Lesson Study Alliance is dedicated to enriching the professional lives of teachers and the academic lives of students by supporting the effective use of Lesson Study, especially in mathematics.
Calculation Nation® uses the power of the Web to let students challenge opponents from anywhere in the world. At the same time, students are able to challenge themselves by investigating significant mathematical content and practicing fundamental skills. The element of competition adds an extra layer of excitement.
“The games on Calculation Nation® provide an entertaining environment where students can explore rich mathematics,” said Jim Rubillo, Executive Director of the National Council of Teachers of Mathematics (NCTM). “Through these games, students are exposed to the same mathematical topics that they see in class as well as those that are recommended in Curriculum Focal Points.”
Calculation Nation® is part of the NCTM Illuminations project, which offers Standards-based resources that improve the teaching and learning of mathematics for all students. Its materials illuminate the vision for school mathematics set forth in NCTM’s Principles and Standards for School Mathematics and Curriculum Focal Points.
Illuminations is also part of Thinkfinity.org, a comprehensive educational website funded by the Verizon Foundation to provide free educational resources to parents, teachers, and students. Thinkfinity.org is the cornerstone of Verizon Foundation’s literacy, education and technology initiatives. The goal of Thinkfinity.org is to improve student achievement in traditional classroom settings and beyond by providing high-quality content and extensive professional development training.
The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students.
T. Nachlieli, Y. Mor, E. Gil, and Y. Kashtan. Eleventh Congress of the European Society for Research in Mathematics Education, 22, Utrecht, Freudenthal Group; Freudenthal Institute; ERME, (2019)
G. Davis, and M. Mcgowen. proceedings of the Annual Meeting of the 26th Annual Meeting of the International Group for the Psychology of Mathematics Education (PME), 2, page 273-280. Norwich, UK, University of Norwich, (July 2002)
A. Waraich. ITiCSE '04: Proceedings of the 9th annual SIGCSE conference on Innovation and technology in computer science education, page 97-101. New York, NY, USA, ACM, (2004)
H. Freudenthal. Educational Studies in Mathematics, 1 (1/2):
3-8(May 1968)Systematization is a great virtue of mathematics, and if possible, the student has to learn this virtue, too. But then I mean the activity of systematizing, not its result. Its result is a system, a beautiful closed system, closed, with no entrance and no exit. In its highest perfection it can even be handled by a machine. But for what can be performed by machines, we need no humans. What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics..
P. Ernest. Why Learn Maths, London University Institute of Education, London, 1. To reproduce mathematical skill and knowledge based capability
The typical traditional reproductive mathematics curriculum has focused exclusively on this first aim, comprising a narrow reading of mathematical capability. At the highest level, not always realised, the learner learns to answer questions posed by the teacher or text. As is argued elsewhere (Ernest 1991) this serves not only to reproduce mathematical knowledge and skills in the learner, but to reproduce the social order and social injustice as well.
2. To develop creative capabilities in mathematics
The progressive mathematics teaching movement has added a second aim, to allow the learner to be creative and express herself in mathematics, via problem solving, investigational work, using a variety of representations, and so on. This allows the learner to pose mathematical questions, puzzles and problems, as well as to solve them. This notion adds the idea of creative personal development and the skills of mathematical questioning as a goal of schooling, but remains trapped in an individualistic ideology that fails to acknowledge the social and societal contexts of schooling, and thus tacitly endorses the social status quo.
3. To develop empowering mathematical capabilities and a critical appreciation of the social applications and uses of mathematics
Critical mathematics education adds in a third aim, the empowerment of the learner through the development of critical mathematical literacy capabilities and the critical appreciation of the mathematics embedded in social and political contexts. Thus the empowered learner will not only be able to pose and solve mathematical questions, but also be able to address important questions relating to the broad range of social uses (and abuses) of mathematics. This is a radical perspective and set of aims concerned with both the political and social empowerment of the learner and with the promotion of social justice, and which is realised in mainstream school education almost nowhere. However, the focus in the appreciation element developed in this perspective is on the external social contexts of mathematics. Admittedly these may include the history of mathematics and its past and present cultural contexts, but these do not represent any full treatment of mathematical appreciation.
4. To develop an inner appreciation of mathematics: its big ideas and nature
This fourth aim adds in further dimension of mathematical appreciation, namely the inner appreciation of mathematics, including the big ideas and nature of mathematics. The appreciation of mathematics as making a unique contribution to human culture with special concepts and a powerful aesthetic of its own, is an aim for school mathematics often neglected by mathematicians and users of mathematics alike. It is common for persons like these to emphasise capability at the expense of appreciation, and external applications at the expense of its inner nature and values. One mistake that may be made in this connection is the assumption that an inner appreciation of mathematics cannot be developed without capability. Thus, according to this assumption, the student cannot appreciate infinity, proof, catastrophe theory and chaos, for example, unless they have developed capability in these high level mathematical topics, which is out of the question at school. The fourth aim questions this assumption and suggests that an inner appreciation of mathematics is not only possible but desirable to some degree for all students at school..(2000)
D. Ingalls, T. Kaehler, J. Maloney, S. Wallace, and A. Kay. OOPSLA '97: Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications, page 318-326. New York, NY, ACM Press, (1997)
M. Mariotti. Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, 1, page 180--195. Stellenbosch, South Africa, PME, University of Stellenbosch, (July 1998)
G. Goldin. Journal for Research in Mathematics Education. Monograph: Journal for Research in Mathematics Education. Monograph: Qualitative Research Methods in Mathematics Education, (1997)
F. Arzarello. the 24th Conference of the International Group for the Psychology of Mathematics Education (PME), 1, page 23--38. Hiroshima, Japan, (2000)