Resource In Mathematics Introduction
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RESOURCE IN MATHEMATICS INTRODUCTION
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Mathematics Department IPGM, Kampus Tuanku Bainun According to Oxford dictionary, resource can be defined as a supply of raw materials, etc which bring a country, person, etc wealth. It is also known as things that can be helpful, support and consolidation when needed. In Mathematics term, resource can be defined as materials that can be used as teaching aids. Examples like a resource file, room, e.g. containing materials can be used by teacher in teaching and learning process.
In Mathematics, resource can be divided into three different kinds, which is printed material, physical manipulative, and audio and visual. Printed materials include books, magazine, encyclopedia, journals, documents, graphs, charts, posters, diagrams, pictures, comic books and many more. Printed materials always refer as paper base materials. In other word, paper base materials are printed materials. Physical manipulative examples are like puppets, globes, specimens and many more. Things that can be hold are called physical manipulative. Examples for audio and visual are TV programs, radio programs, film, movie, music, tapes, and many more. These resources are very helpful in helping students to understand about the topic or the learning area that they are learning.
Teachers always use teaching aids in class. Teaching aids included these three different kinds of resources. Teachers can vary teaching aids by applying these resources in their daily planning in teaching and learning process. Students will not be bored if teachers wisely used these resources in their teaching and learning process. The advantages of using different kinds of resources during teaching and learning process are to enhance students’ ability of understand the learning area and to stimulates their creative thinking. By using resources, students can explore and
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discover an answer by themselves. The most important in teaching aids is to develop students’ style of thinking and stimulate the desire for knowledge.
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RESOURCE IN MATHEMATICS ARTICLE AND SUMMARY/ABSTRACT
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Mathematics Department IPGM, Kampus Tuanku Bainun
ARTICLE AND SUMMARY/ABSTRACT ARTICLE 1
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Mathematics Department IPGM, Kampus Tuanku Bainun Geometry
Geometry is a strand of the K-6 mathematics curriculum that involves the investigation and exploration of shapes, structures and spatial relationships. From a teaching perspective, geometry can be seen as a way for students to relate their notions of shape to the environment in which we live.
There are shapes everywhere and
everything has a shape. Students can use the information learned in their geometry classes to turn tangible ideas into abstract thought.
Geometry in Kindergarten to Grade 8 is finally being taken seriously within the elementary school classroom.
Many teachers were not comfortable with geometry
having associated it with high school and the laborious proofs that were required (Van de Walle,2006). Van de Walle (2006) argues that geometry objectives can be thought of in two different yet related frameworks; spatial reasoning and specific content. Spatial reasoning has to do with the way in which students think and reason about shapes and the space they occupy. Individuals with spatial reasoning have the ability to visualize objects and spatial relationships and without geometric experiences, most people do not grow in their spatial sense or spatial reasoning (Van de Walle, 2006). In classrooms, too much emphasis has been placed on learning geometric terminology rather than
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developing spatial reasoning, causing students to miss a crucial portion of the geometry curriculum (Van de Walle, 2006).
The Van Heile’s explain that that those students who have difficulty understanding spatial ideas and geometric thinking most likely do not have the correct experience to allow growth and development in spatial reasoning
(Van de Walle,
2006)(Tuck, 2005). Each level describes the ways in which student’s process geometric content, as well as the types of geometric ideas students consider while travelling through each level, rather than how much knowledge about the subject they have. The significant differences that are noted from one level to the next are the objects of thought, or more generally, what students are able to understand and consider geometrically (Van de Walle, 2006). At Level 0, the Visualization level, the objects of thought are shapes and what they look like. It is the appearance of the shape that defines it for the student. At this level, a square is a square because, to the student, it looks like a square (Van de Walle, 2006). At Level 1, Analysis, the objects of thought are classes of shapes rather than individual shapes. At this level, students are able to process what makes a square a square by identifying its relevant properties.
The
student is able to identify that a group of shapes go together because of their common properties (Van de Walle, 2006).
At Level 2, Informal Deduction, the Van Heile’s
determined that the objects of thought are the properties of shapes. At this level, the student’s observations go beyond the properties of the shape and begin to focus on logical arguments about the shape based upon these properties (Van de Walle, 2006). Level 3, Deduction, and Level 4, Rigor, are typically not reached until the students enter into high school or University mathematics. Every teacher should provide the tools necessary for each child to experience geometry in a way that they can understand. Geometric thinking should be introduced early on and referred back to throughout the exploration of different mathematics strands with the intention that students develop strong spatial reasoning.
The development of software used in conjunction with the geometry unit is important when teaching geometry. In the article, Developing the 3DMath Dynamic MTE 3105 7 Resource in Mathematics
Geometry Software: Theoretical Perspectives on Design Importance of using 3D Geometric software in the classroom, Jones (2002) states that it is very important and vital to student’s understanding and success in geometry to implement software into the teaching of this subject. Using computer software in the classroom can "enhance both curricula and student learning in geometry" (Jones, 2000). Geometry software can be used successfully in the teaching and learning of geometry because of its interactive style of direct manipulation of geometrical objects (Jones, 2000). For that reason, there is an increased need for more 3D software programs that allow students to manipulate and work with shapes that are 3D in nature. Geometry units in schools are strongly associated with spatial and visual ability. While working with geometric concepts, students are working on and improving cognitive factors such as spatial visualization, reasoning and manipulation. Students who are going to be successful in geometry need to continually improve these skills and find opportunities that allow them to improve.
This improvement may depend on how
geometry is taught in the classroom, what manipulativesare being used, and the time spent teaching it.
Additionally, Jones (2002) explains the danger of placing too much emphasis on 2D shapes in the teaching of geometry. The consecutive approach of teaching 2D geometry and then 3D shapes is not necessarily the best approach for teaching students. If geometry is taught first using 2D shapes and then 3D shapes, the teacher is not fostering proper visual and spatial thinking abilities.
Developing 3D shape
awareness after learning 2D shapes is not easy for students to accomplish and can actually be more confusing, thus you could be setting your students up for difficulty or failure.
It is important for students to have access to and regularly use manipulatives in geometry. Teachers need to use more manipulatives or software programs that focus on both 2D and 3D geometry activities. Jones (2002) stresses the importance of giving students manipulatives to teach geometry instead of using the classic method of showing static pictures of shapes that are intended to represent 3D shapes. MTE 3105 Resource in Mathematics
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In 2002, a research study was conducted examining the effects of computer technology on success in the area geometry for students. The findings of that research study state that "the experiences of a group of learners using computer based representations compared with another group using concrete manipulatives found that while both computer and concrete groups improved significantly, the computer group improved slightly more, with older pupils (fifth grade) benefiting more from the computer-based manipulatives" (Jones 2002).
This research illustrates that both
computer software dealing with geometric principles, and hands on manipulatives given to children during math lessons improve geometric understanding.
The findings
similarly suggest that geometric computer software is slightly more beneficial and significant to students in their comprehension of mathematical principles.
Teachers must ensure that during their lessons they are remembering to challenge their students, by discussing shapes that both reflect a student’s visual perception of a particular shape, and also the irregular version of the shape. Shape’s such as A1 and A2 in Figure 1 are regular versions of shapes but shapes such as B1 and B2 challenge the student’s visual ideas and apply higher order thinking (Mack, 2007). Subsequently, when discussing geometric shapes, especially polygons, teacher’s need to demonstrate non-polygons that resemble a particular shape as well. The lack of this is a concern that was realized by Nancy Mack when teaching a geometry lesson to young students. The students had heard of a right angle and could point one out, but many students thought that there was also something called a left angle. When students first begin to learn about polygons they focus on the visual appearance. If students are only shown polygons with a particular visual appearance, they may not actually understand the mathematical properties related to that polygon. One way to introduce students to the multiplicity of examples is through dynamic geometry computer software, such as Geometer’s Sketchpad. This program allows students to visualize and create shapes they are reading about or discussing in their math classes. Students then understand the ‘big picture’ when it comes to shapes. It is MTE 3105 9 Resource in Mathematics
a program that allows children to explore different geometric shapes, their properties, and examine the multiplicity of shapes that exist.
