A new Elementary Mathematics Curriculum: Practice, Learning and Assessment Some Classroom Episodes
The aim of this paper is to present the new and inn ovative Mathematics Curriculum for elementary levels that is being implemented in the Portuguese basic education system (students from 1 st to 9 grade) through an overview of an ongoing study of implementation/experimentation of this curriculum. A specific mechanism was implemented in the field to provide scientific and pedagogical support to the development of the new elementary mathematics curriculum (NPMEB) implement ation at all grade levels and all over the country. In particular, the NPMEB is being experimented by a set of teachers that teach in their own classes and that have been train ed a d accompanied along the experience by the different authors of the program. We will fo cus on some classroom practices, sharing innovative and creative ideas of teachers and stude n s, grounded on some of the tasks used by the teachers. The preliminary results suggest th at some improvements are already visible, namely regarding students' attitudes and mathematic al competences and teachers' practice. Introduction In the current Portuguese education system there is a new and innovative elementary mathematics curriculum (students from 1 st to 9 grade) the NPMEB (ME, 2007) that includes a series of changes of the government's re sponsibility to improve the conditions of the teaching and learning of that discipline. To th is have contributed the discontent with the results obtained by students in national external e.g. standardized tests, examinations) and international assessments (e.g. Program for Interna tional Student Assessment PISA) This curriculum was designed to gather some disperse cur ricular documents and substitute the current syllabus/curriculum/program, published in t he early 90s, but mainly to provide the sustained development of students' mathematical lea rning focused on the more recent recommendations of mathematics teaching and learnin g. A specific mechanism was implemented in the field t o provide scientific and pedagogical support to the development of the NPMEB implementat ion through all the grade levels and all over the country. This approach was not general ized but applied to a sample of classrooms/teachers. In particular, the NPMEB is be ng xperimented since 2008 by a set of teachers that teach in their own classes and whom h ave been trained and accompanied along the experience by the different authors of the prog ram. At the same time the Ministry of Education named a team of mathematics educators for an evaluation study of the process of implementation/experimentation of the NPMEM for thr ee years. The study was designed in three phases with the following purpose: to describ e, analyze and interpret teaching practices and assessment developed by teachers of the experim entation and/or teachers to teach in the process of generalization; to describe, analyze and interpret the involvement and participation of students in developing their learn ing in the context of the classroom; and to evaluate such practices and other curricular materi als applied. It was expected to have three multiple case studies (one for each cycle of basic education) an evaluative global summary and some recommendations. We propose to present an overview of some of the ta sks used by the teachers and the work of the students in accordance with NPMEB. as well a s the strategies used by the teachers. Data has suggested that some improvements are alrea dy visible, namely regarding students' attitudes and competences and teachers' practice. B efore presenting the method of evaluation of the study and some classroom episodes we began to identify the main ideas of the NPMEB. Main ideas of the NPMEB The NPMEB is no more than a readjustment of the exi sting program, with nearly twenty years, for grades 1 4 (1 st cycle of basic education) 5 6 (2 nd cycle of basic education) and 79 (3 cycle of basic education) (ME, 1990, 1991) whic h points to significant changes on mathematics teaching and learning, and to professio nal practices of teachers. In our opinion, the most innovative aspect of the NPMEB it was to r eplace the three existing programs by a single one that involves all grades from 1 to 9 wit h the same structure and the same mathematical themes. On the other hand transversal skills are addressed in the same way that mathematical topics, i.e. to which were sugges ted methodological guidelines, resources and examples of tasks. The aim of the new curriculum (ME, 2007) is to prom ote, in the students, the acquisition of information, knowledge and experience in mathematic s. On the other hand intends to develop the capacity of integration and mobilizatio n n different contexts and also indicate the development of positive attitudes towards mathe matics and the ability to appreciate this science of all students. Thus three indissociable b asic aspects are pointed out for mathematics education the acquisition