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.  

 

 

Chapter 1: Teaching Mathematics in the 21st Century

“I am definitely not a math person. I am a language person.” That’s what I have been telling myself for the past 10 over years. I am an excellent reader. I love to read and love being read to. Doing comprehension questions was my forte. I excel in my language subjects but fail in math. All I heard from my parents and teachers were practice, practice and practice. I am clueless about why and what I have been doing for those math questions. All I know was getting the right formula to solve the right questions. Till date, I have no idea how I managed to pass the “O” level mathematics. Exam Luck I guess.

 

However, I seemed to have a better understanding of myself after reading the chapters in the book. I realised I may be both a language and a math person! In Chapter 1 of the text, I relate most strongly to the section about The Five Process Standards. 

 

1) Problem solving

 

2) Reasoning and Proof

 

3) Communication

 

4) Connections

 

5) Representation

 

I am good at analysing word problems; I am a whiz at strategy games and beat my brother at RISK every time. Yes, RISK. - The military strategy game that challenges players to complete their military goals before their opponents does. I problem solved and justified my ideas through logical arguments with my brother during the game of RISK. Now don’t you agree it looks like I do have a very mathematical mind since I am so good at strategy games?

 

Also, I realized how important it is for students to see that mathematical concepts are connected to the real world and other disciplines. It is important for them to realize that the ideas behind learning the five content standards in school were preparing themfor the ultimate goal of being savvy, productive, efficient and successful at work in the future.

 

I hope to constantly reviewed and touched upon the content standards in my classroom through hands-on and experiential activities. They are often interlinked to one another. I strongly believe in hands-on activities and for instance in a planting activity, children can learn the above content areas. It is our instructional approach that guides the children's learning and thinking processes.

 

Lastly, I could not agree more that persistence, positive attitude, readiness for change and reflective disposition are definitely the necessary traits in becoming a teacher of mathematics!

Have a good laugh people. :)