Thursday, 12 March 2015

Math Anxiety Caused By Teacher's Teaching Style



Math anxiety can be caused by many factors. But one of the major contributors is that of the math teacher's teaching style. Have you met a teacher's teaching style that does not suit our learning style? It puts us off straight away. If not that, the going will be tough and learning math becomes taxing. It therefore appears that the role of the math teacher very much influence the outcome of our math learning. It makes us like or dislike math. The character or personality of the teacher also affects the interest towards the math subject.

However,looking back, how is the learning experience of our math teachers during their students' day studying for math themselves? Was it exciting then? Or has their math teacher taught them the way they are teaching us now? These are the very questions that we, the students, ponder also. I believe the math teachers, themselves, sometimes do model after their teachers as the image flashes back when they deal with math. The experience formed from the past do affects their teaching style, as a normal human should. If the current math teacher was taught by a dedicated and motivated one, the math learning experience would be a beautiful and enjoyable experience. However, if it was the opposite, then the impression received will goes to their teaching style and attitude towards the math subject.

If the teaching style is positive, math anxiety for the students will be reduced as the teacher are able to express their interest through the way math lessons are conducted. The math lessons and concept maths will be delivered and expressed with excitement and enthusiasm. This teaching style will indirectly affects the learning emotion of the students and the extent of their math anxiety. However,having said that, the math teacher has still to constantly monitor the students' progress. Being confidence with math does not guarantee good math lesson delivery, it only serves as a good starting point where students of the math teacher are less resistant to learning math given a good role model by the math teacher. The learning math journey of the students will not have this favourable headstart given a math teacher who is not confidence and has math anxiety himself.

Therefore, to summarise, math teacher plays an important role for our students and selecting the appropriate teacher becomes more crucial as it decides between a good start and better math learning journey. For math teacher who demonstrates math anxiety, be aware and constantly self-remind that your teaching style has an impact on the outcome of the students' learning. For student, be aware that math teachers are also human with their own feeling and personality. Adjust your learning style to match your teacher's teaching style to reap the best possible result in your math learning and aim to reduce math anxiety.


Heuristics Methods Used in Mathematics - Part 2



Part 2

Heuristics can be divided into 4 main types, which another 2 types would be discussed in this article.

·         The heuristic ‘act it out’ requires pupils to use physical objects or manipulatives to represent information. This skill is used to introduce new concepts and to allow pupils to explore the concepts using manipulatives.


Example:
The figure is made of 17 sticks. Move 4 sticks to form 8 squares.
Solution:

Pupils can use matchsticks to represent the information and use the matchsticks to find the solution to the problem.

Example:
There were some chocolates in a basket. Michael and three of his friends took 8 chocolates each.
25 chocolates were given to Shirley. There were then 11 chocolates left in the basket.
How many chocolates were there in the basket at first?
Solution:
Using the ‘work backwards’ method, first find the number of chocolates taken away by Michael and his three friends.
4 × 8 = 32 chocolates
Then, find the total number of chocolates taken away from the basket.
32 + 25 = 57 chocolates
Number of chocolates in the basket at first = 57 + 11 = 68 chocolates 

·        Pupils can use the ‘before-after concept’ for problems that provide information given before and after the event to find the unknown. This skill allows pupils to compare the information and relate different events together to solve the problems.

Example:

Jacky had $56 more than Jill. When he spent $108, Jill had thrice as much as what he had left.

How much did Jacky have at first?
Solution:  

2 units → $108 - $56 = $52  
1 unit → $52 ÷ 2 = $26  $26 + $108 = $134

Jacky had $134 at first.  

Four: Changing the problem
Example:Find the sum of 10 + 12 + 14 + … + 146 + 148 + 150.
Solution:
         
There are 75 numbers in the sum 2 + 4 + 6 + … + 146 + 148 + 150.
 
There are 4 numbers in the sum 2 + 4 + 6 + 8.
75 – 4 = 71
Hence, there are 71 numbers in the sum 10 + 12 + 14 + … + 146 + 148 + 150.
  
