Our comments on the article "A Practical Framework for Technology Integration in Mathematics Education" by Cheah Ui Hock...
Due to the progress of the society, we cannot live without technology. technology is incorporated everywhere, likle at work, home and outside for entertainment.moreover, pupils can focus on the concept and idea rather than computation. When computation is done by technology, they can know and understand the concept better by paying attention on those. in addition, technology has its advantages and disadvantages. Thus, it is up to the teacher to decide on what, how and when to integrate technology. For instance, not all the topics are suitable to be taught through technology. Therefore, the teachers need to consider the suitability of the content as well.
2) Integaration of technology (based on the article)
- AVAIBILITY
- iNTELLECTUALITY- the knowlegde
- PREPARATION
- THERE MUST BE A CONTINUOUS PROFESSIONAL DEVELOPMENT
Tuesday, October 7, 2008
Tuesday, September 16, 2008
Constructivism vs Constructionism
Constructionism evolved from constructivism. This is as Papert was a Piagetian and his theories had a foundation of Piagetian theories. Yet, what he proposed through contructionism differes slightly from constructivism propsed by Piaget.
Constructivism suggests that knowledge is not simply transmitted from teacher to student, but actively constructed in the mind of the learner.Constructionism the other hand states that constructionism suggests that new ideas are most likely to be created ideas when learners are actively engaged in building some type of external artifact that they can reflect upon and share with others.
Constructivism supports the constructivist viewpoint.However, it emphasizes the particular constructions of external artifacts shared by learners. Although learners can construct and present knowledge or meanings without producing external products, the processes of construction are more evident when learners produce through social interaction with others and share representations of their understanding and thoughts.
Contructivism is promotes science-centered and logic-oriented learning. Constructivism, too, does the same, but, to a lesser degree.
To make a long story short, both are intended for the same goal, yet through different means.
Constructivism suggests that knowledge is not simply transmitted from teacher to student, but actively constructed in the mind of the learner.Constructionism the other hand states that constructionism suggests that new ideas are most likely to be created ideas when learners are actively engaged in building some type of external artifact that they can reflect upon and share with others.
Constructivism supports the constructivist viewpoint.However, it emphasizes the particular constructions of external artifacts shared by learners. Although learners can construct and present knowledge or meanings without producing external products, the processes of construction are more evident when learners produce through social interaction with others and share representations of their understanding and thoughts.
Contructivism is promotes science-centered and logic-oriented learning. Constructivism, too, does the same, but, to a lesser degree.
To make a long story short, both are intended for the same goal, yet through different means.
Monday, September 15, 2008
Tuesday, September 9, 2008
Evaluating Applets - The Table Tree
Evaluating Applets
View SlideShare presentation or Upload your own.
Also available on:
http://www.slideshare.net/emilley/evaluating-applets-presentation
Sunday, September 7, 2008
Fun with MSW LOGO
Hey people!!! Want to learn something fun with MSW LOGO programme??? This software might strike as a complicated one for some students. Thus, it would be a good idea for you introduce this software by teaching these fun activities. They still involve geometry. Therefore, when the form is complete, you can actually discuus with your students about the geometrical shapes that are found in it. All you have to do is to just copy the following commands and paste them in your MSW LOGO and click execute.
1. repeat 100 [fd 78 lt 56 bk 67 circle 34 bk 12]
2. repeat 103 [fd 20 bk 30 rt 57 lt 50 circle 200 lt 45 fd 80]
3. repeat 103 [fd 20 bk 30 rt 57 lt 50 circle 200]
4. repeat 13 [circle 100 lt 30 fd 100]
5. repeat 50 [fd 60 rt 70 fd 23 rt 25 bk 10 lt 20 circle 20]
6. repeat 2000 [fd 90 lt 89 fd 80 rt 89]
1. repeat 100 [fd 78 lt 56 bk 67 circle 34 bk 12]
2. repeat 103 [fd 20 bk 30 rt 57 lt 50 circle 200 lt 45 fd 80]
3. repeat 103 [fd 20 bk 30 rt 57 lt 50 circle 200]
4. repeat 13 [circle 100 lt 30 fd 100]
5. repeat 50 [fd 60 rt 70 fd 23 rt 25 bk 10 lt 20 circle 20]
6. repeat 2000 [fd 90 lt 89 fd 80 rt 89]
Tuesday, September 2, 2008
Something to share with you- LOGO
What is Logo?
Logo is a computer programming language designed for use by learners, including children. It is easy for the novice programmer to get started with Logo writing programs and getting satisfaction doing so, however Logo is also powerful and can be effectively used as a mathematical problem-solving tool without limits.