Geometry is a progressive concept, as seen by the Van Hiele levels of Geometric Thought. Through these levels it is understood that students go through a number of stages; visualization, analysis, informal deduction, deduction, rigour, with each new stage building on the previous (Van de Walle & Folk, 2008). Therefore in order for students to truly understand geometry they must proceed through these levels in a sequential order, moving from concrete to more abstract thought (Carson & Rowlands, 2007). This causes concern with a student’s learning of geometry, as the student may not learn the base they need in one grade to understand the curriculum in the next. It is through geometry that teachers provide their students with this knowledge. In order to provide students with the best education possible, these concerns in geometry must be overcome. Our group definitely agrees with the statements that the research has suggested about using manipulatives within geometry. Our group found it very interesting that much of the research suggests that it is neither helpful, nor beneficial to students to teach 2D shapes before 3D shapes. The research instead suggests that by teaching these two concepts consecutively it actually confuses students more. While out on placement, our group witnessed several geometry lessons. 2D geometry is still being focused on before 3D geometry.
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ARTICLE AND SUMMARY/ABSTRACT ARTICLE 2
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Mathematics Department IPGM, Kampus Tuanku Bainun PRIMARY STUDENTS’ UNDERSTANDING OF TESSELLATION:
Tessellation is included in many mathematics curricula as one way of developing spatial ideas. If students do not understand tessellation in the intended ways, however, the development of other spatial ideas, such as properties of shapes and symmetry, may be compromised. Van Hiele levels were used as a basis for analysing the descriptions of eight different tessellation patterns by 26 Year 5 and 6 students. Responses from some students indicated that they understood the tessellations only as movements of shapes or saw many of the patterns in 3D. Vincent (2003) suggested that exploring tessellations was one approach to investigating the properties of 2D shapes. Serra (1993) included tessellation explorations as one way of developing ideas about symmetry. The notion of MTE 3105 Resource in Mathematics
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using tessellation activities as a means of developing understanding of other aspects of geometry may be compromised if students do not understand the nature of tessellation, or have different perceptions from those assumed by teachers. Level 0 (Visualisation): Students take account only of the appearance of the shape, and describe properties only in terms of its appearance.
Level 1 (Analysis): Students describe properties informally, and can establish the essential conditions through a consideration of component parts.
Level 2 (Abstraction): Students can draw on logic to establish necessary and sufficient conditions when describing the properties of shapes.
Where tessellations were concerned, the understanding demonstrated needed to take account not only of the shapes involved in the tessellation, but also of the transformations applied in order to create the tessellations. At Level 0, students could be expected to identify the shapes involved in the tessellation or the combination of shapes that made up the basic unit that was transformed to create the tiling pattern. Students responding at Level 1 would be expected to describe both the shapes involved and the movements used to transform the shapes but in a disconnected fashion.
How do primary school students describe tessellation patterns?
Are the van Hiele levels useful in describing students’ understanding of tessellation?
Eight different tessellations were presented in pictorial form, and students were asked to identify the shapes used and then to describe in as much detail as possible how the shapes were transformed to create the tessellation. The tessellations included regular and semi- regular patterns, one non-periodic tessellation, and patterns that included MTE 3105 Resource in Mathematics
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pentagons. Van Hiele levels applied to tessellations.
Responses were obtained from 26 Year 5 and 6 students at two Catholic primary schools in Melbourne, Australia. Students coloured in the composite shapes used in each tessellation, and then wrote their descriptions of how the tessellations were made in spaces provided below each design.
The majority of students could describe the tessellations only in a visual manner. The levels of response shown in Table 2 suggest that as the nature of the shapes of which the tessellation was composed became less familiar the level of response was reduced. Tessellation 1, composed entirely of squares, attracted the highest overall levels of response with nearly half of the students responding beyond the visualisation level. In contrast, no students were able to describe Tessellations 6 and 8 at the Abstraction level. Responses of students to each question on the tessellation task.
The highest levels of response overall were elicited by Tessellation 1, with over onequarter of the students reaching Abstraction level. An example of the Abstraction level response is:
Tessellation 3, an irregular tiling pattern produced some somewhat surprising results. The complexity of the pattern seemed to encourage students to apply some level of analysis, although this was not developed further into Abstraction level. A typical response coded at the Analysis level was:
Tessellation 7 was seen only as a set of cubes by 13 (50%) of the students. Only one student explicitly connected the two- and three-dimensional aspects of this tessellation.
This response was coded at the visualisation level. Some students, however, appeared MTE 3105 Resource in Mathematics
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to see three-dimensional shapes in many of the tessellations. One student saw Tessellation 1 as a cube.
The response, however, was coded as irrelevant since the student had not identified the shapes involved correctly.
For some students, the movements used to create the tessellation, rather than the shapes involved, were dominant. This response to Tessellation 4 describes only the movement rather than the shapes involved, and this student described many of the tessellations in a similar fashion:
Few students recognised Tessellations 5 and 6 as being composed of pentagons. Some students saw the composite hexagonal arrangement in Tessellation 5, but several students referred to the shape in Tessellation 6 as “fly wings”. A majority of students in this study described tessellations in terms of the shapes of which they were composed: Visualisation level. Familiar shapes, such as squares and triangles, were more likely to be named whereas only 50 percent of the students could describe Tessellation 8 coherently in terms of the shapes that comprised the design. Familiar shapes also appeared to support higher level descriptions. The complex design of Tessellation 3 appeared to support students to reach Analysis level. Similar comments could be made about Tessellation 2 and Tessellation 6. In order to encourage understanding of tessellation, it would appear that students should experience a wide range of designs, made up of familiar and less familiar shapes and transformations.
The misconceptions shown by some students could compromise their understanding of the properties of 2D shapes, and subsequent development of geometrical ideas.
Using the van Hiele levels as a basis appeared to provide a useful means of identifying primary students’ understanding of tessellation, that included both recognition of the shapes involved and the transformations used to make the design. MTE 3105 15 Resource in Mathematics
Teachers should not assume that all students visualise tiling patterns in the same way.
If tessellation is used as a means of developing students’ geometrical knowledge of the properties of shapes, and of symmetry and transformation, then opportunities are needed for all students to learn about both aspects of tessellation: the nature of the shapes involved and also the kind of transformation applied.
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RESOURCE IN MATHEMATICS TEACHING AND LEARNING KITS
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Mathematics Department IPGM, Kampus Tuanku Bainun Set A – Wheel of Fortune
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Learning Resources and Material
a. Wheel of Fortune b. Flash card (with number on card, 1 - 8)
Development of Lesson
Introduction: 1. Before getting the students about the teaching kit, explain about the Wheel of
Fortune and go over again on 3-Dimensional Shapes again. 2. Explain how to use the Wheel of Fortune.
Methods/Procedures: 1. Ask a student to come in front. MTE 3105 Resource in Mathematics
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2. Ask the student which numbers they want to pick. 3. Tell the student to spin the Wheel of Fortune and yell out which number he/she
pick. 4. When the wheel stops spinning, see the number that the indicator shows. 5. Take the flash cards and pick the same number with the number that the indicator shows. 6. If the flash card shows a3-D shape, ask the student about the properties of the
object. 7. If the flash card shows the properties of a 3-D shape, ask the student which 3-D
shapes it is.
Assessment/Evaluation 1. Students are evaluate if they can recognize the 3-D shapes shown by teacher and identify the properties. 2. Students also will be evaluating if they can recognize which of the 3-D shapes that match with the given properties. Set B - Handouts 3D Shape Properties
Name _____________
This 3D shape is a ________. It has
This 3D shape is a ________. It has MTE 3105 Resource in Mathematics
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This 3D shape is a ________. It has
This 3D shape is a ________. It has
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3D Shape Properties Match the shapes to the correct descriptions.
