Chapter 1- Teaching Mathematics in the 21^st Century

A question to ponder,

“Is the ability to learn mathematics inherited or learnt through teaching?” 

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Mom Stories

I hated math during my school days. Till now I do not like to do count or do calculations.  I always had negative thoughts about Math, “Oh my god, math is impossible”. Somehow I had passed this thinking to my own children. Today my daughter hates math as much as I did in my school days. My son on the other hand, loves this subject and excels in it. Perhaps it is hereditary I thought, as my husband has a flair in this subject as well.

However after reading the chapter, Teaching Mathematics in the 21^st Century, I agree with the authors that “Families and teachers attitudes toward mathematics may enhance or detract from students’ ability to do math. It is important for you and for students’ families to know that mathematics ability is not inherited - anyone can learn mathematics” (p.9).

Child doing Maths

 Now I believe that the ability to do well in mathematics is not inherited just that people tend to develop a love for or dislike for the subject depending on their environment.  After reading chapter 1, I understand that teachers should encourage children to learn mathematics and lay a strong foundation for the young children to abstract essential mathematical skills.

“It is you, the teacher, who will shape mathematics for the students you teach” (p.1).

I understand the important principles and standards for School Mathematics. Each principle emphasizes on how children learn mathematics and the different instructions, strategies used by the teacher for the children to excel in mathematics. Teachers should bring technology into teaching to enhance students’ learning of mathematics in the classroom.

“Teachers help children to think of themselves as mathematicians in the same way as encouraging the children to think of themselves as readers. I understand that teachers can be a better teacher if we are aware of the following two criteria, your knowledge of mathematics and how students learn mathematics are the most important tools you can acquire to be an effective teacher of mathematics” (Van De Walle, Karp, Bay -William, 2013, p.1).

Chapter 2 – Exploring what it means to know and do mathematics

Classroom environment for doing Mathematics

“Students are actively engaged in solving problems, and teachers are posing questions that encourage students to make connections and understand the mathematics they are exploring” (p.14).

I agree with this statement, as I believe children cannot learn “Math” just by observing or imitating the teacher. For young children, math is experience and not something to be merely taught. Children should be actively engaged in their learning and exploring of materials in the class environment. Teacher should provide hands on experience where children can make connections with the real world. It is saddening to see children being pushed into counting or addition, which leads them to learn those skills through memorization instead of true understanding of the concepts or the patterns involved. Rather than having children to sit down and to do worksheets all the time, Children’s learning should take place through child-initiated and self-discovery instead of teacher-directed activities.

Children learn best when they are interested and use experiences to construct their knowledge. Piaget J. (as cited in Fosnot, 1996) believed that young children use experience to construct or build knowledge. “This can happen in two ways-assimilation and accommodation. Assimilation occurs when a new concept “fits” with prior knowledge and new information expands an existing network. Accommodation takes place when the new concept does not “fit” with the existing network so the brain revamps or replaces the existing schema” (Van De Walle, Karp, Bay - William, 2013, p.20). 

Hands on activities

Hands on experience

As stated by the authors, “The worthwhile goal is to create an environment in which students interact with each other and with you. The rich interaction in such a classroom allows students to engage in reflective thinking and to internalize concepts that may be out of reach without the interaction and input from peers and their teachers”(p.22).

References Van de Walle, J.A., Karp, K.S. & Bay- Williams, J.M. (2013). Elementary and Middle School Mathematics: Teaching Developmentally (8thed.) United States of America : Pearson Education, Inc.

Lesson 1                                                                                                                1/4/2013

How children learn and construct their knowledge? 

On the first day of lesson, Dr.Yeap emphasized children's learning will take place in groups referring to Vygotsky's theory as "how children learn in social setting". I also believe that children learn through interaction. As Vygotsky mentions, "Children construct their knowledge through social interaction which simultaneously guides their cognitive development". I trust that children's learning will take place when teachers provide support, coaching, assistance and scaffolding in helping children to achieve the goal. I suggest that teachers should provide cooperative learning experiences where children can share their knowledge with adults and their peers in the learning environment. 

Children learn math with Concrete, Pictorial and Abstract (CPA Approach)

Children learn through interaction

Bring home ideas from today's lesson

• Children are young and new to ideas - Teachers should model and scaffold children's learning.
• Knows about cardinal, ordinal prime and perfect numbers
• Mathematics based on facts not assumptions
• Learnt to observe the patterns in counting and sequencing
• Different ways we use numbers in daily life

End my blog by quoting Dr.Yeap's words, "You cannot count things that are different nouns". Example: Cannot subtract one orange from 3 apple

Lesson 2                                                                                                          2/4/2013

We started our lesson today by discussing the question"What Does it Mean to Understand Mathematics?".

Dr.Yeap explained that children understand mathematics by making connections between existing and new ideas. We referred to the text book, page number 2,3 which provides information on how children understand mathematics. However, one of the interesting and essential ways to understand math is by using manipulative as a tool to teach young children. We learned some important skills through scenarios and from the examples given in class in understanding mathematical concepts. The following are the big ideas that I learnt in class today.  

Scenario

I learnt a new term "subitized" which means the child will be able to tell the number without counting during this discussion.

There is a boy who is not able to count. What will you do as a teacher?

