Fractions...........

4) April 4

I love the way the lecturer explained fractions in such simple term. The numerator respresents the numbers of something while the denominator is a respresentation of something with a different name, like the way we read 4 sweets or 2 apples.

Fraction is a just a convention of language. Fractions are parts of a whole. ( e.g. 1 + 1  = 1 )
Today I learn to read fraction differently –                                                                    2    2

 

2  is read as 2 thirds ,  (instead of saying  two over three.)
3

3   as 3 fourths  ( instead of  three over quarter)
4
 

The Mr R's math video on fractions is a great way to learn through songs. 
 http://mathstory.com

 



@Arthmetic can be fun

 

 

 

Relational understanding....

2)      April 2

Relational Understanding  by Richard Skemp (1978) measure the understanding of the quality and quantity of connection at the two end of the continuum –Knowing what to do and why – to an  instrumental understanding ; doing something without understanding.

• Procedural understanding is simply doing something without understanding
• Conceptual understanding helps children relate new ideas to what is already contexture in them minds.

This is based on the theory of constructivism – knowledge has to be constructed by the learners.

 Authentic Assessment:

Use assessment to plan for learning experience and instruction, including use of varied strategies that provide a comprehensive picture of each child’s progress and needs. Teachers need to continuously evaluate the effectiveness of instruction. Use of teacher designed measures to devise the level of learning.  Early Childhood teachers use concrete tasks, oral questions for informal assessment with young children. Assessment can be conducted while young children engage in independent tasks. Use tasks or oral responses can be conducted during a teaching activity, as part of learning experience enabling the teacher to make more accurate decisions for the instruction of individual students. The teacher uses observation, tasks, and manipulative activities to determine a child’s progress in learning.  Teacher need to know the root cause why the child cannot count.

Teachers must make instructional decisions, both immediate and long term. They must decide how long to spend on a particular math unit. They can use individual task and ongoing observation of class progress, to provide more information that will help them to decide whether to include more experiences, use review activities, skip planned activities or conclude the current topic and move on to a new one.

 @ Scholastic Teaching Resource

 

New insight.......

1) April 1

Today I learn to look at numbers in different ways, and see math as a natural and valuable part of everyday activities.

- Countable are discrete quantifiers that do not have factional parts.

   They have plural form: 1book, 2 books, 3 books.

- Uncountable are continuous quantifiers that always exist as factional parts,

   such as money, water- instead we say;  1 dollar, 2 dollars or 2 cups of water

- Learn to look out for similarity, difference or patterns.  I was constantly challenged to look for more than one way to solve a problem.

- The everyday life of learners offers an endless array, such as how many biscuits to make for the party or how many color pencils are needed to fill this box are real challenges – to learn math naturally.

‘Subitise’ – a mathematical term:  the ability to tell the number of objects in a group without counting them.
 

                                                                              

 

 I enjoy the lesson today. What learners need most is an adult, like Dr Yeap who fosters their interest in math, who encourages them to test their ideas and to keep sharing their reasoning in a supportive, non-judgmental environment. Learners will develop positive attitudes toward and an aptitude for mathematical learning.
 

 Sometimes, teacher too vigor to teach children mathematics,  she can be moving quickly that when a child is able to write and recognize numerals she think the child is ready to accelerate the topic. The child might be far from developmentally ready to acquire those kinds of math skills. Instead, the child might need more concrete experiences with grouping of numbers

There are two differentiated models:

 Acceleration Model – go ahead of topics different content.
 

Enrichment Model– staying with what the content but offer children with more challenging tasks to help develop the math process skills to understand the mathematical relationships around them.

 

 

 

Visualization...

3) April 3


Visualization is the most important skill that teachers need to help children develop in their early years.

Writing numerals are an abstract representation of numbers. Before children are ready to work with writing model of numbers they need to have experiences with concrete and visual models.

According to Jerome Bruner's CPA Approach, children develop concepts of the number system in three stages.

They moved from working with concrete representations of object (such as blocks, unifix cubes, tangram, their fingers) to visual representations (such pictorial drawings) and finally to the abstract conventional number symbols or models

It seemed that most mathematically competent learners in the class had developed in their mind strong visual images of numbers or models. Learners are engaged in the folding or cutting of paper to develop such models. Some time learners were given pencil and paper to work out a problem.

They drew shapes, different symbols, then progressively to drawing arbitrary marking for tens and ones, lines or circles to representing tens. These symbolic images helped learners to develop mental images

Abstract model using conventional numbers symbols were only useful for learners with strong visual image of numbers.

In preparing and planning the lesson; according to Zoltan Dienes' theory of Varability, teacher needs to preamp and expect different responses and perceptual variant

Following the child’s lead, if we watch closely and listen uncritically young children will tell us much about how they think.

The Teaching & Learning Principles

Wow! One needs to be an active learner in learning and doing mathematics through problem solving.  Instructional tasks must be meaningful and relevant to students.

Help students to acquire the disposition of curiosity to learn mathematics.  By giving ample opportunities to help students evaluate their own experiences in such a way that enhances understanding, meaning, relevance, and retention of that information. One way is to allow time for students to talk to one another about the mathematical relationships they see so they can process the information as well as hear other people's perspectives.

Processing information includes verbalising their thinking, reorganizing, questioning, testing, analysing, and summarizing, helps to develop their reasoning skills and sense-making skills.

The more details are added to their existing networks, the more connections they make, the greater consolation takes place.

Can you solve the follow ‘poem’ that has become a problem?

The 7 little dwarfs.
There were 7 little pillows. They found 7 little beds.
They lay down on the 7 little beds.
Along came 7 little dwarfs and lay in the 7 little beds.
They had 7 little dreams.
They dreamed of 7 little gold mines.

 How many all together?

Reflection on chapter 1 & 2

Reflection on chapter 1 & 2

There are two things that stand out in these chapters:

My knowledge of mathematics and how students learn mathematics – these are essential tools I need to acquire to be an effective teacher of mathematics. As the teacher, I play an important role in shaping mathematics for my students.  My beliefs about what it means to know and do mathematics and about how students make sense of mathematics will affect my instructional approach.

First and foremost, having a deeper understanding of what mathematic content should be taught at each grade level., my role in fostering math learning is to integrate experiences with math into children’s everyday play. To make it work, my excitement and interest in children’s inquiries will encourage them to talk through their discoveries. My acceptance of their math reasoning, even when it may seem ‘wrong or illogical, will give them the confidence to keep thinking, questioning, and sharing.  Most often, the feelings stem from my childhood experiences with math that placed too much emphasis on getting correct answers, when the process of finding the answers was not fully understood. So how can I fight the feelings of math anxiety when working with children?

I must remember that I should never ‘teach’ children math. Children learn math by ‘doing’ Math. Children need time to explore and discover math concepts on their own in non-judgmental environment. What children need is an adult to foster interest in them, encourage them to test their ideas and to keep sharing their reasoning with confidence and assurance that it will be accepted, no matter what!

Secondly, I need to know how my students learn mathematics – the awareness of individual development in context; what my students know, are there any common misconceptions and need to learn, then to be able to challenge and support them to learn it well. 

The daily classroom experience that teacher provides has great influence on how and what students learn about mathematics. It provides a repertoire of activities, selection of meaningful instructional tasks and the ability to promote curiosity, questions, develop students reasoning and sense-making skills. Children needs more concrete experiences. They discover relationships among objects. Each new discovery about the physical world, and the thinking that accompanies these discoveries, lays the foundation for later mathematical learning.

“Learning mathematics is maximized when teachers focus on mathematical thinking and reasoning”

(NCTM, 2009, n.d.)