Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

An assessment of legal knowledge of preservice teachers completing accredited teacher education programs in South Florida

The purpose of the study was to assess the legal knowledge of preservice teachers completing their educational training at accredited South Florida universities. The population consisted of 372 preservice kindergarten through twelfth grade teachers completing their educational training in any area of public school education.^ The researcher selected areas of school law to assess based on nationwide studies of litigation involving teachers and school boards, the areas most pertinent to the teachers' daily activities and responsibilities. A forty-item instrument was developed and administered to preservice teachers at six South Florida public and private universities. The areas of school law surveyed were tort liability, teachers' rights as instructors and employees, and students' rights. The research questions asked if preservice teachers possess a fundamental knowledge of school law in any of the identified areas and if a significant difference of legal knowledge existed when comparing preservice teachers by university and comparing preservice elementary and preservice secondary teachers. The criteria for a fundamental knowledge of school law was established as scoring 80% or above on the total survey or any area of school law.^ Conclusions. (1) On the overall survey, the preservice teachers did not exhibit a fundamental knowledge of school law. The mean score was 64.2%, with 11.6% of the respondents scoring at or above the 80% level. (2) The preservice teachers did not possess a fundamental knowledge of school law in any of the three areas of school law, though the survey revealed a difference in the preservice teachers' knowledge in the specific areas. The scores were tort liability, 71.9%; teachers' rights, 65%; and students' rights, 52.3%. (3) A significant difference did not exist between elementary and secondary preservice teachers' knowledge of school law. (4) A significant difference did not exist among the preservice teachers' knowledge of school law when compared by university.^ The study suggested a need for increased instruction in these areas of school law to preservice teachers prior to the beginning of their teaching careers. ^

Teachers' perceptions of the usefulness of Individual Education Plans (IEP)

Since 1997 federal special education policy mandated that all classroom teachers take part in planning and implementation of Individualized Education Plans (IEP) for students with disabilities. This legislation has given teachers new responsibilities because it requires greater participation in the IEP process. The purpose of this study was to examine teachers' perceptions of the usefulness of Individualized Education Plans (IEP). ^ Eighty seven certified Miami-Dade County Public School teachers, 60 general education teachers and 27 special education teachers were surveyed using an updated version of Rheams' (1989) The Teacher Perceptions of the Usefulness of IEPs. Subjects completed a survey form containing a demographic cover page, 18 Likert-scale statements and 3 open ended questions. This study looked at differences in perceptions by teacher group affiliation (general and special), grade level taught (elementary and secondary), and years of experience (<=5 and >5 years). The dependent variables were teacher preparedness; feasibility of IEP implementation; relevancy of IP to classroom instruction; and legal, professional and personal accountability with regard to the IEP. ^ Results of the Multivariate Analysis of Variance (MANOVA) revealed that (a) special education teachers held a more positive perception of overall IEP usefulness than general education teachers, (b) special educators held more positive perceptions concerning issues of feasibility and preparedness, (c) elementary level teachers viewed the IEP more positively than secondary level teachers, specifically in the areas of preparedness and feasibility. ^ Findings of this study indicate that general and secondary educators have not embraced the legislation and incorporated it into their planning and instruction. These findings provide policymakers, institutions of higher education, and school administrators with insight as to how to better translate policy into classroom instructional practice. Consideration should be given to implementing (a) honest communication and shared decision making with regard to IEP directed curriculum and instruction, (b) updated pre and in-service IEP development and implementation training, and (c) opportunities for collaboration and increased plan time, especially on the secondary level. ^

An Investigation of Participants’ Perspectives About a Learning Assistant Program and Their Thinking about Becoming a Mathematics Teacher

A Learning Assistant program that recruits strong STEM undergraduates to become mathematics teachers was explored through a qualitative study. Three program participants were purposely selected and interviewed. The program reaffirmed one participant’s choice to become a teacher and clarified for one that it might be a career for him.