There are 35 pairs of 160 and a ‘80’.
10 + 12 + 14 + … + 146 + 148 + 150 = 35 × 160 + 80  = 5680

Thus, do try to keep in mind the various heuristics and apply them when you are doing problem sums. With regular practice, you will be able to handle problem sums with ease.
The word ‘heuristic’ is taken directly from the Greek verb, heuriskein which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics maths.

Three: Going through the process
·        Pupils can apply the ‘work backwards’ method when given a problem that provides the final result and that requires them to find the initial quantit
·        By restating a problem in another way, pupils can view the problem in another perspective.
·        When facing a complex problem, pupils can split the problem into smaller parts and start by solving the simpler parts. After doing so, the problem is simplified and solving the problem is much easier.

Wednesday, 11 March 2015

Heuristics methods used in Mathematics - Part 1





Part 1


The word ‘heuristic’ is taken directly from the Greek verb, heuriskein which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics maths.
Heuristics can be divided into 4 main types, which will be covered in this 2-part article.

One: Giving a representation

·         Pupils can transform word problems into pictorial representations and represent information with a diagram/model. This skill helps pupils to understand the question better when they see the visual representation of the word problems.
·         A systematic list should be made for word problems that require pupils to identify patterns such as repeated numbers or a series of events that repeat. This skill helps pupils in identifying patterns easily as the list organises all possible answers systematically.

Example:
Michele saved $150 on the first month. On the second month, she saved $60 more than the first month.
On the third month, she saved $70 more than the second month. On the fourth month, she saved $55 more than the third month. How much did she save in four months?
Solution:
Making a list:
1st month → $150
2nd month → $150 + $60 = $210
3rd month → $210 + $70 = $280
4th month → $280 + $55 = $335
 Total amount saved = $150 + $210 + $280 + $335                               = $975
 She saved $975 in four month


Two: Making a calculated guess


·         The ‘guess and check’ method is used for word problems when certain information is lacking. It requires them to make a guess first and check it, and making subsequent guesses and checks until the correct answer is derived. It is often used together with a systematic list as it helps pupils to narrow down the possibilities within a short time frame.


Example:
Jenny has a total of 7 dogs and parrots. The animals have 20 legs altogether.                
How many dogs does she have?
 Solution:
Using the ‘guess and check’ method,
Number of dogsNumber of legsNumber of parrotsNumber of legsTotal number of legsCheck
11 x 4 = 466 x 2 = 124 + 12 = 16X
22 x 4 = 8 55 x 2 = 108 + 10 = 18 X
33 x 4 = 1244 x 2 = 812 + 8 = 20 
She has 3 dogs.


·         The ‘look for patterns’ method is usually used by pupils when they have to identify a certain pattern in a number sequence.

Example:
124513
1191618
16123 X
Solution:

Making a list of possibilities: 
12 - 4 + 5 = 13
11 - 9 + 16 = 18
16 - 12 + 3 = 7
The value of X is 7.


Hence by using the systematic list, it is more effective to find the underlying pattern.

HEURISTICS AND WORD PROBLEMS







Content


Heuristics and its application


What Is Heuristics?+

Heuristics Maths refers to the different strategies that we can adopt to solve unfamiliar or non-routine Maths problems.

How Do We Use Heuristics In Problem Solving?+

There are different types of heuristics and they can be grouped into four categories, based on how they are being used:



Steps to solving word problems

With word problems as an introduction to problem sums for Primary 1 pupils, does your child know the different steps to approaching a word problem?
There are 4 basic steps that pupils can take to solving word problems:

Step 1: Understanding The Problem

It is important for children to understand the word problem that they receive, before they begin solving it.
A good way to help children grasp a question's requirement is to break the question up into smaller parts. Alternatively, parents can also provide guiding questions for the children to help them pick out the important information inside the question.

Step 2: Deciding On An Approach

There are many approaches (different heuristics) to solving word problems.
Children will need to decide on the approach they wish to use based on the question's requirement.

