Identifying and Sequencing of the Elementary Concepts of Proportion (Algebraic Treatment) Through Micro Analysis Technique
Keywords:
Major concept, elementary concept, proportion (algebraic treatment)
Abstract
In this paper attempts have been made (a) to identify all the elementary concepts of the major concept proportion (algebraic treatment) and (b) to find the sequential order of these elementary concepts. Total 74 elementary concepts have been identified and sequenced.
References
Ben Clarke Pacific Institutes for Research in www.centeroninstruction.org, 2006
Chilana, R (1984). Teaching Elementary School Mathematics, The Primary Teacher, 9(4), P-3, New Delhi, India: NCERT.
Malhotra,, O.P. & Gupta, S.K. (2000). Mathematics Today (Revised Edition), Book-3 (for class-3), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-1 (for class-1), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-2 (for class-2), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-4 (for class-4), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
National Council of Educational Research and Training (NCERT) (1996). Let’s Learn Mathematics (Book One), February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (1997). Let’s Learn Mathematics (Book Three), January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (1998). Let’s Learn Mathematics (Book Four), January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2000). Mathematics (with supplement) : A text book for Class-X, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2002). Mathematics: A text book for Class 9, February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2002). Mathematics: A text book for Class 6, February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2003). Let’s Learn Mathematics, Book Two, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2003). Let’s Learn Mathematics, Book Five, December, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2004). Mathematics (Part 1): A text book for Class 7, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2004). Mathematics: A text book for Class 8, January, New Delhi, India: NCERT.
Piaget J. (1973). To Understand is to Invent, Viking, New York.
Pushpanadham. K. (1998). An investigation into the Pupils’ Understanding of Basic Arithmetic Concepts, Quest in Education, 22(2), P-38.
Schiralli, M. and Sinclair, N. (2003), A Constructive Response to where Mathematics Comes From, Education Studies in Mathematics 52: 79-91
Sk Samsul Alam (2003). Sequencing the concepts of subtraction of whole numbers, Journal of Centre for Pedagogical Studies in Mathematics, Thirteenth Issue, PP5 - 13.
Sk Samsul Alam (2003). Sequencing the concepts of addition of whole numbers, Indian Journal of Mathematics Teaching, 29(1&2), PP13 - 23.
Sk Samsul Alam (2005). Sequencing the concepts of multiplication of whole numbers, Journal of Centre for Pedagogical Studies in Mathematics, Joint Issue, 14& 15, PP16 - 22.
Sk Samsul Alam (2005). Sequencing the concepts of division of whole numbers, Indian Journal of Mathematics Teaching, 31(1&2), PP26 - 37.
Sk Samsul Alam (2006). Sequencing of the integral exponent of rational number, Journal of Centre for Pedagogical Studies in Mathematics, Sixteenth Issue, PP15 - 21.
Sk Samsul Alam (2006). Identification and Sequencing of the Mathematical concepts of class-I standard, Quest in Education, 30(3), PP20 - 24.
Sk Samsul Alam (2006). Sequencing the concepts of the operations on algebraic expression, Indian Journal of Mathematics Teaching, 32(1&2), PP. 60-67.
Sk Samsul Alam (2006). Karanir dharanagulir dharabahikikaran, Ganit Parikrama, Bingswati Barsha, 1&2, PP11-19.
Sk Samsul Alam (2007). Sequencing the concepts of International numerals sand Roman numerals, Journal of Centre for Pedagogical Studies in Mathematics, Seventeenth Issue, PP. 17-21.
Sk Samsul Alam (2007). Sequencing the concepts of factorization of algebraic expression, Vigyan Shikshak, 51(1&2).
Sk Samsul Alam (2007). Sequencing the concepts of rational expression, Indian Journal of Mathematics Teaching, 33(1&2), PP26-31.
Sk Samsul Alam (2007). Asannamaner dharanagulir dharabahikikaran, Ganit Parikrama, Ekbingswati Barsha, 1&2, PP4-8.
Sk Samsul Alam (2008). Sequencing the concepts of decimal, Parshad Barta, Chautrishtam Barsha, January ’08, PP 22-32, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2008). Identification and sequencing of the mathematical concepts of class-II standard, Quest in Education, 32(3), PP23-30.
