A continuum to characterise and support teacher interpretation of an innovative curriculum

A continuum for describing the degree to which teachers interpret the various features of a curriculum is presented. The continuum has been developed based upon the observation of classroom practices and discussions with a group of teachers who are using an innovative junior secondary mathematics curriculum. It is anticipated that the ongoing use of the continuum will lead to its improvement as well as the refinement of the curriculum, more focussed support for the teachers,improved student learning, and the building of explanatory theory regarding mathematics teaching and learning.

Recommendations for a mathematical curriculum to be used in conjunction with an oral deaf education program

Students who are deaf or hard of hearing have typically had difficulty in mathematics; however, this problem often is overlooked because of difficulties in language and reading abilities. This study aims to identify the most appropriate mathematics curriculum for deaf or hard of hearing students in an oral deaf education program.

Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Financial Education Through Mathematics and IT Curricula: Pocket Money Management

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

NAPLAN, a high priority or . . . ? Statements about its purpose in Queensland schools

This paper reports on statements from Professional Development participants who were asked to comment on NAPLAN. The participants were involved in a project designed by the YuMi Deadly Centre (YDC) for implementation into 25 Queensland School to enhance the teaching and learning of mathematics to Aboriginal and Torres Strait Islander students and low SES students. Using an action research framework and a survey questionnaire, the preliminary data obtained from participating principals is mixed, with statements indicating that NAPLAN is a high priority for some schools while others indicated that it does not “tell” the whole story of student learning.

Promoting student understanding through complex learning

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.

Grade A Taipei junior high school principals’ self-reported leadership practices

The principal’s leadership and curriculum development are considered the core elements for creating a high performing junior high school. In Taiwan, mathematics curriculum reform has been an ongoing topic since 1994. The pedagogy, classroom interactions, and the underlying philosophy of mathematics education have varied with different versions of guidelines. These changes inevitably increase the requirement for principals’ leadership in order to effectively implement the curriculum reform. Principals’ leadership is essential to the success of the implementation in their school. This study aimed to explore and identify the leadership of junior high school principals whose schools had been judged by the Taipei City Government as Grade A junior high schools. Principals’ implementations of the reformed mathematics curriculum were used as examples to generate insights of their leadership. This study drew upon a multiple-case study approach. Data were collected from interviews, observations, and documentations. Bass and Avolio’s (1997) full range leadership theory provided a structure for gaining insight into these principals’ leadership practices. Five Grade A Taipei junior high school principals participated and shared their leadership concepts and experiences. Findings revealed that the leadership preferences of the five principles varied considerably. Management by exception-active, contingent reward, individualised consideration, and idealised influence were Grade A Taipei junior high school principals’ preferred leadership practices. In addition, principals’ leadership strategies associated with these practices were identified. These principals had adopted a range of leadership strategies according to the staff and school needs. Results of this study have implications for both Taiwanese principals and education departments. Principals can enhance their leadership by gaining more understanding about the Grade A principals’ leadership practices and strategies. Taiwanese education departments can improve school leadership training programs by focusing on these practices and strategies, which may also lead to more effective strategies for implementing national curriculum reform.

Complex learning through cognitively demanding tasks

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of children’s learning potential, as increasingly complex learners capable of dealing with cognitively demanding tasks.

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.

ORIGO Stepping Stones Grade K Student Journal

A mathematics curriculum for the Common Core Curriculum at the Kindergarten level for the USA