Developing assessment literacy through approximations of practice: Exploring secondary mathematics pre-service teachers developing criteria for a rich quadratics task

This study draws on a theoretical model for teacher assessment literacy to investigate the process of how secondary mathematics pre-service teachers (PSTs) might develop theirs through experiencing an approximation of practice. Sixty PSTs participated in designing and then refining assessment criteria for a rich open-ended quadratics task using real student example responses. Data analysis examined variations in the PSTs’ attention to quadratic features and mathematical language as assessment criteria for the task throughout the activity. This paper discusses evidence suggesting that the collaborative analysis of example student responses can make certain, but not all, assessment criteria salient to PSTs.     

How do Dutch secondary teachers and students conceive the purpose of assessment?

How teachers and students deal with assessment practices is largely influenced by the conceptions they hold about the purpose of assessment. This means that, given the current plea for a paradigm shift from Assessment of Learning to Assessment for Leaning with a balance between the formative and summative purposes of assessment, the study of teachers’ and students’ conceptions of the purpose of assessment is of the utmost relevance. In this study Dutch secondary school teachers’ (n = 351) and students’ (n = 712) conceptions of the purpose of assessment were measured using a translation of the teachers’ conceptions of assessment questionnaire and a translated and shortened version of the students’ conceptions of assessment questionnaire. Maximum Likelihood factor analyses resulted in four teacher and five student conceptions of the purpose of assessment. The results indicate that the teachers in our sample did not distinguish between formative and summative purposes of assessment. They did discern classroom assessment (formative as well as summative) from school accountability. In addition, they conceive assessment as being of bad (in terms of measurement errors) or good quality. In contrast with the teachers, students do make a distinction between the formative and summative purpose of assessment. They also refer to school accountability and the affects that assessment triggers in them as further purposes of assessment.     

Students’ formative assessment perceptions,feedback use and mathematics performance in secondary schools in Tanzania

This study investigates the impact of secondary school students’ perceptions of mathematics teachers’ formative assessment practices and feedback delivery on their feedback use, and mathematics performance. The sample consisted of 2767 Form 3 (Grade 11) students from 48 secondary schools in Tanzania. Surveys and focus group discussions were used to measure students’ perceptions of formative assessment, feedback delivery, and feedback use. Structural Equation Modelling (SEM) of survey data showed that students’ perceptions of the quality of teacher feedback delivery and perceived scaffolding positively predicted students’ feedback use whereas perceived monitoring negatively predicted feedback use. In turn, students’ feedback use positively predicted their mathematics performance to a small extent. Content analysis of focus group discussions illustrated that most students valued their mathematics teacher’s assessment practices. The findings imply that in Sub-Saharan African educational systems the quality of teacher feedback delivery and promotion of student feedback use can improve students’ mathematics performance.     

Experienced Middle School Science Teachers’ Assessment Literacy: Investigating Knowledge of Students’ Conceptions in Genetics and Ways to Shape Instruction

Using a framework of assessment literacy that included teachers?? view of learning, knowledge of assessment tools, and knowledge of assessment interpretation and action taking, this study explored the assessment literacy of five experienced middle school teachers. Multiple sources of data were: teachers?? predictions about students?? ideas, students?? written and verbal responses to assessment tasks, teacher background questionnaire, and a videotaped teacher focus group. We investigated middle school teachers?? predictions, interpretations, and recommended actions for formative assessment in genetics. Results documented a variety of ways that teachers would elicit students?? ideas in genetics, focusing on discussion strategies. Findings showed how well teachers predicted student conceptions compared to actual student conceptions. We also found that teachers mostly described general topics they would use to address students?? alternative conceptions. Less often, they explained specific content they would use to challenge ideas or pedagogical strategies for conceptual change. Teachers also discussed barriers to addressing ideas. Teacher professional development should provide more support in helping teachers close the formative assessment cycle by addressing conceptions that are elicited with assessments.     