Sk Samsul Alam (2008). Sequencing the concepts of Quadratic Equation, Journal of Centre for Pedagogical Studies in Mathematics, Eighteenth Issue, PP21-26.
Sk Samsul Alam (2008). Sequencing the concepts of ratio (algebraic treatment), Vigyan Shikshak, 53(1&2), 19-22.
Sk Samsul Alam (2008). Swabhabik sankhyar saraler dharanagulir dharabahikikaran ( Sequencing the concepts of simplification of whole numbers), Annual Bulletin, published in the occasion of : Nineteenth Annual Conference of CPSM.
Sk Samsul Alam (2008). Identification and Sequencing of the Elementary Concepts of Cube and Cube Roots, Indian Journal of Mathematics Teaching, 34(1&2), P39-47.
Sk Samsul Alam (2008). Samay o duratwar dharanagulir dharabahikikaran, Ganit Parikrama, Dwabingswati Barsha, 1&2, PP7-13.
Sk Samsul Alam (2009). Identifying and Sequencing of the Elementary Minor Concepts of the Highest Common Factor (H.C.F.) and the Lowest Common Multiple (L.C.M.) of Numbers, Journal of the Korea Society of Mathematical Education Series D: Research in Mathematics Education, 13(1), 49-61
Sk Samsul Alam (2009). Identification and Sequencing of the Elementary Minor Concepts of Rational Number, Siksha Chintan, 3 , 55-66(March)
Sk Samsul Alam (2009). Sequencing the concepts of linear equation and its graphs, Parshad Barta, panytrishtam Barsha, March-April, PP 25-32, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2009). Identifying and Sequencing of the Elementary Concepts of Measurement of Length, Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 13(2), 123-139
Sk Samsul Alam (2009). Vijganitik rashimalar ga.sa.gu o la.sa.gu-r dharanagulir sanaktakaran abang dharabahikikaran (Identification and Sequencing the elementary concepts of H.C.F & L.C.M of algebraic expressions), Parshad Barta, panytrishtam Barsha, June, PP 10-20, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2009). Identification and sequencing of the mathematical concepts of class-III standard, Quest in Education, 33(3), PP15-23
Sk., Samsul Alam (2009). Identifying and Sequencing of the Elementary Concepts of Measurement of Capacity, Journal of Centre for Pedagogical Studies in Mathematics, Nineteenth Issue, PP25-30.
Sk Samsul Alam (2009). Labh, Khati-o-Batar dharanagulir dharabahikikaran ( Sequencing the concepts of Profit , Loss and Discount), Annual Bulletin, Published in the occasion of : Nineteenth Annual Conference of CPSM.
Sk. Samsul Alam & Samanta, Prof S.K.(2009), Identifying and Sequencing of the Elementary Concepts of Fraction accepted in the 16th Mathematics Conference, BUET, Dhaka, Bangladesh, 17-19 December 2009 for oral presentation.
Sk Samsul Alam (2009). Identification and Sequencing of the Elementary Concepts of Measurement of Temperature, Indian Journal of Mathematics Teaching, 35(1&2), P8-15.
Sk Samsul Alam (2009). Hisab Rakshaner dharanagulir dharabahikikaran(Sequencing the Concepts of Ac- counts/Accounting, Ganit Parikrama, Trayobingswatitam Barsha, 1&2, PP10-14.
West Bengal Board of Primary Education (WBBPE) (1999). Naba Ganit Mukul (Pratham Bhag) December. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2001). Naba Ganit Mukul (Dwitiya Bhag) January. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2001). Naba Ganit Mukul (Chaturtha Bhag)January. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2002). Naba Ganit Mukul (Tritiya Bhag). Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2002). Naba Ganit Mukul (Pancham Bhag) January. Kolkata, India: WBBPE.
West Bengal Board of Secondary Education (WBBSE) (1998). Integrated Ganit (Class 9 & 10) Vol. 1. Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2001). Mathematics for Class 8, Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2004). Mathematics for Class 6, May. Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2005). Mathematics for Class 7, January. Kolkata, India: WBBSE.
This paper is written based on a presentation made in the National Seminar held at Centre for Mathematics Education, Visva-Bharati on February 13-15, 2010
Chilana, R (1984). Teaching Elementary School Mathematics, The Primary Teacher, 9(4), P-3, New Delhi, India: NCERT.