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

The impact of standards-based practices in mathematics on the achievement of low-performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

Propuesta de reestructuración del currículo del bloque matemático de la carrera de matemáticas y física de la Facultad de Filosofía de la Universidad de Cuenca

El presente trabajo consiste en una propuesta de reestructuración del currículodel bloque matemático Carrera de Matemáticas y Física de la Universidad de Cuenca, de manera específica la parte matemática del mismo. Tiene como objetivo ser un documento que oriente los futuros cambios que se impulsen, como consecuencia de la aplicación de las nuevas leyes que regulan el Sistema de Educación Superior. Consta de cuatro capítulos, en el primero se hace una revisión de todos los antecedentes que es necesario conocer para la elaboración de la propuesta, de manera especial, la Constitución de la República, la Ley Orgánica de Educación Superior y su reglamento y el Reglamento de Régimen Académico. La propuesta tiene que ver con una carrera que forma docentes de Educación General Básica y Bachillerato por lo que fue necesario revisar también los documentos correspondientes a estos niveles. En el segundo capítulo se revisa aspectos generales concernientes a la teoría curricular, así como aspectos específicos del currículo y educación matemática. El capítulo tres constituye la propuesta en sí, explica el proceso que se ha seguido para llegar a concretar la idea de un plan de estudios de la carrera. Se establece una relación entre resultados de aprendizaje de la carrera, contenidos a estudiarse en EGB y en el BGU, para luego plantear asignaturas con sus correspondientes números de créditos y carga horaria, obteniendo como resultado el diseño de una malla curricular que responda a las actuales necesidades. Finalmente el capítulo cuatro trata sobre conclusiones y recomendaciones.

O currículo de matemática do 1º ciclo doensino secundário de Cabo Verde na perspectiva de professores

Este estudo tem por objetivo compreender a perspetiva de professores sobre o currículo de Matemática do 1º ciclo do Ensino Secundário cabo-verdiano e conhecer necessidades de formação que identificam, para um melhor desempenho na sua catividade profissional. As questões de estudo são: 1) Como se reveem os professores de Matemática no currículo do 1º ciclo do Ensino Secundário, enquanto agentes que interpretam e implementam esse currículo? 2) Que potencialidades e dificuldades reconhecem nesse currículo? 3) Que áreas consideram haver necessidade de formação, para a melhoria da sua prática docente, nesse nível de ensino? O desenvolvimento do referencial teórico integra duas áreas temáticas como eixos centrais: o currículo, o professor e o professor de Matemática. Foi feita uma análise de normativos cabo-verdianos para a educação, entre os quais se destacam a Lei de Bases do Sistema Educativo, o Plano de estudos para o ensino secundário e o Programa de Matemática do 1o ciclo do Ensino Secundário. A metodologia adotada na investigação segue uma abordagem interpretativa e descritiva, suportada por um design de estudo de caso. São estudados três casos, relativos a professores de Matemática cabo-verdianos do 1º ciclo do Ensino Secundário. A recolha de dados recorre a urna entrevista semiestruturada a cada professor, à observação de três aulas por professor participante e à recolha documental. A análise de dados foi feita utilizando principalmente a técnica de análise de conteúdos. Os professores revêem-se como executores de um currículo uniforme, de cumprimento obrigatório, normativo, emanado centralmente e do qual procuram interpretar as intenções. A sua visão de currículo é centrada nos conteúdos do programa, um dos motivos para que o enquadramento ao nível dos meios institucionais e as competências esperadas ao nível do saber fazer e ao nível do saber ser nem sempre serem conhecidas e/ou cumpridas. Em Acão, revêem-se como figuras centrais do currículo. Todos se reveem com mais competência na implementação curricular à medida que vão adquirindo experiência profissional. Concordam com os temas do programa e um deles sugere a inclusão de um tema. Consideram que os conteúdos nem sempre estão bem organizados e mostram a necessidade de a metodologia do programa ser mais detalhada, evidenciando claramente os seus propósitos. Eventualmente, podem não concordar com a estrutura de currículo em espiral do programa. Os professores identificam mais formação com melhor desempenho. As necessidades de formação são: Metodologia do Ensino da Matemática, Resolução de Problemas, Avaliação e a Geometria ligada à utilização de materiais pedagógicos. O estudo parece indicar que os professores não desenvolvem práticas diferentes por não terem essa vivência e aponta os professores mais jovens como mais abertos à mudança. ABSTRACT: The aim of this study is to understand the perspective of the teacher in relation to the Mathematics curriculum of the 1st cycle of Secondary School of Cape Verde (grades 7-8) and to learn about his/her training needs to develop better skills and performance in their professional activity. The key questions in this study are: 1) how do Mathematics teachers, acting in the capacity of agents who interpret and implement the 1st cycle of Secondary School curriculum, see themselves in this curriculum? 2) What potentialities and difficulties can they recognize in the curriculum? 3) What areas do they consider in need of training to improve teaching capacity within such education grade? The theoretical framework of this investigation integrates two main areas: the curriculum and the teacher. An analysis of Cape-Verdian normative texts for education has been made, including the Lei de Bases do Sistema Educativo (Basis Law of the Educational System), the Study plan for secondary school and the Mathematics program of the 1st cycle of secondary school. ln terms of methodology, we opted for an interpretative approach to our investigation, namely the case study. We looked at three case studies concerning the Cape-Verdian mathematics teacher of the 1st cycle of secondary school. The data collection uses a semi­structured interview for each teacher, the observation of three classes per participating teacher and the documental collection. Content analysis is the main technique used for analyzing the data. Teachers see themselves as practitioners of a uniform curriculum with mandatory compliance and delineated guidelines set by the administration, and they follow their own understanding of its intended purpose. Their vision of the curriculum is focused on program contents, one of the reasons why the expected skills at the level of "how to do" and "how to be" are not always known and/or done. ln their professional setting they see themselves with professional skills growing in tandem with professional experience. They all agree with the program contents but one of them suggests one content to add. ln their opinion the program is not always well organized and they suggest the need for a more comprehensive and detailed methodology of program contents. ln addition, they might not agree with the spiral structure of the program curriculum. They also identified the need for more elaborate professional training including: A Methodology for Mathematics Education, solving problems, Evaluation and the Geometry related to the utilization of pedagogical materials. The study seems to indicate that teachers refrain from developing different practices because of lack of experience but also demonstrates that younger teachers are more open to change.

