Assessment had undergone a major shift from that as a measure of students' performance in pencil and paper test to assessing a broader area that does not only include students' knowledge and understanding but also essential skills. These skills for instance, communication, problem solving, investigation and even thinking skills are few of the intended abilities that are required for teachers to instil in their teaching. These are also one of the aims of the Ministry of Education in the new education system, SPN 21.
In Brunei itself, the secondary schools have begun to implement such task in their curriculum. Brunei Common Assessment Task or better known as BCAT has started in the year 2011. Students are assessed base on their performance on the task by using rubric which comprised of three assessed dimensions. The first dimension is knowledge and understanding while the second dimension includes thinking skill, problem solving and investigation skill and the last one is communication skill.
The Importance of Performance Assessment
Performance assessment, also known as alternative or authentic assessment, is a form of testing that requires students to perform a task rather than select an answer from a ready-made list. It is designed to provide a more complete picture of student achievement in a particular area (Sweet, 1993). In other words, students are assessed through observing their performances and examining the products they have produced throughout the lesson.
The purpose of performance assessment is to evaluate the actual process of doing an object of learning. Students are expected to be able to apply knowledge learnt in class to solve problems in the task. Apart from that, students may need to use their thinking skill in order to complete the task. Teachers as evaluators will be able to judge the quality of their students' abilities, witness their students' progress and facilitate them to a higher level of conceptual and procedural knowledge (Slater, n.d.) during which the task is conducted.
Tasks that are meaningful may enhance students' interest towards mathematics learning as they could make sense of what they learnt while performing (Ng, Koh, Kelly & Yue, 2009). With further understanding on the tasks, students will be able to apply mathematical concepts learnt in real life context (Goldman & Hasselbring, 1997; Lim, Tan & Wei Lin, 2011). Not only that by giving performance assessment tasks students are well guided on their level of achievement as they get immediate feedback based from the rubric assessed by their teachers. Self and peer assessment are also encouraged in order to acknowledge their level of competencies in that particular topic.
The importance of performance task does not focus on the students only. Teachers also benefit from implementing such tasks in their teaching. Different topics could be integrated into one performance task, thus teachers need not to give up certain topics or favourite activities in their classroom and time would be managed efficiently. This kind of integration along with traditional testing would give a comprehensive picture of students' performance. The aforementioned was suggested by Hibbard, Wagenen, Lewbebel et al. (1996) whereby traditional testing should be simultaneously working with the performance task in order to produce a better way to deliver the curriculum (Figure 1).
Figure 1. Students' literacy.
Students' Difficulty in Learning and Understanding on Fractions
The topic being assessed was on fractions in real life. Fraction is considered one of the most difficult topics encountered by students. Many studies had reported of its' difficulties where students struggled in understanding the concept on fractions. Suffolk and Clements (2003) studied students in Form 1 and Form 2 from 27 secondary schools in Brunei had found out that many students were experiencing serious difficulties with elementary fractions tasks.
Another study by Zurina (2003) involving Form 4 (N-Level) students discovered that students had very poor knowledge and understanding of fractions and decimals. The major contributing factors were that teacher spent large amount of time on preparing students for high-stake examination, therefore the traditional 'drill and practice' method was mostly employed by teachers. She further commented that teaching and assessment methods were not generating towards the desired quality of the students.
Description of the Task
The task comprised of six questions with the first four related to each other. The next two questions are the application problems which are quite similar to the first four (refer to Appendix A). Question 1 until 4 assesses the students' knowledge and understanding of their concept on fractions. These include the interpretation of fraction and understanding the key word which is 'remaining' and 'remainder'. Meanwhile Question 5 and 6 are the application of operation in fraction to solve problems, through which the thinking skills, problem solving and investigation, and communication skills are assessed (refer to Appendix B for rubrics). Each dimension were given a score from 1 to 5 depending on the different criteria as stated in Appendix B. Lesson plan for carrying out the task was designed prior the class (refer to Appendix C).
The task was conducted on the 27th September 2012 in an all girls' school in Brunei Darussalam. It was intended for Year 7 students and the topic being assessed was on Fraction in Real Life. There were 22 students involved in this study with an average mathematical ability. The duration of the study followed the mathematics period which was 50 minutes.