Malhotra,, O.P. & Gupta, S.K. (2000). Mathematics Today (Revised Edition), Book-3 (for class-3), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-1 (for class-1), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-2 (for class-2), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
Malhotra,, O.P. & Gupta, S.K. (2002). Mathematics Today (Revised Edition), Book-4 (for class-4), S. Chand & Company Ltd., Ram Nagar, New Delhi-110055.
National Council of Educational Research and Training (NCERT) (1996). Let’s Learn Mathematics (Book One), February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (1997). Let’s Learn Mathematics (Book Three), January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (1998). Let’s Learn Mathematics (Book Four), January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2000). Mathematics (with supplement) : A text book for Class-X, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2002). Mathematics: A text book for Class 9, February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2002). Mathematics: A text book for Class 6, February, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2003). Let’s Learn Mathematics, Book Two, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2003). Let’s Learn Mathematics, Book Five, December, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2004). Mathematics (Part 1): A text book for Class 7, January, New Delhi, India: NCERT.
National Council of Educational Research and Training (NCERT) (2004). Mathematics: A text book for Class 8, January, New Delhi, India: NCERT.
Piaget J. (1973). To Understand is to Invent, Viking, New York.
Pushpanadham. K. (1998). An investigation into the Pupils’ Understanding of Basic Arithmetic Concepts, Quest in Education, 22(2), P-38.
Schiralli, M. and Sinclair, N. (2003), A Constructive Response to where Mathematics Comes From, Education Studies in Mathematics 52: 79-91
Sk Samsul Alam (2003). Sequencing the concepts of subtraction of whole numbers, Journal of Centre for Pedagogical Studies in Mathematics, Thirteenth Issue, PP5 - 13.
Sk Samsul Alam (2003). Sequencing the concepts of addition of whole numbers, Indian Journal of Mathematics Teaching, 29(1&2), PP13 - 23.
Sk Samsul Alam (2005). Sequencing the concepts of multiplication of whole numbers, Journal of Centre for Pedagogical Studies in Mathematics, Joint Issue, 14& 15, PP16 - 22.
Sk Samsul Alam (2005). Sequencing the concepts of division of whole numbers, Indian Journal of Mathematics Teaching, 31(1&2), PP26 - 37.
Sk Samsul Alam (2006). Sequencing of the integral exponent of rational number, Journal of Centre for Pedagogical Studies in Mathematics, Sixteenth Issue, PP15 - 21.
Sk Samsul Alam (2006). Identification and Sequencing of the Mathematical concepts of class-I standard, Quest in Education, 30(3), PP20 - 24.
Sk Samsul Alam (2006). Sequencing the concepts of the operations on algebraic expression, Indian Journal of Mathematics Teaching, 32(1&2), PP. 60-67.
Sk Samsul Alam (2006). Karanir dharanagulir dharabahikikaran, Ganit Parikrama, Bingswati Barsha, 1&2, PP11-19.
Sk Samsul Alam (2007). Sequencing the concepts of International numerals sand Roman numerals, Journal of Centre for Pedagogical Studies in Mathematics, Seventeenth Issue, PP. 17-21.
Sk Samsul Alam (2007). Sequencing the concepts of factorization of algebraic expression, Vigyan Shikshak, 51(1&2).
Sk Samsul Alam (2007). Sequencing the concepts of rational expression, Indian Journal of Mathematics Teaching, 33(1&2), PP26-31.
Sk Samsul Alam (2007). Asannamaner dharanagulir dharabahikikaran, Ganit Parikrama, Ekbingswati Barsha, 1&2, PP4-8.
Sk Samsul Alam (2008). Sequencing the concepts of decimal, Parshad Barta, Chautrishtam Barsha, January ’08, PP 22-32, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2008). Identification and sequencing of the mathematical concepts of class-II standard, Quest in Education, 32(3), PP23-30.
Sk Samsul Alam (2008). Sequencing the concepts of Quadratic Equation, Journal of Centre for Pedagogical Studies in Mathematics, Eighteenth Issue, PP21-26.
Sk Samsul Alam (2008). Sequencing the concepts of ratio (algebraic treatment), Vigyan Shikshak, 53(1&2), 19-22.
Sk Samsul Alam (2008). Swabhabik sankhyar saraler dharanagulir dharabahikikaran ( Sequencing the concepts of simplification of whole numbers), Annual Bulletin, published in the occasion of : Nineteenth Annual Conference of CPSM.
