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Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment

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Abstract

Formative assessment practices for secondary mathematics have been advocated as valuable for students, but difficult for teachers to learn. There have been calls in the literature to increase the emphasis on formative assessment in mathematics teacher preparation courses. This study explored the use of peer-assessment strategies for helping pre-service secondary mathematics teachers (PSTs) cultivate formative assessment principles and practices for assessing school students. Twenty-seven PSTs participated in a peer-assessment cycle comprised of: sourcing a rich mathematics task; constructing an assessment rubric for it; and collecting and analysing a selection of secondary student responses to the task. Each PST then provided written and verbal feedback to a peer on his/her rubric and student solution assessments. We draw on theoretical conceptions of Teacher Assessment Literacy in Practice to characterize the PSTs’ perceptions of their experience of formative assessment processes for learning to assess school students, in terms of cognitive and affective dimensions of their conceptions of assessment. The cohort evidenced a wide range of levels of confidence with the various aspects of formative assessment practices but on average less confidence in assessing school student task responses themselves than in assessing peer work. In addition to highlighting specific changes to different types of assessment knowledge, the PSTs also evidenced an awareness of shifts in their attitudes, in coming to view student task responses with more appreciation and humility.

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Fig. 1

(Source: Xu and Brown 2016, p. 155)

Fig. 2

(Adapted from Reinholz 2016)

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Appendices

Appendix 1: Illustrative rubrics used/adapted by the PSTs

Illustration #1 (adapted from Schwartz et al. 1995)

Assessment criteria

High

Medium

Low

Comments

Modelling: How well does the student build the model for solving the mathematical problem?

    

Manipulating: How well does the student manipulate the mathematical formalism in which the problem is expressed?

    

Inferring: How well does the student apply the results of his or her manipulation of the formalism to the problem situation that spawned the problem?

    

Communicating: How well do students communicate to others what they have done in formulating the problem, manipulating the formalism, and drawing conclusions about the implications of their results?

    

Creativity: How much original is the student’s solution?

    

Illustration #2 (another version from Schwartz et al. 1995)

Assessment criteria

High

Medium

Low

Comments

Understanding the task (e.g. the situation, instructions, data, restrictions)

    

Mathematical thinking (e.g. generalizations, justifications)

    

Manipulations

    

Communication (e.g. explanations, presentation of the solution, mathematical language)

    

Creativity (originality and multiple solutions)

    

Illustration #3 (built on Swan and Burkhardt 2012)

Assessment criteria

High

Medium

Low

Comments

Representing (selecting information, methods and tools)

    

Analysing (e.g. making connections, making calculations, making conjectures and generalizations)

    

Interpreting and evaluating (forming conclusions and arguments, considering appropriateness and accuracy, relating back to the original situation)

    

Communicating and reflecting (e.g. communicating and discussing findings effectively, considering alternative solutions)

    

Appendix 2: Feedback provision by writing an analysis for a peer

Imagine that you are sitting in a team meeting of the mathematics teachers at your school. One of the teachers shares with you the rubric he/she has built to assess student solutions for a certain task. He/she asks you for your opinion on the rubric he/she developed and on the assessment he/she gave with the help of the rubric to the students’ solutions.

  1. 1.

    Read the task, the rubric, the student solutions, and your peer’s student assessments in the report (see the peer’s name below the work to which you are to respond).

  2. 2.

    Give feedback to your peer:

    1. a.

      What is good and what would you improve on the rubric (in accordance with the task chosen)?

    2. b.

      What do you agree with and what aspects would you change in their assessment of student solutions with the rubric? Justify your comments so that your peer can understand them.

In continuation of the ‘conversation’ with your colleague at the teachers’ meeting at school, imagine your peer asked for your advice as to what response you would give to each of their students in order to advance his/her understanding and learning.

  1. 3.

    Offer your peer responses to each student according to his/her task solution. Explain and justify your suggestions.

Appendix 3: Coding scheme with theme frequencies

Coding scheme

Num. PSTs (n = 27)

Cognitive aspects

C1

Increased knowledge about designing rubrics for rich tasks

20

C2

Knowledge of how to distinguish between levels of quality in responses

18

C3

Awareness of the importance of openness to students’ own ways of thinking

16

C4

Increased awareness of needing to align assessment goals, task, and rubric

13

Affective aspects

A1

Confidence in designing mathematical task and assessment criteria

12

A2

Confidence in attending to the details in students’ responses

10

A3

Less confidence in choosing a task and designing appropriate assessment criteria

13

A4

Less confidence in grappling with the subjective nature of certain assessment criteria

18

A5

Less confidence in interpreting students’ thinking

14

A6

Development of humility in responding to students’ work

13

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Ayalon, M., Wilkie, K.J. Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment. J Math Teacher Educ 24, 399–426 (2021). https://doi.org/10.1007/s10857-020-09465-1

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