of knowledg e, ability to use it appropriately and develop general relationship with the discipline. A t a subsequent stage of the program is organized in each cycle, around four major mathemat ical themes (Numbers and Operations, Geometry, Algebra and Organization and Data Analysi s) and three transversal fundamental capacities (Problem Solving, Reasoning and Communic ation) The NPMEB also presents several general methodologi cal uidelines, with emphasis on the need for diversification of tasks and giving partic ular attention to its nature, mainly to the challenge they promote, the role of situations in c o text, the importance of mathematical representations and the connections in mathematics and with extra mathematical aspects, the educational value of group work and moments of coll e tive discussion in the classroom, the importance of appropriate use of technology and oth er materials. It is an opportunity to: value certain features of mathematics that were for gotten or worked in a decontextualized way (e.g. mental computation, number sense, demonst ration, visualization, geometric transformations, patterns, algebra, statistics) in troduce some topics earlier (e.g. rational numbers, algebra) value mathematical processes (pr oblem solving, reasoning and communication) and value the mathematical tasks an d the roles of the teachers and students. The program outlines a set of general principles fo r the evaluation and especially emphasizes the importance of curriculum management h ld at the school level. Such program involves a process of curriculum change and demand for an exploratory teachinglearning with a new kind of classroom culture, wher e students must be much more active and be part of the construction of new knowledge, w here teacher must offer appropriate tasks within a challenging element. The tasks have a crucial importance in this change. It is the teacher who can start by giving a task that use s students' knowledge, while allowing the development of new concepts or processes so that th ey effectively engage in work and interpret correctly the task proposed. This work ca n be done in different ways, discussing and arguing ideas, orchestrated by the teacher, in order to avoid repetition, and highlight what is mathematically essential. In this perspecti v the traditional classroom is replaced by discovery and the development of higher order capab ilities such as testing, conjecturing, reasoning and proof, can be shared by students and te chers. To face these new challenges it is asked for a change of attitude towards mathemati cs nd its teaching, for proper teacher training programs, appropriate educational material s, as well new organizations in schools. NPMEB: The Evaluation Study The Ministry of Education through the Department of Curriculum Development and Innovation (DGIDC) requested under the Process of E xperimentation of the NMPEB a evaluation study, that it's ultimate purpose is to pr duce a set of evaluative synthesis and recommendations that could contribute to regulate a nd/or enhance the development of NPMEB. The DGIDC devised a plan to implement the ne w program in basic schools. This plan provided five actions such as: a) experimentat ion, during 2008/2009, the NPMEB in 40 pilot classes of three cycles of basic education; b the beginning of widespread NPMEB in the academic year 2009/2010; c) the production and distribution of curriculum materials of different nature (e.g. thematic booklets, assignmen ts for use in classrooms; lesson plans) d) a support structure for the beginning of widespread NPMEB in 2009/2010 (e.g. new program coordinators in each group; set of accompan ying teachers) and e) teachers' training. In the training, all teachers experimente rs participated in training throughout the school year (50 hours classroom and 50 hours of aut nomous work) which, in essence, was of the responsibility of NPMEB' authors. Yet develo ped a monitoring process (e.g. visits to classrooms and meetings with teachers experimenters through a coordinator group for each cycle that met on average once a month and all grou ps three times per year. All teachers had reductions in their school hours and shared their c lasses with a pedagogical pair. The process of experimentation began in forty pilot classes equ ally distributed by the 3, 5 and 7th grades. The First Phase included the design of the conceptual framework of the process of the NPMEB' experimentation. So it was taken into ac count: 1) the NPMEB framework; 2) the design of the implementation plan; 3) the struc ture of support for plan implementation; 4) the plan to support the process of experimentati on; 5) the management system of the process; and 6) the teachers experimenters. The dat a was obtained through: interviews to all the 40 teachers experimenters (EP) and 42 other s intervenient (from coordination group, consultative council, authors program, and professi onal and scientific associations, mathematicians and mathematics educators, teachers of the three c