Logo has been around for a long time. It was originally developed at the Massachusetts Institute of Technology in the 1960's and was intended to allow people, even small children, to use computers as a learning tool. Logo was based on LISP, a programming language used in artificial intelligence research. Powerful computer science concepts of the procedure, recursion, programs-as-data are built into Logo. It is the language for learning and is a tool to teach the process of learning and thinking.
Logo's popularity seems to have declined in the United States, however in the past few years there has been new Logo development accompanied by renewed public awareness and enthusiasm. Logo is widely used in the classrooms of Europe and Japan. In England, Logo is a mandated part of the national curriculum. In the United States, Logo's popularity peaked at the time that there was one computer in a classroom. Now that most schools have a lab such that each student can have there own computer, using Logo in the mathematics classroom can be even more powerful.
A computer scientists may not speak very highly of Logo because it is a interpreted language rather than a compiled language. This means that the computer must interpret every command separately while the program is running rather than running a program that "compiles" the entire program into machine code. To keep a long story short, a program that is "interpreted" runs more slowly, but what seems a detriment to a computer scientist is actually a plus if you want to use Logo for education. Students can try their Logo procedures immediately and make changes and additions to their work easily with immediate results.
Recently, versions of Logo have evolved that take advantage of newer hardware and the Windows operating system, such as MSW Logo. Of course the Logo philosophy and the basics of the language remain the same. You will best get a feel for the power of Logo by investigating the activities on this web site.
Why Use Logo?
Logo is not limited to any particular topic or subject, however it has a natural tendency for the exploration of mathematics concepts and for promoting mathematical thinking. Technically, Logo is a programming language, but it would be better described as a learning language that encourages students to explore and to think about the processes involved in developing mathematical ideas. Although Logo was one of the first pieces of educational software available, it is not and will not be outdated.
The very essence of Logo involves a student in thinking about process. The creation of a product becomes more important than the finished product itself. Logo is a natural for students to make the bridge from the concrete to the abstract, particularly with geometry and algebraic thinking.
The use of turtle graphics in Logo leads to natural investigations of geometry concepts with easy-to-learn commands such that the focus is on the math and not the computer. Some very sophisticated figures, concepts and ideas can be easily produced with Logo. While the visual turtle geometry is a good way to introduce logo as a mathematical problem-solving tool, it is not limited to graphics.
So often students, particularly middle school aged students, do not see a reason to use variables, algebraic expressions and equations. Logo provides an arena where students use algebra, need algebra and enjoy the productivity of algebra. After all, a numeric answer is the result of only one question, while a carefully developed algebraic expression is all the answers.
Examining the sample lessons on this web site will give better insight into the use of Logo as a unique and most effective tool for students in the mathematics classroom. There are examples of lessons in geometry, probability, data analysis and number theory. All of these lessons promote skills of number sense, estimation and algebraic thinking.
LOGO as a Programming Language for Educational Applications
by Jim Andris
The LOGO language was developed in 1967 by the Logo Group at MIT under the direction of Seymour Pappert, author of the internationally acclaimed book Mindstorms: Children, Computers, and Powerful Ideas. It was the first language specifically designed to enable children to learn by discovery. According to Billstein, Libeskind and Lott in Logo: Programming and Problem Solving, "Logo is intended to provide an environment in which learners progress through the developmental stages of learning by exploration." (p. 1)
A Language for Integrated, Experimental Learning
Originally designed to conform to the child developmental theories of Jean Piaget, it is the theories of Jerome Bruner, a great promoter of Piagetian theory, which most clearly frame the significance of Logo as a tool £or education. In Studies in Cognitive Growth Bruner and others define three modes of representing knowledge: enactive, iconic, and symbolic. In enactive representation the significance of a stimulus is in the motor reaction it produces. Iconic representation is representing external objects with imaaes, either internal or external. Finally, symbolic representation is linguistic in nature. Each of these three modes of representation has its own characteristics. Children start out with primarily the enactive mode and progress through the dominance of the iconic mode to the modal Western adult form of symbolic representation.
One of the two major capabilities which were designed into Logo is the so-called turtle graphics. A "turtle" composed of a triangle or a turtle symbol may be controlled by commands from the keyboard or from within a Logo program. For example, the command FORWARD 50 RIGHT 90 will cause the turtle to move forward 50 units and turn right 90 degrees. Complex programs for the turtle to follow are built up from a small number of primitives.