Comparison between conceptions and assessment practices among secondary education teachers: more differences than similarities (Comparación entre concepciones y prácticas de evaluación en profesores de Educación Secundaria: más diferencias que semejanzas)

ABSTRACT

Teachers’ conceptions can affect any teaching practice, including assessment. Compared with the previous learning stages in Spain, the accreditation-based focus increases in secondary education. Therefore, it is necessary to study the conceptions teachers have of assessment during this stage and the role these play in their teaching practices. The study participants comprised 219 secondary education teachers. A mixed methodology including a questionnaire, dilemmas and the analysis of test contents was used. An analysis was implemented of the relationship between the conceptions of assessment and the type of tests used, self-assessment and peer assessment, and characteristics of feedback. The teachers reported having a formative conception, but this was incoherent with their assessment methods characterized by a scarce use of self-assessment and peer assessment and a hardly formative feedback. In conclusion, we highlight the relevance of the teaching-related conceptions in the education system and the need for working jointly with teachers to implement an authentically formative assessment in the classroom, with an emphasis on consistency between conceptions and practices.     

Student perspectives on formative feedback as part of writing portfolios

Despite the crucial role that students play in formative assessment practices, student perspectives on such practices are relatively under-researched. Through a qualitative analysis of 128 reflection notes written by student teachers of English, this article investigates the students’ perceptions of formative feedback as part of portfolio assessment at two teacher education institutions in Norway. As such, it contributes to bridging the gap between research and practice. Students received peer and teacher feedback on assignments and wrote reflection notes during the semester. Findings show that students are positive towards teacher feedback and highlight the significance of teacher praise. Main objections raised against peer feedback concern the lack of constructive criticism. However, positive attitudes towards peer discussion groups suggest that they may be a more effective way of implementing peer assessment than formalised written peer commentary. Student reflections suggest that a failure to understand the task and the feedback is a possible hindrance to successfully revising assignments. Overall, students’ positive attitudes towards the portfolio process, which includes multiple drafting, suggest that students in higher education would benefit from more opportunities to revise and resubmit their work, yet they need adequate practice in providing peer feedback, and interpreting and implementing feedback in general.     

Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills

The purpose of this paper is to share a performance assessment task and rubric designed to assess secondary school mathematics preservice teachers’ pedagogical content knowledge and skills. The assessment task and rubric were developed in collaboration with five education faculty, four arts and sciences faculty, and four high school teachers over a period of one year. Over this period, the group met more than 15 times and designed an assessment task and rubric to measure secondary school preservice teachers’ pedagogical content knowledge and skills. The assessment task and rubric were piloted at the end of the year and extensively revised using the pilot data. The redesigned task and rubric were successfully carried out in the second and subsequent years. Other teacher education programs can benefit from this assessment of teacher candidates’ pedagogical content knowledge and skills.     

Mathematics attainment at inner-city schools: Establishing the need for systematic formative evaluation practices

Recently there has been a great amount of research and professional educator interest in at-risk, poor academically attaining students, especially low socioeconomic status students at U.S. inner-city schools. A major factor that has been hypothesized in the research literature as being associated with poor academic attainment is the lack of critical and timely instructional feedback or formative evaluation. Using a sample of 130 inner-city senior high school students, the perceived quality and quantity of formative evaluation received by these students at their elementary and secondary school levels were assessed. in addition, each student was given a mathematics (pre-algebra) assessment using both a one and two-dimensional format (recognition plus confidence) to determine present levels of mathematics attainment. Finally data were collected from the cumulative grade-level folders of a subset of these students, especially norm-referenced data (NRT) in mathematics, to examine their relationship to scores on the Scholastic Aptitude Test-Quantitiative portion. The study finds that in addition to extremely poor mathematics attainment and poor formative evaluation practices there is little association between SAT (quantitative) scores and the grade-level (mathematics) NRT scores. These findings suggest that parents cannot depend on traditional norm-referenced measures to indicate actual mathematics attainment as these students are progressing through the schools. These findings also challenge urban school administrative personnel to reassess the use of NRT measures to monitor student progress and to develop more comprehensive and systematic formative evaluation procedures and practices for individual students as they progress through each grade level.     

