STUDENT PERSPECTIVES ON RUBRIC IN A SECONDARY MATHEMATICS CLASS

M.-Jesús Gallego-Arrufatmgallego@ugr.esMaha A.I. Dandismdandees@ugr.esUniversity of Granada

Keywords:

Students, Assessment, Rubric, Secondary mathematics class

Abstract:

The research presented here is part of a larger project with teachers and secondary school students. It is a case study in which the emphasis is on formative assessment as continuous process developed by various techniques, among them is the rubric. The research interest is the perspectives of students because students are "the key assessment users". This study aims to discuss students' viewpoints regarding the effectiveness of using rubrics in the secondary mathematics class.

The intent of this paper is on one hand to contribute to the limited literature that pertains to the use of rubrics in secondary mathematics class. But mainly aims to promote reflection on whether there are factors such as age or the content of matter on which we should learn more to use (or not use) tools such as assessment rubrics to try to improve learning at the secondary level.

The results showed that the students found positive relationship between using the rubric and their learning, and that using the rubric raised the quality of their answers in problem solving. But they found it difficult and complicated to use, and they gave some recommendation to enhance it.

1. INTRODUCTION

… The student’s point of view matters because of its effect on learning. From the student’s point of view, classroom assessment information is not merely

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information “about” himself or herself. Rather, it forms a major part of his or her learning life, becoming part of the lessons he or she is expected to learn, the relationship he or she has with the teacher and the subject matter, and relationships with peers. (Brookhart, 2003, p. 6)

Stiggins (2001) argued that students are “the key assessment users” (p. 17). In assessment for learning teachers provide students with a clear vision of the learning target from the beginning of the learning, along with samples of strong and weak work, so they can see a progression to competence laid out before them. Also they provide students with continuous access to descriptive (versus evaluative or judgmental) feedback; that is, information that helps to see how to improve the quality of their work. This requires students’ engagement in repeated self assessments so they can watch themselves successfully negotiating the road to competence. Ultimately, then, students learn to generate their own descriptive feedback and to set goals for what comes next in their learning. Each of these specific practices draws the learner more deeply into taking responsibility for her or his own success (Stiggns, 2005).

Isaac (2001) argued that assessment directly contributes to learning both by clarifying what is desirable and by closing a feedback loop between students learning, efforts, and their achievements. Telling the student what is required will assess them to direct their own effort. In order for the assessment for learning to be affective, teachers and students should be partners in the assessment for learning process. The teacher have to share the achievement goals with his students, make his expectations clear, taking in consideration the amount and the time, and the student have to do his best to understand what success looks like, to use the feedback to enhance his performance (Stiggins, 2007).

In Math education, it’s important for the teacher to understand that assessment is a part of a circular process; and that the assessment results help the teacher to understand their students better, and help the students to enhance their academic achievement (Whang, 2004).

After reviewing previous researches that are related to assessment for learning, it is found that there is absence of researches that focus on discovering students’ perspective about using the rubric as an assessment for learning at a secondary school; hence, this study is expected to add to the knowledge assessment for learning.

1. 1. THE BENEFITS OF USING THE RUBRICSRubric is valuable to both teacher and student as a quick and clear summary of performance levels across a scoring scale. The top level of the rubric communicates what exemplary work should look like and involves the student in

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constructive learning and self-evaluation (Hafner and Hafner, 2003).

Goodrich (1997) lists five reasons to use rubrics. Rubrics are used to make the expectations of the teacher clear. They help students become more thoughtful judges of the quality of their own and others’ work. They reduce the amount of time teachers spend evaluating student work. They allow teachers to accommodate heterogeneous classes. Rubrics provide an easy way to explain student evaluation to parents.

Rubrics facilitate student awareness of learning goals as well as the application of feedback, both important in the assessment and learning cycle (Zimmerman & Schunk, 2001).

Although rubrics help students to know what they need to achieve a certain grade, they have other benefits. Rubrics can make the expectations and standards for performance clear to students, parents, teachers, and educators (Cooper & Gargar, 2009). Also, rubrics provide students with feedback about their strengths and areas in needs of improvement. Rubrics support development of understanding and development of students' capacity to judge their own work (Goodrich, 1997; Cooper & Gargar, 2009).

