Monday, 23 July 2012

What i have learnt in 24 hours

First of all, i have gained a clearer perspective on the shift of focus in learning and teaching of math. Some lessons have demonstrated that there is no practicability to certain mathematical problems. Thus, the purpose in doing the sums is not to memorize the strategy and learn arithmetic for arithmetic's sake. Rather, it is to engage children in the process of problem solving (an important life skill) through helping them to see possibilities and allowing them to choose strategies which help them get to the solutions. While problem solving, every individual are encouraged to come up with any methods to solve the problem; this made the process of learning math a flexible one.

In addition, the experience of working through the problems and sharing of diverse methods (which was a BRAIN OPENER) within the class has made me ascertain the value of teaching and learning math as a social activity (as mentioned in chapter 2 of the text).  

Lastly, i have learnt that the language to be used in corresponding to the mathematical problems must be well thought of and applied appropriately. This has never really occurred to me as an important factor in teaching mathematics before this course but it has became a very clear notion to me now.

My remaining questions for teaching math as of now would be:

What is the impact of ability grouping in teaching mathematics?

Would lower-achieving students be confused if they saw more than one way to solve a problem? What kind of instruction can better cater to these children?

Saturday, 21 July 2012

Technology

Our society is now dependent on technology. It helps to make life easier, less manual- should you  need information on any topic?  Look up in the internet! Storing up tons of information? Do it using the computer! Want to keep yourself entertained? Play games or surf the internet on your smart phones!




Technology opens up a whole new world. It's great to have so many resources available at a fingertip!


Technology infuses classrooms with digital learning tools, such as computers and calculators which are easily accessible to students. They support both teaching and learning as they offer richer learning materials, promote critical thinking skills and icreases student motivation while building 21st century skills. As emphasized by Trilling and Fadel (2009), "To be productive contributors to society in our 21st century, you need to be able to quickly learn the core content of a field of knowledge while also mastering a broad portfolio of essentials in learning, innovation, technology, and careers skills needed for work and life”.


Even as my classmates and I are writing entries like this now, we are working towards that goal of being productive contributors of the 21st century as we share our ideas, opinions and information through blogging (online diary). This is how our lecturer integrate technology in his lessons for the benefit of everybody.


"Technology is helping teachers to expand beyond linear, text-based learning and to engage students who learn best in other ways. Its role in schools has evolved from a contained “computer class” into a versatile learning tool that could change how we demonstrate concepts, assign projects and assess progress." (Kessler, 2010)


Friday, 20 July 2012

Relationships with Landmark Numbers (Chapter 11)

During the lesson, our lecturer Mr Yeap explained the usefulness of integrating the use of number bonds into multiplication. I found these strategies very essential for children to figure out problems and realized the amazing use of relationships among numbers.
Interestingly, i found myself connecting my daily experiences to this part of the chapter which also talks about the relationship among numbers; landmark numbers.  Landmarks are well-known objects of a particular landscape. In this case, 'landmark numbers' refer to the well-known numbers which are easy to work with. Understanding the relationship among numbers and landmark numbers can be of practical use in many situations.

While it helps in the development of number sense and place value,  it also helped me in working out some informal methods of computation under such circumstances:
calculating the total amount of my expenditure for the day,
working out the difference in cost for products, etc...

Thus...
it is much easier to work out sums by exploring...the RELATIONSHIP with landmark numbers!

Tuesday, 17 July 2012

Lesson 1

Today's lesson has definitely got me interested to learn more mathematics! I enjoyed my time in class while working on each minilesson. I especially liked the one on arranging the deck of number cards with my partner as i remember both of us feeling amazed and excited when we have taught the cards to be "obedient"! A sense of accomplishment washed over me and my partner has already thought of a person whom she wants to showcase her 'skills' to. Thumbs up for today's activities!
















*A few reminders from Mr Yeap that inspired me:

-Teachers should use the language appropriately (such as saying the nouns while doing counting).
-Content is not important. It is important to generate questions from children.

Sunday, 15 July 2012

Chapter 1: Teaching Mathematics in the 21st Century

 


 

The chapter discusses about the Standards and Principles that act as specific guidelines for teaching pre-K -12 mathematics education.  It gives an overview of the perspectives of forces that effect change within the mathematics classroom.  Just as it is essential for a school to have its own set of philosophies and mission, the Standards and Principles mentioned in this chapter serves the same purpose and importance as they are well supported, big ideas that clearly indicates the goals and beliefs of providing high-quality mathematics education.

Ongoing research on mathematical practices and learning progressions are conducted so as to inform the type and order of instructional experiences of teachers in supporting the understanding and application of mathematic concepts. The teaching focus shifts from time to time as standards are often revised in this ever-changing society. Thus, there is a vast difference between the current mathematics education and what was taught in the past.



Now, as I provide tuition lessons for lower primary students, I noticed the significant change in the teaching of mathematics in schools; the emphasis on problem solving rather than the structured 'get them right' method which was taught in my ‘era’.   It occurred to me then  that our society is moving and changing fast. As such, teachers (like us) would really need to keep abreast of the latest developments in the fast-paced mathematics educational system.


"The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede." ~Edward Gibbon, Decline and Fall of the Roman Empire

Chapter 2: Exploring What It Means to Know and Do Mathematics

More than a decade ago, I remember telling my dad that mathematics is my favourite subject taught in school because I am able to solve the questions. It wasn’t long before I have to stay up late at night to learn how to do division. I could not forget that night; I cried because my dad was mad at me for not being able to understand what he was teaching the whole night. However, when teacher was going through the same questions the next day in school, I remember myself being able to grasp the concept almost immediately.
It was then I started to think that teachers are awesome people who have what it takes to help their students understand things that some others might not be able to (I am still grateful to my dad for teaching me).
Now, as a grown up and being a teacher, I understand that helping students to know and do mathematics is not an easy task. To start with, a teacher must understand what it means to know and do mathematics.














I agree to both the constructivist and sociocultural perspectives that people are constantly applying prior knowledge to make sense of new information (just like how people employ the use of the existing knowledge by counting on fingers while working out a traditional algorithm sum newly taught).Those mental processes work better between and among people in social settings. While in a group, students are able to interact and share their individual ideas with one another. This holds true for me as well; as a student now, i find the ideas i gained from class discussion among peers and lecturers to be valuable take-aways which may be out of reach without the input of others. 

With the interaction among peers and teachers, students can be involved in reflective thinking and better understand the problems. As such, it is crucial for students to be provided with the opportunities to engage in solving problems using their own knowledge in social exchanges.


I also believe in exercising flexibility while learning mathematics and what has been emphasized in the chapter that students can develop a relational understanding if they possess the ability to move among the five representations of mathematical ideas. Applying flexible, transferable knowledge of mathematical ideas has proven to be a critical and fundamental pathway to students’ effective understanding and retention.
To sum it up, teachers must work on providing social opportunities for students by eliciting prior knowledge and create tasks that bring forth students’ critical thinking as well as other proficiencies to promote comprehension in mathematics.