system of education in India is ‘10 + 2 + 3’ model. Education is a state subject and there are 26 states in India. Each state has its own Education Board which is responsible for all matters relating to school education in that state.

This makes the education system nonuniform. Indian education system is highly examination-oriented. The ‘examination mentality’ has had a strong negative influence on everything connected with education in India: textbooks, style of teaching, and teacher preparation. There is little scope for innovation and use of technology in regular teaching.

In the year 2005, the Central Board for Secondary Education took an initiative and issued a directive to all the schools affiliated to it (Figure 1.)

What Math Lab can achieve (CBSE) However, there was no real effect of this circular as no support system was set up. Still, there is no attempt to include really meaningful technology inputs in math education as part of curriculum.

Role of technology in Math education What is technology What is technology? It can be summed up from the perspective of evolution, as:

Slate

Sliderule

Software

It has evolved from oral education and engraving on clay tablets / stones, to writing on palm leaves, to the invention of ink/paper and printing, to digital media in the modern times. Technology hardware: Hand held calculators on one hand and multimedia workstations on the other; digital class rooms on one hand and virtual class rooms on the other are some of the examples of technology playing a role in math education.

ICT, Course distribution over the Internet, use of softwares like Maple, Mathematica, Mupad, Drive, GSP, Cabri, and so on, help to compute and simulate.

Learning management softwares and evaluation tools are playing a vital role in making laborious tasks easy.

Mathematics Laboratory in Schools Concept of Mathematics Laboratory introduced by the Board in 20022003.

Manual titled ‘Mathematics Laboratory in Schools’ published by the Board to give fuidelines and specimen activities.

Aim: To remove the fear for mathematics among chilren and to make the subject more interesting.

All affiliated schools were advised to start the Mathematics Laboratory for classes III onwards and integrate evaluation of practical competencies in Mats with the evaluation of the subject.

Board expects all affiliated schools to have their Mathematics Laboratories by 31st March, 2005.

Circular No. 03/28.01.04 Figure 1. Math Lab aims

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Technology in Math education Education (more so Math education) is in the midst of a change driven by technological developments. Technology is entering many facets of math teaching and learning. Technology is a valuable tool in the teaching and learning of mathematics, for it has the ability to empower mathematics students as well as mathematics instructors. In some cases the use of technology is prompted by the methods that can help a teacher to do some jobs easily and in a better way. In others it is motivated by the belief and effort to impart instructions in a way that will help to achieve the learning goals of students. Integration of technology in education can also be because of nonacademic reasons.

Technology supported e-modules Aims The aim of an e-module should not be to replace a teacher, but to support a teacher. An e-module helps in building intuition and developing independent thinking. Intuitions built at early stages help later in formalisations. Efforts should be made to present numerical, graphical and symbolic representations of various concepts so that a student has the freedom to choose one or more of multiple intelligences.

Recipe for an e-module • Select a topic.

• Revise the basic concepts.

• Give an example of the activity you want them to do.

• Activity should involve observation, analysis of observation based on the concepts revised, conclusion and its justification.

• Give a short quiz to test the assimilation of the concepts.

Maths Laboratory and Internal Assessment in Mathematics Maths Lab provides a conducive ambience for students to learn the subject in a joyful manner through practical activities and interaction.

Teachers need to pay attention to both the transactional strategies and evaluation strategies.

Simple experiments and projects will lead to the development of different skills like numerical, observation, thinking, analytical and so on.

Establishing a Maths Lab does not involve high cost. Improvised aids using inexpensive material can be made.

Space required is also quite limited.

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Circular No. 10/02.03.05 What Math Lab can achieve (CBSE)

• An example of an e-module This module was developed for middle school(age 14-16 years) on the topic of perimeter and areas. It is developed first by typesetting the text in ‘Latex’ and

using the add-on ‘Prosper’, which gives smooth beautifully aligned Power point presentations in pdf format. Here is an outline of the module: • Concepts on rectilinear figures:

Positive aspects of technology use Technology adds new components to teaching and learning of mathematics by providing: • Tools for visualisations/ illustrations.

• Tools to do tedious computations in less time.

• Tools to recognise pattern in a problem.

• Helps to formulate conjunctures.

• Tools to develop problem solving skills.

Technology Enhanced Learning, Visualisations Visualisations can be developed manually (sometimes) or with the help of technology tools provided by calculators/computers. This paper will discuss in details with specific example to illustrate how visualisations can enhance the processes of teaching and learning. The visualisations should be used to: • Explore / Experiment.

