not consider themselves weak. But they thought they performed much better than they did. They first
needed a realistic self-reflection to help them understand what they did not understand to start an
efficient learning process.

CBM is an assessment approach developed and first used by Gardner-Medwin (1995) for teaching
physiology, medicine, and maths at University College London. The genesis of CBM can be traced
back to the desire for a more nuanced and comprehensive assessment methodology that goes beyond
the limitations of traditional grading systems (ibid.). Traditional grading systems often provide a
single numerical score for a student's solution to a problem, leaving little room for insight into the
students' thought process or the level of confidence in their answer (ibid.). So, instead of assigning a
fixed score to a solution, CBM allows students to express their confidence in their answers. Students
typically provide the solution to a problem and add a confidence rating, such as high, medium, or
low, influencing the grading (e. g. see Table 1). Certainty-based marking encourages students to think
critically about their responses and reflect on their understanding of the material. This approach
recognizes that learning is a dynamic process, and students may possess varying degrees of
confidence even when their answers are correct. By incorporating certainty levels into assessment,
educators gain insights into students' self-awareness and understanding of the subject matter.

Later, Yuen-Reed and Reed (2015) simplified the confidence rating to two confidence levels and
grades without malus points, in contrast to Gardner-Medwin (1995). The two options of "unsure" and
"very unsure" are combined into just one option of "unsure" because Yuen-Reed and Reed (2015)
argue that this distinction is very subjective.

Today, studies on various facets of CBM are available. It has been used in assessment but more in
self-assessment and summative assessments (Gardner-Medwin, 2019). In Germany, CBM was, for
example, conducted at the RheinMain University of Applied Sciences in a mathematics course with
43 third-semester students in the Department of Engineering (Kanzinger & Gehrig, 2022). Four tests
were conducted, each with five subject-specific single-choice questions and CBM. Results were sent
to the students at the end of the day the tests had been conducted. An online survey among the students
as an evaluation of CBM took place at the end of the semester. Results indicate that CBM could
promote the students' ability to self-reflect on tests during the semester. Almost all students stated
that CBM helps them to reflect on their learning. There was no control group in this study (ibid.).
Following these ideas, integrating formative assessment with CBM could represent a powerful and
nuanced approach to understanding and enhancing student learning, particularly in disciplines like
mathematics. It has been tried in medicine (Hendriks et al., 2019) but only in one assessment inside
a series of assessments and in veterinary (Valero & Cárdenas, 2017). Foster (2016) used CBM in
mathematics in school (and called it Confidence Assessment, CA) and investigated how pupils deal
with this approach and respond. For this purpose, a ten-task questionnaire on negative numbers and
a certainty grading with ten steps was carried out with different classes from age 10 to age 13. Based
on this test, Foster (2016) stated that the pupils were well-calibrated but demanded to repeat the test
since they then understood their certainty better. According to Foster (2016), research is needed into
what effects will be there if CBM is done more often. A further study by Foster (2022) showed mixed
results regarding the effects of summative assessment. Conducted in four schools with n=475 pupils,
but varying in time (from 3 weeks to an entire school year), Foster found that in schools pupils became
better than the control group, and in others, they did not.
Formative assessment takes place parallel to the learning unit or course to support the learning process and to improve individual learning (cf. Geisen & Zender, 2023; see also Brookhart, 2010; Cizek, 2010; Maier, 2010; Gikandi et al., 2011) and enables teachers to adapt learning opportunities to the needs of the respective learners (cf. Black & William, 2009). Introducing CBM within formative assessment could take this process a step further. Students could receive feedback on their answers and be prompted to self-reflect and express their confidence levels in their answers, for which they also receive feedback. This dual-layered evaluation could acknowledge the dynamic nature of learning and encourage metacognition – the ability to think about one's thinking. The integration of formative assessment with CBM could cultivate a learning environment that is responsive, adaptive, and focused on continuous improvement. On the one hand, students could become active participants in their learning journey. On the other hand, educators could receive valuable data, not only one-dimensional, on how much the students did correct, but also a second dimension, which is how certain they are. This leads to new insights if a topic remains unclear for the students, although they did perform well. Alternatively, students could be very confident in a topic but answer the questions wrongly, which can uncover misconceptions. Based on the data, educators can tailor their instructional strategies to the different types in this now two-dimensional outcome.

The literature shows that CBM is used in the university context (and mainly in medicine) but not much in school so far. It is also not commonly known or used in Germany. Therefore, the study presented below can be seen as a starting point for using CBM in the context of formative assessment in school mathematics lessons.

# A weekly CBM test in mathematics lessons - an exploratory study in fifth grade

## Objectives

CBM is rare and plays a minor role in assessment. Nevertheless, the wide range of Gardner-Medwin's publications (e. g. 2019) show a promising use of CBM in self-assessments. However, there is a need for research concerning CBM in the context of formative assessment. Furthermore, self-reflection should already be used at school. Using CBM in formative assessment could train pupils at school to reflect on their knowledge and improve on this reflection, a necessary skill for individual learning. Therefore, self-reflection should be initiated early in a learner's biography. However, there is still a need for research in this area. An exploratory study is therefore being conducted to investigate the influence of CBM in formative assessment on middle school pupils' mathematical self-reflection. Instead of directly measuring self-reflection, the accuracy of the confidence in the answers was measured by how often a student was correct when sure about the answer or how often a student was not correct when unsure about the answer.

## Method and sample

To measure the influence of CBM, an experimental fifth-grade class was chosen from a full-time German grammar school. The class had n=15 pupils aged 10 and 11 (six male and nine female). The pupils came from the same elementary school, and their respective performance levels in math lessons were heterogeneous. They had six hours of mathematics lessons each week, in which the last lesson of each regular week (excluding vacations, weeks in which there were reports and in which a class test was written) was used for a short test on the content of the previous lessons in that week. By the time this article was written, sixteen tests had been set. The tests were conducted weekly and
contained eight open questions (no multiple choice). Additionally, they had a certainty question after each mathematical problem about how sure the students were about their solution. There were two checkboxes: “I am ☐ sure ☐ not sure.”. Based on the concept of Yuen-Reed and Reed (2015), the certainty levels were reduced from three to two to make it simpler for the pupils because of their age. The rating was 2 points for a correct and sure answer, -2 points if the answer was wrong but sure, 1 point for a right but unsure answer, and 0 points if the answer was wrong and unsure. If no checkbox was used, 0 points were assigned regardless of whether the answer was correct or wrong (see Table 1). So, it is always better to state at least to be unsure than not using the checkbox. Consequently, the pupils have used the checkboxes. Also, in this system, it is easy to understand that it is better to be honest about the certainty of your answer.

