“I am just not a maths person.” We often hear this exasperated cry from people of all ages, whether children or adults. What could be the cause of this statement? Some feel that they are not good in calculations, others develop anxiety while solving math problems. These feelings of low level of competency in mathematics are developed in childhood and get strengthened when difficulty level increases at higher grade levels.
This phenomenon should be a cause of concern for parents. Research has found that not only does this lead to low self-efficacy and a negative attitude towards maths, low scores in maths have a great impact on students’ overall achievement in academics. And, as a 2012 study also found, that the motivation level of students is also affected.
So, what can be done to help children love maths and enjoy the subject? In my 18 years of experience working as a mathematics educator, I have observed that the teaching of maths follows a progression. It is a journey of concept development. Mathematical concepts are not to be rote learned. They require a journey of construction of knowledge from concrete, hands on tangible experiences to abstract symbols and ideas. There are countless research studies that conclude that children need sensory impressions of mathematical concepts to be able to understand and become fluent in solving mathematical problems. In order to provide children with these sensory impressions, we must introduce children to maths manipulatives.
Manipulatives are tangible items that students can manipulate through hands, involving senses. These include teaching aids and tools similar to base ten blocks, Tangrams and abacus that help children understand abstract mathematical concepts. When they work with these tangible items, they receive information and hence build concepts. Cockett & Kilgour (2015) conducted a research titled, “Mathematical Manipulatives: Creating an Environment for Understanding, Efficiency, Engagement, and Enjoyment” which involved 32 students of lower primary working with different types of manipulatives.
They concluded that manipulatives helped the students to stay motivated, engaged and happy while doing maths problems. They also concluded that there is a positive impact of manipulatives on developing self-efficacy among the students. Not only do young children benefit from hands on manipulatives, but students at higher elementary level also benefit with them as investigated by Golafshani in 2013.
Goracke (2009) also conducted an action research with the students of grade eight to investigate the impact of manipulatives on students’ attitudes and understanding. He discovered that students were fully engaged in using manipulatives and were happy with the opportunity to socialise during the exploration time, while working with manipulatives. This shows that hands-on activities not only provide deeper understanding of concepts, but help students become confident and develop positive attitude towards their maths class.
The experience with these concrete objects helps the students to move towards abstract reasoning with ease but this does not happen automatically. Teachers play an important role in making this transfer happen. Knowledge of using manipulatives is important for receiving the benefits embedded in them. Therefore, a teacher’s role is essential in helping the students receive the information through thought provoking questions leading to exploration of these concepts.
The choice of manipulatives must be according to the age of students and help to serve the purpose of achieving the set curriculum targets. Maths manipulatives are only able to benefit a student if a qualified teacher is present to supervise the process. And for a teacher to become qualified in this new method of pedagogy, he or she needs to be given the relevant training regarding the proper use of these manipulatives.
During my experience of teaching students and training teachers about the use of manipulatives, I found that teachers themselves feel that there is a need for a platform that provides them proper training regarding maths education. To validate my observations, I conducted a survey involving 200 maths teachers from private schools in Karachi ranging across grade levels from KG to grade 10. The results were astounding.
Ninety five percent of the teachers felt that there is a need for teacher training sessions on the topic of using manipulatives for maths education. It was also surprising that while teachers are aware of the benefits of the manipulatives, they do not know about the specific manipulatives that exist for teaching the concepts. The survey also revealed that the teachers of pre-primary use manipulatives more frequently as compared to the teachers of primary level.
Secondary teachers barely use the manipulatives in their classrooms. When the teachers were asked about the reason for not using the manipulatives, it was revealed that many are not aware of the manipulatives used for teaching each particular concept and if they are aware of them, they don’t know the correct use and methodology of teaching across different grade levels. They don’t feel confident enough to teach maths with manipulatives. Other hindrances as shared by the teachers were time constraints due to the coverage of set curriculum, lack of PD or professional development sessions at school, classroom management and the management of manipulatives in the class.
Low scores in maths is also a major problem in Pakistan as reported by Aser 2017. There is a great need of awareness and professional development programs for maths teachers training to improve the quality of math education.
The writer is Founder/CEO of Concrete to Abstract, an organisation set up to promote better ways to teach maths, to train teachers to become better educators through manipulatives
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