• Observe / Conjuncture • Convince / Prove • Extrapolate / Extend Example: Let a student be shown the following picture:

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triangle, rectangle, square, parallelogram and rhombus are revised.

Computations of areas of these figures is demonstrated by flash animations.

Non rectilinear figures are introduced.

Problems involved in finding the perimeter and area of a circle are exhibited by the use of applets.

Show with the help of animations how these can be determined.

Historical background of defining and determining π and its uses are illustrated.

A short session with hands-on activities on these concepts is included.

A quiz is given to evaluate the impact of the module.

draw any conclusions/conjectures about the geometrical shapes involved? It may help to look at the figure on the right hand side shows a rearrangement of the shapes in figure on the left hand side. May be naming the sides will help in thinking: a b

c

Does this enable students to think and respond? If still not, the following picture can be shown: b

a b T

T

c

b×b

a T

T

T C×C T

a×a T

T

This should help to motivate most of the students to conjuncture: Area of figure on left hand = Area of figure on right hand 4 × Area of triangle + Area of square = 4 × Area of triangle + Area of two squares, and hence a2 + b2 = c2 This is the called Pythagoras Theorem.

Given the information that in the first figure, inside quadrilateral is a square, students can be asked if they can

These explorations are much more captivating when shown digitally.

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Use of e-module and Feedback from Kendriya Vidyalaya, I.I.T. Bombay

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One of the e-module was used in a Math Lab for middle level (8th standard) on the topic of areas and the another for senior secondary (12th standard) students on the topic of derivatives in calculus at different schools. Students (total number of students: 77) were asked to tick one choice in each column of the questioner:

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The way the lab was The contents of the lab conducted were

Would you like to have more such labs?

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Very interesting (46.15% ) Difficult ( 6.41%)

Very much (41.02% )

Interesting (42.30% )

Moderate (78.20%)

Yes (52.56%)

OK (11.53%)

Easy ( 15.38%)

No (6.41%)

Some general comments • Activities were new and interesting. Concepts are much clearer now.

• It cleared my fundas. Would like to attend more.

• We need such labs in Integration also.

• Actually such labs are really good, but I need to be intelligent enough to grasp things!

• It was time consuming, but still interesting.

• Boring!!

• gre8!

• Sir, please conduct these types of labs more often • This is something that I had not done before, helped me to understand graphs.

• This kind of labs should be conducted for chemistry also.

• Excellent, just a bit slow.

• Cool! Expecting more such in future.

• Amazing mental exercise! Too good, making concepts crystal clear.

• I really liked it from the down of my heart.

• A new look at calculus, amazing! Thanks a lot!

• Thank you very much, sir.

Conclusions Negative aspects of Technology use • One of the biggest drawback of technology is that it needs resources: both financial as well academic.

Given that schools/colleges have limited resources, there are difficult choices to make on how to invest the resources.

• Technology enables a false sense of accomplishment to deceive the school/college and community.

• For teachers, using technology increases workload to learn technology. Also it puts pressure on them since they have to change their teaching approach. In their enthusiasm, teacher may loose perspective and aim of instruction.

• For students, learning to use technology itself may be time consuming and frustrating.

• Using technology can lead to an easy way of getting answers for students. This can lead to weakened conceptual understanding and basic skills.

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Technology is not versatile and its functions are limited. After all it is the product of human mind. Technology by itself cannot promote learning.

More often than not, it needs a facilitator.

Some questions Some of the questions one asks are: • Is the use of technology required for learning in general, or for learning math in particular?

Is there evidence that students learn mathematics better with any technology or with specific technology?

Is it worth spending on technology when there is a shortage of resources, both financial and academic?

Can technology compensate for the lack of qualified instructors?

Some answers • Technology is not a universal tool and an omnipotent aid that can always help. Technology often provides convincing demonstration of ideas, helps to conjuncture, but does not replace ’proof’.

• Nor does constructing a proof rules out the use of technology.

• This distinction must be emphasised and the importance of both must be appreciated.

• Technology cannot replace live class room teaching nor it can compensate lack of qualified teacher. In terms of valid reasons, from a learning standpoint, there actually is some evidence that specific technology can improve students’ learning of mathematics when implemented properly.

• Learning does not take place in the technology. Learning takes place in the interaction between motivated faculty and motivated students. Whenever possible, technology can be used to provide such environments.

• Used properly, technology can help the teacher to impart instructions in a more effective way that will enhance students understanding and motivate them to learn. \\

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