This 3D shape has no flat faces and no straight edges. It has just one curved face. It is a ________________.
This 3D shape has one curved face and one flat face. The flat face is a circle. It is a ________________.
This 3D shape has 6 flat square faces, 12 straight edges and 8 corners. It is a ________________.
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This 3D shape has one curved face and 2 flat circular faces. It is a ________________.
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Learning Resources and Material
a. The Crosswords b. The Word Search c. Nets and Solids d. 3D Properties Development of Lesson
Introduction: 1. Go over again on the 3-D shapes topic
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1. Distribute the handouts one after another after the students finished the one before. 2. Ask the students to complete the handouts within 10 minutes.
Assessment/Evaluation 1. Students will be evaluated with the correct answer answered within 10 minutes.
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RESOURCE IN MATHEMATICS MULTIMEDIA PRESENTATION SOFTWARE
Mathematics Department IPGM, Kampus Tuanku Bainun Geometry Sketchpad Learning Resources and Materials: •
Computer
•
Geometer’s Sketchpad (software)
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•
Geometric shapes handout
•
Pencils
Development of Lesson: •
Introduction: ○ Before getting the students linked to Geometer’s Sketchpad, explain and go over what the different geometric shapes are and what defines them. ○ Explain that there are several ways to go about constructing shapes. ○ Explain that they will use Geometer’s Sketchpad software to construct the shapes.
•
Methods/Procedures:
1.
The students will log onto Geometer’s Sketchpad.
2.
The students will be given a worksheet with the different geometric shapes that they are to construct. They will have different dimensions that they are to incorporate into their shapes. Each student will have different shapes to construct.
3.
The students will be given the freedom to make the shapes their own (adding colors, etc.).
Accommodations/Adaptations: ○ The students will be given geometric shapes that vary in difficulty depending on their skill level.
Assessment/Evaluation: ○ The students will be evaluated based on their handout. The students will be graded based on if they constructed the correct shapes in the correct way. MTE 3105 Resource in Mathematics
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○ A test will be given at the end of the unit to assess the students' knowledge on geometric shapes.
Closure: The students and the teacher will have a discussion about geometric shapes. Where are the different shapes found in the environment? They will discuss what their thoughts were about Geometer’s Sketchpad. What could be done differently? What could be done to make this more fun? Did the students enjoy this activity?
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RESOURCE IN MATHEMATICS WHAT ARE RESOURCES?
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Mathematics Department IPGM, Kampus Tuanku Bainun According to Oxford dictionary, resource can be defined as a supply of raw materials, etc which bring a country, person, wealth and etc. It is also known as things that can be helpful, support and consolidation when needed. In Mathematics term, resource can be defined as materials that can be used as teaching aids. Examples like a resource file, room, e.g. containing materials can be used by teacher in teaching and learning process.
In Mathematics, resource can be divided into three different kinds, which is printed material, physical manipulative, and audio and visual. Printed materials include books, magazine, encyclopedia, journals, documents, graphs, charts, posters, diagrams, pictures, comic books and many more. Printed materials always refer as paper base materials. In other word, paper base materials are printed materials. Physical manipulative examples are like puppets, globes, specimens and many more. Things that can be hold are called physical manipulative. Examples for audio and visual are TV programs, radio programs, film, movie, music, tapes, and many more. These resources are very helpful in helping students to understand about the topic or the learning area that they are learning.
Our group had done several teaching aids based on variability of different resource. In printed materials, several worksheets were listed out by our group. The worksheets are called “The Crosswords”, “The Word Search”, “Nets and Solids”, and “3D Properties”. These worksheets also teach the visual spatial intelligence. In order to the “The Crosswords”, “The Word Search”, and “Nets and Solids”, students are required to visualize and use their imaginary to picture in their minds what will the object be. In “3D Properties”, students have to recall back their learning in 3D properties topic. MTE 3105 Resource in Mathematics
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Printed material are said to enhance students understanding, vocabulary, and their visual spatial intelligence.
A set of teaching and learning kits based on audio and visual resources also made by us. A set of detective presentation and 3D properties from Microsoft Power Point 2007 were made and we also made a lesson plan using the Geometry Sketchpad (GSP). In the presentation, students will be ask on several properties like edges, vertices, lines, and many more. Thus, it can deepen the understanding of the concept of shapes. This eventually will enhance and generate their thinking method on finding the answer. In GSP, students will ask to make a 3D shapes based on the given worksheets and try to generate a solids by themselves. Thus, this will stimulate their creative thinking. A set of multimedia presentation also had been made using the Microsoft Power Point 2007. “Properties of 3D Shapes” are made in order to enhance students understanding in the properties of the 3D shapes. “Shapes Detective” is a specialized activity for students to force their memory to answer what is the shape based on the properties shown.
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RESOURCE IN MATHEMATICS HOW TO USE RESOURCES?
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Mathematics Department IPGM, Kampus Tuanku Bainun As we can see now, teachers often refer to resources in teaching and learning process in any subjects. Teachers nowadays know that if they only rely on the text book, students will get bored easily and discourage to learn through the day. That is why teachers now rely on different resources in order to make their teaching and learning process more interactive. Although relying on resources is a good way to more interactive learning, but teacher must realize that students cannot understand about the concept. So, both teaching from the teacher and the usage of different resources are crucial.
Many types of resources are made and being used in the teaching and learning process. But a teacher always lacks on giving proper instructions and never do an instructions paper for students to try the resources by themselves. In this task, many kinds of resources are made by us and we listed down the methods and ways to use it. We are using the printed materials, computer soft wares, Geometry Sketchpad and many more.
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Firstly, let us see the teaching and learning kits that we had prepared. In this teaching and learning kits, we had prepared 2 types of teaching kits, they are the Wheel of Fortune and handouts. How to use the Wheel of Fortune? This Wheel of Fortune only works after the students had learned about the properties of the 3D shapes. This lesson focuses about the basic 3D shapes and the properties of the shapes. The objective is to evaluate if students remember the properties of the basic 3D shapes. The teacher will hang up the Wheel of Fortune at the blackboard. Then, pick a student to come in front and pick any number that he/she wants. Then ask him/her to spin the wheel. To make the spinning more interactive, tell the student to yell out the number that he/she picked before. When the spin stops, take a look at the number which the indicator shows. Then, take the flash card which has the same number as the indicator shows. If the flash card is a 3D shape, ask the student on the 3D shape’s properties. If the flash card shows the properties of a 3D shape, ask the student to answer what is the 3D shape is. Handouts that we made have 4 different topics. Distribute the handouts one after another after finished the one before. Students are ask to finish a handout within 10 minutes each. This activity will control the class and force their memory to recall what they had learned before.
Secondly, we had made a set of the multimedia presentation. We had made it using the Microsoft Power Point 2007 and Geometry Sketchpad. Two of the Power Point’s presentation is about the properties of the 3D shapes. It explains about the faces, edges, vertices, and many more. This way, students will recognize and understand the concept of the properties in 3D shapes. In “Shapes Detective”, students will play the role as detective where they have to guess what the shape is based on the properties given. It also got an example on things that can be found in our daily life. In Geometry Sketchpad, The students will log onto Geometer’s Sketchpad. The students will be given a worksheet with the different geometric shapes that they are to construct. They will have different dimensions that they are to incorporate into their shapes. Each student will have different shapes to construct. The students will be given the freedom to make the shapes their own (adding colors, etc.).
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RESOURCE IN MATHEMATICS HOW RESOURCES GIVE BENEFITS TO YOU? MTE 3105 Resource in Mathematics
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Mathematics Department IPGM, Kampus Tuanku Bainun Learning in the 21st century requires new skills, new tools, and new knowledge. One of the challenges that our institutions face is ensuring that each of the students is equipped to flourish within the wide array of learning and work communities. They must develop skills and habits of learning that will serve them for a lifetime. Therefore, teaching and learning process must be interactive, entertaining, interesting, attractive, and useful assisted by the resource stated above to enhance the students’ interest. Students must be perfect in many aspects in order for them to adapt and mingle themselves with a world full of challenges.