Rubrics provide opportunities for reflection, feedback, and continued learning. They can help both teachers and students to review their own work or their peer’s work, in this way students learn to become self-directed. Besides, they will have the opportunity to understand how they and others learn. In 2002, a team work conducted a study that aimed to explore the effects of using analytical rubrics on teacher’s beliefs about teaching, learning, and the portfolio process. The study revealed that using analytical rubrics as a lens for examining their professional portfolios facilitated a more reflective approach to teaching, and can help both students and teachers to become expert problem solvers, decision makers, and goal getter (Moss, Gosnell, Brookhart, and Haber, 2002).

1. 2. PURPOSE OF THE STUDYThe current study intend to develop an understanding of students’ perspective about using the rubric in a mathematics classroom, the advantages and disadvantages of using the rubric, how to improve this rubric, and the effect of this rubric on their peers, since scholars agreed that involve students in developing and creating assessment rubrics, and involve them more as they become competent in doing so. Will help them to better understand what must be done to reach expectation, this encourages them to be independent and to manage their own learning. “Students not only assess their own work, but they also help identify the criteria for assessment and design the tools for measuring the quality of the performance” (Yoshina & Harada, 2007, p.11)

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Perlman (2003) argued that if we expect our students to do their best possible work, teachers should share the rubric with the students, sharing the rubric with student empower them to evaluate their own work (Perlman, 2003).

Stevens and Levi (2005) list three good reasons for involving students in rubric constructions: (1) prevents misunderstanding and misinterpretation before they affect students work; (2) involve students in the educational process; (3) cut down teachers work load by letting students to create parts of their assessment tools. Also we think that students’ involvement in the process of designing a rubric develops their understanding, their ability to become self-directed and help them develop insight into how they and others learn.

So, the main focus of this research is exploratory, descriptive and interpretive in nature. This study will spot the light on the rubrics as an assessment for learning format which teachers and students can use in the classroom to collect information that helps them to understand and support both learning and teaching processes.

1. 3. RESEARCH QUESTIONSThe study addresses the following research questions:

1. What are the advantages and disadvantages of using the rubric on a secondary mathematics classroom from students’ perspective?

2. What is needed to enhance this rubric from the students’ perspective?

3. What are the rubrics effects on their peers from the students’ perspective?

2. RESEARCH METHOD

2. 1. PARTICIPANTS AND SCHOOL DESCRIPTIONThe study population consists of Mathematics’ students of 3rd Secondary Education, in the academic year 2010-2011. The sampling method is the purposeful sampling. A Mathematics’ teacher who was interested in using rubrics for assessment was involved. The teacher had along teaching experience (19 years). The students (N=15) participate in the research were in 3rd ESO (14 to 16 years of age).

2. 2. INSTRUMENTATIONStudents’ open-ended questionnaire was used to explore their perceptions about rubrics as a method of learning and assessing. In this paper we report the results of the analysis of open responses.

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3. RESULTS

3. 1. THE POSITIVE AND NEGATIVE OF USING THE RUBRICMost of the students found positive relationship between using the rubric and their learning. Students wrote that solving the problem with previous knowledge of assessment standards forced them to improve the way in which they used to study the learning content of a topic. They wrote that they had to study the topic content more thoroughly than before knowing the assessment standards.

Students used to provide numerical answers to math questions. However, using the rubric forced them to explain what they had learnt in words. Therefore, students should understand every step in problem solving to be able to explain it to the teacher. Thus, according to students, the rubric forced them to study more and subsequently they learn more.

Other students found it difficult to use the rubric in problem solving since it requires much explanation and consumes longer time than usual. Those students found it difficult to complete solving the problem according to the rubric.

Some students found it difficult to understand the matrix and the scoring system.

Some students complained for difficulty in assessing their peers

Some students claimed that using the rubric in problem solving raised the quality of their answers.

