Chapter 1 & 2 Reflections ( EDU 330)

Blog Entries Reflection (Elementary Mathematics)

Chapter 1:

Teaching Mathematics in the Era of the NCTM standards

As I read this chapter, I began to realize how meaningful and impactful the NCTM standards are. I looked at the Pre -K2 standards found in Appendix A and I remember during my time or Era in my preschool years, mathematics was route learned. There was no flexibility in expressing understanding. Those days were just one way, because it’s like that and it’s like that, no questions asked.

 Then, teachers were not really patient and I as a student was not really interested in this subject. I also didn’t have the motivation and persistence.

Furthermore, the teachers I had for math were also not really encouraging or dynamic. I enjoyed language subjects but didn’t really manage to cultivate the love or passion for math even up to my primary years of schooling and secondary school years too.

Reflecting on this chapter as a teacher and learner, I realized that the NCTM standards provide expectations that are more concrete and well-defined. I found the standards to be meaningful with ample reasoning given. The NCTM allows a child to make meaning and not just only know concepts but experience concepts. Knowing the WHY’S are important as it’s not just about knowing a certain formula. Therefore, when children inquire and desire to know why and how the problem is solved this way, it allows challenge and reasoning experiences into their mathematics learning. Also, as I pondered upon the five content standards I realized and agree that the five process standards direct the methods or processes of doing all mathematics learning and teaching.

5 Content standards

·         Numbers and Operations

·         Algebra

·         Geometry

·         Measurement

·         Data Analysis and Probability

5 Process Standards

·         Problem Solving

·         Reasoning and Proof

·         Communication

·         Connections

·         Representation

I also like the saying which I read from pg 4 of the book which says that, “we should teach in a way that reflects these process standards because it is one of the best definitions of what it means to teach according to the standards.”

As I read Appendix B, Two standards came across my mind.

1: Reflection on my teaching practice (Standard 7)

2. Reflection on Learning Environment (Standard 4)

I thought as an Educator it is important and good to check if meaningful teachings are taking place and whether a good learning environment is set up, one that cultivates active learning and also fosters respect towards each individual child needs and way of learning.

As I read about the data from NAEP, I realized that American students don’t really perform in math. There must be some factor that causes this and I believe mathematic passion has to be nurtured as well as cultivated and teaching has to be done meaningfully with proper goals. Instead of focusing to do everything I agree it is important to do a depth of study on each topic. It is more meaningful and therefore I like the idea of the Curriculum Focal points.

 In that way, students get to focus on a topic and have to put in their effort as well. This spurs more focused concentration and attention.

Chapter 2:

Exploring What it means to know and do mathematics!!

I agree with what I read in chapter two. To know and do Mathematics  means “generating strategies for solving problems , applying those approaches, seeing if they lead to solutions and checking to see if the answers make sense”. As said in the book, “Doing Mathematics in classrooms should closely model the act of doing mathematics in the real world”. (Pg 13) I believe, giving students concrete hands on experiences is essential. Creating a proper classroom environment for doing mathematics is strongly needed. Children must be comfortable in an environment where they can discuss ideas free of risks. Also as an educator, I believe that it is important to have a personal feel for doing Mathematics. Knowing the Science and Order of Math is very much vital as it helps us connect with our students’ predicament. We as educators have to remind ourselves how each unique child understands the problem and solves it. And when doing Math, using justification is also necessary as when we problem- solve, it helps determine if an answer is correct, because eventually when it comes to the real world there are truly no “answer books”.

Constructivist theory and Sociocultural theory.

Constructivist theory:

As I read about the constructivist theory, I begin to understand the figure 2.8 model better (pg 20) - We use the ideas we already have (blue dots) to construct a new, idea (red dot), developing in the process a network of connections between ideas. The more ideas used and the more connections made, the better we understand. This is where I think the 2 theories work hand in hand and they are quite similar. Pg 21 says, “…when considering classroom practices that maximize opportunities to construct ideas, or to provide tools to promote mediation, they are quite similar.”Ideas can be discussed in classroom interactions and that’s where we learn from each other and expound on more ideas. We can grow ideas together. To do this once again, the classroom culture and environment must be one that cultivates respect, sharing and a safe risk-free learning environment. And so, I agree with the points on pg 22

1.     Provide opportunities to talk about mathematics

2.    Build in opportunities for reflective thought.

3.    Encourage Multiple Approaches

4.    Treat errors as opportunities for learning.

5.    Scaffold new content

6.    Honor Diversity

What does it mean to understand Mathematics???

Pg 23- “ One way we can think about understanding is that it exists along a continuum from a relational understanding-knowing what to do and why- to an instrumental understanding- doing without understanding.

Relational Understanding and Instrumental Understanding

Pg 24 – Figure 2.11 says, understanding is a measure of the quality and quantity of connections that a new idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding.”

And therefore I believe, relational understanding is very important as it provides reasoning and meaning to one’s work. It’s not just a “formula-basis” experience with math. Last but not least, I have learnt that to know and do math should be a purposeful and meaningful experience.