Step 3: Solving The Problem

After deciding on the approach, children will proceed on to solve the word problem with the selected approach. Over here, children will need to have a good knowledge of the approach selected in order to solve the problem.

Step 4: Checking The Solution

The last step for children to take when solving word problems will be to check their worked solution to ensure that they have solved the problem correctly.
For this step, children will need to make reference to the question provided and do the necessary comparison.

Worked example

Here we have a worked example using the 4 steps introduced above:

Question:

At a café, there are 3-legged stools and 4-legged stools for customers to sit on.
Vincent counts 15 stools with a total of 50 legs altogether.
How many 3-legged stools are there in the café?

Solution:

Step 1: Understanding the problem (through asking guiding questions).
Step 2: Deciding on an approach.
To use the “Guess and Check” strategy.
Step 3: Solving the problem with the "Guess and Check" strategy.
The total number of stools must always be the given number, 15.
Step 4: Check the solution.
Number of legs for ten 3-legged stools:
3 x 10 = 30
Number of legs for 4-legged stools:
50 – 30 = 20
Number of 4-legged stools:
20 4 = 20

Tuesday, 10 March 2015

Can Learning Heuristically Join Forces With Education?



There are now waiting lines for pre-school. Yes, two years before my boy steps foot into his pre-school, he gets put on a waiting list. This must be the ivy league of pre-schools.

I had a fluke event during kindergarten reading hour (which morphed into nap time). My friend Davy was lying down next to me, on my left. I don't remember the story being read, but I distinctly remember what happened next.

The fluorescent light above us began to flicker. As I stared at the light in awe, the light popped and broke on one end. Something inside me forced me to push Davy--into a row of desks, bloodying his nose. The weight of the light dangling from one end proved too heavy, and the light crashed directly where we had been lying.

Davy was crying. He failed to see that I'd saved his frickin' life. His nose was bleeding, the teacher was screaming, little girls peed their pants. Nap time was over.

This was the beginning of my education. And make no mistake, I liked learning. Still, the very act of sitting in rows staring at a teacher never made sense. How is a test going to really going to prove you've learned something? Answer: It doesn't.

My son will enter this school system soon, a system that closely resembles the one I trudged through. Classrooms with ~30 kids regurgitating what the Education Department believes is important.

I have already drawn up my plan towards my sons' classes. I plan to know his teacher better than most. I want to know where he/she has been and where they're going. I want to know where they stand and how they grew up. I want to know if they've travelled. I want to hear them tell a story and tell a joke. I plan on holding them to a higher standard. When you give a kid responsibility and trust, they shine. So will my teacher.

Our educational system shows signs of being inflationary. The degrees needed when I went to university are only the beginning of what is needed today. Tuitions are astronomical and are not matched by quality. Textbooks are obsolete before they're finished printing. I must face the reality that this is not a world I've seen before. We must gaze at our environment with new lenses.

How can we (an obese nation, by the way) move our classrooms out of an actual 'room'? Biology in a nearby field, language at a public speech, Heuristics Maths...well, anywhere but behind a chalk board.

Everyone learns in their own special way. I won't get into it, but I know that you can read 10 books on starfish, but until you see one in its own habitat, you don't know starfish. We live in a world where everything is digital. There will come a day when "I've actually seen a starfish!" means more than anything.

This isn't about entertaining kids. It's about knowing the world around them, writing about what they see, and learning actively.

Just look at them--sitting in their seats in neat little rows, all day-dreaming...reminds me of the unemployment line.


Are You Looking For More On Math Online



One in every of the fantastic perks with the on-line is usually that schooling is now accessible for any person and everyone. Those who have missed out on school whenever they were younger can initiate downloading programs internet based and get a certification and even a graduate or post-graduate diploma.

