Abstract
Today’s widespread concern with mathematical literacy indicates the educators’ commitment to the old principle, formulated more than three decades ago by Hans Freudenthal: “The child should be able to use in society what [he or she] has learned at school.” As obvious and uncontestable as this maxim seems to be, the question of how the term mathematical literacy should be interpreted and implemented has been an object of debates and disagreements. One position on this issue has been presented by Paul Goldenberg in the preceding chapter. With Paul’s critical statement serving as a point of departure, the authors of this chapter tackle such questions as What do we have in mind while talking about mathematical literacy? Should we give in to the utilitarian approach to school mathematics that seems to transpire from this latter term, whatever its interpretation? And even if we agree that the students’ ability to broadly apply mathematics should be fostered, will we ever be able to overcome the inherent situatedness of learning? How? Coming from a diverse groups of writers—two researchers in mathematics education, a psychologist, a mathematician, and a policy maker—the five attempts at answering these questions may sounds too diverse to end up in agreement. Still, they certainly make for an interesting, important, and ultimately useful conversation.
With contributions by
Abraham Arcavi, Weizmann Institute of Science, Rechovot, Israel
Ron Livné, Mathematics Institute, The Hebrew University of Jerusalem, Jerusalem, Israel
Iddo Gal, Ph.D., Department of Human Services, The University of Haifa, Haifa, Israel
Hannah Perl, Israel Ministry of Education, Jerusalem, Israel
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Notes
- 1.
Common Core State Standards Initiative: see http://www.corestandards.org/, retrieved August 2, 2012.
- 2.
Program for International Student Assessment: see http://www.oecd.org/pisa/, retrieved August 2, 2012.
- 3.
Scholastic Aptitude test: see http://sat.collegeboard.org/home, retrieved August 2, 2012.
- 4.
Advanced Placement: see http://apcentral.collegeboard.com/apc/Controller.jpf, retrieved August 2, 2012.
- 5.
I was unable to get this and similar statistics from an official source, and had to compute them by dividing the number of people taking the exam (given by the administrating authority) in a given year by a official estimate of the age group (the Bureau of Census of the country or the CIA tables; the country entry in Wikipedia is a good place to start). These figures should be viewed as approximations.
- 6.
For Achieve’s agenda of “college and career readiness” see http://www.achieve.org/.
- 7.
Organisation for Economic Co-operation and Development: see http://www.oecd.org/, retrieved August 2, 2012.
- 8.
This is evidenced by numerous publications on the drop in enrollment to mathematics-related university subjects (e.g. Garfunkel and Young 1998; Gilbert 2006; OECD 2006) and by the frequent calls for research projects that examine ways to reverse this trend (see e.g. TISME initiative in UK, http://tisme-scienceandmaths.org/). The decline in young people’s interest in mathematics and science is generally considered these days as one of the most serious educational problems, to be studied by educational researchers and dealt with by educators and policy makers.
- 9.
This basic tenet, that builds on ideas of the philosopher Ludwig Wittgenstein and the psychologist Lev Vygotsky, defines the approach to the study of thinking and learning known as communicational, or commognitive (this last term, the portmanteau of the words communication and cognition, signals that the two ingredients are members of the same category). For justification and elaboration of the idea, as well as for a survey of its implications for the theory and practice of teaching and learning mathematics see Sfard (2008).
- 10.
The PISA 2012 Definition of Mathematical Literacy: “Mathematical literacy is an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognize the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens.” (PISA 2012 Mathematics Framework, Draft, November 30, 2010 http://www.oecd.org/pisa/pisaproducts/46961598.pdf).
- 11.
Such tracking has been practiced in a number of countries, with England (the special program is known as Functional Mathematics; see QCA 2005) and South Africa (see Venkatakrishnan and Graven 2006) among them. A similar tendency exists in Israel, where there is a plan to allow students with the history of low achievement to “compromise” on mathematical literacy (see, for instance, the newspaper publication in Hebrew, http://www.nrg.co.il/online/1/ART2/333/661.html, retrieved on 21.07.12).
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Sfard, A. (2014). Reflections on Mathematical Literacy. In: Fried, M., Dreyfus, T. (eds) Mathematics & Mathematics Education: Searching for Common Ground. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7473-5_10
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