How do we define learning in the 21st century? According to NIE Senior Education Research Scientist Dr David Huang, learning should not only involve the ability to acquire knowledge efficiently, but also be able to innovatively transfer the newly acquired knowledge beyond specific contexts and instances, a process called “creative transfer”. In this article, he shares more about his research project that focuses on creative transfer in Math.

Creative transfer occurs when students synthesize, expand, combine and adapt their knowledge in transfer so as to create novel concepts and procedures. “An example of creative transfer is a student creating a solution method for a question in a curriculum topic they have never learned before,” says Dr David Huang.

His research project consists of two sub-studies, the first of which (Study 1) was conducted on primary school students across three local schools. Study 1, he explains, explores the extent to which the learners’ domain knowledge of the already learned topics of fraction multiplication and whole number division can influence their creative transfer to the untaught topic of fraction division.

“In Study 1, we found that procedural flexibility and conceptual knowledge are particularly important for transfer to take place,” he notes.

Discovering Learners’ Potential for Creative Transfer

In the initial stages of the study, the research team found that there were a number of students who already had prior exposure to fraction division before it was introduced in the formal curriculum.

“After realizing this situation, we took the opportunity to compare creative transfer (by students who had no prior exposure to fraction division) versus application of knowledge in usual transfer (by students who had prior exposure),” he explains.

The direct comparison between the two groups of students led to the finding that procedural flexibility of (previously learnt) whole number division and fraction multiplication was particularly important for those students who had prior exposure to fraction division. Meanwhile, for those who did not have prior exposure, their conceptual knowledge of whole number division and fraction multiplication was important for them to invent their own methods in solving fraction division problems.

“Teachers and researchers were also pleasantly surprised to note that students developed many novel creative transfer approaches to solve fraction division problems, suggesting that students in Singapore have good potentials in creative transfer,” he shares.

Further Implications of the Study

The research project has important implications on how teachers can change their approach in teaching new topics and at the same time, foster deep learning in the classroom.

David shares that the research team has given feedback to teachers that students had difficulties in answering conceptual questions, for example drawing models to illustrate and explain mathematical relationships.

“Based on our observations, many students answered the questions by providing procedural steps instead,” he states. “This suggests a need for developing students’ conceptual knowledge, as well as strengthening the disciplinary language in explaining concepts and mathematical relationships.”

Furthermore, the study has shown that students who do not have prior exposure to fraction division have used their prior conceptual knowledge on whole number division and fraction multiplication to solve novel problems on fraction division.

Thus, this implies that having procedural knowledge, while necessary, is not sufficient. “A deep conceptual understanding of a topic would not only help students learn the topic well, but also prepare them to use the conceptual understanding to deal with new curriculum topics later on,” he explains.

Meanwhile, for students who already had prior exposure to fraction division, their procedural flexibility of whole number division and fraction multiplication predicts their transfer in solving fraction division problems.

“To strengthen students’ procedural flexibility, teachers can encourage them to solve problems using as many methods as possible, even if some methods are not as efficient,” he shares. “This flexibility could help students integrate the old curriculum topics they had learned before with new topics they are currently learning.”

Enhancing Our Understanding of Creative Transfer

David shares that Study 2 will be rolled out in May 2022.

“Study 1 has provided us with an understanding on the different forms of domain knowledge that can influence creative transfer in learners,” he says.

“Study 2, meanwhile, seeks to examine ‘compare and contrast’ as a pedagogy in developing students’ domain knowledge. It also looks at whether improving domain knowledge of already learned curriculum topics increases students’ performance in creative transfer.”

The creative transfer of knowledge, he emphasizes, should be an essential feature in education. The payoff for meaningful instruction lies in not just an immediate retention of the learned information, but also in transfer to novel situations in future.

“As future novel situations may not be known to the present teachers and learners, students need to be capable of dealing with transfer tasks that teachers cannot (or do not) directly prepare them for,” he adds. “Hence, developing students’ ability for creative transfer empowers them to be the future pillars of tomorrow.”