‘Why do we have to do this?’ Primary trainee teachers' views of a subject knowledge audit in mathematics

This paper examines theoretical and empirical evidence related to primary teachers' subject knowledge in mathematics and considers the relevance of an audit of higher‐level subject knowledge to the subject knowledge required for teaching primary mathematics. Questionnaires and interviews were carried out to determine the views of generalist primary trainee teachers. Their views suggest that an audit of higher‐level subject knowledge may be seen as relevant to the teaching of primary mathematics due to increased confidence levels. There is little evidence to suggest that the audit is supporting the trainee teachers in developing a connected view of mathematics that may be more indicative of an effective teacher.     

The Collaborative Programme Between CTS,ICMI and UNESCO

Previous research has highlighted challenges associated with embracing an inquiry approach to science teaching for primary teachers, often associating these challenges with insecurity linked to the lack of content knowledge. We argue that in order to understand the extent to which primary student teachers are able to embrace science teaching informed by scientific literacy for all, it is important to take into account various, sometimes competing, science teacher and primary teacher Discourses. The aim of this paper is to explore how such Discourses are constituted in the context of learning to teach during a 1-year university-based Post Graduate Certificate of Education course. The empirical data consist of semi-structured interviews with 11 student teachers. The analysis identifies 5 teacher Discourses and we argue that these can help us to better understand some of the tensions involved in becoming a primary teacher with a responsibility for teaching science: for example, in terms of the interplay between the student teachers' own educational biographies and institutionally sanctioned Discourses. One conclusion is that student teachers' willingness and ability to embrace a Discourse of science education, informed by the aim of scientific literacy for all, may be every bit as constrained by their experience of learning science through ‘traditional schooling’ as it is by their confidence with respect to their own subject knowledge. The 5 Discourses, with their complex interrelations, raise questions about which identity positions are available to students in the intersections of the Discourses and which identity positions teacher educators may seek to make available for their students.     

Assessment of mathematics and reading performance: An examination of the correspondence between direct assessment of student performance and teacher report

Teacher judgments have been identified as a primary source of information regarding student academic achievement. Research examining the accuracy of teachers' judgments in assessing students' academic abilities has shown relatively high accuracy. However, previous studies have relied primarily on norm‐referenced measures to obtain estimates of students' achievement in reading and mathematics. Recent developments in the assessment of students' academic skills, such as Curriculum‐Based Measurement (CBM), provide a direct estimate of students' skill levels in basic areas such as reading and mathematics. The purpose of the present study was to examine the extent to which teachers' perceptions of students' reading and mathematics skills corresponded to direct estimates of students' reading and mathematics skills. Two second‐grade teachers estimated the reading and mathematics skills of 33 second‐grade students. Results of this study indicated that teachers were not accurate in assessing their students' mathematics functioning. Teachers were more accurate in assessing the occurrence of Mastery mathematics levels in basic addition, but were very inaccurate in assessing the occurrence of Mastery, Instructional, or Frustrational mathematics levels in all other skills assessed. In reading, teachers' judgment accuracy varied as a function of grade‐level material and instructional level. Specifically, teachers experienced considerable difficulty accurately identifying students who were reading at a Mastery level in grade‐level or above‐grade‐level material. © 2006 Wiley Periodicals, Inc. Psychol Schs 43: 247–265, 2006.     

浅谈小学数学课堂教学中问题意识的培养

数学既是小学阶段就开始接触的学科,也是对小学生数学思维运用和解题能力要求较高的学科,没有问题可“问”的小学数学课堂无疑是枯燥和无趣的,难以真正实现对小学生思维能力的培养,因此,本文结合目前小学数学课堂出现的问题,探究怎样在小学数学教学中将学生问题意识培养起来。     

Examining the implementation of the mathematics strand of the Key Stage 3 Strategy: What are the bases of evaluation?

