Where is math 2.0? Alarming trends and hopeful frameworks circa 2010

General Summary

The proposed chapter addresses critical analysis of the presence of mathematics in online communities that include children and teens. The chapter sections are:

1. Descriptive analysis of the presence of mathematical ideas and artifacts in social communities on the web

a. Introduction and review of educational framework relevant to social internetb. Preliminary summary of existing trendsc. Representative examples illustrating the trends

2. A study of mathematical behavior on the web among young people, teachers and parentsa. Survey design and difficulties in data collection due to the situated nature of

behaviors and parents’ low level of awarenessb. Data analysis

3. Conclusions and implications: toward a framework for building math-rich online communities

Frameworks summary

Community learning is a complex phenomenon that can benefit from multi-disciplinary approach and synthesis of multiple frameworks. The following framework clusters are necessary to underpin the current study:

Communities of practice and legitimate peripheral participation (Lave & Wenger, 1991) with the shift from communities to distributed open networks and affinity spaces (Barton & Tusting, 2005)

Studies of trends in interactive media (Churches, 2009; Dede, Honan, & Peters, 2005; Moravec, John, 2009)

Serious gaming (Michael & Chen, 2005) Educational semiotics and studies of representations (Hoffmann, Lenhard, & Seeger,

2005), to analyze new forms and roles of referents, signs and social objects Frameworks based on meaning and significance (Csikszentmihalyi, 2008; Wesch,

2008), to focus on the ways internet effects and shapes human quest for meaning Psychology of mathematics education and learning theories, including metaphor

studies (Droujkova, 2004), developmental studies (Kozulin, Gindis, Ageyev, & Miller, 2003; Piaget, 1971), and enactivist models for the growth of mathematical understanding (Droujkova, Berenson, Slaten, & Tombes, 2005)

Preliminary trend analysis

The ongoing descriptive analysis, together with accumulating interview data, suggests several trends. The main trend is the lag of mathematics behind other subjects in class-centered web

2.0 communities for children, and an even larger lag in informal, recreational communities. Children’s mathematics remains very much confined to classes, homework, and standardized tests, or activities that closely imitate them. Most class-centered mathematical communities are not sustainable, in that they dissolve after the class ends, even if the artifacts stay available online. Many existing sustainable math-oriented communities are intellectually elitist and demographically exclusive.

Picture 1. Sharp drops in math-related web searches during school vacation times.

The data gathered for the study includes comparison of mathematical behavior on and off the web; comparison of behavior in math-related and other activities; and comparison of behavior among different demographics.

Math You Make: Toward a framework for mathematical culture shift

Math You Make is a framework where mathematical education is viewed within a cultural context, defining learning as taking on roles in communities and networks. Changes in mathematics education, then, are culture shifts that include many events at individual, family, local community and group, and global network levels. A framework encompassing these events can help bring about mathematics education changes, and, in particular, to orient individual web 2.0 educational projects to wider vision and goals.

Picture 2: Math You Make framework

Math You Make, a practical and conceptual framework, has roots in the theoretical frameworks discussed above. It identifies five directions for the culture shift toward widespread algebraic, statistical and geometric literacy, currently estimated at about five percent of the adult US population. These five directions are: mathematical authoring; community mathematics; humanistic mathematics; executable mathematics; and psychology of mathematics learning and education. The chapter will discuss the role of the social internet in support of each of these directions of the mathematical culture shift, providing a comprehensive review of current examples and future trends:

Tools and practices of user-generated content, as well as the internet participatory trends of co-production, crowdsourcing, and open educational resources can powerfully support mathematical authoring.

For community mathematics, free, well-designed communication platforms such as nings, blogs, wikis, microblogging, forums, aggregators, and distributed content mash-ups can support online and local math clubs and math circles, topical discussion and study communities, and networks growing around a variety of particular math endeavors: competitions, educational philosophies, comic strips, books, or curricula.

It is said that mathematics is not a spectator sport. The culture of setting up mathematical activities to require knowledge of relatively advanced formal math to make any sense is cited as one of barriers preventing the majority of population from appropriating mathematics as their own endeavor, or expressing any interest and joy in the field (Lockhart, 2008). Humanistic mathematics approach promotes activities that an audience can enjoy. On the web, this includes infusing mathematics into robust artistic and musical communities; creation and viral spread of appealing math-rich media; and developing newbie-friendly tools and communities supporting authoring of such media.

The idea that manipulating carefully prepared objects can support powerful mathematics is rather old, with examples including abacus (2500 BC) or Napier’s bones (1600s), and 20th century sets by Montessori, Cuisenaire, and Mortensen. Web 2.0 brings several crucial changes to this field of executable mathematics, including zero-cost distribution of virtual manipulatives; an invitation for everybody to create their own math-rich objects through programming or “construction set” mash-up environments; situating math objects in multi-user virtual worlds; and ease of sharing and continuing development in open educational resource communities.

Psychology of mathematics education incorporates theories of teaching and learning, studies and practices of meta-cognition, developmental awareness, and support of emotional well-being such as math anxiety reduction. Web 2.0 requires a shift toward more social views on the psychology of mathematics education and its role, within this framework, of supporting the other four dimensions.

Math 2.0 includes efforts of thousands of people, organizations and networks, from making professional math blogs a bit more accessible for beginners to helping a neighbor kid to learn to program; from creating and forwarding beautiful math videos to hosting free webinars; from running math clubs to building manipulative depositories. The goal of the Math You Make framework is to help educators, parents, researchers and social media specialists to analyze roles of their actions and projects, however small, in the global events of our times. If each of us is more aware of how our internet actions co-create larger culture shifts, we can be more coordinated and purposeful.

About the authorMaria Droujkova, PhDDirector, Natural Math, LLC309 Silvercliff TrailCary, NC 27513919-388-1721http://www.naturalmath.commaria@naturalmath.com

Maria Droujkova is a mathematics education researcher interested in early algebra, multiplicative reasoning and communities of practice. Maria has BS in Mathematics from Moscow State University (1994), MS in Applied Mathematics from Tulane University (1997) and PhD in Mathematics Education from North Carolina State University (2004). Since the early nineties, Maria has been organizing mathematical communities, teaching workshops and classes, consulting for universities and businesses, and presenting her research at the National and International conferences.

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