Pre-course reading - Chapter 2 (Exploring What It Means to Know & Do Mathematics

On page 13 of the text book Elementary and Middle School Mathematics Teaching Developmentally (8th Edition), the authors mentioned that when an odd number multiply with an odd number, would always generates an odd answer; when an even number multiply with an even number, would always generates an even answer; when an odd number multiply with an even number, would always generates an odd answer but why I always have an even answer?  Can clarify?  Thanks you.

In the text book, I enjoy solving the problem sums from page 15 to page 18, though I did not get 100% right for my answer.  The Star and Jump Numbers: Searching for Patterns and One Up, One Down really interesting.  Now I know why people can do their mental sum so quick.

On page 14, I total agreed with the authors that having a conducive environment for learning Maths will enhance children's learning.  During Maths lesson, teachers must provide adequate materials and engaging manipulative for children to learn through hands-ion; allow children to share their leads and encourage them to listen to their peers and learning from others; make a list of solution and brainstorm the possible answer; allow mistakes, as children can learn from mistakes, hence, it create opportunity in learning.

In this chapter I read about Jean Piaget, the constructivism theory and Les Vygotsky, the social-cultural theory, whom talk about children learn through the process of assimilation and accommodation, and zone of proximal development respectively.  Additional, I have learnt a new concept, i.e.  semiotic mediation; which is using diagram, pictorials and visuals to exchange information of one's beliefs.

The below diagram is found in page 24 of the text book; which I agreed that Maths should be taught through the 5 representation.