<table><caption>Table 1: CBM points scheme (based on Yuen-Reed & Reed, 2015)</caption><thead><tr><th></th><th>sure</th><th>unsure</th><th>nothins</th></tr></thead><tbody><tr><th>correct</th><td>2</td><td>1</td><td>0</td></tr><tr><th>incorrect</th><td>-2</td><td>0</td><td>0</td></tr></tbody></table>

## Empirical analysis and initial findings

Regarding accuracy, the class test results were investigated in two ways: first, by how many correct answers the pupils gave and whether they were sure about this, and second, by how many incorrect answers the pupils gave and whether they were unsure about this. The results are displayed in Table 2.

<table><caption>Table 2: Pupils' prospective validity in percent</caption><thead><tr><th></th><th>Test 1</th><th>Test 2</th><th>Test 3</th><th>Test 4</th><th>Test 5</th><th>Test 6</th><th>Test 7</th><th>Test 8</th></tr></thead><tbody><tr><th>sure and correct</th><td>67%</td><td>70%</td><td>66%</td><td>59%</td><td>83%</td><td>86%</td><td>75%</td><td>87%</td></tr><tr><th>unsure and incorrect</th><td>52%</td><td>63%</td><td>68%</td><td>66%</td><td>85%</td><td>67%</td><td>80%</td><td>64%</td></tr><tr><th>mean</th><td>59%</td><td>67%</td><td>67%</td><td>62%</td><td>84%</td><td>77%</td><td>78%</td><td>76%</td></tr></tbody></table>
<table><thead><tr><th></th><th>Test 9</th><th>Test 10</th><th>Test 11</th><th>Test 12</th><th>Test 13</th><th>Test 14</th><th>Test 15</th><th>Test 16</th></tr></thead><tbody><tr><td>sure and correct</td><td>88%</td><td>83%</td><td>89%</td><td>79%</td><td>76%</td><td>84%</td><td>84%</td><td>83%</td></tr><tr><td>unsure and incorrect</td><td>57%</td><td>77%</td><td>61%</td><td>49%</td><td>58%</td><td>69%</td><td>52%</td><td>58%</td></tr><tr><td>mean</td><td>72%</td><td>80%</td><td>75%</td><td>64%</td><td>67%</td><td>77%</td><td>68%</td><td>71%</td></tr></tbody></table>

The first four tests looked almost the same, but something changed, and the pupils started to rank higher. The diagrams in Figure 1 (see next page and page after next) show each pupil represented by one dot. The dot is positioned on the x-axis based on how many points the pupil got in the test and on the y-axis based on how many correct answers were given by this pupil. A perfect accuracy would mean the pupil is on a straight line with a gradient of ½. The diagrams show that the points move towards that line over time, especially after the fourth test.

## Conclusions and Discussion

This paper focuses on using CBM within formative assessment in school mathematics lessons, a strategy that could enhance the prospective validity of pupils' answers to mathematical problems. Understanding one's expertise can lead to improved self-reflection, a crucial skill for adjusting one's learning process. Therefore, it is necessary to investigate the influence of CBM in formative assessment on the mathematical self-reflection of pupils at school. Furthermore, research is needed into the potential effects of more frequent CBM testing (Foster, 2016). To address these questions, we conducted an empirical study, testing a class of 5th graders at a German grammar school with CBM tests almost every week for a school year. At the time of writing this article, we had administered sixteen tests. After the first four tests with nearly the same prospective validity, the rate suddenly went up. Pupils got better at telling what they had learned and what not. As stated in the methods section, the self-reflection itself was not measured, but a better accuracy could speak in favour of a better self-reflection. At least, one must know about one's knowledge as a basis of self-reflection. If the pupils used their knowledge to learn and practice precisely what they had identified as their weaknesses before, this would be a step towards self-regulated learning. However, there has been no further investigation into the consequences of the test results for the pupils so far.

While the category “sure and correct” remains on a high level, the opposite, “unsure and incorrect” seems not to benefit from the CBM treatment. One possible conclusion is that the repeated use of CBM manages to reduce overconfident pupils, but on the other hand, it may create some insecurities. Regarding the origin of CBM, this effect is desired in the case of medical doctors but it may not be so much in favour when it comes to pupils in school. Open questions are whether this effect mainly concerns weaker pupils, who are generally more insecure about their mathematical knowledge.

The presented exploratory study is a starting point and is still ongoing, so the findings must be interpreted cautiously. In addition, these findings relate exclusively to one experimental group, so to a small sample. Therefore, the study will initially be continued in the current groups and then expanded to include further groups so that future results will be based on a broader database.
<figure><img src="image_93.png" /><figcaption>Test2</figcaption></figure>

<figure><img src="image_94.png" /><figcaption>Test3</figcaption></figure>

<figure><img src="image_95.png" /><figcaption>Test4</figcaption></figure>

<figure><img src="image_96.png" /><figcaption>Test5</figcaption></figure>

<figure><img src="image_97.png" /><figcaption>Test6</figcaption></figure>

<figure><img src="image_98.png" /><figcaption>Test7</figcaption></figure>

<figure><img src="image_99.png" /><figcaption>Test 8</figcaption></figure>

<figure><img src="image_100.png" /><figcaption>Test 9</figcaption></figure>

<figure><img src="image_101.png" /><figcaption>Test 10</figcaption></figure>

<figure><img src="image_102.png" /></figure>
<figure><img src="image_103.png" /><figcaption>Figure 1: Test results of the CBM class (Each point represents the results of one pupil. The x-axis is the final score, while the y-axis is the number of correct answers.)</figcaption></figure>

## References

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- Brensing, M., Dannewald, T., Kanzinger, A., Mayer, U., & Zender, J. (2021). Counselling in the introductory phase of studies. *Zeitschrift für Hochschulentwicklung, 16*(1), 117–136.

- Brookhart, S. M. (2010). *Formative assessment strategies for every classroom: An ASCD action tool*. Association for Supervision and Curriculum Development.

- Cizek, G. J. (2010). An introduction to formative assessment: History, characteristics, and challenges. In Andrade, H., Cizek, G. J. (Eds.), *Handbook of formative assessment* (pp. 3–17). Routledge. https://doi.org/10.4324/9780203874851

- Foster, C. (2016). Confidence and competence with mathematical procedures. *Educational Studies in Mathematics, 91*(2), 271–288. https://doi.org/10.1007/s10649-015-9660-9
Foster, C. (2022). Implementing confidence assessment in low-stakes, formative mathematics assessments. *International Journal of Science and Mathematics Education, 20*(7), 1411-1429.