This article presents findings from a comparative case study examining the implementation of the mathematics strand of the Key Stage 3 Strategy in two contrasting schools—one using setting and whole‐class teaching, the other incorporating mixed‐ability grouping and individualised learning. A number of ‘outcomes’ of implementation are considered, including teachers' and students' experiences, changes in pedagogic practice and students' attainment. Whilst both schools achieved highly in relation to similar schools, higher attainment gains between Key Stage 2 and Key Stage 3 in the school using setting/whole‐class teaching were associated with increasing student disaffection and dependence on teachers. In contrast, the attainment gains at the school using individualised learning were associated with increasing enthusiasm and independence. The mixed picture of outcomes and their complex interconnections suggest that evaluations of implementation resting on attainment‐based outcomes are problematic in terms of longer‐term aims of increasing the proportions of students choosing to study mathematics and developing the skills of independent learning.     

Student primary teachers improving their mathematics subject knowledge: cognition and affect intertwined

This paper describes a study conducted with a random sample of 80 student primary teachers drawn from all four years of the Bachelor of Education (BEd) programme at a teacher education institution in Scotland, with a view to determining why there were such differing levels of engagement with an online maths assessment. The assessment was created in an attempt to address deficiencies in subject knowledge in order to reduce the amount of time spent on mathematics remediation, and to raise awareness of the levels of mathematics competence required in the primary classroom. Study of the reasons behind the differing patterns of engagement with the assessment revealed that two thirds of the group were able to reach a competence threshold and often to improve upon it by some way; a worrying third of the students, however, made little attempt to use the tool to improve their subject knowledge. A further finding indicated that students who engaged with the online assessment reported improving levels of confidence in mathematics.     

Classroom management and students' mathematics achievement: The role of students’ disruptive behavior and teacher classroom management

Establishing a well-organized classroom conducive to learning is a key element of high-quality teaching. However, less is known about the degree to which the classroom management process is affected by the specific students in the classroom. Using two large-scale datasets of German secondary school students, the present two studies examined the effectiveness of teachers' classroom management in mathematics while taking into account students' disruptive behavior in the classroom. When controlling for the average level of disruptions in the classroom, both students' disruptive behavior and teachers' monitoring activity were negatively associated with students' mathematics achievement, whereas no associations occurred for teachers' structure and rule clarity. The results suggest that teachers' monitoring activity needs to take into account students’ disruptive behavior in the classroom, highlighting the complexity of effective classroom management.     

Teachers as writers: learning together with others

In the context of renewed interest in teachers' identities as writers and the writers as artist‐educators, this paper reports upon the findings of “Teachers as Writers” (2015–2017). A collaborative partnership between two universities and a creative writing foundation, the study sought to determine the impact of writers' engagement with teachers on changing teachers' classroom practices in the teaching of writing and, as a consequence, in improving outcomes for students. The project afforded opportunities for writers and teachers to work together as learners in order to improve student outcomes. The study involved two complementary datasets: a qualitative dataset of observations, interviews, audio‐capture (of workshops, tutorials and co‐mentoring reflections) and audio‐diaries from 16 teachers; and a randomised controlled trial (RCT) involving 32 primary and secondary classes. The findings reveal that the teachers' identities and assurance as writers shifted significantly. The Arvon experience also led to pedagogic shifts which the students reported impacted positively upon their motivation, confidence and sense of ownership and skills as writers. However, these salient dispositional shifts did not impact upon the young people's attainment. The professional writers gained new understandings which substantially altered their conceptions of writers' potential contribution in schools.     

Teachers' Opinions about Inclusion: A pilot study in a Palestinian context

The present study explored teachers' opinions about the inclusion of students with disabilities and special needs in regular primary schools in a Palestinian context, and factors that influenced such opinions. The sample consisted of 90 teachers at six schools. Eighty-seven (97%) of them had students with disabilities or special needs in their classes. Fifty-four (60%) of the teachers were of the opinion that students with disabilities and special needs should have an opportunity to attend public schools. Opinion-related factors were identified and compared to results of previous studies. Eighty-one (90%) of the teachers expressed a need for changes in the public schools in order to meet the needs of students with disabilities and special needs. Their focus of interest for building their own competence was on knowledge and skills that could empower them as teachers, not on knowledge about the students' disabling impairments.     

