Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases

As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.     

An analysis of teachers’ self-reported competencies for teaching metacognition

For successful reading experiences in native and/or foreign/second language, individuals need to benefit from not only cognitive strategies but also metacognitive strategies. Although research found reading comprehension and performance increase following metacognitive trainings, such findings may not transfer into mainstream classrooms as easily for several reasons. This study, therefore, aimed to disseminate the phenomenon of teaching metacognition with an emphasis on teacher’s instrumental role during classroom learning. More specifically, it investigated language instructors’ metacognition and their self-reported competencies for teaching metacognition. It also examined whether and how self-reported competencies changed following a professional development (PD) module of teaching for metacognition. Utilising Metacognitive Awareness Inventory (MAI) and think aloud protocols for instructional planning, this study found most participants were either highly metacognitive or metacognitive individuals. It was also found that most participants were initially not knowledgeable about and/or competent in teaching metacognition. Following PD, highly metacognitive teachers developed authentic lesson plans manifesting metacognition instruction while metacognitive teachers adopted similar instructional designs presented during the PD. Besides, half of the participants appreciated teaching metacognitively following the PD. Finally, under the light of these findings, future research and policy adjustments were proposed.     

The development of elementary pre-service teachers’ professional noticing of students’ thinking through adapted Lesson Study

The purpose of the study was to investigate how Lesson Study influences pre-service teachers’ learning to professionally notice students’ mathematical thinking. The initial and last video-recorded discussions were analysed using a qualitative method. Findings suggest that Lesson Study can be useful means to improve pre-service teachers’ noticing expertise in reviewing and planning lessons. However, to maximise the effect of Lesson Study on developing pre-service teachers’ noticing expertise, several modifications need to be made to the Lesson Study protocol, which are discussed.     

Characterizing a highly accomplished teacher’s noticing of third-grade students’ mathematical thinking

This study investigated a highly accomplished third-grade teacher’s noticing of students’ mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom teaching as opposed to professional development environments. Noticing was conceptualized as both attending to different elements of classroom instruction and making sense of classroom events. The teacher paid most attention to student thinking and was able to offer a variety of rich interpretations of student thinking which were presented in an emergent framework. The results also indicated how the teacher’s noticing might influence her instructional decisions. Implications for both research methods in studying noticing and teacher learning and practices are discussed.     

“It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths

Learning to name and notice students’ mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students’ mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students’ mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students’ mathematical strengths. The paper concludes with implications for future research in teacher education.

     

The development of an instrument to measure teachers’ inquiry habit of mind

In the present study the construct inquiry of mind explored and an instrument to measure it is proposed. Using three different samples, explorative and confirmative factor analyses were performed, resulting in three empirical dimensions that correspond to the three theoretical dimensions: 1) ‘value deep understanding,’ 2) ‘reserve judgment and tolerate ambiguity,’ and 3) ‘taking a range of perspectives and posing increasingly focused questions.’ Our findings suggest the teachers’ inquiry habit of mind scale has good psychometric properties making it useful not only for research that investigates teachers’ research attitude and intention to do research but also as an evaluation tool for the development of an inquiry habit of mind in both student teachers and teacher educators (in teacher education) as well as in experienced teachers (participating in professional development).     

Preservice teachers’ articulated noticing through pedagogies of practice

Elementary preservice teachers at six universities engaged in a task that provided them opportunities to articulate their professional noticing within video representations, written decompositions, and animated approximations of practice. The preservice teachers’ written accounts indicated that a majority attended to students or student thinking; however, when asked to illustrate their noticing through animation, focus shifted to the classroom teacher. Findings indicate the extent to which preservice teachers articulated specific mathematics concepts within and across pedagogies of practice and highlight the critical importance for selecting and utilizing multiple types of tasks to better understand preservice teacher noticing. Implications for eliciting and supporting preservice teacher noticing are discussed.     

Development of pre-service teachers’ information and communication technology (ICT) in education competencies in a mainland Chinese university

This paper examines how the design and implementation of a core teacher education course develops pre-service teachers’ information communication technology (ICT) in education competencies in a mainland Chinese university. This course adopted a four-component instructional design system to develop its curriculum, incorporated an inquiry-based learning approach to develop pre-service teachers’ pedagogical competencies, and used an online learning platform to facilitate the sharing of experiences of using ICT for teaching and learning. This case study demonstrates that innovative pedagogies together with more relevant course content supported by an online learning platform may enhance the effectiveness of a core ICT in education course.     

