DAY TWO

Children problem solving

I placed the Tangrams in my Math (and Science discovery) learning centre last two weeks.  
I get my children to manipulate with them as I facilitate them during the learning centre time (earlier today in school.) 
I am amazed; they actually figured out to complete the Tangrams accordingly 
in a short period of time!

Back at Seed Institute:

CRITICAL THINKING.  I think creative critical thinking sounds better. 

 So, CREATIVE CRITICAL THINKING for Day two EDU 330 Elementary Mathematics.

'Learning is more than the acquisition of the ability to think; it is the acquisition of many specialised abilities for thinking about a variety of things."

Lev Vygotsky

To lead the child to right path, we need to teach the child the right way.  Hence, here is the methods of teaching;

One, Modelling; explaining is not a good instructional method.

Two, Scaffolding, I do, you do, we do; "Scaffolding is …of instructional process which works in a task-sharing situation between the teacher and the student.”

Three, Independent; “The greatest sign of success for a teacher... is to be able to say, "The children are now working as if I did not exist."”-Maria Montessori.

PROBLEM 5

7, SEVEN, 7, SEVEN,7.....

7 blah, seven blah, 7 blah, seven blah...

Tough calculation. 

Then again, the fundamental in Maths; we cannot count things that has different nouns.

Rationale counting

Rational counting refers to a child's ability to assign a number to the objects she is counting. As she counts a set of objects, the child must understand that the last number is equivalent to the total number of items in the set. Rational counting requires a mastery of rote counting and one-to-one correspondence.

One, To be able to count, you need to classify.

Two, Rote counting comes first before to be able to rationale counting (Counting by rote is a skill that come quite naturally to most children)

Three, One-to-one correspondence.

Four, Cardinal number (to appreciate the last number represent  the size of object.)

SUBITIZE.

In very young children, right-brain dominancy gives the ability to "subitize" large quantities. Wikipedia defines subitizing as a "rapid, accurate and confident judgment of number." This is something we can all do up to a small number of items - usually around 4 or 5. After that, we are either guessing or counting.

PROBLEM 6

BEANS, BEANS, BEANS

The music video from Debbie and Friends could be a good tuning in or introduction for the children to start off a good mathematics lesson.  Of course, the video must be related to what we are going to bring in for Math lesson. 

Kidney beans

Countdown by 1 or 2 to get ZERO!

Subtracting and we figured out the bad numbers;  multiples of 3 and 4.

Numbers

Cardinal: how many

Cardinal is counting.

   Ordinal: position

Ordinal says what order things are in.

Nominal: name

Nominal is a Name. 

PROBLEM 7

It is good to expose children with 10 frame.  Counting, sorting, dividing, subtracting, one-to-one correspondence...

Make 10 method

5 +7 +6= 18

/  \

5  1

PROBLEM 8

 Let's divide!

What if there are 51 beans that needs to be divided between Jack, Jill and Mother?  How many does each has?  How many ways can you divide the 51 beans?

51  /  3  =  17

/    \

30  21

After so many years, I have found the easiest way to divide!

Hands- on on Day 1,

Creative critical thinking on Day 2,

Day 3, here I come!

DAY ONE.

 PROBLEM ONE.

My NAME is NUR SHAHIRA- When I have 10 letters in my name and I was told to find 99th letter in my name, I felt like I have 99 problems instead.  

My brain had to work, yes, creative critical thinking. 

I rote count and listed down the numbers very carefully.  I tried to spot any pattern, multiples or any other clues so as to easily figure out the 99th letter in my name.  
I practically trying hard to stay focus when the more numbers I saw on my paper, my brain cells tend to have their way of shutting down.

I decided to cheat and minus NUR the mathematical way and so I am left with

S    H    A    H    I    R    A.

1    2     3     4    5    6    7
 13  12   11   10   9    8        

      14   15   16  17  18  19

25  24   23   22   21  20      

.

.

.

               99

I figured 'A' as my my 99th letter in my name.

PROBLEM TWO.

Ahh this one made me feel like I am one genius Math magician.  Suddenly I felt like WOAHHH, 
MATH IS MAGIC.

CARD TRICK :

 

Children will be definitely be amazed with the Card Trick!

It is actually a fun way to introduce to children numerals and learning the number words.   

I shall show my children my magic, getting them to learn number words the magical way.  

PROBLEM THREE.

 

A tangram is a Chinese puzzle consisting of 7 shape:

• Two large right triangles

• One medium sized right triangle

• Two small right triangles

• One small square

• One parallelogram 

Like building blocks, TANGRAMS can teach children about spatial relationships.

They may help children learn geometric terms and develop stronger problem solving skills and even help children perform better in general mathematics.

Arranged correctly, the shapes can be fitted together as a large square, rectangle, or triangle.  

I explored many different ways to create rectangle and square using 7 shapes or less.  

Tangrams too, can actually used to create different creative designs.  

PROBLEM FOUR.