A Framework for Transition: Supporting 'Learning to Learn' in Higher Education

In this paper, a framework for developing first‐year students' learning is proposed. Its aim is to increase university managers' and teachers' awareness of two issues: (1) that the currently predominant ‘skills’ approaches to the enhancement of student learning are based on a deficiency model and achieve little more than remedying the overt problems of individual students and (2) that a holistic, subject‐specific approach is needed to support all students in the complex process of learning to learn in higher education. The framework aims at facilitating transition to university by helping students to understand what is expected from them at university, by addressing their conceptions of learning and knowledge and by gradually developing their competence as independent learners as well as their competence in constructing knowledge in their discipline. Different contexts are used to apply complementary methods for the development of learning. As the framework relies on the engagement of academic teachers, it is critical that university managers and policy makers give appropriate recognition to effective teaching. This involves instigating changes in conceptions of teaching, providing opportunities for educational development and setting incentives for teachers' commitment to student learning.     

Person and Context in Becoming a New Teacher

The influence of, and the interplay between biographical and contextual factors in new teachers' professional learning and development during their first years of teaching are examined. Data were gathered through semi-structured interviews and a questionnaire. Findings suggest the powerful influence of prior experiences as students, the low impact of Initial Teacher Education on new teachers' socialisation and the strong effect of workplace conditions in shaping beginning teachers' practices and attitudes towards teaching. It is argued that more importance needs to be given to the structural and organisational factors of the workplace if a 'learning culture' is to be fostered in schools. Implications for Teacher Education and Induction are discussed.     

Chinese primary school mathematics teachers working in a centralised curriculum system: a case study of two primary schools in North‐East China

Mainland China has a highly centralised curriculum development system. A study of two schools in northeast China, one in a rural area and the other in an urban area, indicates that the primary mathematics curriculum has been widely adopted by teachers at the classroom level. Feeling the intense pressure generated by the national mathematics Olympiad,1 1. The mathematics Olympiad is a type of ‘extracurricular’ activity that aims to promote students' interest and improve their ability in mathematics. Students participating in the competition are required to complete some challenging and non‐routine mathematical operations. The international mathematics Olympiad is held every year. In Mainland China, this competition is commonly organised at city, provincial and national level. Students who perform exceptionally well are exempted from the highly competitive national university entrance examinations for entry to universities View all notes teachers in the urban school tended to give more difficult mathematics problems to their students in the hope that above‐average students would perform well in the competition. In the rural school, the ability of students was more varied and generally lower. Teachers there worked very hard to push their students to meet the national requirements. The driving force behind this was the county‐wide public examination in which students' performance was taken as an indicator of teachers' competence. Teachers in both schools also have not taken effective steps to adapt the curriculum for students' individual differences. A comparison of the practices between the teachers in the two schools suggests that teachers' beliefs, their professional knowledge and skills shape their inclination and ability in curriculum adaptation and differentiation.     

An examination of the professional development needs of out-of-field mathematics teachers

This paper presents an empirical study examining the professional development needs of out-of-field mathematics teachers in the Irish context (n = 202). An online questionnaire gathered data on cohort demographics and confidence with regard to teaching mathematics. A paper-and-pencil test evaluated teachers' cognitive and conceptual proficiency with curriculum-aligned mathematical content. Low achievement levels and high occurrence of conceptual errors indicate inadequate subject content knowledge and difficulties with the content of the curriculum. Additionally, these teachers described themselves as either somewhat or very confident in teaching all content. The discrepancies which exist between confidence levels and content proficiency highlight the importance of designing appropriate professional development programs that are situated and practice based.     