Sk Samsul Alam (2008). Identification and Sequencing of the Elementary Concepts of Cube and Cube Roots, Indian Journal of Mathematics Teaching, 34(1&2), P39-47.
Sk Samsul Alam (2008). Samay o duratwar dharanagulir dharabahikikaran, Ganit Parikrama, Dwabingswati Barsha, 1&2, PP7-13.
Sk Samsul Alam (2009). Identifying and Sequencing of the Elementary Minor Concepts of the Highest Common Factor (H.C.F.) and the Lowest Common Multiple (L.C.M.) of Numbers, Journal of the Korea Society of Mathematical Education Series D: Research in Mathematics Education, 13(1), 49-61
Sk Samsul Alam (2009). Identification and Sequencing of the Elementary Minor Concepts of Rational Number, Siksha Chintan, 3 , 55-66(March)
Sk Samsul Alam (2009). Sequencing the concepts of linear equation and its graphs, Parshad Barta, panytrishtam Barsha, March-April, PP 25-32, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2009). Identifying and Sequencing of the Elementary Concepts of Measurement of Length, Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 13(2), 123-139
Sk Samsul Alam (2009). Vijganitik rashimalar ga.sa.gu o la.sa.gu-r dharanagulir sanaktakaran abang dharabahikikaran (Identification and Sequencing the elementary concepts of H.C.F & L.C.M of algebraic expressions), Parshad Barta, panytrishtam Barsha, June, PP 10-20, Paschim Banga Madhya Shiksha Parshad.
Sk Samsul Alam (2009). Identification and sequencing of the mathematical concepts of class-III standard, Quest in Education, 33(3), PP15-23
Sk., Samsul Alam (2009). Identifying and Sequencing of the Elementary Concepts of Measurement of Capacity, Journal of Centre for Pedagogical Studies in Mathematics, Nineteenth Issue, PP25-30.
Sk Samsul Alam (2009). Labh, Khati-o-Batar dharanagulir dharabahikikaran ( Sequencing the concepts of Profit , Loss and Discount), Annual Bulletin, Published in the occasion of : Nineteenth Annual Conference of CPSM.
Sk. Samsul Alam & Samanta, Prof S.K.(2009), Identifying and Sequencing of the Elementary Concepts of Fraction accepted in the 16th Mathematics Conference, BUET, Dhaka, Bangladesh, 17-19 December 2009 for oral presentation.
Sk Samsul Alam (2009). Identification and Sequencing of the Elementary Concepts of Measurement of Temperature, Indian Journal of Mathematics Teaching, 35(1&2), P8-15.
Sk Samsul Alam (2009). Hisab Rakshaner dharanagulir dharabahikikaran(Sequencing the Concepts of Ac- counts/Accounting, Ganit Parikrama, Trayobingswatitam Barsha, 1&2, PP10-14.
West Bengal Board of Primary Education (WBBPE) (1999). Naba Ganit Mukul (Pratham Bhag) December. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2001). Naba Ganit Mukul (Dwitiya Bhag) January. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2001). Naba Ganit Mukul (Chaturtha Bhag)January. Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2002). Naba Ganit Mukul (Tritiya Bhag). Kolkata, India: WBBPE.
West Bengal Board of Primary Education (WBBPE) (2002). Naba Ganit Mukul (Pancham Bhag) January. Kolkata, India: WBBPE.
West Bengal Board of Secondary Education (WBBSE) (1998). Integrated Ganit (Class 9 & 10) Vol. 1. Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2001). Mathematics for Class 8, Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2004). Mathematics for Class 6, May. Kolkata, India: WBBSE.
West Bengal Board of Secondary Education (WBBSE) (2005). Mathematics for Class 7, January. Kolkata, India: WBBSE.
This paper is written based on a presentation made in the National Seminar held at Centre for Mathematics Education, Visva-Bharati on February 13-15, 2010
How to Cite
Dr.Sk.Samsul Alam. (2015). Identifying and Sequencing of the Elementary Concepts of Proportion (Algebraic Treatment) Through Micro Analysis Technique. International Journal of Current Research in Science and Technology, 1(1), 33-44. Retrieved from https://crst.gfer.org/index.php/crst/article/view/5
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