Problem solving:

Two machines, one job

Ron's Recycle Shop, started when Ron bought a used paper-shredding machine.  Business was good so Ron bought a new shredding machine.  The old machine could shred a truckload of paper in 4 hours.  The new machine could shred same truckload in only 2 hours. How long will it take to shred a truckload of paper if Ron runs both SHREDDERS at the same time?

In 1 hour, the new machine will do half of the truckload.  In 1 hour, the old machine could do quarter of the paper.  So in 1 hour, the two machines have done three-quarter of the truck, and there is quarter left.  

What is left is one-third as much as what they already did, so it should take the two machines one-third as long to do that part as it took to do the first part. One-third of an hour is 20 minutes.  

That means it takes 1 hour and 20 minutes to do it all.   

Four Math problems covered for the evening.  

Oh MATH, you're so FUN-BULOUS! 

GROW WITH MATH

In our rapidly changing world,  today’s mathematics students need a repertoire of knowledge and skills that are more diverse, complex, and integrated than any previous generation. 

Principles and Standards for School Mathematics is a guide for focused, sustained efforts to
 improve students’ school mathematics.  Principles and Standards includes four grade bands:pre-k-2, 3-5, 6-8 and 9-12.  
There is a common set of five content standards throughout the grades: Number and operation, algebra, geometry, measurement and date analysis and probability. Each content standard includes a set of goals applicable to all grade bands followed by grade-band chapters that provide specific expectations for what students should know.

Problem solving is an integral part of mathematics.  By solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and positive confidence.

Mathematical reasoning and proof offer powerful ways of developing and expressing insights about a wide range of phenomena.  By exploring phenomena, justifying results, and using mathematical conjectures in all content areas and—with different expectations of sophistication—at all grade levels, students should see and expect that mathematics makes sense.

Mathematical communication is a way of sharing ideas and clarifying understanding.

Connections-Mathematics is not a collection of separate strands or standards.  Through instruction that emphasizes the interrelatedness of mathematical ideas, students learn not only mathematics but also about the utility of mathematics.

Mathematical ideas can be represented in a variety of ways: pictures, concrete materials, tables, graphs, number and letter symbols, spreadsheet displays, and so on. The ways in which mathematical ideas are represented is essential to how people understand and use those ideas. 

"Doing mathematics means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see weather your answers make sense.  Doing mathematics in classrooms should closely model the act of doing mathematics in the real world." (Van de Walle,J)  

 

The layout and physical resourcing of the classroom environment can significantly affect how students and teachers work within it.  With proper structures and supports, classrooms will assist the students to make sense of mathematics of what they know.  Students will be mentally engaged for the new ideas to be interconnected in a rich web of interrelated ideas.  Students must find relevant ideas they possessed and to bring forth on the development of the new idea.  Thus, students will reflective when they engage  in interesting problems in which they use their prior knowledge as they search for solutions and create new ideas in process.  

According constructivism (Jean Piaget) and sociocultural (Lev Vygotsky) theories,  the best learning opportunities are those engage learners in using their own knowledge and experience to solve problems through social interactions and reflections. 

Mathematics is a creative discipline.  It stimulates a child's thinking and allow the child to discover a more efficient solution to a problem or figuring out the hidden connections with much perseverance and positive attitude. 

 Mathematics utilizes a universal language that is shared all over the world.  With the basics of math skills, your children will be able to solve real-life problems, learn to reason and to connect ideas logically.  Moreover, having solid math skills will opens a world of opportunity for your child to have better access to higher-level careers. 

DEAR PARENTS

A Parents' guide

It is suggested that we shift the emphasis from teaching to learning, from our experience to the children's, in fact, from our world to their world.

-Zoltan Dienes

Math looks different these days.
 When you visit your child's Maths classroom, 

you are more likely to see your child solving real Maths problems.  

Definitely different from what you remember what Math lessons used to be.

Mathematics is problem-based.  

Teachers want children to understand that Math is not only used within the classroom, but also, helps them solve everyday problems.  

Hence, teachers use activities that are connected the the children's real lives. 

 Children are like mathematicians; they solve problems that may take them few minutes, an hour or more to solve. This way, children will figure and know that there are many ways to solve a problem. 

Children need to be expose to mathematics at both home and school.

Parents can help out by showing their children when they use math as simple as helping your child estimate in the grocery store or how many slices can we cut equally from a one whole pizza for a number of people. 

Teachers encourage children not only to work independently but also, in groups.  Children working together helps with understanding;  it allows more time for the children to talk, share and discuss about what they know and do not know. 

Working together as a team also helps to create good communication skills among the teachers and children. 

Teachers are engage with the children during group problem-solving.  

They actively listening to the children's  reasoning which, in turn, helps them understand their children's thinking and problem solving techniques they used. 

Homework may look different from when you were in school.  

The amount of it may be different too.
Practice is still important and children need to continue to do that. Children will still need to memorize basic facts.  Children need to be expose to activities and tasks that allow for a deeper understanding of the math. These tasks may take longer to solve, therefore, fewer problems are assigned to them. But these problems will help children understand how significant math is in their lives and for their future. 

We know that every child is capable of achieving in math. 

Math is everywhere! 

Look out for it with your children!