Reflection: Chapters 1 and 2

After reading chapter one and two, I feel that the author is trying to convey the message that we should encourage children to be actively process thinkers, explorers and investigator in learning mathematical concepts instead of just spoon feeding children with procedures and explanation that might lead to memorisation of concepts.


I definitely agree with this message as I too believe that children need to understand the concept before being able to grasp the concept fully. Therefore, one of the ways that I try to make use of and the authors have mentioned in one of the implications for mathematics would be to build in opportunities for reflective thought. For instance, when I was teaching my children multiplications, the children were initially unable to come up with an explanation for their approach towards a sum during a class activity. However, after modelling and asking these questions a few times, the children soon were more confident and were more willing to attempt explaining their method’s to the class. For example, they were asked to explain how they had the answer 3twos after looking at the pictures in the questions. One of the children explained that there are three groups of two, thus, she derives the answer of 3twos. Another child mentioned that there are altogether 3 rectangles that represents as groups and in each rectangle, there are two birds. The first child based her explanation on her knowledge of equal numbers that she had learned before this topic while the other child tried to explain more explicitly in his own words.

Also, as a teacher, I agree with the authors that we must treat errors as opportunities for learning. I would always try to make it a point to sit with the students who made errors in their work to work with them to see if they could identify their own mistakes or at times, I would notify the child that she has made an error and would ask her to try to resolve or problem solve the error by herself until she needs my help. This implications has indirectly boast the children’s confidence and interest in mathematics as they no longer feel upset about making mistakes but instead, have the drive to want to solve the error.

Lastly, I would use concrete materials and counting manipulative such as cubes, wooden blocks and etc to incorporate it into my teaching to provide a visual image to help them better understand the concepts. After reading the text about ineffective manipulatives, I realise children with difficulties understanding the concept was carrying out mindless procedure as their focus was on trying to get the answer instead of the process. Thus, this would be definately something that I would like to reflect upon and work with these children to focus on their process with them. However, I failed to imply the encouragement of the use of various methodologies to a problem as initially, I thought it would become a foundation to all children to learn the same method so that they would be better able to understand the next concept that I would be teaching. Nevertheless, I am willing to change and imply it into my classroom setting. Also, I agree with the authors that we should inculcate technology-based models into our teaching as it would act as a tool for children to develop their own network of methodologies and understanding of the concepts.

In conclusion, as a learner and a teacher, I believe that helping children develop relational understanding between concepts and making connections is more beneficial than just developing procedural understanding in children as they will be truly able to understand and retain each concept in their mind and assimilate and accommodate new knowledge prior to what they already know.

The boy is trying to count in twos with the aid of the straws.

the child is using the abascus to figure out how many beads makes the numeral 14.

The children are exploring with the balancing scale by selecting different items based on their choice to see which of them are heavy or light.