The session started with a brief review on the topic specifically on the four operations of fractions. After 5 minutes, the task sheets were distributed to the students including the rubrics. Students were given an explanation of what they should do for the task and what was expected according to the rubric. Students were asked to work together in a pair and the use of calculators was allowed. Teachers involved were making rounds while giving help when necessary to the students throughout the lesson.
During the lesson, most of the students were working on their task with few of the students did not communicate with their partners. It could be observed that few students were struggling in understanding the first question. These students managed to shade the boxes with their colour pencils. However, they did not label their shadings as they were instructed in the question.
Furthermore, students were found having difficulty to proceed to the next question. Since the second question was asking the students to shade three-eighths of the remainder, few students had shaded three boxes on their diagram. More problems arose as they moved on to the next question where students were found to shade ten boxes rather than four, which was the actual answer. As for the fourth question, since they got it wrong from the second and the third question, their final solution was also incorrect.
Questions 5 and 6 were the application problems. Students need to understand the problems and think before they could proceed. The first part of the question was an easy and straight forward question which a lot of the students managed to answer. Whereas the second part of Question 5 was difficult for students to solve even though it was a similar problem to those in Questions 1 to 4. Question 6 was the least answered by the students during the lesson.
Results and Discussions
Mean Scores for Each Dimensions
Knowledge and Understanding
Thinking Skills, Problem Solving and Investigations
From the analysis of the rubrics, it was found that the mean score for each dimension were as shown in Table 1 above. Based from the results, most students were able to show correct fraction diagrams in Question 1, 2 and 3. This showed that the students had basic knowledge on fractions but little on understanding the problem. Meanwhile, students only managed to apply a strategy and obtain incomplete solutions to both application problems which indicated that they were unable to reach the standard intended for their level. This further affected their communication skills by which they were unable to illustrate and reason their solutions.
From the observations, teachers found out that there was a slight improvement throughout the lesson for knowledge and understanding dimension only. This was because the students spent more time trying out Questions 2 and 3 compared to the rest of the questions, a reason why Question 6 was the least answered. This was also the reason why the teachers involved were unable to rate the students on the other two dimensions during the lesson conducted..
Analysing at each question, all the students had no problem with attempting Question 1. However, students were having difficulty in finding the right number of squares to be shaded in Question 2 and 3. This was mainly due to the misunderstanding of the word 'remaining' in the question. Students were using the original number of squares to find the number of squares to be shaded in Questions 2 and 3. This led to their inability to find the correct response for Question 4.
With regards to Questions 5 and 6, students were also having similar problem of understanding the word 'remaining' and 'remainder' as posted in the previous questions. This brought an impact towards the overall performance of the students for these two application questions. Few tried the questions but were unsuccessful in getting the correct answers, others left it unattempted.
Reflection and Conclusion
From the above discussion, it could be concluded that overall the lesson ran smoothly and only the first objective was achieved as indicated from the mean scores of the rubric. Students were found to be quite engaged in the activity. Students' thinking could be observed through their working and when they asked questions clarifying their difficulties.
However less communication with their partner could be observed during the lesson. Low students' interaction resulted in different scores achieved by few groups. Apart from that, students were seen more focused on finishing the first task rather than the application problems. Perhaps, this is because the first activity targeted on the basic understanding on fractions in real life and students assumed that the questions were easy since diagrams were provided. Feedback from the students was asked towards the end of the lesson where commonly they claimed that the tasks were overly difficult. This kind of response had shown that the students who participated in this task were not exposed to this kind of assessment approach.
It was also found from the above analysis that there were few limitations on the task. Firstly, difficulty in rating students' scores was encountered. This is because few of them had left their task unanswered and the rubric designed had specified one mark for no attempt in the third dimension, the communication skill. This had shown that the rubric itself was lacking of fairness. This should be modified in the future if one would implement the task in their class. Secondly, a proper classroom observation checklist which assesses other attributes apart from what the rubrics had specified should have been developed. At least, from this checklist, a wider perspective such as students' interaction with their peers and also with the teachers involved could be further evaluated. Finally, as discussed before, the tasks only concentrate on a key word 'remaining' which is a confusing concept to the students. This can be modified by adding different concept rather than focusing on just one.