Gardner-Medwin, A. R. (1995). Confidence assessment in the teaching of basic science. *ALT-J, 3*(1), 80-85.

Gardner-Medwin, T. (2019). Certainty-based marking. In Clegg, K. (Ed.), *Innovative Assessment in Higher Education: A Handbook for Academic Practitioners*, 141–150.

Geisen, M. & Zender, J. (2023). Formative Assessment in online courses – Ideas and Experiences. In M. Ludwig, S. Barlovits, A. Caldeira, & A. Moura (Eds.), *Research On STEM Education in the Digital Age. Proceedings of ROSEDA 2023: Research Online STEM Education in the Digital Age* (pp. 25-32). WTM-Verlag.

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Valero, G., & Cárdenas, P. (2017) Formative and Summative Assessment in Veterinary Pathology and Other Courses at a Mexican Veterinary College. *Journal of Veterinary Medical Education, 44* (2), 331–337. https://doi.org/10.3138/jvme.1015-169R

Yuen-Reed, G., & Reed, K. B. (2015). Engineering Student Self-Assessment through Confidence-Based Scoring. *Advances in Engineering Education, 4*(4), 1–23.
Posters
# Assessment in the mathematics classroom in relation to how students are in(ex)cluded in mathematics

Maria Silwer

Malmö University, Malmö, Sweden; maria.silwer@mau.se

Keywords: Classroom assessment, students' perspectives, teachers' perspectives, mathematical reasoning.

## Introduction and background

In this poster I would like to discuss the design of my PhD-project on assessment in the mathematics classroom in relation to how students are in(ex)cluded in mathematics, in early school years (ages 10-12), in Sweden. This poster uses in(ex)clusion as a concept for inclusion and exclusion. Here inclusion in mathematics is when students can access and participate in mathematics learning (Roos, 2019b, referred to in Roos, 2023). Exclusion is always present in the process, when working for inclusion (Valero, 2021, referred to in Roos, 2023).

This poster uses the following definition of assessment practice: All decisions the teacher makes when assessing, e.g., what is assessed, which tasks to use, when and in which situations (Boistrup, 2017). Hence, assessment is a part of learning and education, and therefore also in mathematics education. In mathematics classroom assessment the teacher gathers information about students’ mathematical knowing to support learning but also to improve teaching practice (Nieminen et al., 2023). Assessment affects how the students are positioned when learning mathematics due to roles and responsibilities (Nieminen et al., 2023). This could indicate that students meet different kinds of assessment practices in different classrooms, which in turn in(ex)clude the students in relation to learning mathematics. Hence, this poster assumes that assessment is present in all teaching and is shown to the student when given as feedback (Boistrup, 2017).

## Plan for upcoming study

The tentative aim of this study is to build an understanding of assessment in the mathematics classroom in relation to how students are in(ex)cluded in mathematics. The mathematical focus will be reasoning due to two reasons. One, different kinds of reasoning are generated by problem solving (Boesen et al., 2010, referred to in Säfström et al., 2024), which in turn is shown to be beneficial for students’ learning of mathematics (Liester & Cai, 2016, referred to in Säfström et al., 2024). Two, reasoning can exist regardless of mathematical content, e.g. arithmetic or geometry. Hence, this study will explore students’ perspectives on assessment in mathematics and how students are in(ex)cluded in relation to learning mathematics through reasoning in the classroom. The teacher matters in the classroom (Terhart, 2011) and in the assessment, so this study will also focus on the teacher. By doing this, it will be possible to gain insights into how equity-driven assessment practices could be used in the mathematics classroom. To meet the aims of this study, its design will be developed systematically structured by the following parts.

First, the aim is to examine how students are in(ex)cluded in relation to learning mathematics in the classroom. The tentative research question is: What traces of in(ex)clusion can be identified in interviews with students and teachers? To answer this question interviews will be conducted with
students and teachers, with a focus on their perspectives of assessment in the mathematics classroom.
The results will be presented in the first article.

Second, the aim is to compare responses from students and teachers, to identify potential differences
in assessment practices in relation to in(ex)clusion, within and between classrooms. The tentative
research questions are: What similarities and differences due to in(ex)clusion can be identified in
students' and teachers' perspectives on assessment in mathematics? What similarities and differences
regarding assessment practices within and between classrooms can be identified? The earlier
interviews will be used as a pilot study to design a survey with multiple-choice questions, to further
examine students' and teachers' perspectives on assessment in the mathematics classroom. The
results will be presented in the second article.

Third, the aim is to examine assessment practices in relation to how students are in(ex)cluded in relation to reasoning in mathematics education. The tentative research question is: How do different assessment practices in(ex)clude students in relation to reasoning in mathematics? A survey with open-ended questions will be used to examine teachers' perspectives on their own assessment practice. The results will be presented in the third article.

Fourth, the aim is to find ways to assess students reasoning in mathematics, on a classroom level, where the assessment practice promotes equity for all students. The tentative research question is: What can an assessment practice that promotes equity for all students look like? This case study will draw on findings from the earlier partial studies to develop assessment practices together with a teacher, in the mathematics classroom. The results will be presented in the fourth article.

References

Boistrup, L. B. (2017). Assessment in mathematics education: A gatekeeping dispositive. In H. Straehler-Pohl, N. Bohlmann, & A. Pais (Eds.), *Disorder of Mathematics Education: Challenging the Sociopolitical Dimensions of Research* (pp. 209–230). Switzerland: Springer International Publishing.

Nieminen, J. H., Bagger, A., Padilla, A., & Tan, P. (2023). Student Positioning in Mathematics Assessment Research: A Critical Review. *Journal for Research in Mathematics Education, 54*(5), 317–341. https://doi.org/10.5951/jresematheduc-2022-0030

Roos, H. (2023). Students' voices of inclusion in mathematics education. *Educational Studies in Mathematics, 113*(2), 229–249. https://doi.org/10.1007/s10649-023-10213-4

Säfström, A. I., Lithner, J., Palm, T., Palmberg, B., Sidenvall, J., Andersson, C., Boström, E., & Granberg, C. (2024). Developing a diagnostic framework for primary and secondary students’ reasoning difficulties during mathematical problem solving. *Educational Studies in Mathematics, 115*(2), 125–149. https://doi.org/10.1007/s10649-023-10278-1

Terhart, E. (2011). Has John Hattie really found the holy grail of research on teaching? An extended review of Visible Learning. *Journal of Curriculum Studies, 43*(3), 425–438. https://doi.org/10.1080/00220272.2011.576774
# The importance of formative assessment in developing student teachers' teaching practice

Daniel de Oliveira Lima¹

¹University of the State of Rio de Janeiro, Cap-UERJ, Department of Mathematics and Drawing, Rio de Janeiro, Brazil; danielprof2006@gmail.com

Keywords: Mathematics assessment, pedagogical practices, teacher training, formative assessment, teacher development.

