Chapter 2: Exploring What It Means To Know And Do Mathematics

I always believe that math is about memorizing formulas, facts and rules until I read the chapters. If a person has never been exposed to thinking about math as thinking, reasoning, and problem solving, our lenses, which we view math will be very narrow. 

The big idea from chapter 2 is in order to be an effective math teacher there are two broad components: 

1.  Teacher needs an understanding of how children learn math.

2. Teachers need to understand math.  There is a difference between knowing a way to solve a problem and knowing why the formula or procedure works.

The best learning opportunities according to Jean Piaget - constructivism and Led Vygotsky - sociocultural theories are that it engage learners in using their own knowledge and experience to solve problems through social interactions and reflection.

As educator, we need to constantly reflect on how to elicit prior knowledge by designing task that reflect the social and cultural backgrounds of students, to challenge students to think critically and creatively and to include a comprehensive and holistically strategy and teaching as we plan and design our teaching instructions in mathematics.

• Creating opportunities for students to interact with teachers and peers which allows them to be engaged in reflective thinking;

 

• Encouraging multiple approaches for children to demonstrate their understanding through sharing  ways to solve a problem with different solutions;

 

• Honouring diversity to recognise each learner is unique with different collection of prior knowledge and cultural experiences;

Learning and knowing math is a complex system.  It is important we understand the difference in knowing a procedure and understanding the concept. In which, both are inter-related.