1. Assess the child through concrete materials

2. Perhaps he is able to count using real things

3. Possible to do 1 to 1 correspondence and rote counting

We conclude that the child may be not able to count by looking at the object(visual)but may be able to count using real things.

I agree with Dr.Yeap statement "Teachers should know the root cause of the problems and must know possible strategies". 

Dr.Yeap quoted this "some concrete things are real, but not natural which we use things 

to illustrate". 

This may sound confusing, but it is meaningful. There is no such thing like a "Square block which exist in the world". 

Concept of big and Small

Use same images to teach children the concept of big and small

I always use small fruit (rambutan for small) and watermelon for big) to teach the small and large concept. After this lesson I understand that we should use small watermelon and large watermelon to teach this concept. This is a big idea that I learnt from today's lesson. I also understood that mathematics and languages are connected in children's learning. 

Word problems 

(pictures from Dr.Yeap's blog)

We discuss a variety of word problems. Initially  I thought all word problems were of the same type. However, I noticed that there is difference in each and every problem sum. Some written statements are simple and some are complicated. It caters to children's different level of abilities to solve the word problems.  

Lesson plan

Learnt about substantative lesson plan and poor lesson plan. the information that Dr. Yeap gives is very useful from today's lesson,
Dr.Yeap says that we should never tell the children, "Fewer means subtraction, altogether means addition. 

Lesson 3                                                                                                                             3/4/2013

Humpty-Dumpty

We analyse "Humpty Dumpty song" and discuss how we can use this literary work as a stimulus to teach mathematical concept. We can derive few mathematical concepts that can be taught like measurement, length, concept of balance (science activity) and counting. I realized that language activities can be used to teach mathematical skills for young children.

Dr. Yeap asked us, "What is the difficult math concept to teach young children?".

Some of my classmates and I said, grouping, Money, Time, Counting in 2's & 4's.

I get some ideas on how to teach money concepts for young children. We reviewed paperclips in the can activity. My estimation fro a few of the containers was correct. Today's topic is about fractions and we learnt 3/4 is 3 out of 4 and not 3 upon 4. I like the song about fraction today, "numerator - is never under, denominator is for down". 

Dr. Yeap quotes this,

"Teach money concepts in real situations and not in artificial environment". 

"You cannot show fractions".

"You cannot show numbers as numbers are abstract and things you are showing are 

nouns".

What do you need to do for K2 children?

This answer is very important and useful for me as a K2 teacher. I understood that we should 

give visual literacy experience to the children and start with concrete materials. I learnt that 

exposing children to visuals is very important for them to learn future essential skills in formal 

schooling.

We ended up this session by quote "Teacher job is building knowledge structure".

Lesson 4                                                                                                                            4/4/2013

Today's lesson we started with the theory, "How children construct knowledge?" Jean Piaget believed that young children use experiences to construct or build new knowledge. It is a two way process in which the first part is a assimilation whereby a new element of experience are incorporated into existing structures and the other part is known as accommodation whereby a child either modifies or create new scheme.

Exercise:Tangram shapes (pre-cut pictures)

We learnt about Tangrams shapes and adapt some ideas on how to compare the area. I explored how shapes fit together to form larger shapes and larger shapes can be made of smaller shapes. This activity enhances me with a higher level of thinking and I am able to find out what makes these shapes alike and different. During the process, I was thinking about the following. 

1. How many 2's can be fit in piece 4? (I rearrange and overlap)

2. In 1 and 2, I compare the half of piece 1 with the half of piece 2. (fold overlap, rearrange)

3. For 2 and 3, I figure out 3 is 4 times larger than 2.

We learnt to compare the area in today,s lesson and also to pronounce the word "area"

Dr.Yeap quote this in class, "Nobody is born clever"

Lesson 5 & Lesson 6                                                                                         5/4/2013

Dr.yeap says that,

• Teaching of Numeracy is not in isolation.Teacher should know the structure of mathematics, so we can help children to construct knowledge". Learning opportunities should be given to children in preschool to learn social skills and motor skills.
• The concrete objects that we use to teach mathematical concepts must be identical and avoid different length of concrete objects.
• By the end of K2, the children must be able to work with one noun and they should understand that 25 are 2 tens and 5 ones.  
• Use the term "greater instead of bigger" to represent large quantity.
• Math is a common way to teach visualization.

Exercise 1

98-89 = 9

45-45= 9

32-23= 9

We found  a pattern during this exercise. whenever a 2 digit number, where the digits are 

consecutive, is subtracted from the same 2 digit number but with an opposite order, the number 

9 is obtained. The goal of the lesson is to practice subtraction by renaming. 

Dr. Yeap mentions that, 

• What is important is never to focus on teaching but to focus on learning.
• Teachers should know "What do I want the students to learn?
• How do I know the child's learning?
• What if they cannot (Teachers do remediation and revisit the process)
• What if they already can? (Differentiated instruction for advance learners)
• Teachers should know "Learning Goal"

Dr.yeap emphasized 4 teaching strategies, Modelling, scaffolding, do themselves, and 

explanation (Adapted from the article "What is a professional Learning Community?" 

Exercise 2 

 

Representing age group through graph

Age in years	20-29	30-39	40-49	50-59
Number	14	10	16	5

Our group represent the age group through bar graph. The smallest size represents the least 

number of people in that group. The largest size represents the most people in that age group. 

The size of the bar varies based on the number of people in the group.