ESL teacher profiles of ICT integration in their classroom practices and assessment activities : a portrait viewed through the lens of some Quebec teachers’ social representations

Abstract : Information and communication technologies (ICTs, henceforth) have become ubiquitous in our society. The plethora of devices competing with the computer, from iPads to the Interactive whiteboard, just to name a few, has provided teachers and students alike with the ability to communicate and access information with unprecedented accessibility and speed. It is only logical that schools reflect these changes given that their purpose is to prepare students for the future. Surprisingly enough, research indicates that ICT integration into teaching activities is still marginal. Many elementary and secondary schoolteachers are not making effective use of ICTs in their teaching activities as well as in their assessment practices. The purpose of the current study is a) to describe Quebec ESL teachers’ profiles of using ICTs in their daily teaching activities; b) to describe teachers’ ICT integration and assessment practices; and c) to describe teachers’ social representations regarding the utility and relevance of ICT use in their daily teaching activities and assessment practices. In order to attain our objectives, we based our theoretical framework, principally, on the social representations (SR, henceforth) theory and we defined most related constructs which were deemed fundamental to the current thesis. We also collected data from 28 ESL elementary and secondary school teachers working in public and private sectors. The interview guide used to that end included a range of items to elicit teachers’ SR in terms of ICT daily use in teaching activities as well as in assessment practices. In addition, we carried out our data analyses from a textual statistics perspective, a particular mode of content analysis, in order to extract the indicators underlying teachers’ representations of the teachers. The findings suggest that although almost all participants use a wide range of ICT tools in their practices, ICT implementation is seemingly not exploited to its fullest potential and, correspondingly, is likely to produce limited effects on students’ learning. Moreover, none of the interviewees claim that they use ICTs in their assessment practices and they still hold to the traditional paper-based assessment (PBA, henceforth) approach of assessing students’ learning. Teachers’ common discourse reveals a gap between the positive standpoint with regards to ICT integration, on the one hand, and the actual uses of instructional technology, on the other. These results are useful for better understanding the way ESL teachers in Quebec currently view their use of ICTs, particularly for evaluation purposes. In fact, they provide a starting place for reconsidering the implementation of ICTs in elementary and secondary schools. They may also be useful to open up avenues for the development of a future research program in this regard.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Primary students' success on the structured number line

Number lines are part of our everyday life (e.g., thermometers, kitchen scales) and are frequently used in primary mathematics as instructional aids, in texts and for assessment purposes on mathematics tests. There are two major types of number lines; structured number lines, which are the focus of this paper, and empty number lines. Structured number lines represent mathematical information by the placement of marks on a horizontal or vertical line which has been marked into proportional segments (Figure 1). Empty number lines are blank lines which students can use for calculations (Figure 2) and are not discussed further here (see van den Heuvel-Panhuizen, 2008, on the role of empty number lines). In this article, we will focus on how students’ knowledge of the structured number line develops and how they become successful users of this mathematical tool.

Stepping stones : teacher lesson plans : year 1

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website