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Resource are said to be an assistant in the enhancing the students ability in daily teaching and learning process. However, how true is this statement? We will discuss here after some experience and investigations.
Firstly, if we use different resources in our daily teaching and learning process, student will not bored easily. Researches were said that student can only stand for 30 minutes for a teaching and learning process for a subject. That is why different resources are used in order to get the students’ optimum attention in the teaching and learning process. Colourful teaching kits and different types of them can attract students more effectively compared the one-and-only text books. This is the power of the resource material.
Secondly, there are positive impacts on students’ achievement using different resources. Steven W. Lett (2007) once said that once a person sees something, it is more likely they will remember or at least retain it for a longer period than if it was just told to them. Students will see more concepts of the topic that they are learning through variation of teaching and learning kits that consist of different types of resources. Example, if teacher only say, “A cube has 6 faces of square”, students will have the complication to imagine how the cube has 6 squares. Compare to a teacher say, “This is a cube with 6 faces of squares” while showing and giving the students the chance to feel, to touch the cube itself, it will enhance the students understanding.
Thirdly, children will learn more effectively through concrete object or things especially for primary school. According to the principle of Child Development, one of the principle is children are at the best when learning using concrete objects. So, using physical manipulative with different resources give more understanding to students. Cognitive scholar like Jean Piaget and Lev Vygotsky theorizes that the growth of a children’s’ mental or cognitive develop through an interaction with the environment. Students learn the best when they interact with nature, because they experience it through their senses, it is also called “a firsthand knowledge”. MTE 3105 Resource in Mathematics
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The students’ present mental structures are inadequate to explain the knowledge and they must be altered. It means that by interactions with the environment, students can stimulate new structures and enhance cognitive skills. According to scholars, there are several factors that can develop children’s mental structure, which is interaction with the environment, maturations and learning, from a simple to more complexes, and social interaction and environment.
Firstly, we look at the printed materials that we had prepared. In this printed materials, it is a good way to control the class and prevent from students running in class, noise, and many more. This printed materials benefits to students because it can show whether the students remember or not about the 3D properties.
Secondly, we take a look at the teaching and learning kits that we prepared. The Wheel of Fortune is an interactive game that can attract the students to play it. We can control the class by saying, “If you want to play this game, keep quiet and stay at your own place.” Give some motivational to the students when they answer the question correctly. This game will enhance their understanding on which 3D shapes have these properties.
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RESOURCE IN MATHEMATICS CONCLUSION
Mathematics Department IPGM, Kampus Tuanku Bainun As a conclusion, resources must be used up to the maximum level so that the students can get the advantages and benefits on it. Instead of using the traditional way MTE 3105 Resource in Mathematics
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in our teaching and learning process, why don’t we try something new in the process. New resources will attract students to pay attention and give more understanding on the topic. Research had said that a normal human brain can only stand only about 25 to 30 minutes max and get bored. If we use different resources in one or more period of time, students will be more energetic to learn because using different resources like wearing a pair of torn shoe every 25 minutes. Students will use their brain exceed the human limit if the resource that we use is very interactive and attractive. Experience with the environment is essential since the interaction with it is how new structures are made. Piaget distinguishes between two types of experience, namely concrete and abstract. It is important to remind ourselves that knowledge is constructed through experience.
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RESOURCE IN MATHEMATICS REFLECTION
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Mathematics Department IPGM, Kampus Tuanku Bainun Mohd Ihsan bin Faharol Razi
This semester, third semester Mathematics group had undergo MTE 3106 which is the Resource in Mathematics. The assignment of this course is to find articles and write a summary on each article, make a teaching kit, a multimedia presentation and a report on resources. This assignment is a pair work. I was assign to pair with Afizal in order to do this assignment. So, the journey to finish this assignment starts.
At first, we don’t know how to start with. Then, our lecturer, Mr. Chuah guided us on how to do the assignment. He also showed a sample of the senior’s assignment. Both of us astonished by the sample assignment because it stated very clear on every detail. Even the report of this assignment is excellent. So, both of us determined to do well in t his assignment to. We start of from doing the teaching kit because when we calculate the probability, this assignment is based on the teaching kits that we made. So, we decided to finish our teaching kits first. Both of us tried to think hard to make simple but meaningful teaching kits. Then, the idea of Wheel of Fortune came. At first, we had a little bit trouble on doing the Wheel of Fortune. We could not find the method to make the wheel spin. At the very last moment, we just do simple trick to make the wheel spins.
The report is easy when our teaching and learning kits finished. The current of the flow are very fluent. We were very happy with our assignment.
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There are many things that I can learn from this assignment. Firstly, resources are not limited to things that we made, but everything around us is the resources itself. A simple rock can be used as manipulative kits in counting, addition, and subtraction. Pens also can be used as our resources too. I learned that in order to be a good teacher, there’s no need impressive teaching and learning kits, it is how well I used the resource around me. Secondly, I now know the important of resource in teaching and learning process.
Afizal bin Abdul Ghani
I received an assignment from my Mathematics lecturer, Mr. Chuah. This assignment is pair work. My friend and I was got the topic about shape and space from that topic, we should provide the material kids to use when are teaching and also discover about resources of material, article about this topic and so on. From that I have done some research in internet and other sources like a book in library to find the other resources and information about shape and space. A task like this requires thinking process that helps us to remember and know properly the way to solve it. We also can learn how to provide the best material to teach pupils in future. We also know how to attract pupils in classroom to learn our lesson. Strategy and the way to find the solution was helped me and my friends to discover many ways and interrupt each others. I was apply maximum affords to do this assignment very well. It is tough for me to discover the task. I had asked my friends about these tasks to find get some idea and to share our information and knowledge. The way I take to finished up this assignment was increased my confident level because I need to communicate and make collaborations with other peoples. From this assignment, I gained many benefit. Such as, it’s developing my current knowledge about the strategy in teaching and learning. I hope, finished this assignment will help me in practicum and school soon. The way to complete this assignment was enable me to apply my knowledge in ICT by using Power Point. Completed this assignment, was encourage my own teaching skills to apply it in future. It also builds my MTE 3105 Resource in Mathematics
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confidence level to be a Math teacher. It is also an interesting and enjoyable way to know the subject properly. It also encourages my co-operative skills among my classmate and lecturer. This assignment required us and teaches me to think, be flexible and creative. Hopefully, completely this assignment will developed more positive attitude towards about this subject. That’s all, thank you.
RESOURCE IN MATHEMATICS COLLABORATION FORM
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Mathematics Department IPGM, Kampus Tuanku Bainun Collaboration Form
Name
: Mohd Ihsan bin Faharol Razi : Afizal bin Abdul Ghani
Group
: Program Ijazah Sarjana Muda Perguruan: Matematik
Semester
:3
Year
: 2009
Course
: MTE 3106 – Resources in Mathematics
Lecturer
: Mr. Chuah Boon Keat
Date
MTE 3105 Resource in Mathematics
Agenda
Comment
Signature
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RESOURCE IN MATHEMATICS BIBLIOGRAPHY/REFERRENCE
Mathematics Department IPGM, Kampus Tuanku Bainun Hatfield, M., Edwards, N., Bitter, G., & Morrow, J,. (2005) Mathematics methods for elementary and middle school teachers (5th Edition). Hoboken, NJ: John Wiley & Sons, Inc.
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Mark Spikell, Behrouz Aghevli (October, 1999) The Workshop Method of Teaching: An Example from the Discipline of Mathematics Education.
Vygotsky, L. (1962). Thought and Language. Trans. E. Haufmann nad G. Vakar. Campbridge, MA: MIT Press.