Some students claimed that the rubric forced them to focus on memorisation in order to be able to explain each step in solving the problem. Before using the rubric, students did not have to explain and there was no need to memorise math concepts.

Most students found using the rubric in problem solving is more difficult and more complicated than solving without the rubric.

Some students found it difficult to understand the rubric, they asked for more practice and training. According to them two or three hours of training is not

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enough to understand what a rubric is and how to use it in problem solving and in scoring.

Some students claimed that using the rubric facilitate understanding the topic content. According to them, before using the rubric, they and the teacher have to solve several problems in order to understand the topic content. However, with the rubric it is enough to solve one or few problems to understand.

Most students considered that solving a problem using the rubric takes much time. They considered this as a disadvantage of the rubric.

Some students claimed that it is easy to get some scores in the exam. One student wrote

“You can have some scores in the exercise; learn the subject better, but it takes a lot of time” [S11]

However, students considered it very difficult to have full mark because there is much explanation in short time. One student mentioned:

“It is difficult. We have to know everything very well in order to get maximum grade” [S6]

Most of students criticized the time of rubric application. The rubric was introduced to the students for the first time during the third semester. Students express their dissatisfaction with this sudden introduction and state that it would be more beneficial to them if the rubric was introduced in the first semester. Some students advise that students should be exposed to rubric at primary years of their study.

According to students, the time did not allow training, practicing and good understanding of the rubric.

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3. 2. THE RUBRICS EFFECTS ON PEERSSome students perceive that the rubric enhanced their peers’ grades, as answering any question according to the rubric requires a lot of explanation, they had to study the content day by day, and consequently they understand the content very well.

Some students noticed that using the rubric make the student always have some grades, it’s very difficult to have a zero, since this method evaluate students mathematical knowledge and strategic knowledge and explanation. On the other hand, four students noticed that the rubric had a bad effect on their peers, they said that with the use of the rubric the students had lower grades than usual, it is very difficult to use and it hearts all the students.

One student wrote, “Using the rubric affect the students’ grades badly” [S14]

Four students were not sure about the effect of the rubric on their partners. One student asserted, “Some students got lower grades than usual, but others got higher than usual, and cost them less effort “[S6]

Other student noted, “In some cases it was good, and in some cases it was bad, for out of time and the need to explain everything”. [S4]

3. 3. PERSPECTIVES TO ENHANCE THE RUBRIC Students made some recommendations in order to enhance the rubric:

1. Students asked for more training and practice of using rubrics in general and this rubric in specific.

2. Students recommended introducing rubrics at early stages in their education such as primary stages.

3. Students asked for better design of this rubric. Students suggest designing the rubric in a way that does not require detailed explanation and much study from students. In addition, they advise to make it shorter by removing some sections. Some students recommend enhancing the scoring system.

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4. DISCUSSION

The students found using the rubric in problem solving is more difficult and more complicated than solving without the rubric, since it requires much explanation and consumes longer time than usual. Those students found it difficult to complete solving the problem according to the rubric. Also students used to provide numerical answers to math questions. However, using the rubric forced them to explain what they had learnt in words. Therefore, students should understand every step in problem solving to be able to explain it to the teacher. Thus, according to students, the rubric forced them to study more and subsequently they learn more. Moss, Gosnell, Brookhart, and Haber (2002) asserted that using analytical rubrics can help both students and teachers to become expert problem solvers, decision makers, and goal getter.

Most of students criticized the time of rubric application. As the rubric was introduced to the students for the first time during the third semester. Students express their dissatisfaction with this sudden introduction and state that it would be more beneficial to them if the rubric was introduced in the first semester. Some students advise that students should be exposed to rubric at primary years of their study. According to students, the time did not allow training, practicing and good understanding of the rubric. Some students found it difficult to understand the rubric, they asked for more practice and training. According to them two or three hours of training is not enough to understand what a rubric is and how to use it in problem solving and in scoring. Since it was the first time they used rubric.

Also for the students is difficult to understand the rubric scoring system. A possible explanation of this finding is that the teacher designed the exam in a way that the questions have unequal scores however (Question 1 equals two points, Question 2 equals three points and Question 3 equals five points, while the rubric is designed to assess each question with a fixed score that equals 10). Students faced difficulty in the conversion of scores for each question.

