Saturday, August 20, 2011

Chapter 2

Upon reading Chapter 2, I have identified two concepts among all that I recognize of utmost importance. Hence, I shall summarize and reflect on what I have learnt upon understanding them.

The first concept would be



The Setting for Doing Mathematics:

Ideas are the currency of the classroom
To regard all ideas expressed by anyone in equal respect as it has the potential to contribute to everyone's learning.

Students have autonomy with respect to the methods used to solve problems
Students to understand that methods have to be understood by others and also, there is no 'one-method' in solving a problem.

The classroom culture exhibits an appreciation for mistakes as opportunities to learn
Mistakes can be dealt with constructively, instead of hiding it. They are opportunities for furthur exploration in reasoning and problem solving.

The authority for reasonability and correctness lies in the logic and structure of the subject, rather than in the social status of the participants
Embrace the culture of learning - Allow students to come up with individual approaches rather than being dependent on the teacher.

Opinion:
I selected this concept of "The Setting for Doing Mathematics" as I felt that this is something I can identify with, especially with the particular point that the classroom culture exhibits an appreciation for mistakes as opportunities to learn.

My personal experience when I was younger was that if I made mistakes, my mathematics workbook would be thrown to the ground and I would have to pick it up and redo the problems on my own until I get the correct answer. On the contrary, students who get the problems right could have their free time to chit chat, do drawing or their own activities. Hence, I quickly learnt that the product rather than the process have to be right. I often 'covered up' my own mistakes by erasing my answer and writing in the correct ones (that majority of my friends had) before handing it up. I recognize that this is not a strategy to be used in class because it teaches students the wrong concepts. This is an example of how a student has to feel safe to make mistakes in the classroom environment in order to be a learner of depth.

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The second concept would be



Implications for Teaching Mathematics:

Build new knowledge from prior knowledge
Students should have the leeway to develop, or invent, strategies for doing mathematics using their prior knowledge - demonstrating comprehension between the connections of these maths concepts.

Provide opportunities to talk about mathematics
To create an environment in which students interact with each other and the teacher, leading to reflective thinking.

Build in opportunities for reflective thought
Students to find relevant ideas from a new idea in order to bear the development of the new idea.

Encourage multiple approaches
Provide opportunities for students to build connections between what they know and what they are learning.

Treat errors as opportunities for learning
Students may make errors as they misapply their prior knowledge to what they have learnt. These errors are opportunities for learning as teachers can scaffold and lead students to engage in self-reflective thought process.

Scaffold new content
Scaffolding in mathematics requires use of tools like manipulatives or more assistance from peers.

Honor diversity
Each learner is unique and possess a different collection of prior knowledge and cultural experiences. Effective teaching incorporates what each student bring to the classroom.

Opinion:
Similar aspects I identified that re-appeared in implications for teaching mathematics are "Treat errors as opportunities for learning" and "honor diversity", both points which were presented differently in 'The Setting for Doing Mathematics' while in essence, the same.

I like how the author puts it, that errors are misapplication of student's prior knowledge in a new situation. This makes sense in a way that learners are continuously tapping onto their prior knowledge when solving problems, and when faced with a challenge their errors are most probably because they do not understand what is the most useful approach to use for the new situation. These are misconceptions that the teacher use it as opportunities for the student to engage in reflective thought.

Honoring diversity was also highlighted in 'The Setting for Doing Mathematics' as "Ideas are the currency of the classroom". Technically, the essence of both factors is for the teacher to respect and honor the ideas/prior knowledge that unique individuals bring into the classroom. Effective teaching can then be done as new ideas taught are built onto those prior experiences. Certainly all the factors are important as they all play a role, but I feel that factors that re-appear are of utmost importance in the learning and teaching experience for both learners and teachers.

Reference:
Van De Walle, J., Karp, K. & Bay-Williams, J. (2010). Elementary & middle school mathematics. Teaching developmentally (7th ed.). Boston, MA: Allyn and Bacon

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