Relating turtle graphics back to Bruner's forms of representation, it can be seen why Logo is such a powerful tool for educators. The concept of a geometric figure, say a square, can be translated into enactive mode. The child may be instructed to walk forward 10 paces, turn right, walk forward 10 more paces, and so forth, until a square has been described on the floor. A connection can be made between these movements and the symbols FD 10 RT 90 FD 10 in this way, giving a concrete interpretation of a symbolic language. Finally, what the child sees as these commands are executed, is a visual image of a turtle drawing a square on the monitor--the iconic mode.
A more contemporary approach to holistic education emphasizes "whole-brain learning". Most of us are now familiar with the concepts of "right-brained" and "left-brained" thinking. The right brain tends to specialize in schematic thinking and detailed visual imagery, the left brain, in categorical and linguistic thinking. Symbols such as FD 50 RT 90 are processed by the left brain (or if they are processed by the right brain, are processed as pictures rather than symbols). Images such as a square drawn on the monitor screen are processed by the right brain. Logo turtle graphics makes it possible to have these two modes working in concert, or if a learner has a preferred modality, Logo allows that modality to dominate.
In fact, one might even think of Logo as a language which literally allows the left brain to communicate with the right brain. The learner inputs a symbolic string at the keyboard, and observes a moving turtle tracing geometric forms on a screen. This is a perfect setup for experimental learning. Add to this the fact that children love to draw, and we have a formula for learning by doing. In order to draw a certain geometric figure, the child can experiment with different strings of symbols until the desired result is achieved. With just a little prompting from the teacher, the child is on his or her own schedule of learning.
A Language for Learning Problem Solving Skills
The advantages of turtle graphics for integrated learning are almost immediately obvious to anyone observing a child use Logo. At a somewhat more subtle level, Logo is tailor-made to encourage a problem solving approach to problems. However, we need to carefully deliniate the meaning of this assertion, for there are many definitions and levels of problem solving in education.
If we look carefully at human activity, we can see that our problem solving activity grows out of our creativity. That is, we are continually conceiving of goals or broader aims that we desire, but which we have not achieved. Out of our attempts at goal-achievement grow our problem-solving endeavours. Those of us who are systematic in our goal achievement recognize the importance of a self-conscious approach to problems, i.e. the importance of being able to document the steps in our approaches to solving problems. In other words, we have a procedural outlook: we attempt to identify sets of steps which constitute solutions to our problems. On the other hand, it is important not to become so caught up in methodology that we block the generation of novel solutions to problems.
The Logo language is procedural in just this desired sense. The learner can experiment with several lists of Logo elementary commands, or primitives. When from this experimentation emerges a list of commands that solves the problem at hand (say to draw a small circle), that list of commands can be given a name. This is done in Logo by typing the word "TO" followed by the name of the procedure, followed by the list of commands, followed by the word "END". From that point on, it is no longer necessary to type in the list of commands. Simply typing the name of the procedure will execute the entire list of commands. On the other hand, used properly, Logo can illustrate that there is nothing sacred about a particular list of commands, and alternative procedures for solving the same problem can be developed and given names, e.g. CIRCLEl and CIRCLE2.
At still a deeper level of the Logo language (beyond its procedurality), we can discern still other ways in which it significantly reflects the characteristics of human problem solving. Human problem solving is recursive, general, and hierarchical. The Logo language reflects all of these characteristics, some better than others. Perhaps if we trace the solution of a problem through its phases of development we can illustrate these characteristics of human problem solving as they manifest themselves in Loao.
Recursion may be defined as repetition. For example the procedure
TO SQUARE FD 50 RT 90 FD 50 RT 90 FD 50 RT 90 FD 50 RT 90 END
will solve the problem of finding a way to draw a square in Logo. On the other hand, the procedure
TO SQUARE REPEAT 4[RT 90 FD 50] END
solves the same problem without writing out the directions for drawing each side of the square. Instead, it simply says "draw a side, four times." Incidentally, this is called finite recursion, because we are counting to a finite number. The procedure
TO SQUARE RT 90 FD 50 SQUARE END
solves the same problem with an infinite recursion. (P.S.: CTRL-S to stop!) Recursion is an extremely important characteristic of human problem solving and it is reflected in nearly all computer languages.
Another important characteristic of human problem solving is its generality. We would prefer to solve a problem for a whole set of cases rather than have to solve the problem separately for each case in the set. Translated into our square problem, we might ask, why write a procedure for drawing a square of fixed size, when one can be written for drawing a square of any size? The procedure
TO SQUARE :N REPEAT 4[FD :N RT 90] END
solves the problem of drawing a square of size N. Perhaps and even more amazing demonstration of the power of recursion and generality combined is based on the fact that the exterior angles of a regular polygon are given by the formula 360/s, where s is the number of sides of the polygon. The following procedure draws a regular polygon of side, n, and number of sides, s.