For a lot of the internet based maths courses you need to sign-up and fork out a tiny payment while there is a number of far more courses which might be without cost. There are actually numerous choices in maths itself you can nearly pick and opt for the subjects that you simply want like calculus, differentiation, trigonometry, geometry and so on. As soon as you wish to get Maths activity class therefore you never have the time to go out and meet with anyone, acquiring the knowledge over the internet stands out as the finest solution. This kind of online maths is practical for teenage pupils and all those in superior school. They will get all of the particulars and allow that they will need without needing to go away place and can get extra done in a smaller amount time. It's also possible to get this math tutoring online any time in the day or evening and this makes it a whole lot more effective for everyone to perform clearly. A good amount of college students have study techniques and many people can only examine underneath a number of issues and at several instances of day. As you appearance in the way that this can be performed via the internet, you're able to see how advantageous it happens to be for most persons. With mathletics there to assist you every action within the way with your maths, you will see that you just improve your grades tons swifter and quicker. This can be viewed as the subsequent generation in math tutoring and getting 100 % on the internet dependent it truly is most suitable for all students.

While you make use of the mathematics strategy you will find that it performs so much more beneficial than the previous conventional procedures of gaining a math tutor from a class. It makes use of entertaining video games and remarkable approaches that can aid you to remember the math and basically know it additional. Most internet based mathematics lessons begin the process of with concentrating on most of the general procedures that will involve addition, subtraction, coupled with order of operations. Aside from the basic principles, these affordable web based programs concentration within the totally different types of figures like decimals, fractions, percentage, absolute worth, radical signs, exponents and ratios. Online maths software programs are one of the hottest instructional coursewares between all topics remaining provided above the net. You can find countless educational establishments, some non-public and some will be the most desirable globally who are offering zero cost downloads of different maths assignments, tutorials as well as other coursewares. Almost all of the compact tutorial centered courses are for free but there are actually selected certification programs too for which you ought to spend a minimum charge depending on the topics. Learning math is a little diverse than studying for other subjects. Math can be a vital thinking study course and is realized by actively doing dilemmas. It's essential for students to complete the assigned research and even more math complications for practice. Doing research and practice function aids college students understand formulas and strategies they need to know. This also facilitates boost trouble fixing and crucial imagining abilities.

Learning for math begins from the classroom. It truly is essential for students to get duty for learning and becoming conscious of strengths and weaknesses. Attending just about every class is crucial. Not only attending, but becoming an energetic participant with the classroom, combined with taking notes. Examination material is typically coated in class, so it's always crucial that pupils pay awareness.

Making Math More Fun Review



For the greater majority, mathematics is one subject that doesn't interest quite a few individuals. It is meant to be hard, stressful and requires plenty of logical thinking. Well, this is the most popular misconception of individuals about mathematics. Unless they've heard of Making Math More Fun ebooks, then they will have a different view of this subject area, seeing maths is fun.

1. Each Child's Ultimate Games Book.

Making Math More Fun is not your ordinary textbook wherein the basics are taught. That way, kids are given a various view of what mathematics is all about. Having a fun concept of the subject will make them appreciate it a lot more. In fact, in performing the activities, they'll not even understand that they are learning the fundamental mathematical abilities at the exact same time. Since the e-books come in four different parts and of distinctive sets of games, kids can have their pick from board games to puzzles and other fun-filled activities which are meant for the subject to be as easy as ABC.

2. A Teacher's Effective Teaching Companion.

Just as kids have difficulty in understanding mathematics, teachers too have a difficult time on tips on how to teach the subject effectively to students. With Making Math More Fun [http://hubpages.com/hub/Making-Math-More-Fun-Review], a teacher's resources are unlimited. 1 can pick from the quite a few board games and puzzles that can be discovered inside the four distinctive books. Because of this, keeping the kids' attention will never be challenging once more.

This book may be purchased on the web and can be downloaded and thereafter printed. Imagine acquiring something in just a couple of clicks of your mouse. It'll also save you from a great deal of effort and hassles.

3. A Parent's Welcome Relief.

Making Math More Fun is each and every parent's tool in teaching their youngsters the way to do well in mathematics. Since most of the activities are some thing the children will surely take pleasure in, teaching them becomes less stressful. Since it's inexpensive, parents can also save additional money from buying unique resource materials. Very best of all, the activities are something that everybody in the family will surely appreciate. It promotes family bonding by providing 1 activity that the entire family will definitely love performing.