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# Teaching Mathematics by hands-on approach

I hear I forget,
I see I remember,
I do I learn.
When I read this quote in an article on learning strategies, I realised how important it is to use hands on activities for teaching learning Mathematics. In year 2K we established a Maths lab in our school with a mission of creating interest in the subject using hands on activities and recreational Math which is not a part of any syllabus of any grade. In a year or two we came to notice a remarkable change in the attitude of students towards learning of Mathematics. It was in the year 2003 C.B.S.E. in India made it mandatory for all schools to have a Maths lab in school. I contributed in preparing a Laboratory Manual of C.B.S.E for grades 9 and 10. In the year 2006 , I came to know about blogging and created my blog for sharing Math lab activities at Planet Infinity
Are you teaching the same way?
What other strategies you are using for teaching Math. Please share.

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### Replies to This Discussion

We are also using maths lab activity in our school. I observe that the students are more motivated in learning mathematics and grasping the concepts through maths lab activities. I am so happy maths lab period is included in our school time table from classes 6.
In "Deriving the Formula for the Volume of a Cylinder," you claim that the Length of the cuboid is 1/2 the circumference of the top circle. This is untrue, and would confuse a discerning student. You are better off by showing them the limiting process and letting their imaginations see the conclusion.

The length of the cuboid is approximately half the circumference of the top circle. The approximation is "off" by the difference between the length of an arc and the length of the secant. This difference, or error, is clearly (to students) related to the "curvature" of the arc. The smaller the arc, the less the difference. So if you started by cutting the cylinder into two pieces, then three, then four, etc. the students can quickly see that when you cut the cylinder into " a zillion" pieces the resulting cuboid is almost exactly a rectangular solid, so they can give the Volume = Length x breadth x height formula.
Another point about showing this method of calculation by approximation is that you can motivate students by telling them that this is something they will learn to do themselves when they take Calculus!

It shows them that something they may think is distant and unattainable is actually much closer and easier than they thought. It can be quite empowering.
All the information that is being done in the above activities can easily be achieved by a simply process of folding the circle (doing) and observing (seeing) with attention to the information generated and discussing with others the observations (listening). To begin with; listening, seeing, and doing should never have been separated.

Folding circles is the one activity that has been left out of mathematics and other disciplines because we have convinced ourselves the picture we draw is the circle. When you cut the circle from a rectangular paper have students notice the difference between the drawn image and the circle. From that students should be able to logically deduce the only information that directs them to fold the circle in half. The question then; "what do we have that has been generated that was not there before?" By observing how you do the folding, a generalization can be made about touching two imaginary points on the circumference together, checking for alignment, then creasing. We all do this when folding a circle. So mark the imaginary points first, then you can see there are four points on the circumference and one diameter. In drawing lines connecting the four points you are only making visible what is already there in relationship. Common language is all that is needed to express observations, then mathematical terms can be introduced to add preciseness and clarity. By observing the multifunctional relationships and movement functions of the parts withing the circle there are over one hundred and twenty mathematical functions that can be observed by discussing the information generated by this one fold. If you go to my website you will see other things that can be done with the circle : wholemovement.com
You are very right . In Maths laboratory children actually learn through this approach. They cut slices into more number of parts and tend to get more closer to result. Basic idea is visualisation of formula using hands on approach.

Dr. Steven B Tesser said:
In "Deriving the Formula for the Volume of a Cylinder," you claim that the Length of the cuboid is 1/2 the circumference of the top circle. This is untrue, and would confuse a discerning student. You are better off by showing them the limiting process and letting their imaginations see the conclusion.

The length of the cuboid is approximately half the circumference of the top circle. The approximation is "off" by the difference between the length of an arc and the length of the secant. This difference, or error, is clearly (to students) related to the "curvature" of the arc. The smaller the arc, the less the difference. So if you started by cutting the cylinder into two pieces, then three, then four, etc. the students can quickly see that when you cut the cylinder into " a zillion" pieces the resulting cuboid is almost exactly a rectangular solid, so they can give the Volume = Length x breadth x height formula.
Hi All,

I agree that hands-on learning is very important, especially at junior and middle years, when students are transforming concrete understandings to theoretical knowledge. We are using many of the Maths300 activities at Hawkesdale P12 College, which are mostly open-ended and problem solving tasks that progress from hands-on to computer simulations.
One of the recent activities was finding the maximum volume of a rectangular prism, using a fixed area of paper (10 x 20cm). Only after we had made a range of different sized containers using the paper rectangles were some students able to understand the concept of volume and how it could be calculated. Graphing the different volumes against the height of the container we found that the maximum volume was somewhere between 2 and 3 cm.