Developing an approach to the performance-oriented testing of science teachers’ action-related competencies

ABSTRACT

Measuring teachers’ skills to carry out the complex tasks required in teaching is an important means of evaluating the effectiveness of teacher education but remains a challenging activity to conduct in practice. It is necessary to optimise approaches for usability and effectiveness along a continuum from low-effort and low-authenticity measures such as paper-and-pencil tests to high-effort, high-authenticity measures such as extended classroom observations. The first part of the paper reviews a range of efforts toward measuring the competencies of teachers and other professionals in carrying out the tasks that make up their work. These include performance tests such as computer-based simulations or simulations using actors, as well as the use of tasks requiring participation in or responses to video vignettes. Video vignette approaches typically have been less interactive than performance tests and interactivity is seen as a desirable feature. A novel framework for developing performance-oriented testing is then outlined. The second part of the paper exemplifies this framework in relation to providing explanations in physics classrooms. The development of a novel test instrument following the framework is described, and findings on construct validity are presented to support the applicability of the presented approach.     

Sociomathematical and mathematical norms related to definition in pre-service primary teachers’ discourse

This study is part of a wider research program, which seeks to investigate the existence (or not) of relationships between sociomathematical and mathematical norms at different academic levels. Here, we consider the norms that arise in the interaction between primary student teachers when they solve a mathematical task related to the mathematical definition. We hypothesize that in the colloquial mathematical discourse between these students coexist two types of discourse as follows: sociomathematical and mathematical, each one with its specific norms. This coexistence can originate commognitive conflicts. We have been able to identify different commognitive conflicts that arose from the simultaneous existence of sociomathematical norms and mathematical norms linked to defining, approaching their generation.     

Development of an instrument measuring student teachers’ perceived stressors about the practicum

The Stressors about Practicum Inventory, a self-report measure of perceived stressors about the practicum, was designed to provide those responsible for the training of primary school teachers with an informative, inexpensive and psychometrically sound tool. The present study describes the development and validation of the 94-item inventory in a sample of 138 Greek primary student teachers. It also investigates its initial factor structure and reliability. The scale was administered both before and after a four-week period of practicum. Content validity was examined using a panel of experts and student teachers, whereas convergent validity was assessed with the use of a measure of neuroticism. Factor analyses revealed four sources of perceived stress. No gender differences were found. However, the experience of the practicum significantly reduced student teachers’ perceived stress. All perceived stressors were moderately correlated with neuroticism, but after the practicum the size of the correlations was reduced.     

Practicum experiences as sources of pre-service teachers’ self-efficacy

This study examines physical education pre-service teachers’ (PTs) self-efficacy and practicum experiences as self-efficacy sources through a mixed-method approach. For the quantitative phase, a self-efficacy questionnaire was applied to 141 PTs. Results showed a stronger self-efficacy in the relationship with students and discipline promotion. Lower self-efficacy was linked to instructional strategies. Concerning the qualitative phase, eight PTs were interviewed. PTs with higher self-efficacy reported professional experiences before practicum as mastery experiences. During the practicum they highlighted as mastery experiences: classes’ characteristics, planning and teaching practice; lesson observation as vicarious experiences; and post-lesson conversations as verbal persuasion. PTs with lower self-efficacy reported classes’ characteristics and teaching practice as failure experiences. Lesson observation was linked to negative vicarious experiences and post-lesson conversations were associated to negative emotions and the absence of verbal persuasion. This study’s results have implications inasmuch as they confirm the role of the practicum in teacher education programmes and the importance of training supervisors in the implementation and management of the training experience, thus contributing to PTs’ self-efficacy development.     

Evolution of pre-service teachers’ attitudes towards learning science during an introductory science unit

Primary teachers, despite their critical role in fostering student interest in science, lack confidence and have negative attitudes towards teaching science, with this trend starting during initial teacher education. Though research on attitudes towards teaching science is well established, less is known about attitudes towards learning science. In order to advance our understanding in this area, this study mapped the entry and evolution of attitudinal profiles towards learning science of 108 primary education pre-service teachers undertaking a first-year science unit. Participants completed an online survey tapping on self-determination, grade motivation, self-efficacy, difficulty, interest, anxiety and enjoyment in science before the commencement of the unit (T1) and at the end of it (T2). Clustering methods were used to group participants into homogenous attitudinal profiles at both points in time. Subsequently, daughter profile analysis was used to examine qualitative changes in final profiles respective to entry. Four distinct attitudinal profiles were identified with 47% of the participants exhibiting the least favourable profiles at the start of the science unit. Migration (T1 to T2) was more prevalent from the least to the most favourable profiles, however, it did occur in the opposite direction. Findings revealed that, though pre-service teachers increased their confidence in their ability to learn science, their self-determination decreased in all but one of the eight resulting daughter profiles.     