Factors related to teachers' attitudes towards the inclusive education of students with severe intellectual disabilities in Riyadh,Saudi

In Saudi Arabia, the majority of students with severe intellectual disabilities are still educated in special schools that do not meet their unique needs for interaction with their typically developing peers in public schools settings where they could improve social, communication and academic skills. One of the most significant obstacles to inclusion of this group of students is teachers' perspectives regarding inclusive education for this category of students. As a result, this study examined teachers' perspectives regarding the inclusion of students with severe intellectual disabilities using a quantitative approach. In addition, this study also examined the relationship between teachers' perspectives regarding the inclusion of students with severe intellectual disabilities and current teaching position, training, teacher's levels of education, previous teaching experience with any kind of disabilities in inclusive settings, grade level being taught, teacher's gender and whether they have a family member with a disability. Three hundred and three teachers responded to the Opinions Relative to inclusion of Students with Disabilities (ORI: Arabic version) survey, including 161 males and 139 females, and three non‐specified gender. A two‐way analysis of covariance (ANCOVA), a one‐way analysis of variance (ANOVA) and an independent t‐test were used to answer the research questions. The findings of the study indicate that teachers have slightly negative perspectives towards the inclusive education of students with severe intellectual disabilities. Significant factors regarding teachers' perspectives towards the inclusion of this group of students included their current teaching position, previous teaching experience with students who had any kind of disability in inclusive settings and the teacher's gender.     

Does emotional intelligence predict student teachers' performance?

There are good theoretical grounds for seeing emotional intelligence (EI) as important in the teachers' skill set. Yet there is a lack of data on whether student teachers' levels of EI are associated with their teaching performance. This question was addressed, with gender and prior academic attainment also being explored as possible contributors to teaching performance. No association between the three independent variables and teaching performance was found. This raises serious questions for our understanding of emotions and teaching.     

Teacher interpersonal competence for Dutch secondary multicultural classrooms

In the Netherlands, as in many European countries, classrooms display a growing cultural diversity. There are only very limited empirically supported data on the interpersonal competence teachers need in Dutch classrooms and studies from other countries cannot be generalized because of differences in the composition of the student population. This paper reports on an exploratory study in two schools on teachers' experiences in multicultural classes followed by an in‐depth case study of one expert teacher. We use this study to answer the question to what degree this teacher displays interpersonal competence (teaching behaviours, knowledge and attitudes) specific for teaching in multicultural classrooms by comparing this teacher's competence with generic interpersonal teaching competence. The teacher studied seems to be aware of special needs of students from different cultures and to use this knowledge to apply specific teaching strategies and interpersonal cues to create a positive classroom atmosphere and to cater for needs of diverse students. Further, the results indicate that many elements of this teacher's interpersonal competence in teaching a multicultural class can be considered aspects of generic teaching competence. It seems that the multicultural classroom puts heavier demands on this competence than a less diverse classroom.     

Outdoor mathematics trails: an evaluation of one training partnership

Outdoor education has received greater attention in the United Kingdom with the launch of the Learning Outside the Classroom Manifesto. However, teachers' lack of confidence and competence appear to be key factors underpinning the extent of outdoor learning provision in schools. This paper reports on a partnership project in which student teachers worked alongside classroom teachers to create outdoor activities in primary mathematics. Findings suggest that such a partnership provides a supporting framework for both teachers and student teachers to develop confidence, competence and enthusiasm for the provision of future outdoor learning experiences.     

Exposing Student Teachers' Content Knowledge: Empowerment or debilitation?

Previous governments and other commentators have emphasized the relationship between a teacher's knowledge of the subject material being taught and the quality of learning outcomes. This has been reflected in the entry requirements to Initial Teacher Training (ITT) (primary) of public examination performance in the core subjects. However, disquiet has been expressed as to the efficacy of such qualifications as indicators of knowledge and skills at the entry point. Recent changes to ITT (primary) regulations require students' actual knowledge of the content of the three core subjects to be audited. This paper reports and reflects on the effects that re-examining their knowledge and skills in mathematics has had on the confidence of primary trainee teachers. It presents some key questions that must be addressed if the current audit regulations are indeed to benefit our future teachers and to enhance the learning of our pupils.     

试论数学教学中如何激发学生的求知欲

在数学教学中,教师可通过多种方法激发学生的求知欲,从而不断提高数学教学效率,提高学生的数学学科核心素养。文章探讨在数学教学中激发学生求知欲的有效策略:联系实际,创设情境;教学设计活动化;鼓励学生参与操作,得出结论;注意提问、批改作业的方式、技巧;跳出“思维定式”,让学生感受创新的快乐。