TO POLY :S :N REPEAT :S[FD :N RT 360/:S] END
Hierarchicality is perhaps the most significant characteristic of human problem solving. This is the quality of analyzing a complex task down into subtasks, and those subtasks into still other subtasks. Every complex human procedure from writing or playing a symphony to balancing a checkbook displays hierarchicality. Logo is outstanding in its ability to reflect this important quality in its procedure. The key here is the fact that if one writes the name of procedure A as a step in procedure B, procedure A is automatically executed in proper sequence. The following procedure for drawing a house demonstrates hierarchicality, in that it is broken down into a square and a triangle, which are accomplished with the procedure POLY.
TO HOUSE :N POLY 4 :N FD :N RT 30 POLY 3 :N END
http://www.donbeaty.com/ictm/default.asp
Logo is a computer programming language designed for use by learners, including children. It is easy for the novice programmer to get started with Logo writing programs and getting satisfaction doing so, however Logo is also powerful and can be effectively used as a mathematical problem-solving tool without limits.
Logo has been around for a long time. It was originally developed at the Massachusetts Institute of Technology in the 1960's and was intended to allow people, even small children, to use computers as a learning tool. Logo was based on LISP, a programming language used in artificial intelligence research. Powerful computer science concepts of the procedure, recursion, programs-as-data are built into Logo. It is the language for learning and is a tool to teach the process of learning and thinking.
Logo's popularity seems to have declined in the United States, however in the past few years there has been new Logo development accompanied by renewed public awareness and enthusiasm. Logo is widely used in the classrooms of Europe and Japan. In England, Logo is a mandated part of the national curriculum. In the United States, Logo's popularity peaked at the time that there was one computer in a classroom. Now that most schools have a lab such that each student can have there own computer, using Logo in the mathematics classroom can be even more powerful.
A computer scientists may not speak very highly of Logo because it is a interpreted language rather than a compiled language. This means that the computer must interpret every command separately while the program is running rather than running a program that "compiles" the entire program into machine code. To keep a long story short, a program that is "interpreted" runs more slowly, but what seems a detriment to a computer scientist is actually a plus if you want to use Logo for education. Students can try their Logo procedures immediately and make changes and additions to their work easily with immediate results.
Recently, versions of Logo have evolved that take advantage of newer hardware and the Windows operating system, such as MSW Logo. Of course the Logo philosophy and the basics of the language remain the same. You will best get a feel for the power of Logo by investigating the activities on this web site.
Why Use Logo?
Logo is not limited to any particular topic or subject, however it has a natural tendency for the exploration of mathematics concepts and for promoting mathematical thinking. Technically, Logo is a programming language, but it would be better described as a learning language that encourages students to explore and to think about the processes involved in developing mathematical ideas. Although Logo was one of the first pieces of educational software available, it is not and will not be outdated.
The very essence of Logo involves a student in thinking about process. The creation of a product becomes more important than the finished product itself. Logo is a natural for students to make the bridge from the concrete to the abstract, particularly with geometry and algebraic thinking.
The use of turtle graphics in Logo leads to natural investigations of geometry concepts with easy-to-learn commands such that the focus is on the math and not the computer. Some very sophisticated figures, concepts and ideas can be easily produced with Logo. While the visual turtle geometry is a good way to introduce logo as a mathematical problem-solving tool, it is not limited to graphics.
So often students, particularly middle school aged students, do not see a reason to use variables, algebraic expressions and equations. Logo provides an arena where students use algebra, need algebra and enjoy the productivity of algebra. After all, a numeric answer is the result of only one question, while a carefully developed algebraic expression is all the answers.
Examining the sample lessons on this web site will give better insight into the use of Logo as a unique and most effective tool for students in the mathematics classroom. There are examples of lessons in geometry, probability, data analysis and number theory. All of these lessons promote skills of number sense, estimation and algebraic thinking.
LOGO as a Programming Language for Educational Applications
by Jim Andris
The LOGO language was developed in 1967 by the Logo Group at MIT under the direction of Seymour Pappert, author of the internationally acclaimed book Mindstorms: Children, Computers, and Powerful Ideas. It was the first language specifically designed to enable children to learn by discovery. According to Billstein, Libeskind and Lott in Logo: Programming and Problem Solving, "Logo is intended to provide an environment in which learners progress through the developmental stages of learning by exploration." (p. 1)
A Language for Integrated, Experimental Learning
Originally designed to conform to the child developmental theories of Jean Piaget, it is the theories of Jerome Bruner, a great promoter of Piagetian theory, which most clearly frame the significance of Logo as a tool £or education. In Studies in Cognitive Growth Bruner and others define three modes of representing knowledge: enactive, iconic, and symbolic. In enactive representation the significance of a stimulus is in the motor reaction it produces. Iconic representation is representing external objects with imaaes, either internal or external. Finally, symbolic representation is linguistic in nature. Each of these three modes of representation has its own characteristics. Children start out with primarily the enactive mode and progress through the dominance of the iconic mode to the modal Western adult form of symbolic representation.