Geometry Skecthpad Lesson Plan. Retrieved on 23rd March 2009. http://www.lessonplanspage.com/MathCIGeometricShapesWithGeometersSketc hpad7.htm
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RESOURCE IN MATHEMATICS APPENDIX
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Mathematics Department IPGM, Kampus Tuanku Bainun
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Mathematics Department IPGM, Kampus Tuanku Bainun According to Oxford dictionary, resource can be defined as a supply of raw materials, etc which bring a country, person, etc wealth. It is also known as things that can be helpful, support and consolidation when needed. In Mathematics term, resource can be defined as materials that can be used as teaching aids. Examples like a resource file, room, e.g. containing materials can be used by teacher in teaching and learning process.
In Mathematics, resource can be divided into three different kinds, which is printed material, physical manipulative, and audio and visual. Printed materials include books, magazine, encyclopedia, journals, documents, graphs, charts, posters, diagrams, pictures, comic books and many more. Printed materials always refer as paper base materials. In other word, paper base materials are printed materials. Physical manipulative examples are like puppets, globes, specimens and many more. Things that can be hold are called physical manipulative. Examples for audio and visual are TV programs, radio programs, film, movie, music, tapes, and many more. These resources are very helpful in helping students to understand about the topic or the learning area that they are learning.
Teachers always use teaching aids in class. Teaching aids included these three different kinds of resources. Teachers can vary teaching aids by applying these resources in their daily planning in teaching and learning process. Students will not be bored if teachers wisely used these resources in their teaching and learning process. The advantages of using different kinds of resources during teaching and learning process are to enhance students’ ability of understand the learning area and to stimulates their creative thinking. By using resources, students can explore and
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discover an answer by themselves. The most important in teaching aids is to develop students’ style of thinking and stimulate the desire for knowledge.
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RESOURCE IN MATHEMATICS ARTICLE AND SUMMARY/ABSTRACT
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Mathematics Department IPGM, Kampus Tuanku Bainun
ARTICLE AND SUMMARY/ABSTRACT ARTICLE 1
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Mathematics Department IPGM, Kampus Tuanku Bainun Geometry
Geometry is a strand of the K-6 mathematics curriculum that involves the investigation and exploration of shapes, structures and spatial relationships. From a teaching perspective, geometry can be seen as a way for students to relate their notions of shape to the environment in which we live.
There are shapes everywhere and
everything has a shape. Students can use the information learned in their geometry classes to turn tangible ideas into abstract thought.
Geometry in Kindergarten to Grade 8 is finally being taken seriously within the elementary school classroom.
Many teachers were not comfortable with geometry
having associated it with high school and the laborious proofs that were required (Van de Walle,2006). Van de Walle (2006) argues that geometry objectives can be thought of in two different yet related frameworks; spatial reasoning and specific content. Spatial reasoning has to do with the way in which students think and reason about shapes and the space they occupy. Individuals with spatial reasoning have the ability to visualize objects and spatial relationships and without geometric experiences, most people do not grow in their spatial sense or spatial reasoning (Van de Walle, 2006). In classrooms, too much emphasis has been placed on learning geometric terminology rather than
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developing spatial reasoning, causing students to miss a crucial portion of the geometry curriculum (Van de Walle, 2006).
The Van Heile’s explain that that those students who have difficulty understanding spatial ideas and geometric thinking most likely do not have the correct experience to allow growth and development in spatial reasoning
(Van de Walle,
2006)(Tuck, 2005). Each level describes the ways in which student’s process geometric content, as well as the types of geometric ideas students consider while travelling through each level, rather than how much knowledge about the subject they have. The significant differences that are noted from one level to the next are the objects of thought, or more generally, what students are able to understand and consider geometrically (Van de Walle, 2006). At Level 0, the Visualization level, the objects of thought are shapes and what they look like. It is the appearance of the shape that defines it for the student. At this level, a square is a square because, to the student, it looks like a square (Van de Walle, 2006). At Level 1, Analysis, the objects of thought are classes of shapes rather than individual shapes. At this level, students are able to process what makes a square a square by identifying its relevant properties.
The
student is able to identify that a group of shapes go together because of their common properties (Van de Walle, 2006).
At Level 2, Informal Deduction, the Van Heile’s
determined that the objects of thought are the properties of shapes. At this level, the student’s observations go beyond the properties of the shape and begin to focus on logical arguments about the shape based upon these properties (Van de Walle, 2006). Level 3, Deduction, and Level 4, Rigor, are typically not reached until the students enter into high school or University mathematics. Every teacher should provide the tools necessary for each child to experience geometry in a way that they can understand. Geometric thinking should be introduced early on and referred back to throughout the exploration of different mathematics strands with the intention that students develop strong spatial reasoning.
The development of software used in conjunction with the geometry unit is important when teaching geometry. In the article, Developing the 3DMath Dynamic MTE 3105 7 Resource in Mathematics
Geometry Software: Theoretical Perspectives on Design Importance of using 3D Geometric software in the classroom, Jones (2002) states that it is very important and vital to student’s understanding and success in geometry to implement software into the teaching of this subject. Using computer software in the classroom can "enhance both curricula and student learning in geometry" (Jones, 2000). Geometry software can be used successfully in the teaching and learning of geometry because of its interactive style of direct manipulation of geometrical objects (Jones, 2000). For that reason, there is an increased need for more 3D software programs that allow students to manipulate and work with shapes that are 3D in nature. Geometry units in schools are strongly associated with spatial and visual ability. While working with geometric concepts, students are working on and improving cognitive factors such as spatial visualization, reasoning and manipulation. Students who are going to be successful in geometry need to continually improve these skills and find opportunities that allow them to improve.
This improvement may depend on how
geometry is taught in the classroom, what manipulativesare being used, and the time spent teaching it.
Additionally, Jones (2002) explains the danger of placing too much emphasis on 2D shapes in the teaching of geometry. The consecutive approach of teaching 2D geometry and then 3D shapes is not necessarily the best approach for teaching students. If geometry is taught first using 2D shapes and then 3D shapes, the teacher is not fostering proper visual and spatial thinking abilities.
Developing 3D shape
awareness after learning 2D shapes is not easy for students to accomplish and can actually be more confusing, thus you could be setting your students up for difficulty or failure.
It is important for students to have access to and regularly use manipulatives in geometry. Teachers need to use more manipulatives or software programs that focus on both 2D and 3D geometry activities. Jones (2002) stresses the importance of giving students manipulatives to teach geometry instead of using the classic method of showing static pictures of shapes that are intended to represent 3D shapes. MTE 3105 Resource in Mathematics
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In 2002, a research study was conducted examining the effects of computer technology on success in the area geometry for students. The findings of that research study state that "the experiences of a group of learners using computer based representations compared with another group using concrete manipulatives found that while both computer and concrete groups improved significantly, the computer group improved slightly more, with older pupils (fifth grade) benefiting more from the computer-based manipulatives" (Jones 2002).
This research illustrates that both
computer software dealing with geometric principles, and hands on manipulatives given to children during math lessons improve geometric understanding.
The findings
similarly suggest that geometric computer software is slightly more beneficial and significant to students in their comprehension of mathematical principles.
Teachers must ensure that during their lessons they are remembering to challenge their students, by discussing shapes that both reflect a student’s visual perception of a particular shape, and also the irregular version of the shape. Shape’s such as A1 and A2 in Figure 1 are regular versions of shapes but shapes such as B1 and B2 challenge the student’s visual ideas and apply higher order thinking (Mack, 2007). Subsequently, when discussing geometric shapes, especially polygons, teacher’s need to demonstrate non-polygons that resemble a particular shape as well. The lack of this is a concern that was realized by Nancy Mack when teaching a geometry lesson to young students. The students had heard of a right angle and could point one out, but many students thought that there was also something called a left angle. When students first begin to learn about polygons they focus on the visual appearance. If students are only shown polygons with a particular visual appearance, they may not actually understand the mathematical properties related to that polygon. One way to introduce students to the multiplicity of examples is through dynamic geometry computer software, such as Geometer’s Sketchpad. This program allows students to visualize and create shapes they are reading about or discussing in their math classes. Students then understand the ‘big picture’ when it comes to shapes. It is MTE 3105 9 Resource in Mathematics
a program that allows children to explore different geometric shapes, their properties, and examine the multiplicity of shapes that exist.