What do we know and where do we go? Formative assessment in developing student teachers’ professional learning of teaching science

In the context of teacher education, it could well be suggested that assessment activities that build on formative interactions between student teachers and teacher educators might offer new windows into better understanding teaching and learning. This paper presents findings from a study into a primary science teacher education initiative that seeks to build the foundations on which 24 primary science student teachers, through the use of formative assessment of their science teaching and learning, can begin developing their pedagogical content knowledge (PCK). In the project, formative assessment consists of activities used by teacher educators to stimulate interactions, self- and peer-assessment in order to provide insights into how student teachers develop their PCK during a semester. Content Representations (CoRes), were used as a tool to unpack the student teachers’ approach to teaching a science topic and the reasons for that approach. The results indicate that the use of CoRes, together with subsequent self-assessment and formative interactions with teacher educators and peers, do have the potential for PCK development for student teachers. The results further highlight the need for developing reliable and valid tools for capturing and assessing student teachers’ PCK in pre-service teacher education.     

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

The purpose of this study was to examine and elaborate upon elementary prospective teachers’ (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs’ conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs’ performance on tasks to elaborate upon PSTs’ conceptions of the operation of partitive division. This study contributes new insights into PSTs’ conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.     

Pre-service teacher planning for differentiation of instruction in mathematics classrooms

This study investigated how 46 pre-service teachers (PSTs) planned for differentiation of instruction in mathematics. Content analysis was utilized to explore the differentiation strategies included and student characteristics considered in PST plans and how PSTs used differentiation strategies and student characteristics to differentiate lesson content, process, product, and environment. In addition, a rubric was designed and utilized to analyze the level of detail PSTs provided in their plans. Results indicated that overall, PSTs were developing in their planning for differentiation of instruction, using general terms to describe the modifications they would make to meet student needs. Moreover, results revealed that PSTs included strategies to differentiate lesson content and environment most often in their plans and frequently considered student readiness levels when planning for differentiation. Findings also revealed that PSTs need support in learning how to plan for differentiation based on student cultural backgrounds. Implications for mathematics teacher preparation are discussed.

     

The impact of an alternative professional development model on teacher practices in formative assessment and student learning

Among contemporary means of enhancing student learning, formative assessment is perhaps one of the most important and effective. While formative assessment ideas and practices have been shown to have a proven record enhancing student learning, these practices are slow to be fully integrated into teachers’ day-to-day classroom practices. This study describes a collaborative effort among university faculty and public school partners to train teachers in the skills and practices of formative assessment. Regarding teachers’ involvement in the formative assessment professional development, findings highlight that 1) teachers’ participation in the professional development efforts did strengthen their understanding of both general knowledge of formative assessment and the use of formative assessment practices, 2) teachers’ plans to use the strategies in the future were related to their understanding of these strategies, and 3) in-depth and comprehensive understanding of formative assessment practices were critical to concrete applications of such practices in their classrooms. With respect to the impact on student learning, an overall effect size of .41 was found for teachers who utilized a formative assessment strategy compared with district averages for similar learning objectives when the practices were not used.     

The Teacher as Examiner: the case of mathematics coursework

Recent developments in curriculum and assessment in the UK have led to increased involvement of teachers in high‐stakes summative assessment of their own students. Case studies of experienced secondary school mathematics teachers reading and assessing General Certificate of Secondary Education (GCSE) coursework texts show that they experience tensions between their various roles and responsibilities as teachers and as examiners. Moreover, different teachers appear to resolve these tensions in different ways, adopting various positions in relation both to the content of the written coursework texts and to the student‐authors of the texts. Variations in teachers’ approaches to reading and assessing mathematics coursework may lead to differences in the ranks or grades allocated and, even where they do not, the meanings of the grades given by different teachers may be substantially different. Through examining teachers’ assessment practices, questions are raised both about the validity of such assessments and about the compatibility of the coursework examination system with the aims of the curriculum development which gave rise to it.     

Effects of a rubric for mathematical reasoning on teaching and learning in primary school

Rubrics are assessment tools that help students gain complex competencies. Our quasi-experimental study aimed to evaluate whether rubrics help teachers teach and assess mathematical reasoning in primary school and whether such an instrument might support student learning. In two Swiss cantons, 762 students in 44 5th- and 6th-grade primary classes worked on their reasoning competencies, and half of them additionally employed our standards-based rubric. All of the teachers received a 1-day training and participated in the final project evaluation. To standardise and support the teachers during the implementation phase, they received a detailed curriculum. An achievement test and questionnaires for students and teachers were administered before and at the end of the intervention. The results of our quantitative longitudinal analyses indicate that the rubric fosters the teachers’ perceived diagnostic skills but only indirectly impacts their use of formative feedback. Based on the students’ perceptions, however, we observed a direct effect of the rubric on formative feedback and student self-assessment. Effects on students’ outcomes could not be observed, but there are indications of effects mediated by self-regulation and self-efficacy.     

