Monday 23 July 2007

Origami

Origami is an art of paper folding. This technique can be utilised in teaching various mathematical concepts.It is known that when we fold a paper, a crease is formed. On that crease a line segment of desired length can be drawn. And by folding that paper again, in such a way that the extreme points of the line segment concides,one can get the mid point of the line segment.Because this technique is based on "working with hands" domain, so the learning of a concept is maximum .The students can visualise the theoritical geometrical concepts taught in the classroom .
Nearly everyone has made paper airplanes or tried origami when we were children. Take these memories further when you download dozens of 3D-Papercraft projects for free.

http://cp.c-ij.com/english/3D-papercraft/

Thursday 12 July 2007

Brain teasers/ videos

We teachers all the time are discussing problems given in the text books and the students also get use to accept this as a regular feature. When there is an inter school mathematics competition or general Olympiads, we expect good results from the students. On the real side we actually are not training the young achievers to solve the non routine problems. In the process a stereotype approach of doing /solving math problems gets registered permanently into the young minds. I personally feel that if we would spend some time on taking up variety of problems in the classroom, it will surely help the students to tackle the non routine problems asked in various competitive examinations.
One way could be taking up simple brain teasers. It is an excellent way to improve the critical thinking, develop on logical thinking and problem solving skills of the students.
Recently, I visited http://www.teachertube.com/ and found various videos on math teasers. It is really a pool of useful resources. You can reach there by the following URL http://www.teachertube.com/groups_home.php?urlkey=BrainTeasers.

Wednesday 11 July 2007

Fear of solving word problems

Fear of solving word problems.
There is a fear of solving a word problem in mathematics among the students .About 80% of the students try to avoid it during the examination. Once I had a survey in my class and I asked the students to solve two word problems from the chapter mensuration in class X.
30% students do not even read the problems.
35% do not understand what is being asked in the question?
15% tried to form correct equations but failed.
20% attempted the questions correctly.

There is no way…to skip word problems. But yes we can make solving word problems interesting for students. It is a challenge for a teacher to add a creative element to a dullest and boring work. The first effort made by a teacher could be to inculcate in students an attitude of doing/learning all kinds of problems which are essential for them. The second and the most important aspect is visualizing a problem. If the students visualize a concept, it helps them to learn/grasp the concept quickly. We can use the resources available on the web for making them visualise the concept.

Story telling


Story telling is a strategy which could help math teachers to bind students close to mathematics.There are various true tales/anecdotes of mathematicians which could add a long lasting impact on students to explore mathematics deeply. In my free periods as well as in class teacher period or in House meetings I am using this strategy of story telling.
Here I am sharing some incidents about a famous Mathematician Gauss.
Gauss was a child prodigy (a teenager who acclaimed success at a young age), of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager.
At the age of three he corrected, in his head, an error his father had made on paper while calculating finances.
Once in primary school his teacher, J.G. B├╝ttner tried to occupy pupils by making them add up the integers from 1 to 100. The young Gauss produced the correct answer within seconds by a flash of mathematical insight, to the astonishment of his teacher,J.G.Buttner.
He added the integers from 1 to 100 in the following manner
S=1+2+3+4+-------------100
S=100+99+98+------------1

2S = 101+101+101+-------------101 (100 times)
S= 10100/2 = 5050.

Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on.

If you are sharing some real stories of mathematicians in your classrooms ,Please do share.

Tuesday 10 July 2007

eways Probability

In class X C.B.S.E. Mathematics syllabus, the concept of Probability is introduced for the first time to the students. The students more or less cram the idea and do the questions using the formula. But when they actually experiment on probability they ask the questions like I tossed the coin two times and both the times head appeared so the probability of getting a head is 1 instead of 1/2.
I think this way they will not correctly learn the actual probabilty concepts. To make them understand the actual meaning and interpretation of probability,in my classroom teaching of probabilty I have used the probability Applets given on the web for generating the readings.
E.g. if a coin is tossed 100 times then how many times a head appeared and how many times a tail appeared.Then I ask my students to compare the results with the results which they have learned.
And if we increase the number of throws to 200, 300 or more then the students can actually learn the correct interpretation of probability.
I have designed various probability problems. I am sharing some of them.
Throw a pair of die 200 times .Note down the readings. Calculate the probability of the following
getting sum more than 8 on both the dies.
getting a multiple of 3 on first die .
getting prime number on both the dies.
getting an even sum
I have used the following links for generating the readings.

Tuesday 3 July 2007

eways coordinates

Here I am sharing, how I have used the cam studio software in my math teaching. I have prepared a lesson plan on the chapter plotting coordinates of points on a graph paper. This topic is introduced for the first time in class IX. The students are not so comfortable in plotting points correctly on a graph paper. They normally commit mistakes while plotting the points and labeling even correct axes. This was bothering me, so I tried a new strategy for teaching this concept to the students. I used open source software Geogebra and created a video lesson using Cam studio. The complete activity was as follows
10 Points were generated on the x-axis and by observing the readings of the coordinates generated, the students quickly answered the coordinates of any general point on the x-axis is (x, 0)
10 Points were generated on y-axis and by observing the readings of the coordinates generated; the students were able to tell the coordinates of any general point on the y-axis.
10 Points were generated in the I quadrant and the students noted their coordinates and visualizing them they noted the observation of any general point in the first quadrant is (x, y)
Similarly points were generated in the remaining three quadrants to note the coordinates of any general point in the remaining 3 quadrants.
This is how I introduced this concept to my students.
Then I gave them the assignment based on the activity.
During the lesson, the whole class was attentive, because their attention was captured by the activity running on the screen. Few of my students have downloaded Geogebra at home, to explore more.

Different Proofs


In class X mathematics syllabus Pythagoras Theorem is taught. The students simply cram the theoretical proof of the theorem given in the N.C.E.R.T. book and thus could not do the application part of it. I think if we could provide the students with various proofs of the theorem, then the students would be able to understand it in a better manner.


Click on these links for Interesting Pythagoras theorem proofs
http://www.teachertube.com/view_video.php?viewkey=1540bc52912baf3aa709
http://sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
http://www.ies.co.jp/math/java/samples/pytha2.html
http://www.frontiernet.net/~imaging/pythagorean.html
 

Apture