## Introduction

Assessment is essential in teacher education as it elucidates how and what enhances students' school performance in class. For instance, Lima (2022) delves into the significance of teacher training in comprehending assessment in mathematics. At the University of State of Rio de Janeiro (UERJ), student teachers learn about pedagogical practices in mathematics during their mathematics undergraduate studies. This course's curriculum emphasizes preparing students for the challenges they will encounter in their future school classes. The course content integrates concepts from primary education with a focus on active methodologies and formative assessment. Ideas from Anderson and Palm (2018), Buchholtz, et al. (2018) and Lima (2022) inspire reflective discussions regarding formative assessment. This article aims to explore the role of formative assessment in the course and whether having a focus on formative assessment in an undergraduate mathematics can benefit student teachers in their teaching practice.

## Theoretical framework

According to Anderson and Palm (2018), assessment is a process that involves teachers and their students in collecting, analyzing, interpreting, discussing, and utilizing information regarding students' learning. Assessment fulfills two roles: summative and formative. The former involves assessing school students' performance, allowing teachers to rank students and provide an overview of their learning progress. The latter concentrates on the learning process and emphasizes feedback and offers detailed personalized feedback.

Lima (2022) suggests that formative assessments aim to enhance learning, essentially making them integral to the teaching process. Formative assessment, when conducted solely by the teacher, becomes an intrinsic part of teaching. It's important to note that since teaching methods vary, so do assessment methods. It is necessary to highlight that there are different ways of teaching, so there are other ways of evaluating. Buchholtz, et al. (2018) argue that any assessment can be either formative or summative, contingent upon the teacher's perspectives.

Lima (2022) distinguishes between summative and formative feedback. Summative feedback centers on grades and occurs at the culmination of a process, evaluating a student's overall performance. In contrast, formative feedback transpires throughout the process, pinpointing errors and devising strategies to address weaknesses. Moreover, it facilitates students' self-regulation and fosters autonomy.
**Research questions and aim**

Lima (2022) argues that mathematics undergraduate programs must incorporate assessments in mathematics. Consequently, as the author and professor specializing in pedagogical practices in mathematics, he introduced this subject in his class. Building upon this premise and drawing from the research of Lima (2022) and Buchholtz, et al. (2018) the present study aims to explore the research question: How has a focus on formative assessment in their undergraduate mathematics degree benefited student teachers in their teaching practice?

**Analyzing some answers from students**

To address the research question, two student reports about student experience in the course were analyzed. Out of eight students, these were the ones who participated the most in class and showed higher levels of engagement. The reports were analyzed through qualitative research using document analysis.

Student A expressed, "In this specific subject, I performed well; I learned extensively and gained insights into classroom dynamics, student challenges, and effective strategies for addressing individual learning processes". This student emphasized the importance of recognizing and addressing student difficulties, which is often overlooked, particularly among math educators.

Student B shared, "The course significantly enhanced my ability to create inclusive and engaging learning environments for my students. I've noticed a substantial increase in their participation and enthusiasm". Despite acknowledging that more consistent attendance could have benefited her learning, she found the course instrumental in improving her teaching practices.

**Conclusions**

Throughout the course, students were challenged to create lesson plans and activities, apply active methodologies, and receive specific feedback. Additionally, the class examined the significance of teacher development, encompassing knowledge, professional culture, pedagogical tact, teamwork, and social commitment. It is evident that the course had a positive impact on students' preparations for their future careers as educators.

**References**

Andersson, C. & Palm, T. (2018). Reasons for teachers' successful development of a formative assessment practice through professional development – a motivation perspective. *Assessment in Education: Principles, Policy & Practice, 25*(6), 576–597.
https://doi.org/10.1080/0969594X.2018.1430685

Buchholtz, N. F., Krosanke, N., Orschulik, A. B., & Vorholter, K. (2018). Combining and integrating formative and summative assessment in mathematics teacher education. *ZDM Mathematics Education, 50*, 715–72. https://doi.org/10.1007/s11858-018-0948-y

Lima, D. (2022). *Concepções de professores de matemática sobre a avaliação escolar: o caso da Escola Sesc de ensino médio* [Doctoral dissertation, Federal University of Rio de Janeiro]. Theses and Dissertations Archive. https://pemat.im.ufrj.br/index.php/pt/producao-cientifica/teses/104-2022/379-concepcoes-de-professores-de-matematica-sobre-avaliacao-escolar-o-caso-da-escolas-de-ensino-medio.
# Perceptions of Effective Formative Feedback: A comparative Analysis Between Undergraduate Students and Mathematics Lecturers

Samah Taha, George Kinnear and Paola Iannone

University of Edinburgh, School of Mathematics; Samah.taha@ed.ac.uk; G.kinnear@ed.ac.uk and Paola.innone@ed.ac.uk

*Keywords: Formative feedback, feedback framework, comparative judgement.*

In the context of formative e-assessment in mathematics, students often demonstrate misconceptions, which underlie their mistakes. This prompts an exploration of the role of feedback as cornerstone of formative e-assessment. Given the increasing reliance on technology in education and the need for adaptable assessment methods to meet the evolving needs of learners in the digital age, focusing on e-assessment becomes imperative (Evans, 2013). What feedback should mathematics lecturers provide within e-assessment to effectively support student learning? This poster presents the perspective of both undergraduate students and mathematics lecturers to the feedback provided by fourteen mathematics lecturers in response to a fictional student response to a formative e-assessment task.

High-quality feedback may influence student achievement (Mulliner & Tucker, 2017). However, despite substantial time and effort invested in generating feedback, there is a noticeable lack of research in higher education regarding its effectiveness (Price et al., 2010). Despite evidence of students' desire for feedback from their lecturers, the National Students Survey in the UK has documented student dissatisfaction since 2005, with students expressing discontent over the nature and timing of feedback (Price et al., 2010). In contrast, academics often believe their students are receiving timely, extensive, and informative feedback (Mulliner & Tucker, 2017).

