Introduction In 1976 Skemp published an important discussion paper setting out the differences between relational and instrumental understanding as they apply to the teaching and learning of mathematics. Skemp highlights two false loves, the first is understanding. Skemp defines understanding in two ways: 1) instrumental understanding and 2) relational understanding. The second false friend is the word mathematics which he describes as two different subjects being taught. I considered Skemp's article in four sections.1. False friends2. Instrumental and relational understanding3. The discrepancy4. Implications for Mathematics TeachingKey Terms: Outline; false friends; Instrumental understanding; relational understanding; mathematics.Setting the sceneIt is extremely difficult to define understanding. Skemp attempts to assimilate it into some form of appropriate or inappropriate pattern which depends on many variables such as language, environment, beliefs, tradition and culture. Could understanding be an abstract thing, a brain pattern or a rule? Skemp uses the term "faux amis" to mean that language can have different meanings to different people even if the original roots of the words are the same. He looks at French and English and identifies what he calls a “mismatch.” He uses analogies and understandings based on his own experience and that of others in his community of practice (Mellin-Olsen, 1981). This discrepancy, according to him, is the root of many difficulties in teaching mathematics, including the word mathematics itself. This assignment attempts to evaluate his arguments in relation to other literature and my own experience. A schema is a mental structure that we use to organize and simplify our knowledge of the world around us...... middle of paper.... ..). Understanding of proportion and ratio concepts among ninth grade students in Malaysia. International Journal of Mathematical Education in Science and Technology, Volume 31, Number 4, 1 July 2000, pp. 579-599(21) Skemp, R. (1976). 'Relational understanding and instrumental understanding', Mathematics Teaching 77, 20–26.Von Glasersfeld, E.: 1991, 'Introduction' to (E. Von Glasersfeld, Ed.) RadicalConstructivism in Mathematics Education, Kluwer, Dordrecht.Von Glasersfeld, E.: 1995, Radical Constructivism: A Way of Knowing and Learning. Falmer, London. White, P. (1991). Rules versus understanding. Australian Senior Mathematics Journal, 5(1), 9-10.Wood, T. (1995). 'From alternative epistemologies to educational practice; Rethinking what it means to teach and learn' in Steffe, L.P. & Gale, J. (eds) Constructioism in Education, Lawrence Erlbaum.