Some students complained for difficulty in assessing their peers, as they are not accustomed to assess each other, it create problems between them.

Students’ opinion about the effect of using the rubric on their peers was classified in three parts: the first part and the biggest, asserted that the rubric affect their class partner positively in a way that they got higher grades and they understood the subject more; the second part saw that the rubric affect their class partners negatively, they get lower scores; and the third part added that with some students the effect was positive and with other the effect was negative. Some students’ grades were less than usual, but other got better than they got usual, and also cost them less time and effort.

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The student noted that to enhance this rubric first, it should be put it into practice from inferior courses, second should be designed in a way that doesn’t oblige them to study very much, in a way that doesn’t require explaining a lot, because they have to explain every step which takes a lot of time. Third it’s very long it’s better to be shorter by removing some part, since there are some parts are similar or repeated. Finally it should be designed and explained in a way that students can understand; also the rubric scoring strategy should be enhanced. Indicate that it is important to involve students in revising and finalizing the rubrics, with a discussion about the characteristics of the excellent work, and to engage students in the learning experiences they hope to achieve. Moreover the study revealed that rubrics allow students to learn in new ways and can improve communication between teacher and students. And that rubric student had the opportunity to learn from one another, and that rubrics can help students form and adapt lifetime standards for assessing performance.

5. ACKNOWLEDGEMENTSFinancial support provided by the AECID is gratefully acknowledged, as is additional support from the the Ministry of Education, Culture and Sport of Spain (research project R+D entitled Servicio federado de erúbricas para la evaluación de los aprendizajes (EDU2010-15432).

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Brookhart, S., Moss, C. & Long, B. (2008). Formative assessment that empowers. Educational Leadership, 66 (3), 52-57.

Cooper, B. & Gargan, A. (2009). Rubrics in education old term, new meanings. Phi Delta Kappan, 91(1), 54.

Goodrich, H. (1997). Understanding Rubrics, Educational Leadership, 54 (4).

Hafner. J. & Hafner. P. (2003).Quantitative analysis of the rubric as an assessment tool: an empirical study of student peer-group rating. International Journal of Science Education, (25), (12), 1509.

Isaac, G. (2001). Assessment for learning, teaching and learning in higher education series, the university of Queensland.

Moss, c, Kathleen A. Gosnell, M. Brookhart, s, & Haber, J. (2002). The Role of Rubrics in Reflective Practice: Moving Pre-Service Teachers from “Goal Seeking” to “Goal Getting” Dispositions. Center for Advancing the Study of

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Teaching and Learning, Department of Foundations and Leadership, School of Education, Duquesne University, Retrieved on 2/2/2011 at: http://www.duq.edu/castl/_pdf/CASTL_Technical_Report_3_02.pdf

Stevens, D. & Levi, A. (2005). Introduction to Rubric. An assessment tool to save grading time. Convey effective feedback and promote students learning. h t t p : / / b o o k s . g o o g l e . e s / b o o k s ?id=LIxWgDn8_N0C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

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Stiggns. R. (2005). Assessment for learning Define, Retrieved at: http://www.assessmentinst.com/wp-content/uploads/2009/05/afldefined.pdf

Stiggins, R. (2007). Assessment Through the Student's Eyes, Educational leadership, 4 (8). Retrieved at: http://www.ascd.org/publications/educational-leadership/may07/vol64/num08/Assessment-Through-the-Student's-Eyes.aspx

Whang, W. (2004). Mathematics assessment in Korea. Paper presented (by the Korean Presentation Team) at the Tenth International Congress on Mathematical Education, Copenhagen, Denmark. Retrieved at: http://www.mathlove.com/new3/.

Zimmerman, B., & Schunk, D. (2001). Self-Regulated Learning and Academic Achievement: Theoretical Perspectives (2nd Ed.). Mahwah, NJ: Lawrence Erlbaum. Retrieved on 5/5/2012 at: books.google.com.

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