Geometry is a progressive concept, as seen by the Van Hiele levels of Geometric Thought. Through these levels it is understood that students go through a number of stages; visualization, analysis, informal deduction, deduction, rigour, with each new stage building on the previous (Van de Walle & Folk, 2008). Therefore in order for students to truly understand geometry they must proceed through these levels in a sequential order, moving from concrete to more abstract thought (Carson & Rowlands, 2007). This causes concern with a student’s learning of geometry, as the student may not learn the base they need in one grade to understand the curriculum in the next. It is through geometry that teachers provide their students with this knowledge. In order to provide students with the best education possible, these concerns in geometry must be overcome. Our group definitely agrees with the statements that the research has suggested about using manipulatives within geometry. Our group found it very interesting that much of the research suggests that it is neither helpful, nor beneficial to students to teach 2D shapes before 3D shapes. The research instead suggests that by teaching these two concepts consecutively it actually confuses students more. While out on placement, our group witnessed several geometry lessons. 2D geometry is still being focused on before 3D geometry.
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ARTICLE AND SUMMARY/ABSTRACT ARTICLE 2
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Mathematics Department IPGM, Kampus Tuanku Bainun PRIMARY STUDENTS’ UNDERSTANDING OF TESSELLATION:
Tessellation is included in many mathematics curricula as one way of developing spatial ideas. If students do not understand tessellation in the intended ways, however, the development of other spatial ideas, such as properties of shapes and symmetry, may be compromised. Van Hiele levels were used as a basis for analysing the descriptions of eight different tessellation patterns by 26 Year 5 and 6 students. Responses from some students indicated that they understood the tessellations only as movements of shapes or saw many of the patterns in 3D. Vincent (2003) suggested that exploring tessellations was one approach to investigating the properties of 2D shapes. Serra (1993) included tessellation explorations as one way of developing ideas about symmetry. The notion of MTE 3105 Resource in Mathematics
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using tessellation activities as a means of developing understanding of other aspects of geometry may be compromised if students do not understand the nature of tessellation, or have different perceptions from those assumed by teachers. Level 0 (Visualisation): Students take account only of the appearance of the shape, and describe properties only in terms of its appearance.
Level 1 (Analysis): Students describe properties informally, and can establish the essential conditions through a consideration of component parts.
Level 2 (Abstraction): Students can draw on logic to establish necessary and sufficient conditions when describing the properties of shapes.
Where tessellations were concerned, the understanding demonstrated needed to take account not only of the shapes involved in the tessellation, but also of the transformations applied in order to create the tessellations. At Level 0, students could be expected to identify the shapes involved in the tessellation or the combination of shapes that made up the basic unit that was transformed to create the tiling pattern. Students responding at Level 1 would be expected to describe both the shapes involved and the movements used to transform the shapes but in a disconnected fashion.
How do primary school students describe tessellation patterns?
Are the van Hiele levels useful in describing students’ understanding of tessellation?
Eight different tessellations were presented in pictorial form, and students were asked to identify the shapes used and then to describe in as much detail as possible how the shapes were transformed to create the tessellation. The tessellations included regular and semi- regular patterns, one non-periodic tessellation, and patterns that included MTE 3105 Resource in Mathematics
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pentagons. Van Hiele levels applied to tessellations.
Responses were obtained from 26 Year 5 and 6 students at two Catholic primary schools in Melbourne, Australia. Students coloured in the composite shapes used in each tessellation, and then wrote their descriptions of how the tessellations were made in spaces provided below each design.
The majority of students could describe the tessellations only in a visual manner. The levels of response shown in Table 2 suggest that as the nature of the shapes of which the tessellation was composed became less familiar the level of response was reduced. Tessellation 1, composed entirely of squares, attracted the highest overall levels of response with nearly half of the students responding beyond the visualisation level. In contrast, no students were able to describe Tessellations 6 and 8 at the Abstraction level. Responses of students to each question on the tessellation task.
The highest levels of response overall were elicited by Tessellation 1, with over onequarter of the students reaching Abstraction level. An example of the Abstraction level response is:
Tessellation 3, an irregular tiling pattern produced some somewhat surprising results. The complexity of the pattern seemed to encourage students to apply some level of analysis, although this was not developed further into Abstraction level. A typical response coded at the Analysis level was:
Tessellation 7 was seen only as a set of cubes by 13 (50%) of the students. Only one student explicitly connected the two- and three-dimensional aspects of this tessellation.
This response was coded at the visualisation level. Some students, however, appeared MTE 3105 Resource in Mathematics
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to see three-dimensional shapes in many of the tessellations. One student saw Tessellation 1 as a cube.
The response, however, was coded as irrelevant since the student had not identified the shapes involved correctly.
For some students, the movements used to create the tessellation, rather than the shapes involved, were dominant. This response to Tessellation 4 describes only the movement rather than the shapes involved, and this student described many of the tessellations in a similar fashion:
Few students recognised Tessellations 5 and 6 as being composed of pentagons. Some students saw the composite hexagonal arrangement in Tessellation 5, but several students referred to the shape in Tessellation 6 as “fly wings”. A majority of students in this study described tessellations in terms of the shapes of which they were composed: Visualisation level. Familiar shapes, such as squares and triangles, were more likely to be named whereas only 50 percent of the students could describe Tessellation 8 coherently in terms of the shapes that comprised the design. Familiar shapes also appeared to support higher level descriptions. The complex design of Tessellation 3 appeared to support students to reach Analysis level. Similar comments could be made about Tessellation 2 and Tessellation 6. In order to encourage understanding of tessellation, it would appear that students should experience a wide range of designs, made up of familiar and less familiar shapes and transformations.
The misconceptions shown by some students could compromise their understanding of the properties of 2D shapes, and subsequent development of geometrical ideas.
Using the van Hiele levels as a basis appeared to provide a useful means of identifying primary students’ understanding of tessellation, that included both recognition of the shapes involved and the transformations used to make the design. MTE 3105 15 Resource in Mathematics
Teachers should not assume that all students visualise tiling patterns in the same way.
If tessellation is used as a means of developing students’ geometrical knowledge of the properties of shapes, and of symmetry and transformation, then opportunities are needed for all students to learn about both aspects of tessellation: the nature of the shapes involved and also the kind of transformation applied.
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RESOURCE IN MATHEMATICS TEACHING AND LEARNING KITS
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Mathematics Department IPGM, Kampus Tuanku Bainun Set A – Wheel of Fortune
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Learning Resources and Material
a. Wheel of Fortune b. Flash card (with number on card, 1 - 8)
Development of Lesson
Introduction: 1. Before getting the students about the teaching kit, explain about the Wheel of
Fortune and go over again on 3-Dimensional Shapes again. 2. Explain how to use the Wheel of Fortune.
Methods/Procedures: 1. Ask a student to come in front. MTE 3105 Resource in Mathematics
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2. Ask the student which numbers they want to pick. 3. Tell the student to spin the Wheel of Fortune and yell out which number he/she
pick. 4. When the wheel stops spinning, see the number that the indicator shows. 5. Take the flash cards and pick the same number with the number that the indicator shows. 6. If the flash card shows a3-D shape, ask the student about the properties of the
object. 7. If the flash card shows the properties of a 3-D shape, ask the student which 3-D
shapes it is.
Assessment/Evaluation 1. Students are evaluate if they can recognize the 3-D shapes shown by teacher and identify the properties. 2. Students also will be evaluating if they can recognize which of the 3-D shapes that match with the given properties. Set B - Handouts 3D Shape Properties
Name _____________
This 3D shape is a ________. It has
This 3D shape is a ________. It has MTE 3105 Resource in Mathematics
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This 3D shape is a ________. It has
This 3D shape is a ________. It has
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3D Shape Properties Match the shapes to the correct descriptions.
This 3D shape has no flat faces and no straight edges. It has just one curved face. It is a ________________.