Assessment feedback includes all feedback exchanges generated within assessment design, occurring within and beyond the immediate learning context, being overt or covert (actively and/or passively sought and/or received), and importantly, drawing from a range of sources (Evans, 2013). A comprehensive review by Lipnevich and Panadero (2021) presents fourteen models, complete with accompanying diagrams, explaining how feedback operates and identifying variables that may contribute to student engagement with it. Within this complex landscape of factors and interactions, our study draws a narrow focus on the content of the feedback message that mathematics lecturers provide to undergraduate students on formative e-assessment tasks. In this poster, we address two questions:

RQ1: Do mathematics lecturers generally agree on the characteristics of the effectiveness of formative feedback?

RQ2: Do the lecturers' perceptions of effective feedback align with those of their students?

Building upon the research conducted by Evans et al. (2022), which highlights the efficacy of comparative judgment in studying the quality of mathematical explanations, we adopt this approach to analyse the quality of feedback given on e-tasks. Comparative judgment is a widely utilised method in educational research, employed to evaluate student's essays, laboratory reports, and abstract constructs such as conceptual understanding, problem-solving, and mathematicians' proof
conceptions (Evans et al., 2022). For our study, we collected feedback from mathematics lecturers
in response to a prompt on a common error made by undergraduate students. The task is derived from
a digital module in integral calculus, designed to support undergraduates in finding areas enclosed by
functions, as highlighted by Kontorovich and Locke (2023). Using a comparative judgment
approach, two groups of judges – lecturers and students – will assess pairs of feedback for
effectiveness. This will generate two scores for each item of feedback: one from lecturers and one
from students. To address RQ1, we will compute the split-halves reliability measure for the group of
lecturers, using the method described by Evans et al. (2022). This gives a number between 0 and 1,
with values above 0.7 indicating a good level of agreement between the lecturers. To address RQ2,
we will compute the correlation between the scores produced by the lecturers and the scores produced
by the students. A high correlation (close to 1) indicates strong agreement on feedback effectiveness,
while a low correlation (close to 0) suggests limited agreement.

If undergraduate students and mathematics lecturers share a common understanding of high- and low-quality mathematical feedback, this agreement motivates further investigation in two directions: evaluating alignment with established frameworks for high-quality feedback, and exploring potential differences in the underlying mechanisms and considerations influencing students and lecturers' choices. Conversely, any conflict in feedback perceptions between students and lecturers prompts an exploration of the factors contributing to the disparity. Addressing these factors is crucial for enhancing students' engagement with feedback.

References

Evans, C. (2013). Making Sense of Assessment Feedback in Higher Education. *Review of Educational Research*, 83(1), 70–120. https://doi.org/10.3102/0034654312474350

Evans, T., Mejía-Ramos, J. P., & Inglis, M. (2022). Do mathematicians and undergraduates agree about explanation quality? *Educational Studies in Mathematics*, 111(3), 445–467.
https://doi.org/10.1007/s10649-022-10164-2

Kontorovich, I., & Locke, K. (2023). The Area Enclosed by a Function Is Not Always the Definite Integral: Relearning Through Collaborative Transitioning Within a Learning-Support Module. *Digital Experiences in Mathematics Education, 9*(2), 255–282. https://doi.org/10.1007/s40751-022-00116-z

Lipnevich, A., & Panadero, E. (2021). A Review of Feedback Models and Theories: Descriptions, Definitions, and Conclusions. *Frontiers in Education, 6*. https://doi.org/10.3389/feduc.2021.720195

Mulliner, E., & Tucker, M. (2017). Feedback on feedback practice: Perceptions of students and academics. *Assessment & Evaluation in Higher Education, 42*(2), 266–288.
https://doi.org/10.1080/02602938.2015.1103365

Price, M., Handley, K., Millar, J., & O'Donovan, B. (2010). Feedback: All that effort, but what is the effect? *Assessment & Evaluation in Higher Education, 35*(3), 277–289.
https://doi.org/10.1080/02602930903541007
# Design of tasks for assessing Diophantine equations on the new Mexican School

Alejandra Fabiola Huitrado Mora¹ and Carolina de Haro Calderón¹

¹Teaching Updating Center in Zacatecas, Mexico; alejandrafabiola@camzac.edu.mx; carolina-calderon@camzac.edu.mx

*Keywords: Diophantine equations, modeling, mathematical curriculum.*

## Linear Diophantine equations

In mathematics an equation is an algebraic statement in which it is shown that two amounts are equal using mathematical symbols like numbers, variable or unknown values joined by arithmetic symbols, and it is true for some values. This is an essential tool for modeling real life situations. Moreover, Amorim (2020) reminds us that one of the challenges in the initial training of mathematics teachers is to articulate the contents studied in the disciplines at the university with the themes of primary and secondary school. In this research we focus on the Diophantine equations as they are part of the new curriculum 2022, National Strategy for the Improvement of Normal Schools, in Mexico.

Given polynomial equations with integer coefficients and which solutions are also integer numbers are called Diophantine equations. For now, we focus on linear equations, more precisely with two variables, i.e., equations like the following: $ax + by = c$, with a, b and c integers numbers.

## Curriculum 2022 National Strategy for the Improvement of Normal Schools

Recently, the basic education curriculum in Mexico has been updated with the aim of covering the needs of the development of individuals. For this, the new curriculum 2022 in its approach of the mathematics teaching and learning degree states that:

> Mathematics is understood as a complex social and cultural construction; On the one hand, it is a set of heterogeneous knowledge in permanent construction, dynamic and situated, and on the other, it is a scientific discipline with its own knowledge production procedures, which must be learned and taught among new generations. Its value lies in the fact that it allows the subject to situate himself, order and understand the world. (Secretaría de Educación Pública [SEP], 2022, p. 1)

> Below I explain the treatment given to the design of the tasks for the evaluation of the topic "Diophantine equations".