Peer assessment in a test-dominated setting: empowering, boring or facilitating examination preparation?

The literature suggests that peer assessment contributes to the development of student learning and promotes ownership of assessment processes. These claims emerge from research conducted primarily in Western contexts. This exploratory paper reports on the perspectives that a class of Hong Kong primary school students and their teachers have on their engagement with peer assessment. It draws on data collected through extensive interviews and classroom observations from a 2-year case study. The findings indicate that student perceptions about the usefulness of peer assessment follow from their perspectives on quality of peer feedback, peer language proficiency, and the novelty or repetitiveness of its processes. Teachers and students also viewed peer assessment as assuming a wider role in preparing for examinations and future secondary schooling. A key implication is that assessment practices are deeply cultural and, in test-dominated settings, peer assessment may have most potential when explicit links are drawn with preparation for summative assessment.     

Scaffolding peer-assessment skills: Risk of interference with learning domain-specific skills?

Giving students complex learning tasks combined with peer-assessment tasks can impose a high cognitive load. Scaffolding has proven to reduce cognitive load during learning and improve accuracy on domain-specific tasks. This study investigated whether scaffolding has a similar, positive effect on the learning of peer-assessment tasks. We hypothesised that: (1) domain-specific scaffolding improves domain-specific accuracy and reduces time on task and perceived mental effort, and (2) peer-assessment scaffolding improves peer-assessment accuracy and reduces time on task and perceived mental effort. Additionally, we explored whether there was an interaction between domain-specific and peer-assessment scaffolding. In a 2x2 experiment with the factors domain-specific scaffolding (present, absent) and peer-assessment scaffolding (present, absent), 236 secondary school students assessed the performance of fictitious peers in an electronic learning environment. We found that domain-specific accuracy indeed improved with domain-specific scaffolding, confirming our first hypothesis. Our tests of the second hypothesis, however, revealed surprising results: peer-assessment scaffolding significantly increased accuracy and mental effort during learning, it had no effect on peer-assessment accuracy at the test and led to reduced domain-specific accuracy, even when combined with domain-specific scaffolding. These results suggest that scaffolding students' peer assessment before they have mastered the task at hand can have disturbing effects on students’ ability to learn from the task.     

Formative assessment of students from a Confucian heritage culture: Insights from Japan

Abstract

Since the turn of the century there has been increasing interest in educational assessment and the ways in which it can encourage or discourage effective learning processes. Much of this interest has centered around formative assessment and those practices which can promote student learning through the act of being assessed. Societies that have a Confucian heritage culture are widely believed to prioritize summative assessment at the expense of formative assessment. This will inevitably impact the ways in which students from these countries approach and engage with assessment tasks. The present study seeks to understand the dispositions of students from one Confucian heritage culture though the analysis of quantitative and qualitative data. The conceptions and experiences of university students in Japan were studied in order to provide direction for the development of formative assessment practice. Two data collection instruments were used: a self-report survey and a narrative frame task. The results indicate that students from Japan approach assessment tasks in a way that is at odds with some popular Confucian categories, such as intense competition, a desire to please the family, and the priority of book knowledge above practical skill. The paper concludes with pedagogical implications for teachers.     

Using Performance Task Data to Improve Instruction

Two well-accepted ideas among educators are (a) performance assessment is an effective means of assessing higher-order thinking skills and (b) data-driven instruction planning is a valuable tool for optimizing student learning. This article describes a locally developed performance task (LDPT) designed to measure critical thinking, problem solving, and written communication skills of elementary and middle school students in a large school district. An investigation was conducted to determine how middle school teachers use LDPT responses to inform instruction and to ascertain how students are reflecting on their performance. Results from an analysis of documents indicated teachers were engaged in formal data-informed practices within professional learning communities. Moreover, educators examined student work samples and planned instruction based on student-specific needs. Strategies to reinforce proficiency in the skills assessed by the district's LDPT are reported.