One of the two major capabilities which were designed into Logo is the so-called turtle graphics. A "turtle" composed of a triangle or a turtle symbol may be controlled by commands from the keyboard or from within a Logo program. For example, the command FORWARD 50 RIGHT 90 will cause the turtle to move forward 50 units and turn right 90 degrees. Complex programs for the turtle to follow are built up from a small number of primitives.
Relating turtle graphics back to Bruner's forms of representation, it can be seen why Logo is such a powerful tool for educators. The concept of a geometric figure, say a square, can be translated into enactive mode. The child may be instructed to walk forward 10 paces, turn right, walk forward 10 more paces, and so forth, until a square has been described on the floor. A connection can be made between these movements and the symbols FD 10 RT 90 FD 10 in this way, giving a concrete interpretation of a symbolic language. Finally, what the child sees as these commands are executed, is a visual image of a turtle drawing a square on the monitor--the iconic mode.
A more contemporary approach to holistic education emphasizes "whole-brain learning". Most of us are now familiar with the concepts of "right-brained" and "left-brained" thinking. The right brain tends to specialize in schematic thinking and detailed visual imagery, the left brain, in categorical and linguistic thinking. Symbols such as FD 50 RT 90 are processed by the left brain (or if they are processed by the right brain, are processed as pictures rather than symbols). Images such as a square drawn on the monitor screen are processed by the right brain. Logo turtle graphics makes it possible to have these two modes working in concert, or if a learner has a preferred modality, Logo allows that modality to dominate.
In fact, one might even think of Logo as a language which literally allows the left brain to communicate with the right brain. The learner inputs a symbolic string at the keyboard, and observes a moving turtle tracing geometric forms on a screen. This is a perfect setup for experimental learning. Add to this the fact that children love to draw, and we have a formula for learning by doing. In order to draw a certain geometric figure, the child can experiment with different strings of symbols until the desired result is achieved. With just a little prompting from the teacher, the child is on his or her own schedule of learning.
A Language for Learning Problem Solving Skills
The advantages of turtle graphics for integrated learning are almost immediately obvious to anyone observing a child use Logo. At a somewhat more subtle level, Logo is tailor-made to encourage a problem solving approach to problems. However, we need to carefully deliniate the meaning of this assertion, for there are many definitions and levels of problem solving in education.
If we look carefully at human activity, we can see that our problem solving activity grows out of our creativity. That is, we are continually conceiving of goals or broader aims that we desire, but which we have not achieved. Out of our attempts at goal-achievement grow our problem-solving endeavours. Those of us who are systematic in our goal achievement recognize the importance of a self-conscious approach to problems, i.e. the importance of being able to document the steps in our approaches to solving problems. In other words, we have a procedural outlook: we attempt to identify sets of steps which constitute solutions to our problems. On the other hand, it is important not to become so caught up in methodology that we block the generation of novel solutions to problems.
The Logo language is procedural in just this desired sense. The learner can experiment with several lists of Logo elementary commands, or primitives. When from this experimentation emerges a list of commands that solves the problem at hand (say to draw a small circle), that list of commands can be given a name. This is done in Logo by typing the word "TO" followed by the name of the procedure, followed by the list of commands, followed by the word "END". From that point on, it is no longer necessary to type in the list of commands. Simply typing the name of the procedure will execute the entire list of commands. On the other hand, used properly, Logo can illustrate that there is nothing sacred about a particular list of commands, and alternative procedures for solving the same problem can be developed and given names, e.g. CIRCLEl and CIRCLE2.
At still a deeper level of the Logo language (beyond its procedurality), we can discern still other ways in which it significantly reflects the characteristics of human problem solving. Human problem solving is recursive, general, and hierarchical. The Logo language reflects all of these characteristics, some better than others. Perhaps if we trace the solution of a problem through its phases of development we can illustrate these characteristics of human problem solving as they manifest themselves in Loao.