## Tasks-design for future teachers on the topic Diophantine equations.

Linear equations with one variable are perhaps the simplest tool for modeling and solving problems, but what happens when more than one unknown value appears? Moreover, what happens when we try to design activities to contextualize them, where there is also implicit information that the individual destined to pose and solve a problem must identify to use it in the correct modeling of the situation? A problem proposed for a group of 2^nd^ semester of teachers in training to try to answer both questions was: On the "Pozolito" farm there are ducks and dogs. Mr. Genaro told his grandson that counting only the legs of the animals there are, there is a total of 54. Write an equation that describes the situation and finds at least one solution (if it is possible). Explain your answer.
The students took 15 minutes for solving the problem. Answering the first question, the most common error that occurred was that the implicit information (number of legs of both animals) was identified but the same variable was used, so the equation $2x + 4x = 54$ was proposed, and they quickly responded that reducing similar terms, i.e., $6x = 54$ the solution was $x = 9$. However, they do not differentiate between how many of them are ducks and how many of them are dogs. Later we will see, that 9 has no sense with the correct answers. Now for the second question, common errors were also identified. In this case, several of the students identified that the number of ducks was a variable $x$, and the number of dogs another variable $y$, but they did not use the implicit information (number of legs of both animals), so they proposed the equation $x + y = 54$, giving a long list of possible solutions, which was obviously incorrect because the implicit information was really fundamental for the statement and subsequent resolution. These difficulties were also reported by Edo (2013).

Then, what was the answer to the problem? As a first step, formulate the correct equation, that is, $2x + 4y = 54$, and then proceed to solve it. Clearly, the first thing to do is check that the equation does indeed have integer solutions, which are the ones that interest us and that they are clearly solutions to the contextualized problem, because even when we know that the equation has an infinite number of solutions in real numbers, we are not interested in saying that there are 3.5 dogs. It is easy to verify that this problem has integer solutions. Now, although in general we look for integer solutions for a Diophantine equation, and we have established that they are an infinite quantity, if they exist, for problems that model a situation of real life we must take in account which answers really are important to us, because in this case we are not interested in solutions like having -3 ducks either. Thus, the solutions reduce to $x = 1 + 2t, y = 13 - t, t \in Z, 1 \le t \le 12$.

The assessment of this problem, it was found that only a sixth of the group completely solved the task, and in total a quarter partially solved it, even intuitively, by trial and error. Due to all the factors observed, it is planned to replan the work with the contextualization of the contents, particularly with Diophantine equations, to improve future evaluations and the design of exercises paying attention in these and other factors that we can detect because they are an example of modeling simple real life.

## Acknowledgment

To the Teaching Updating Center in Zacatecas for the supporting to this work.

## References

* Amorim, M. É., Pietropaolo, R. C., Galvão, M. E. E. L., & Da Fontoura G. S., A. (2020). A sequence of activities for teaching Diophantine Equations: Possibility to expand the knowledge base of future mathematics teachers. *Acta Scientiae*, 22(5), 207-225.
[https://doi.org/10.17648/acta.scientiae.6080](https://doi.org/10.17648/acta.scientiae.6080)

* Edo, S. I., Ilma, R., & Hartono, Y. (2013). Investigating secondary school students’ difficulties in Modeling Problems PISA-Model Level 5 and 6. *Journal on Mathematics Education, 4*(1).
[https://doi.org/10.22342/jme.4.1.561.41-58](https://doi.org/10.22342/jme.4.1.561.41-58)

* Secretaría de Educación Pública [SEP] (2022, 03 March). *Anexo 12. Plan de estudio de la licenciatura en enseñanza y aprendizaje de las matemáticas*. [9FUnbRJp85-ANEXO_12_DEL_ACUERDO_16_08_22.pdf](9FUnbRJp85-ANEXO_12_DEL_ACUERDO_16_08_22.pdf) (sep.gob.mx)
# Exploring instrumental orchestration practices in the context of formative assessment with technology

Min Chen¹, Rogier Bos², Michiel Doorman³ and Paul Drijvers⁴

Freudenthal Institute, Utrecht University, The Netherlands; m.chen3@uu.nl; r.d.bos@uu.nl; m.doorman@uu.nl; p.drijvers@uu.nl

*Keywords: Instrumental orchestration, formative assessment, digital technology.*

## Introduction

In guiding instrumental genesis teachers need to assess students' progress, and teachers' interventions involving digital tools can be described using the theory of instrumental orchestration (Trouche, 2004). We would like to study how assessment is part of these interventions of instrumental orchestration to better understand formative assessment in teaching with technology.

## Background of the study

Digital tools have greatly increased the possibilities and potential for mathematical teaching and learning as well as for formative assessment (e.g., Baird et al., 2017). Much research on digital technology in mathematics education has been done with respect to learning with technology, and the significance of the instrumental view is central to current research on digital tools in mathematics teaching and learning (e.g., Drijvers et al., 2010; Trouche, 2004). Instrumentation theory stresses the importance of teachers carefully designing activities and selecting appropriate artefacts for students, to facilitate instrumental genesis in a meaningful and natural way. Regular whole-class teacher-centered teaching orchestration can be enriched with other formats, such as student-centered practices where students can actively explore mathematics activities through digital tools (Drijvers & Sinclair, 2023). These student-centered activities help to collect whole class information. Moreover, the integration of digital tools in the mathematics classroom requires careful consideration of how to orchestrate the lessons and the impact on assessment practices (Panero & Aldon, 2016). Thus, exploring teachers' orchestration preferences is crucial for aligning teaching practices with formative assessment using digital technology in mathematics classrooms.

## Relation to the conference theme and dimension

According to Hollebrands & Okumuş (2018), effective instrumental orchestration involves selecting appropriate technological tools and guiding their use to foster meaningful learning experiences. In the context of formative assessment, technology can provide immediate feedback, facilitate personalized learning, and enable teachers to monitor student progress in real-time (Spector et al., 2016). This alignment of technology with pedagogical goals enhances the formative assessment process by making it more dynamic, responsive, and supportive of student learning trajectories (Black & William, 2009). Thus, the relationship between instrumental orchestration and formative assessment with technology could be synergistic, integrating digital tools to create a more effective and nuanced approach to evaluating and supporting student learning. This study adopts the instrumental orchestration theory to study the ways in which teachers' orchestrate formative assessment practices through digital technology. In other words, we want to study the role of formative assessment in how teachers develop orchestration strategies and implement them.
## Setup of the study

The research question of this study is: How do teachers conduct formative assessment as part of their orchestration practices when using digital technology in mathematics classrooms?

We answer this question by studying classroom videos of technology-rich lessons. This study uses a convenience sampling method and participants are secondary school mathematics teachers from JiangSu Province in China. We choose videos of the 2022 "JiangSu Province ICT-integrated High-Teaching Quality Course Competition" for observation and analysis, because we expect that these videos could illustrate successful examples of technology-rich classroom practices. When analyzing the data, we focus on understanding how the orchestration types employed by teachers provide them with opportunities to gauge the progress of their students and to assess their work. The results examine teachers' orchestrations and classroom assessment practices with the aim to illustrate teachers' specific orchestration practices with a particular emphasis on assessing students' performance in a formative way. Hopefully, our findings can be used to demonstrate how teachers can create more adaptive and responsive learning environments that enhance student outcome by effectively orchestrating digital tools within formative assessment practices.