This 3D shape has one curved face and one flat face. The flat face is a circle. It is a ________________.
This 3D shape has 6 flat square faces, 12 straight edges and 8 corners. It is a ________________.
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This 3D shape has one curved face and 2 flat circular faces. It is a ________________.
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Learning Resources and Material
a. The Crosswords b. The Word Search c. Nets and Solids d. 3D Properties Development of Lesson
Introduction: 1. Go over again on the 3-D shapes topic
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1. Distribute the handouts one after another after the students finished the one before. 2. Ask the students to complete the handouts within 10 minutes.
Assessment/Evaluation 1. Students will be evaluated with the correct answer answered within 10 minutes.
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RESOURCE IN MATHEMATICS MULTIMEDIA PRESENTATION SOFTWARE
Mathematics Department IPGM, Kampus Tuanku Bainun Geometry Sketchpad Learning Resources and Materials: •
Computer
•
Geometer’s Sketchpad (software)
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•
Geometric shapes handout
•
Pencils
Development of Lesson: •
Introduction: ○ Before getting the students linked to Geometer’s Sketchpad, explain and go over what the different geometric shapes are and what defines them. ○ Explain that there are several ways to go about constructing shapes. ○ Explain that they will use Geometer’s Sketchpad software to construct the shapes.
•
Methods/Procedures:
1.
The students will log onto Geometer’s Sketchpad.
2.
The students will be given a worksheet with the different geometric shapes that they are to construct. They will have different dimensions that they are to incorporate into their shapes. Each student will have different shapes to construct.
3.
The students will be given the freedom to make the shapes their own (adding colors, etc.).
Accommodations/Adaptations: ○ The students will be given geometric shapes that vary in difficulty depending on their skill level.
Assessment/Evaluation: ○ The students will be evaluated based on their handout. The students will be graded based on if they constructed the correct shapes in the correct way. MTE 3105 Resource in Mathematics
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○ A test will be given at the end of the unit to assess the students' knowledge on geometric shapes.
Closure: The students and the teacher will have a discussion about geometric shapes. Where are the different shapes found in the environment? They will discuss what their thoughts were about Geometer’s Sketchpad. What could be done differently? What could be done to make this more fun? Did the students enjoy this activity?
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RESOURCE IN MATHEMATICS WHAT ARE RESOURCES?
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Mathematics Department IPGM, Kampus Tuanku Bainun According to Oxford dictionary, resource can be defined as a supply of raw materials, etc which bring a country, person, wealth and etc. It is also known as things that can be helpful, support and consolidation when needed. In Mathematics term, resource can be defined as materials that can be used as teaching aids. Examples like a resource file, room, e.g. containing materials can be used by teacher in teaching and learning process.
In Mathematics, resource can be divided into three different kinds, which is printed material, physical manipulative, and audio and visual. Printed materials include books, magazine, encyclopedia, journals, documents, graphs, charts, posters, diagrams, pictures, comic books and many more. Printed materials always refer as paper base materials. In other word, paper base materials are printed materials. Physical manipulative examples are like puppets, globes, specimens and many more. Things that can be hold are called physical manipulative. Examples for audio and visual are TV programs, radio programs, film, movie, music, tapes, and many more. These resources are very helpful in helping students to understand about the topic or the learning area that they are learning.
Our group had done several teaching aids based on variability of different resource. In printed materials, several worksheets were listed out by our group. The worksheets are called “The Crosswords”, “The Word Search”, “Nets and Solids”, and “3D Properties”. These worksheets also teach the visual spatial intelligence. In order to the “The Crosswords”, “The Word Search”, and “Nets and Solids”, students are required to visualize and use their imaginary to picture in their minds what will the object be. In “3D Properties”, students have to recall back their learning in 3D properties topic. MTE 3105 Resource in Mathematics
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Printed material are said to enhance students understanding, vocabulary, and their visual spatial intelligence.
A set of teaching and learning kits based on audio and visual resources also made by us. A set of detective presentation and 3D properties from Microsoft Power Point 2007 were made and we also made a lesson plan using the Geometry Sketchpad (GSP). In the presentation, students will be ask on several properties like edges, vertices, lines, and many more. Thus, it can deepen the understanding of the concept of shapes. This eventually will enhance and generate their thinking method on finding the answer. In GSP, students will ask to make a 3D shapes based on the given worksheets and try to generate a solids by themselves. Thus, this will stimulate their creative thinking. A set of multimedia presentation also had been made using the Microsoft Power Point 2007. “Properties of 3D Shapes” are made in order to enhance students understanding in the properties of the 3D shapes. “Shapes Detective” is a specialized activity for students to force their memory to answer what is the shape based on the properties shown.
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RESOURCE IN MATHEMATICS HOW TO USE RESOURCES?
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Mathematics Department IPGM, Kampus Tuanku Bainun As we can see now, teachers often refer to resources in teaching and learning process in any subjects. Teachers nowadays know that if they only rely on the text book, students will get bored easily and discourage to learn through the day. That is why teachers now rely on different resources in order to make their teaching and learning process more interactive. Although relying on resources is a good way to more interactive learning, but teacher must realize that students cannot understand about the concept. So, both teaching from the teacher and the usage of different resources are crucial.
Many types of resources are made and being used in the teaching and learning process. But a teacher always lacks on giving proper instructions and never do an instructions paper for students to try the resources by themselves. In this task, many kinds of resources are made by us and we listed down the methods and ways to use it. We are using the printed materials, computer soft wares, Geometry Sketchpad and many more.
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Firstly, let us see the teaching and learning kits that we had prepared. In this teaching and learning kits, we had prepared 2 types of teaching kits, they are the Wheel of Fortune and handouts. How to use the Wheel of Fortune? This Wheel of Fortune only works after the students had learned about the properties of the 3D shapes. This lesson focuses about the basic 3D shapes and the properties of the shapes. The objective is to evaluate if students remember the properties of the basic 3D shapes. The teacher will hang up the Wheel of Fortune at the blackboard. Then, pick a student to come in front and pick any number that he/she wants. Then ask him/her to spin the wheel. To make the spinning more interactive, tell the student to yell out the number that he/she picked before. When the spin stops, take a look at the number which the indicator shows. Then, take the flash card which has the same number as the indicator shows. If the flash card is a 3D shape, ask the student on the 3D shape’s properties. If the flash card shows the properties of a 3D shape, ask the student to answer what is the 3D shape is. Handouts that we made have 4 different topics. Distribute the handouts one after another after finished the one before. Students are ask to finish a handout within 10 minutes each. This activity will control the class and force their memory to recall what they had learned before.
Secondly, we had made a set of the multimedia presentation. We had made it using the Microsoft Power Point 2007 and Geometry Sketchpad. Two of the Power Point’s presentation is about the properties of the 3D shapes. It explains about the faces, edges, vertices, and many more. This way, students will recognize and understand the concept of the properties in 3D shapes. In “Shapes Detective”, students will play the role as detective where they have to guess what the shape is based on the properties given. It also got an example on things that can be found in our daily life. In Geometry Sketchpad, The students will log onto Geometer’s Sketchpad. The students will be given a worksheet with the different geometric shapes that they are to construct. They will have different dimensions that they are to incorporate into their shapes. Each student will have different shapes to construct. The students will be given the freedom to make the shapes their own (adding colors, etc.).
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RESOURCE IN MATHEMATICS HOW RESOURCES GIVE BENEFITS TO YOU? MTE 3105 Resource in Mathematics
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Mathematics Department IPGM, Kampus Tuanku Bainun Learning in the 21st century requires new skills, new tools, and new knowledge. One of the challenges that our institutions face is ensuring that each of the students is equipped to flourish within the wide array of learning and work communities. They must develop skills and habits of learning that will serve them for a lifetime. Therefore, teaching and learning process must be interactive, entertaining, interesting, attractive, and useful assisted by the resource stated above to enhance the students’ interest. Students must be perfect in many aspects in order for them to adapt and mingle themselves with a world full of challenges.