Recursion may be defined as repetition. For example the procedure
TO SQUARE FD 50 RT 90 FD 50 RT 90 FD 50 RT 90 FD 50 RT 90 END
will solve the problem of finding a way to draw a square in Logo. On the other hand, the procedure
TO SQUARE REPEAT 4[RT 90 FD 50] END
solves the same problem without writing out the directions for drawing each side of the square. Instead, it simply says "draw a side, four times." Incidentally, this is called finite recursion, because we are counting to a finite number. The procedure
TO SQUARE RT 90 FD 50 SQUARE END
solves the same problem with an infinite recursion. (P.S.: CTRL-S to stop!) Recursion is an extremely important characteristic of human problem solving and it is reflected in nearly all computer languages.
Another important characteristic of human problem solving is its generality. We would prefer to solve a problem for a whole set of cases rather than have to solve the problem separately for each case in the set. Translated into our square problem, we might ask, why write a procedure for drawing a square of fixed size, when one can be written for drawing a square of any size? The procedure
TO SQUARE :N REPEAT 4[FD :N RT 90] END
solves the problem of drawing a square of size N. Perhaps and even more amazing demonstration of the power of recursion and generality combined is based on the fact that the exterior angles of a regular polygon are given by the formula 360/s, where s is the number of sides of the polygon. The following procedure draws a regular polygon of side, n, and number of sides, s.
TO POLY :S :N REPEAT :S[FD :N RT 360/:S] END
Hierarchicality is perhaps the most significant characteristic of human problem solving. This is the quality of analyzing a complex task down into subtasks, and those subtasks into still other subtasks. Every complex human procedure from writing or playing a symphony to balancing a checkbook displays hierarchicality. Logo is outstanding in its ability to reflect this important quality in its procedure. The key here is the fact that if one writes the name of procedure A as a step in procedure B, procedure A is automatically executed in proper sequence. The following procedure for drawing a house demonstrates hierarchicality, in that it is broken down into a square and a triangle, which are accomplished with the procedure POLY.
TO HOUSE :N POLY 4 :N FD :N RT 30 POLY 3 :N END
http://www.donbeaty.com/ictm/default.asp
LOGO in Geometry- TURTLE GEOMETRY
This is a very interesting link where we have to make a plan for the turtle in order to create geometry....
http://nlvm.usu.edu/en/nav/frames_asid_178_g_2_t_3.html?open=activities
http://nlvm.usu.edu/en/nav/frames_asid_178_g_2_t_3.html?open=activities
Monday, August 25, 2008
Gaming with numerals
Pupils tend to come to school with pre-set mind that mathematics is difficult. Thus, in the long run, they grow to hate it. This results in their lack of practice in mathematics and their competence in this subject does not advance. This may not necessarily be the truth for all pupls in a class, but most do fall into this category allright. So, as teachers, we must take up the responsibity of nurturing a love of numbers in the young hearts and minds of our pupils or future-pupils. This is definitely not an easy task as it demands a lot of creativity, experience and understandings in the fields related. Games is the easiest way to do this, say many. Yes, indeed, as children naturally enjoy games. They lihgten up at every opportunity they get to play something. So, what we would like recomend to you is, try this site out!!!
http://www.primarygames.com/math.htm
This link is full of various games of mathematics. This site offers a chance to the pupils to see that numerals can be fun. As teachers, we should make use of the various games in this site to promote learning mathematics. Our personal favourite game in this site is Puzzle Sudoku. (I actually bumped into this site while surfing for online Sudoku games as I'm a Sudoku fan). This is a slightly altered version of Sudoku that can give a change for those bright kids who are tired of messing with the same traditional type of Sudoku.
So, happy gaming we'd like to wish you and adios for now.
http://www.primarygames.com/math.htm
This link is full of various games of mathematics. This site offers a chance to the pupils to see that numerals can be fun. As teachers, we should make use of the various games in this site to promote learning mathematics. Our personal favourite game in this site is Puzzle Sudoku. (I actually bumped into this site while surfing for online Sudoku games as I'm a Sudoku fan). This is a slightly altered version of Sudoku that can give a change for those bright kids who are tired of messing with the same traditional type of Sudoku.
So, happy gaming we'd like to wish you and adios for now.
Monday, August 11, 2008
Some useful items!
We found a website at
http://www.primaryresources.co.uk/maths/maths.htm
It has actually explored more on the primary maths topics.
Interesting activities and power point presentations with colorful pictures and flash cards which will be useful for us as maths teachers. So check out people!
http://www.primaryresources.co.uk/maths/maths.htm
It has actually explored more on the primary maths topics.
Interesting activities and power point presentations with colorful pictures and flash cards which will be useful for us as maths teachers. So check out people!
Tuesday, August 5, 2008
Homework Well Done.