## References

Black, P., & William, D. (2009). Developing the theory of formative assessment. *Educational Assessment, Evaluation & Accountability, 21*, 5–31. https://doi.org/10.1007/s11092-008-9068-5

Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. *Educational Studies in Mathematics*, 75(2), 213–234. https://doi.org/10.1007/s10649-010-9254-5

Dalby, D., & Swan, M. (2019). Using digital technology to enhance formative assessment in mathematics classrooms. *British journal of educational technology*, 50(2), 832–845. https://doi.org/10.1111/bjet.12606

Drijvers, P., & Sinclair, N. (2023). The role of digital technologies in mathematics education: Purposes and perspectives. *ZDM*, 1–10. https://doi.org/10.1007/s11858-023-01535-x

Panero, M., & Aldon, G. (2016). How teachers evolve their formative assessment practices when digital tools are involved in the classroom. *Digital Experiences in Mathematics Education, 2*(1), 70–86. https://doi.org/10.1007/s40751-016-0012-x

Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. *International Journal of Computers for Mathematical Learning*, 9, 281–307. https://doi.org/10.1007/s10758-004-3468-5

Spector, J. M., Ifenthaler, D., Sampson, D., Lan (Joy) Yang, Mukama, E., Warusavitarana, A., ... & Gibson, D. C. (2016). Technology enhanced formative assessment for 21st century learning. *Journal of educational technology & society*, 19(3), 58–71.

Hollebrands, K., & Okumuş, S. (2018). Secondary mathematics teachers’ instrumental integration in technology-rich geometry classrooms. *The Journal of Mathematical Behavior*, 49, 82–94. https://doi.org/10.1016/j.jmathb.2017.10.003
# Self-assessment in long-term problem solving STEM contexts

Julia Schäfer¹ and Gero Stoffels¹

¹University of Cologne, Institute of Mathematics Education, Cologne, Germany;
[julia.schaefer@uni-koeln.de](mailto:julia.schaefer@uni-koeln.de); [gero.stoffels@uni-koeln.de](mailto:gero.stoffels@uni-koeln.de)

*Keywords: Self-assessment, problem solving, mathematics in STEM, authenticity.*

## MINTco@NRW a project fostering long-term problem solving

MINTco@NRW is a cooperation between the University of Siegen and the University of Cologne. This project is a follow up of the extracurricular project "Authentic-STEM" (Stoffels, 2024). Its aim is to integrate systematically long-term problem solving in authentic contexts into regular classrooms at secondary level in North Rhine-Westphalia. To make this possible, companies collaborate in the project and provide several authentic mathematics related unsolved problems that are solved by German and U.S. students in solver-teams. During a cycle the students work four months on the problems. At the end of each cycle, the solutions developed are presented to the companies. Through MINTco@NRW this activity will be transferred into regular classrooms. Therefore, there is a need for tasks and materials fitting the curriculum as well as testing adequately the participating students for grading. Both need to be connected to the core ideas of the project. These are, that through long-term and intensive engagement with authentic problems the students deepen their 21st century skills (Radmehr & Vos, 2020), enhance their mathematical and STEM competencies (e.g. problem solving, modeling, using theories and communicate) and explore their self-efficacy (Bandura, 1997).

## Self-assessment for testing more than mathematical and STEM competencies

Various studies have already shown that there is a strong correlation between students' learning, performance, and formative assessments. Feedback and its quality also play a central role in the above-mentioned context. Feedback should point out the main errors and their probable causes and explain how to avoid those errors in the future. All three aspects can be addressed by students' self-assessment, since self-criticism and self-evaluation have a major influence on students' own learning processes (Shepard, 2005). Also, self-evaluation plays a central role in many mathematical metacognitive processes, e.g. the verification phase in mathematical problem solving (Rott et al., 2021) or the validating phase in mathematical modeling (Blum & Borromeo-Ferri, 2009). The long-term approach of this project (Stoffels & Holten, 2022) as well as the complexity of the real problems, give many opportunities for the students to evaluate their own problem solving activity. Also, the setting with multiple stakeholders involved can add other perspectives to the students' self-assessment. An example for this aspect is the evaluation of the students' own views about the mathematicality of the problems. Similar questions are raised in the sociologically informed conceptualization of authenticity given by Vos (2018).

The main research questions are: how adequate self-assessment formats look like, which capture both more general skills and competencies as well as the quality of mathematical processes; and who, among the stakeholders, should take part in which way to strength the capability of students' self-assessment? Therefore, during the project period, one focus of the self-assessment will lay on the students' zone of proximal development (Vygotsky 1978) also monitoring the project's environment.
**Methodological considerations and expected outcomes**

The project consists of a half year pilot cycle in Spring 2024, which is still in an extracurricular format. During this cycle material (e.g. logbooks, Impulse formats) for supporting the students' problem solving are evaluated using structuring content analysis. Parallel to this identification formats for the self-assessment of students and tests for grading are identified and adapted to the core ideas of the project. In the following two years starting summer 2024, the program will be implemented in at least six regular classrooms in North-Rhine Westphalia, so two design research cycles will be carried out to improve the formats and evaluate their effectiveness. Over each cycle, portfolios are kept as "digital logbooks", which might be a candidate for examination formats.

The presented project aims to contribute to the development of adequate assessment formats for long-term cooperative problem solving as well as the evaluation of the adequacy of these formats regarding their ability to foster students' self-assessment and self-regulatory processes.

**Acknowledgment**

MINTco@NRW is funded by the Ministry of Education of North-Rhine Westphalia.

**References**

Bandura, A. (1997). *Self-Efficacy: the exercise of control*. W. H. Freeman and Company.

Blum, W., & Borromeo Ferri, R. (2009). Mathematical Modelling: Can It Be Taught And Learnt? *Journal of Mathematical Modelling and Application*, 1(1), 45–58.

Radmehr, F., & Vos, P. (2020). Issues and challenges for 21st century assessment in mathematics education. *Science and mathematics education for 21st century citizens: Challenges and ways forwards*, 437-462 [http://doi.org/10.13140/RG.2.2.18537.77927](http://doi.org/10.13140/RG.2.2.18537.77927)

Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. *ZDM–Mathematics Education*, 53(4), 737-752. [https://doi.org/10.1007/s11858-021-01244-3](https://doi.org/10.1007/s11858-021-01244-3)

Shepard, L. A. (2005). Linking formative assessment to scaffolding. *Educational leadership*, 63(3), 66-70.

