“What does math have to do with my everyday life?” your student might ask. To some, solving math questions has no relation to the problems they encounter in their daily lives. But math questions that draw on real-life scenarios can help us appreciate the usefulness of math.

One of the aims of math education is to teach students the value of math in their daily lives.

According to Math professor Alan Schoenfeld, well-known for his book Mathematical Problem Solving, many students feel that math has little or no relation to the real world (cited in Fan et al., 2008). Many also mistakenly assume that there can only be one answer to any math problem.

Consider this question:

How many answers can you come up with? Does you answer include Mrs Lim joining the cruise?

This is an example of a performance task. There is more than one answer for this question, and more than one way to go about solving the problem.

What Is Performance Assessment?

Performance tasks are used in performance assessment. The math tasks are usually open-ended and authentic. They use real-life scenarios to assess students’ learning and often have more than one solution.

“Such tasks cannot be answered by simple recall,” explains Associate Professor Fan Lianghuo, who teaches math education at NIE. “Students need to explore and engage in processes such as looking for patterns, gathering data, and logical reasoning.”

Performance assessment is useful for gathering data on the students’ learning. Lianghuo was interested to find out how such assessment can affect students’ learning of math.

Alternative Methods of Assessment

In recent years, greater emphasis has been placed on developing students’ skills in problem solving, higher-order thinking, co-operation and communication.

Traditional methods have been useful in assessing recall of knowledge, often acquired through rote learning. But these methods have been found to be inadequate in testing areas such as students’ learning processes, interests and appreciation of math.

Lianghuo says that when using traditional assessment methods like MCQs, the teacher may not know if the students’ thinking processes are wrong, even though they get the right answer.

“Teachers need to know their students’ thinking processes,” he emphasizes. “That’s where performance tasks come in. When students do performance tasks, teachers can understand their students better – their thinking processes, their weaknesses, their strengths – so they can make informed instructional decisions.”

The Benefits

According to research, higher-order thinking processes and problem-solving skills can be better assessed by performance assessments (Fan, 2006).

The teachers in this study found that complementing their teaching with performance tasks helped them gain an understanding of their students’ learning.

The students also enjoyed doing the performance tasks. They had to apply different methods to solve the problems, which helped them develop their creativity in problem solving.

These methods helped develop their higher-order thinking skills, and they were able to use these tasks to reflect on their own learning process. (Fan et al., 2008)

The Challenges

As with any new method, however, the students and teachers encountered several challenges.

• Time constraints
  Finding time to implement this method was an issue as teachers are constantly under pressure to complete the syllabus. Teachers should decide on the frequency of using these tasks and implement them gradually into their teaching to avoid a sudden increase in workload.
• Lack of resources
  Although the resources available online are growing, there is still a lack of resources suitable for the local context. Teachers can work together to develop these materials. Lianghuo recommends attending professional workshops and seminars, such as those organized by NIE’s Math department, to gain knowledge on how to design these tasks.
• Feeling lost
  A number of students found some of the tasks too challenging, and some felt lost when doing these tasks (Fan et al., 2008). “Students may have no idea what to do, especially at the beginning,” explains Lianghuo.”Teachers must make their expectations clear and show them how they can approach the task,” he suggests. “At the later stage, they should give their students more freedom to be more independent.”

Worth It All

“Schools need to create a culture that encourages the use of performance assessment,” stresses Lianghuo. Already, some schools are using performance tasks in their continual assessments. Increasingly, such questions are also being included in the PSLE.

The benefits of performance assessment may not be immediately evident in the exam results, but Lianghuo assures us that these efforts are worthwhile.

“Using performance tasks, students can appreciate the relevance of math in their daily lives,” he says, “and they can show creativity and make their own decisions.”

References
Fan, L. (2006). Making alternative assessment an integral part of instructional practice. In P. Y. Lee (Ed.), Teaching secondary school mathematics: A resource book (pp. 343-354). Singapore: McGraw-Hill.

Fan, L. (Ed.). (2008, September). Performance assessment in mathematics: Concepts, methods, and examples from research and practice in Singapore classrooms [Resource booklet]. Singapore: National Institute of Education.

Fan, L. et al. (2008). Integrating new assessment strategies into mathematics classrooms: An exploratory study in Singapore primary and secondary schools (Final Res. Rep. for CRP 24/03 FLH). Singapore: National Institute of Education, Centre for Research in Pedagogy and Practice.