I should say this week's presentation by Fifi and the group was indeed exciting. It was short, simple yet very attention-grabing and entirely interactive presentation. I for one was totally engaged in the activity even though my mind was entirely elsewhere thinking of the assignment to be handed in the next day. I am sure we all agree about the activity's effectiveness in getting all to take part and follow what they presented even though it was a pretty simple thing. Their justificaition of why the Geomater's Sketchpad is useful in teaching various topics in Mathematics was indeed superb. Clearly they have done some real good homework.
The polygon Song.
Polygons are part of geometry and since we are discussing geometry lately my group thinks it would be appropriate to be posted here. I mean what good it could possibly be for the children to use Geometer's Sketchpad if they cannt even remember the polygons. so this one is a simple way to teach them polygons.
Monday, July 28, 2008
Calculator in Classroom.. Applicable?
After reading the article, we have come out with some thoughts in relation to Malaysian context.Undoubtedly, children of all ages should be proficient with calculators, and they need to learn to figure on paper and pencil work, but these methods alone will not meet contemporary needs.
We agree with the point that teachers should not completely reject the use of calculator in primary classroom, the keyword here is "HOW", in which how are we going to integrate the use of calculator in primary classroom. By using calculator, instead of worrying about computation mistakes, focusing on reasoning and problem solving benefits the pupils even better. Teachers can help students see patterns, check estimates against reality, and solve complex problems, like those encountered in daily life, through the structured use of calculators. Children introduced to the calculator when they are young will find it easy and effective to use. moreover, our opinion is also supported by reserchers who said that -Students who use calculators within a mix of instructional styles do not lose their paper and pencil skills. - more to come..
We agree with the point that teachers should not completely reject the use of calculator in primary classroom, the keyword here is "HOW", in which how are we going to integrate the use of calculator in primary classroom. By using calculator, instead of worrying about computation mistakes, focusing on reasoning and problem solving benefits the pupils even better. Teachers can help students see patterns, check estimates against reality, and solve complex problems, like those encountered in daily life, through the structured use of calculators. Children introduced to the calculator when they are young will find it easy and effective to use. moreover, our opinion is also supported by reserchers who said that -Students who use calculators within a mix of instructional styles do not lose their paper and pencil skills. - more to come..
Tuesday, July 15, 2008
Calculator with Patterns!
Here's an online calculator to share with you guys!!
http://www.teachers.ash.org.au/jeather/rainforestmaths/RFMF/DIY5wds/DIY5calc.swf
http://www.teachers.ash.org.au/jeather/rainforestmaths/RFMF/DIY5wds/DIY5calc.swf
Using Calculator To Teach Patterns
The Example of Activity Using Calculator To Teach Patterns
Activity Three Students will demonstrate their ability to recognize numerical
patterns/relationships and apply this knowledge to problem solving.
•
Place students into cooperative learning groups.
•
Pass out 100 centimeter cubes and calculators to each group.
•
Explain to each group that they are going to model the patterns of the ants in the story the students and teacher are about to read.
•
Review characteristics of patterns with the class.
•
Read the first four pages of One Hundred Hungry Ants by Elinor J. Pinczes.
•
Ask the students to model the pattern of the ants (one by one). Discuss if this is an efficient method of moving from place to place.
•
Ask the children to use their calculator to count by ones the numbers of ants (use the constant arithmetic feature 0+1=,=,=,=,=…). Stop at 100.
•
Return to the story and read the next two pages of the story. Ask the children to model 2 rows of 50, using centimeter cubes. Count, using the calculator (constant arithmetic feature 0+2=,=,=,=…). Stop at 100.
•
Return and read the next two pages. Ask the children to model four rows of twenty-five, using the centimeter cubes. Count, on the calculator (use constant arithmetic feature, 0+4=,=,=,=,=…). Stop at 100.
•
Return and read the next two pages. Ask the children to model five rows of twenty, using the centimeter cubes. Count, using the calculator (use the constant arithmetic feature 0+5=,=,=,=…).
•
Return and read the next two pages. Ask the children to model ten rows of ten. Count, using the calculator (use constant arithmetic function 0+10 =,=,=,…).
•
Finish reading the story.
Evaluation:
•
Students will decide which patterns and relationships were most efficient and justify their conclusions. Evaluation is based on the criteria given in the attached rubric (Teacher Resource #4).
•
After finishing activity, collect materials. Discuss patterns noticed in modeling/calculator activity.
•
Handout hundreds chart (Teacher should have one to model, either overhead or chart). Use hundreds chart to record patterns discovered during activity (Teacher models counting starting at 2 up to 100). Children should color each pattern found differently to see relationships.
•
In their math journals, children will describe which models were most efficient in moving the ants and which ones were not. Justify the patterns/relationships found.