Developing pre-service teachers’ understanding of children’s risky play

This study examines the effectiveness of an intervention course for changing early childhood pre-service teachers’ understanding of children’s risky play. Twenty-six of the early childhood pre-service teachers who were enrolled in this course filled out an open-ended questionnaire at the beginning and end of the six-week course. Data from the pre and post surveys were triangulated with data obtained through the researcher’s reflective notes and participants’ brief evaluations and drawings. The results of the data analysis indicated that participation in the intervention course had changed pre-service teachers’ beliefs. As a result of the course, pre-service teachers’ positive perspectives on children’s risky play increased and their understanding became enhanced. Results are discussed in relation to the literature and the implications of examining early childhood education programs are explored.     

Just add hours? An assessment of pre-service teachers’ perception of the value of professional experience in attaining teacher competencies

This study compared pre-service teachers’ perceptions of their professional competencies at two campuses of a large regional teacher education university, where one campus provided students 22% more hours of professional placement in schools and related educational settings. Students who had experienced more hours in schools and such settings were more positive about their, ability to apply their knowledge of students and how they learn, classroom management, professional knowledge and practice, and community engagement; however, when students felt well supported during professional experience, such differences diminished. Additional hours were not associated with pre-service teachers’ perceptions of their ability to apply subject content and teaching; plan, assess and report; and effective student communication. Researchers argued that this pointed to the crucial role of good classroom mentors in teacher professional experience but also the value of students’ tertiary teacher education in preparing them for classroom teaching.     

Fostering aspects of pre-service teachers’ data literacy: Results of a randomized controlled trial

The present study reports the results of a randomized controlled trial aimed at fostering specific aspects of pre-service teachers’ data literacy. The 6-h intervention focused on data types, reference norms, scale transformations, graphic displays of the properties of frequency distributions, and judgments about the magnitude of mean differences. Pretest-posttest comparisons of a data literacy test showed a large and significant effect of the intervention. Furthermore, main effects but no significant interaction effects with pretest scores were found for personal and motivational covariates (academic self-concept, value beliefs, study interest) on posttest data literacy.     

Preservice teachers’ knowledge of proof by mathematical induction

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.

Prospective elementary school teachers’ professional noticing of children’s early numeracy

The goal of this study is to develop the professional noticing abilities of prospective elementary school teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, ninety-four prospective elementary school teachers from three institutions participated in a researcher-developed five-session module that progressively nests the three interrelated components of professional noticing—attending, interpreting, and deciding. The module embeds video excerpts of diagnostic interviews of children doing mathematics (representations of practice) to prepare the prospective teachers for similar work. The module culminates with prospective teachers implementing similar diagnostic interviews (approximations of practice) to gain experience in the three component skills of professional noticing. A pre- and post-assessment was administered to measure prospective teachers’ change in the three components. A Wilcoxon signed ranks test was conducted and found the prospective elementary school teachers demonstrated significant growth in all three components. Selected prospective elementary school teacher responses on the pre- and post-assessment are provided to illustrate sample growth in the prospective teachers’ abilities to professionally notice. These results, the first in an ongoing study, indicate the potential that prospective teachers can develop professional noticing skills through this module. Continued data collection and analysis from the ongoing study by these authors and future, longer-term emphasis on professional noticing for prospective teachers should be studied.     

Discomfort as a means of pre-service teachers’ professional development – an action research as part of the ‘Research Literacy’ course

This paper focus on defining a research question while conducting action research among third-year students attending a course on Research Literacy at a teacher education college. This paper discusses the process of preparing for and conducting action research among third-year students attending a course on Research Literacy at a teacher education college. The students were asked to conduct an action research on their classroom activities. The aim of this article is to present the process and pinpointing the discomfort of the students in formulating a research question suited to action research thanks to two prerequisite conditions: the ‘safe space’ and the ‘tender spot’. The research findings illustrate that the students had difficulty defining their ‘tender spot’. It was necessary to create a ‘safe space’. Furthermore, the findings show that the ‘tender spot’ issues were associated with disciplinary content far more than with generic lesson management or classroom management issues. The approach discussed here is leading to positive change and it may be that this professional development tool can facilitate the induction of novice teachers everywhere.