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Resource are said to be an assistant in the enhancing the students ability in daily teaching and learning process. However, how true is this statement? We will discuss here after some experience and investigations.
Firstly, if we use different resources in our daily teaching and learning process, student will not bored easily. Researches were said that student can only stand for 30 minutes for a teaching and learning process for a subject. That is why different resources are used in order to get the students’ optimum attention in the teaching and learning process. Colourful teaching kits and different types of them can attract students more effectively compared the one-and-only text books. This is the power of the resource material.
Secondly, there are positive impacts on students’ achievement using different resources. Steven W. Lett (2007) once said that once a person sees something, it is more likely they will remember or at least retain it for a longer period than if it was just told to them. Students will see more concepts of the topic that they are learning through variation of teaching and learning kits that consist of different types of resources. Example, if teacher only say, “A cube has 6 faces of square”, students will have the complication to imagine how the cube has 6 squares. Compare to a teacher say, “This is a cube with 6 faces of squares” while showing and giving the students the chance to feel, to touch the cube itself, it will enhance the students understanding.
Thirdly, children will learn more effectively through concrete object or things especially for primary school. According to the principle of Child Development, one of the principle is children are at the best when learning using concrete objects. So, using physical manipulative with different resources give more understanding to students. Cognitive scholar like Jean Piaget and Lev Vygotsky theorizes that the growth of a children’s’ mental or cognitive develop through an interaction with the environment. Students learn the best when they interact with nature, because they experience it through their senses, it is also called “a firsthand knowledge”. MTE 3105 Resource in Mathematics
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The students’ present mental structures are inadequate to explain the knowledge and they must be altered. It means that by interactions with the environment, students can stimulate new structures and enhance cognitive skills. According to scholars, there are several factors that can develop children’s mental structure, which is interaction with the environment, maturations and learning, from a simple to more complexes, and social interaction and environment.
Firstly, we look at the printed materials that we had prepared. In this printed materials, it is a good way to control the class and prevent from students running in class, noise, and many more. This printed materials benefits to students because it can show whether the students remember or not about the 3D properties.
Secondly, we take a look at the teaching and learning kits that we prepared. The Wheel of Fortune is an interactive game that can attract the students to play it. We can control the class by saying, “If you want to play this game, keep quiet and stay at your own place.” Give some motivational to the students when they answer the question correctly. This game will enhance their understanding on which 3D shapes have these properties.
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RESOURCE IN MATHEMATICS CONCLUSION
Mathematics Department IPGM, Kampus Tuanku Bainun As a conclusion, resources must be used up to the maximum level so that the students can get the advantages and benefits on it. Instead of using the traditional way MTE 3105 Resource in Mathematics
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in our teaching and learning process, why don’t we try something new in the process. New resources will attract students to pay attention and give more understanding on the topic. Research had said that a normal human brain can only stand only about 25 to 30 minutes max and get bored. If we use different resources in one or more period of time, students will be more energetic to learn because using different resources like wearing a pair of torn shoe every 25 minutes. Students will use their brain exceed the human limit if the resource that we use is very interactive and attractive. Experience with the environment is essential since the interaction with it is how new structures are made. Piaget distinguishes between two types of experience, namely concrete and abstract. It is important to remind ourselves that knowledge is constructed through experience.
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RESOURCE IN MATHEMATICS REFLECTION
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Mathematics Department IPGM, Kampus Tuanku Bainun Mohd Ihsan bin Faharol Razi
This semester, third semester Mathematics group had undergo MTE 3106 which is the Resource in Mathematics. The assignment of this course is to find articles and write a summary on each article, make a teaching kit, a multimedia presentation and a report on resources. This assignment is a pair work. I was assign to pair with Afizal in order to do this assignment. So, the journey to finish this assignment starts.
At first, we don’t know how to start with. Then, our lecturer, Mr. Chuah guided us on how to do the assignment. He also showed a sample of the senior’s assignment. Both of us astonished by the sample assignment because it stated very clear on every detail. Even the report of this assignment is excellent. So, both of us determined to do well in t his assignment to. We start of from doing the teaching kit because when we calculate the probability, this assignment is based on the teaching kits that we made. So, we decided to finish our teaching kits first. Both of us tried to think hard to make simple but meaningful teaching kits. Then, the idea of Wheel of Fortune came. At first, we had a little bit trouble on doing the Wheel of Fortune. We could not find the method to make the wheel spin. At the very last moment, we just do simple trick to make the wheel spins.
The report is easy when our teaching and learning kits finished. The current of the flow are very fluent. We were very happy with our assignment.
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There are many things that I can learn from this assignment. Firstly, resources are not limited to things that we made, but everything around us is the resources itself. A simple rock can be used as manipulative kits in counting, addition, and subtraction. Pens also can be used as our resources too. I learned that in order to be a good teacher, there’s no need impressive teaching and learning kits, it is how well I used the resource around me. Secondly, I now know the important of resource in teaching and learning process.
Afizal bin Abdul Ghani
I received an assignment from my Mathematics lecturer, Mr. Chuah. This assignment is pair work. My friend and I was got the topic about shape and space from that topic, we should provide the material kids to use when are teaching and also discover about resources of material, article about this topic and so on. From that I have done some research in internet and other sources like a book in library to find the other resources and information about shape and space. A task like this requires thinking process that helps us to remember and know properly the way to solve it. We also can learn how to provide the best material to teach pupils in future. We also know how to attract pupils in classroom to learn our lesson. Strategy and the way to find the solution was helped me and my friends to discover many ways and interrupt each others. I was apply maximum affords to do this assignment very well. It is tough for me to discover the task. I had asked my friends about these tasks to find get some idea and to share our information and knowledge. The way I take to finished up this assignment was increased my confident level because I need to communicate and make collaborations with other peoples. From this assignment, I gained many benefit. Such as, it’s developing my current knowledge about the strategy in teaching and learning. I hope, finished this assignment will help me in practicum and school soon. The way to complete this assignment was enable me to apply my knowledge in ICT by using Power Point. Completed this assignment, was encourage my own teaching skills to apply it in future. It also builds my MTE 3105 Resource in Mathematics
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confidence level to be a Math teacher. It is also an interesting and enjoyable way to know the subject properly. It also encourages my co-operative skills among my classmate and lecturer. This assignment required us and teaches me to think, be flexible and creative. Hopefully, completely this assignment will developed more positive attitude towards about this subject. That’s all, thank you.
RESOURCE IN MATHEMATICS COLLABORATION FORM
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Mathematics Department IPGM, Kampus Tuanku Bainun Collaboration Form
Name
: Mohd Ihsan bin Faharol Razi : Afizal bin Abdul Ghani
Group
: Program Ijazah Sarjana Muda Perguruan: Matematik
Semester
:3
Year
: 2009
Course
: MTE 3106 – Resources in Mathematics
Lecturer
: Mr. Chuah Boon Keat
Date
MTE 3105 Resource in Mathematics
Agenda
Comment
Signature
62
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RESOURCE IN MATHEMATICS BIBLIOGRAPHY/REFERRENCE
Mathematics Department IPGM, Kampus Tuanku Bainun Hatfield, M., Edwards, N., Bitter, G., & Morrow, J,. (2005) Mathematics methods for elementary and middle school teachers (5th Edition). Hoboken, NJ: John Wiley & Sons, Inc.
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Mark Spikell, Behrouz Aghevli (October, 1999) The Workshop Method of Teaching: An Example from the Discipline of Mathematics Education.
Vygotsky, L. (1962). Thought and Language. Trans. E. Haufmann nad G. Vakar. Campbridge, MA: MIT Press.
Geometry Skecthpad Lesson Plan. Retrieved on 23rd March 2009. http://www.lessonplanspage.com/MathCIGeometricShapesWithGeometersSketc hpad7.htm
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RESOURCE IN MATHEMATICS APPENDIX
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Mathematics Department IPGM, Kampus Tuanku Bainun
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