Extension/Follow Up:
A possible writing extension activity would be to create and publish a big book following the format of one of the books read during the unit.
As a math extension activity, the students could create a series of one-step, multi-step and process problems using the story they wrote.
In a cooperative learning activity, the students could make several sets of puzzle cards for problem solving. See Cooperative Problem Solving with Pattern Blocks for modeling.
Synopsis of the story "One Hundred Hungry Ants".
Activity Three Students will demonstrate their ability to recognize numerical
patterns/relationships and apply this knowledge to problem solving.
•
Place students into cooperative learning groups.
•
Pass out 100 centimeter cubes and calculators to each group.
•
Explain to each group that they are going to model the patterns of the ants in the story the students and teacher are about to read.
•
Review characteristics of patterns with the class.
•
Read the first four pages of One Hundred Hungry Ants by Elinor J. Pinczes.
•
Ask the students to model the pattern of the ants (one by one). Discuss if this is an efficient method of moving from place to place.
•
Ask the children to use their calculator to count by ones the numbers of ants (use the constant arithmetic feature 0+1=,=,=,=,=…). Stop at 100.
•
Return to the story and read the next two pages of the story. Ask the children to model 2 rows of 50, using centimeter cubes. Count, using the calculator (constant arithmetic feature 0+2=,=,=,=…). Stop at 100.
•
Return and read the next two pages. Ask the children to model four rows of twenty-five, using the centimeter cubes. Count, on the calculator (use constant arithmetic feature, 0+4=,=,=,=,=…). Stop at 100.
•
Return and read the next two pages. Ask the children to model five rows of twenty, using the centimeter cubes. Count, using the calculator (use the constant arithmetic feature 0+5=,=,=,=…).
•
Return and read the next two pages. Ask the children to model ten rows of ten. Count, using the calculator (use constant arithmetic function 0+10 =,=,=,…).
•
Finish reading the story.
Evaluation:
•
Students will decide which patterns and relationships were most efficient and justify their conclusions. Evaluation is based on the criteria given in the attached rubric (Teacher Resource #4).
•
After finishing activity, collect materials. Discuss patterns noticed in modeling/calculator activity.
•
Handout hundreds chart (Teacher should have one to model, either overhead or chart). Use hundreds chart to record patterns discovered during activity (Teacher models counting starting at 2 up to 100). Children should color each pattern found differently to see relationships.
•
In their math journals, children will describe which models were most efficient in moving the ants and which ones were not. Justify the patterns/relationships found.
Extension/Follow Up:
A possible writing extension activity would be to create and publish a big book following the format of one of the books read during the unit.
As a math extension activity, the students could create a series of one-step, multi-step and process problems using the story they wrote.
In a cooperative learning activity, the students could make several sets of puzzle cards for problem solving. See Cooperative Problem Solving with Pattern Blocks for modeling.
Synopsis of the story "One Hundred Hungry Ants".
In One Hundred Hungry Ants by Elinor J Pinczes, illustrated by Bonnie Mackain (Houghton Miffin, ISBN 0395631165), a soft breeze carries the suggestion of a picnic to 100 hungry ants. The littlest ant tells the other ants that marching in single file will take too long, so organises them into lines of 50, then 25, then 20, then ten. Will they get there before all the food is eaten?
Read and enjoy the book with the children the day before you intend to use it for a mathematical focus. Have fun with the story, and get the children to join in with the obvious choruses such as:
We’re going to a picnic! A hey and a hi dee ho!
And
There’ll be lots of yummies for our hungry tummies, A hey and a hi dee ho!
Monday, July 14, 2008
Mathematics and Technology
Mathematics and taechnology. I've always believed that mathematics is part of technology. I mean how can technology survive without mathematics. Take, for instance, computer. Every operation in it has a basic of mathematics, right?
Now that we are actually learning how use it in teaching mathematics its got to be interesting!!! There is so much to be exploreed and discovered to be inegrated into our mathematics lessons.
so, here I would like share with you guys some links that can come in handy for us throughout this course:
http://frank.mtsu.edu/~itconf/papers96/kimmins.html
http://futureofmath.misterteacher.com/
http://www.researchinformation.co.uk/time.php
Now that we are actually learning how use it in teaching mathematics its got to be interesting!!! There is so much to be exploreed and discovered to be inegrated into our mathematics lessons.
so, here I would like share with you guys some links that can come in handy for us throughout this course:
http://frank.mtsu.edu/~itconf/papers96/kimmins.html
http://futureofmath.misterteacher.com/
http://www.researchinformation.co.uk/time.php
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