Stoffels, G., & Holten, K. (2022). MINT-Pro²Digi: Authentisches projektorientiertes mathematisches Problemlösen in außerunterrichtlichen digitalen Kontexten. *MINTUS – Beiträge Zur Mathematisch-Naturwissenschaftlichen Bildung*, 47-71. [https://doi.org/10.1007/978-3-658-36764-0_3](https://doi.org/10.1007/978-3-658-36764-0_3)

Stoffels, G. (2024). *Authentic-STEM: Opening long-term domains of experience for fostering students' and mentors' self-efficacy through mathematics* (P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya, Eds.). HAL Archives Ouvertes; Alfréd Rényi Institute of Mathematics. [https://hal.science/hal-04420539](https://hal.science/hal-04420539)

Vos, P. (2018). “How real people really need mathematics in the real world”—Authenticity in mathematics education. *Education Sciences, 8*(4), 195. [https://doi.org/10.3390/educsci8040195](https://doi.org/10.3390/educsci8040195)

Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. In *JSTOR*. Harvard university press. [https://doi.org/10.2307/j.ctvjf9vz4](https://doi.org/10.2307/j.ctvjf9vz4)
# The role of elicitation in formative assessment

Kristoffer Arvidsson<fnref n="1" /> and Torulf Palm<fnref n="2" />

Keywords: Formative assessment, elicitation, feedback, mathematics education.

## Introduction and aim

Research has shown that formative assessment has a large potential for accomplishing positive effects on student learning (Black & William, 1998; Hattie, 2009; Andersson & Palm, 2017). One main function of formative assessment is to adapt teaching strategies to students’ learning needs (SLN). Adaption of teaching to SLN requires that information about these needs be elicited and understood. However, studies examining feedback effectiveness most often do not focus on how the quality of the acquired information influences the impact of feedback on student achievement.

My poster will describe a study that is part of a larger project that seeks to contribute to the development of a theory of action for formative assessment. This includes identifying mechanisms by which formative assessment affects student learning. The study presented in this poster contributes to the project by identifying how a mathematics teacher elicits information about SLN when they seek help during task solving. The study aims to describe different ways of eliciting relevant information, how these ways influence the quality of information acquired and how these affect possibilities to adapt the feedback to meet the SLN.

This poster will describe the study and emphasise the importance of elicitation in the formative assessment practice. In doing so, describe the different ways of elicitation the teacher uses and how they may relate to the adjustment of feedback the teacher makes.

## Method

This qualitative case study focuses on in-depth insights into the practice of one experienced middle school teacher. The data consists of 15 audio recordings of the teacher's mathematics lessons in a year 6 class over the span of one year. During this time the teacher was a part of a professional developmental program which focused on improving formative assessment practises in the classroom. During the recorded lessons, the teacher helped students individually when they sought help during task-solving. The data will be analysed in a thematic approach by identifying ways of elicitation, types of feedback and the relations between them.

## Tentative findings

Preliminary findings suggest that the teacher's way of eliciting may influence the type and relevance of information gathered about SLN. The teacher's feedback seems to align more closely with SLN when the elicitation process yields sufficient information, i.e. to enable the adjustment of feedback specifically to those needs. In cases where elicitation does not provide sufficient information, but the teacher proceeds to give feedback, this feedback often misses addressing the actual learning need. Instead, it may focus on task completion, which could be a separate issue from the learning need.

<footnote n="1">¹Umea University, Science and Mathematics Education, Sweden; kristoffer.arvidsson@umu.se</footnote>

<footnote n="2">²Umea University, Science and Mathematics Education, Sweden; torulf.palm@umu.se</footnote>

<footnote n="1">¹,²Umea Mathematics Education Research Centre (UMERC)</footnote>
Thus, it is important to explore how various elicitation ways might affect the outcome of elicitation and subsequently, how this outcome might shape the adaptation of feedback to students' learning needs.

Following are transcripts of two teacher-student interactions that depict two different ways of dealing with elicitation. The first transcript shows how the teacher elicits information about the learning need, continues to elicit information when she doesn't receive sufficient information and by the end of the conversation, the student's learning needs are resolved. The second transcript shows how the teacher elicits information but proceeds to give feedback before having received sufficient information about the learning needs. In the end, the learning needs of the student are not resolved, prompting the conversation to loop back, with the teacher needing to start again with the elicitation process.

Transcript 1

Student: I don't get it...

Teacher: What are you supposed to find out? What is the assignment? Can you tell me?

Student: I must figure out the circumference and area of this thing...

Teacher: OK, what help have you received [from the textbook] to be able to solve it?

Student: Ehh... all sides are 1 cm.

Teacher: Yes, OK, what about it do you find difficult?

Student: I don't know... I don't understand. Should I count all of them, like that?

Teacher: Yes?... What do you think... How do you calculate the circumference?

Student: But I'm going to... You add everything together.

Teacher: Yes, you already knew that! Great!

Transcript 2

Teacher: OK, what assignment are you working with?

Student: 128. I have done like this [shows previous work] and the thing I don't get is...

Teacher: [Interrupts] Wait, where are you? Explain the assignment.

Student: [Explains the assignment]

Teacher: What formula have you used?

Student: I don't know... or what do you mean?

Teacher: [Explains the formula for calculating area]

Student: I have used that formula already.

Teacher: Oh? I see, right... Then what was your problem?

[Conversation continues...]

A key distinction between these two ways of eliciting is the persistence in continuing until sufficient information is acquired. The poster session will offer a chance to explore additional examples.

References

Andersson, C., & Palm, T. (2017). The impact of formative assessment on student achievement: A study of the effects of changes to classroom practice after a comprehensive professional development programme. *Learning and Instruction*, *49*, 92–102. https://doi.org/10/f3t4k7

Black, P., & William, D. (1998). Assessment and classroom learning. *Assessment in Education: Principles, Policy & Practice*, *5*(1), 7–74. https://doi.org/10/fpnss4

Hattie, J. (2009). *Visible learning: A synthesis of over 800 meta-analyses relating to achievement*. Routledge.
FAME 1 Proceedings

Feedback & Assessment in Mathematics Education

5-7 June, 2024 - Utrecht, The Netherlands

14th ERME Topic Conference (ETC14)

ISBN: 978-90-393-7788-8

DOI: 10.5281/zenodo.14231455

<figure><img src="image_104.png" /></figure>

Utrecht
University