Giving and receiving feedback on mathematics tasks: Insights gleaned from exploring teachers' and students' perspectives
ABSTRACT. In this presentation, I will employ theoretical frameworks of Assessment Literacy to elucidate the perceptions of mathematics teachers and students regarding their involvement in formative assessment processes, exploring both cognitive and affective dimensions. Specifically, I will focus on participants’ perceptions of their experience of constructing, giving, and/or receiving feedback, considering cognitive aspects such as role enactment [My role] and knowledge [I know], and affective dimensions including the expression of feelings [I feel], beliefs [I believe], and self-efficacy [I am/am not confident]. I will illustrate how engagement with diverse formative assessment scenarios, involving interactions with both "real" and "fictitious" partners, gives rise to varied opportunities and challenges associated with feedback. I will propose that recognizing feedback as an interactive process in which feedback "receivers" are actively involved, though posing certain challenges for teachers and students, is indispensable for realizing the potential of feedback to enhance learning and sustain formative assessment processes in the classroom.
Enhancing Teacher Training in Mathematics Education: A Model for a Semiotic Approach to Feedback and Interpretative Knowledge
ABSTRACT. This research introduces a comprehensive model for a teacher training course centered on Semiotic Interpretative Knowledge (SIK) in mathematics education. Highlighting the critical need for specialized training, the course is designed to refine teachers’ abilities to interpret student’s responses through a semiotic lens, especially when conceptual knowledge remains hidden behind difficulties related to patterns of sign use. It focuses on equipping educators with advanced semiotic interpretation skills, thereby enhancing their capability to offer deeper, more meaningful, and effective feedback in mathematics classrooms. The model not only delineates the key features of the designed course but also lays a foundation for future investigations into its feasibility and impact.
Exploring formative assessment and peer feedback in technology-enhanced mathematics learning environments through bar model virtual manipulatives
ABSTRACT. The increased integration of technology in educational settings has correspondingly led to an uptick in the adoption of digital assessment, significantly impacting both the method and content in the assessment of mathematics education. Technology not only transforms the assessment approach but also holds crucial implications for how teachers assign tasks and shapes the way students engage in mathematical reasoning. In our modern, data-rich world, much of our daily experiences and interactions have progressively moved into the digital space, a trend matched by advancing technology in videography. This paper explores how educators leverage this innovation to enhance mathematics assessment and feedback, using screencasts to capture students’ on-screen interactions as the primary method for data collection. In the study, students’ digital interactions while solving word problems using the bar model, a web-based virtual manipulative, were recorded. Analysis of data collected may suggest possible feedback about students’ specific competencies and deficiencies and inform teaching practices to be adapted to students’ learning needs. Digital feedback may be expanded to include peer assessment and self-evaluation when students engage, interact, and share ideas in real-time using screen mirroring functionalities, another innovation seamlessly supported by classroom connectivity.
Exploring metrics: elementary mathematics teachers' evaluation of digital geometry assessment activities
ABSTRACT. This study concentrates on metrics that guide teachers in perceiving Digital Formative Assessment (DFA) as suitable for formative assessment for students and aligning with the curriculum. This is part of a larger study that explores the efficiency of a digital formative assessment platform for elementary school geometry. The research utilized open coding to analyze responses from a teacher questionnaire, exploring elementary math teachers' perspectives on DFA. This research was conducted with nine mathematics teachers from diverse Israeli elementary schools. Using a teacher questionnaire and 12 DFA activities, the study identified 11 codes categorized into three categories: Information provided, type of task, and student interaction.
Using e-assessment for interactive example-generation tasks
ABSTRACT. The paper concerns the use of e-assessment systems to advance students’ example spaces of mathematical concepts. We report on a pilot study with seven first-year students of Linear Algebra. Three students engaged with the static version of the e-task, which asked them to generate three examples that were as different as possible. The remaining students were prompted by an interactive e-task that assessed the provided examples and asked for another one with different properties. The analysis of a single task about matrices showed that the students who worked with the interactive e-task were more successful than those working with the static e-task, in terms of the number and the range of generated examples. These preliminary findings open the doors to further study of the design and use of interactive example-generation tasks in university mathematics education.
Conception of two informative tutoring feedback strategies for mathematical tasks with STACK
ABSTRACT. The increasing presence of computer-based teaching and learning opportunities in recent years offers new approaches for providing informative tutorial feedback (ITF). For mathematical tasks, the tool STACK can be a possible approach. STACK enables the automated evaluation of even open mathematical tasks with any number of correct solutions and the provision of immediate feedback for learners. This paper will therefore investigate the question of how STACK could be used to design ITF-strategies for mathematical tasks. As a result of this question, two different strategies are presented, which differ when the cause of an erroneous answer is not clear. While in one strategy learners are provided with solution-specific hints for processing the task, in the other strategy, they enter a task loop in which they must work out these hints on their own. Finally, the strategies are compared in terms of their characteristics and possible effects on students’ learning processes.
Students’ experiences with automated final answer diagnoses for mathematics tasks
ABSTRACT. Model Backtracking (MBT) is a novel technique for automated detailed diagnoses based on final answers. In this small-scale pilot study, we answer research questions about nine 15 to 17-year-old mid-achieving students’ experiences with MBT diagnoses. The students practiced linear extrapolation in a learning environment that provides error-specific feedback and selects appropriate subtasks using MBT. Data included screen captures of students navigating the environment and interviews on students’ experiences with the environment. Results showed approaches ranging from correcting an error after receiving feedback to trial-and-error behavior while repeatedly consulting the worked-out solution. Furthermore, students preferred error-specific feedback over worked-out solutions. They found that worked-out solutions provide an insightful overview; yet, errors are not pinpointed, and worked-out solutions reduced motivation for further practice.
A mathematics teacher’s implementation of formative assessment: Overcoming obstacles with adaptive professional development support
ABSTRACT. This paper focuses a mathematics teacher’s implementation of formative assessment (FA) when helping students solve mathematics tasks. Such FA practice has great potential, but is non-trivial, and teachers will need substantial support for developing their beliefs and practices. We have studied why an engaged and experienced mathematics teacher who had participated in a comprehensive professional development program made certain changes but not others and how additional support helped her overcome obstacles she experienced. The study exemplifies the significance of first-hand information from teachers' classroom practices together with adapted feedback when providing professional development support for their FA development.
Expert design and implementation of effective classroom discussions for formative assessment
ABSTRACT. We present the first results of a long-term study aimed at characterizing an expert design and implementation of effective classroom discussions for formative assessment. For the analysis of the data collected in this study we combine the use of three different theoretical constructs concerning: the expert teacher’s roles during classroom discussions; shared attention; formative assessment key-strategies. The presented results concern, on one side, the expert’s use of a specific digital technology (an interactive whiteboard) to empower specific MAEAB roles to promote shared attention and, on the other side, the effects of the empowered MAEAB roles in the activation of specific FA strategies.
The students' use of visual representation for stimulating their metacognitive strategies: Teachers' perspectives
ABSTRACT. Visual representation is effective in enhancing mathematical learning and thinking processes. This study focuses on visual representations automatically provided by the formative assessment platform to describe students' mathematical strategies. We examined the teachers' perspectives on how the students' metacognitive strategies could be stimulated by visual representation of strategy (VRS) provided by a formative assessment platform in assignments for comparing fractions. Twenty-five teachers participated in this study. Based on different data resources, we were able to identify three categories where the teachers considered the VRS as a tool for stimulating students' use of metacognitive strategies: as part of class management, as part of task requirements, and as part of feedback information.
