Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

The challenge of generic competences to science education

Since 2000 there has been pressure on education systems for develop in students a number of competences that are described as generic. This pressure stems from studies of the changing nature of work in the Knowledge Society that is now so dominant. The DeSeCo project identified a number of these competences, and listed them under the headings of communicative, analytical and personal. They include thinking, creativity, communication skills, knowing how to learn, working in teams, adapting to change, and problem solving. These competences pose a substantial challenge to the manner in which education as a whole, and science education in particular, has hitherto been generally conceived. It is now common to find their importance acknowledged in new formulation of the curriculum. The paper reviews a number of these curriculum documents and how they have tried to relate these competences to the teaching and learning of Science, a subject with its own very specific content for learning. It will be suggested that the challenge provides an opportunity for a reconstruction of the teaching and learning of science in schools that will increase its effectiveness for more students.

A comparison of Chinese and Australian early childhood mathematics

In the 21st century mathematics proficiency is synonymous with a numerate citizenry. In the past few decades young children’s ability to reason mathematically and develop mathematical proficiencies has been recognised. This paper explores the history of early childhood mathematics (ECME) that may explicate differences in Chinese and Australian contexts. Results of this review established that China and Australia are diametrically positioned in ECME. Influencing each countries philosophies and practices are their cultural beliefs. ECME in China and Australia must be culturally sustainable to achieve excellent outcomes for young children. Ongoing critique and review is necessary to ensure that ECME is meeting the needs of all teachers and children in their particular context. China and Australia with their rich contrasting philosophies can assist each other in their journeys to create exemplary ECME for the 21st century.

Mathematics learning in prep

Most teachers recognise the importance of mathematics teaching and learning in early years but there is not consensus on how and when this learning should occur. Young-Loveridge (cited in de Vries, Thomas, and Warren, 2010) suggests that quality early mathematical experiences are a key determinant to later achievement.

Alternatives to the World Bank’s strategies for education and development

Over the past several decades, policy has become increasingly global. In economics, for example, policy has followed the so-called Washington Consensus of privatization, liberalization, and deregulation. In education, global policy has included the proliferation of strategies including standardized testing, paraprofessional teachers, user fees, and privatization. There are many problems with these neoliberal policies. Foremost among them, is the havoc they wreak on the lives of so many children and adults. Poverty, inequality, and myriad associated problems have reached new heights in this neoliberal era. Moreover, these policies have been adopted uncritically and alternative policies have been ignored, which leads to our focus here.

Skill development and social inclusion via peer assisted learning in first-year higher education : an evaluation of student experiences across two law units

Because professions seek graduates who can 'collaborate, share skills and knowledge, and communicate' (Kruck and Reif, 2001, p 37), it is important that university graduates are not equipped solely with the content knowledge of their discipline, but also with prospective employment skills. Furthermore, when students 'interact more in positive ways with their teachers and peers, they gain more in terms of essential skills and competencies, such as critical thinking, problem~solving [and] effective communication' (NSSE, 2000, p 2)./n this way, peer assisted fellowing has the potential to enhance students' professional development, and provide the social inclusion and engagement necessary for effective learning. This session describes two peer assisted learning models embedded within first year QUT Faculty of Law units. Through a partnership between teaching staff, student mentors and mentees, the models aim to facilitate student socialisation whilst supplementing understanding of substantive law with the development of academic and work·related skills. Mentor and mentee perceptions, and program implications, are considered.

Education for social responsibility: Ethics and imagination for engaging students and teachers in educational reform

In this chapter we make assumptions about the primary role of education for the life of its beneficiaries and for society. Undoubtedly, formal education plays an important role in enhancing the likelihood for participation in future social life, including enjoyment and employment, by the student as well as the development of the well being of society in general. Similarly, education is often seen as a main means for intergenerational transmission of knowledge and culture. However, as Dewey (1916) argues, in liberal societies, education has the capacity of enhancing democratic participation in society that goes beyond passive participation by its members. One can argue that the achievement of the ideals of democracy demands a free and strong education system. In other words, while education can function as an instrument to integrate students into the present society, it also has the potential to become an instrument for its transformation by means of which citizens can develop an understanding of how their society functions and a sense of agency towards its transformation. Arguably, this is what Freire (1985) meant when he talked about the role of education to “read and write” the world. A stream of progressive educators (e.g., Apple (2004), Freire, (1985), Giroux (2001) and McLaren (2002)) taught us that the reading of the world that is capable of leading into writing the world is a critical reading; i.e., a reading that poses “Why” questions and imagines “What else can be” (Carr & Kemmis, 1987).

Grenada, Education and Revolution, 1979-83

Grenada’s New Jewel Movement, led by Maurice Bishop, was the first indigenous political grouping in the history of the English-speaking Caribbean to overthrow an existing government by armed force. Yet most of the four and a half years of the Revolution (1979-83) were characterized by considerable popular support for the new People’s Revolutionary Government before it came to it’s tragic, unexpected and shocking end in October 1983. Social, economic and political change seems possible in the 1970s and ‘80s. People in newly decolonizing countries were encouraged by the beginnings of the Non-Aligned Movement of Third World nations demanding new international economic order that would win them some economic justice after the ravages of colonialism. People also saw that some radical regimes, such as that led by Michael Manley in Jamaica and the Sandinistas in Nicaragua, were articulating and implementing basic rights that held the promise of countering the social and political oppression that they had endured throughout the centuries of colonial history. A majority of Grenadians committed themselves to fighting by the side of the People’s Revolutionary Government for such new goals. This chapter will analyse how the Grenada Revolution reconceptualised the education, planned new goals, and implemented bold new educational policies. It will discuss the extent to which the government and people were able to reshape education as a tool for national reconstruction and the raising of national consciousness.

The Cuban Revolution and Internationalism: Structuring Education and Health

The Capacity to Share is the first book to document how Cubans share their highly developed educational services with other low-income states, especially those in Africa, Latin America, and the Caribbean. A variety of international and Cuban authors break new ground in presenting this research. They investigate the experiences of people who have studied in Cuba on scholarships from the Cuban government, the implications for their home countries, and the work of Cuban teachers and administrators to support education in other countries. The authors discuss how the Cuban "solidarity" approach prioritizes global educational cooperation for mutual support, rather than imposing conditional aid. The book offers original and unusual insights into issues of culture, education, aid, development, and change as they relate to low-income states.

Cuba's Education System: A Foundation for "The Capacity to Share"

The Capacity to Share is the first book to document how Cubans share their highly developed educational services with other low-income states, especially those in Africa, Latin America, and the Caribbean. A variety of international and Cuban authors break new ground in presenting this research. They investigate the experiences of people who have studied in Cuba on scholarships from the Cuban government, the implications for their home countries, and the work of Cuban teachers and administrators to support education in other countries. The authors discuss how the Cuban "solidarity" approach prioritizes global educational cooperation for mutual support, rather than imposing conditional aid. The book offers original and unusual insights into issues of culture, education, aid, development, and change as they relate to low-income states.