Chapter 2

What?
Learning is the development of neuronetworks and the brain is "strengthened" through use of pathways and the connections made to information. Cognitive development is building a variety of pathways to information and linking them together. Studies show the importance of tow different mindsets, fixed vs growth. The growth mindset understands their limitations and is on a mission to figure out what they can do to change them and grow in the weaker areas. We now are accepting of the fact that the brain is affected by genetics and environment.
Piaget's theory is characterized by individual constructivism with a role of the environment. Also that cognitive development is affected by interaction with peers. Factors in cognitive development include biological maturation, active exploration of the environment, social experiences, and a process of equilibration where the brain is taking in information using assimilation (putting info with something we already know) or accommodation (making a new place or adapting a space for new info). Piaget's theory works in stages (not quite like the ages given). As a future teacher we may have students in any of the last three stages of development.
Vygotsky's theory is about socio-cultural learning, the role of the culture and interaction with adults, using guided participation (to help students do things like adults do), using cognitive apprenticeship (to help them think like adults do), having peer interaction, and that play has on the development of a child. He believes that all the information we have in our heads, we got from somewhere in the environment-nothing began in our heads. Vygotsky has the "Zone of Proximal Development" where no one is in any certain level or stage at the same time. It's very individual and allows for differences from child to child. We can teach our students using differentiation by customizing our classroom instruction to the needs of those in our class.
So What?
It is important for me as future teacher to understand the different levels of thinking and reasoning that my student's will be on so that I can teach and instruct accordingly. I'm not going to be able to teach a concept in just one single way and expect that every student will understand and remember it just like that. Especially in the math field, logic and reasoning are a large part of high school algebra, geometry, and higher level classes for them to understand how all the mathematical concepts fit together. Also understanding how the students are going to try to assimilate or accommodate the new information given in a non-threatening, less stressful way. If I can help make some of those connections and it's not just a bunch of random facts, they'll be able to better link those in their mind and build pathways as well.
Now What?
I still need to make connections myself as to how all the mathematical concepts fit together in the big picture. I'm starting to see it as I have advanced into higher classes and I want to be able to make those connections for my students in a simpler way. Also I need practice applying assimilation and accommodation activities and finding those ways of establishing disequilibrium in my students so they find a place for the information.