Wednesday, April 28, 2010

MATHEMATICS HBMT 2203

Teaching Fractions with Tortillas
a) (i) Two strengths

1. As a Physical Materials
Teaching fractions with tortillas is one way of the variety of physical materials that used to show the meaning of a fraction as “part of a whole”. This method will provide a graduated and conceptually supported framework for students to create a meaningful connection among concrete, representational and abstract levels of understanding. Beginning with visual, tactile and kinaesthetic experiences to establish understanding, students expand their understanding through pictorial representations of concrete objects and move to the abstract level of understanding.

2. As a Hands-On And Learning Experience
"Hands-on and learning by experience are powerful ideas, and we know that engaging students actively and thoughtfully in their studies pays off in better learning (Rutherford, 1993, p. 5).” This activity also provides students with a similar set of experiences so everyone can participate in discussions on a level playing field regardless of their socio-economic status. In this way, special benefits are not awarded to those who, by virtue of their wealth or background, have a greater number of experiences under their belts. It is also forces student thinking by requiring interpretation of the observed events, rather than memorization of correct responses.

3. To Build Self Confidence
Let the pupils do as many things by himself or herself. Young children need to be watched closely. However, they learn to be independent and to develop confidence by doing tasks. It's important to let them make choices, rather than deciding everything for her. Encourage them to play with other children and to be with adults who are not family members. The pupils need social opportunities to learn to see the point of view of others.
Young children are more likely to get along with teachers and classmates if they have had experiences with different adults and children.

(ii) Two weaknesses
1. Hard To Make The Tortillas
Teaching fractions with tortillas is so hard for a teacher. It is because the teacher has to make these tortillas about one to two kilograms and then fry it. Soon in the school, these tortillas have to wait for the teaching and learning time. It soon will be melting or damage and cannot be use anymore. When the pupils touch these tortillas, it will dirt their hands and may be also their shirts and uniforms. Pupils also will not focus on teacher’s instructions and they will play with these tortillas.

2. The Size Of The Tortillas Is Not In A Standard Size
The size of the tortillas that with different radius and diameter and the shapes also are the problems for teacher and pupils to recognize one half, one quarter and three quarters. It is because after the pupils fold it into half or quarter, it will have different size or tear off into different sizes. Teacher also faces the difficulties to make tortillas with the same size. The thickness of the tortillas will also interrupt pupils thinking and understanding about fractions. They still cannot understand that fractions divide an object into equal parts.

3. Not Easy To Cut Into Same Size
Pupils will have difficulties to cut into same size especially for kids. They do not have the skills to use and hold the knife to cut the food or tortillas into same size with same radius or diameter into ½, ¼ and ¾.

Fraction Circle Set
(i) Two strengths

1. To Stimulate Students To Participate In The Teaching and Learning Activities
The benefits of hands-on-learning in the school revolves around those children who are either not as academically "talented" or have not shown "interest" in school. This method tends to stimulate these type of students into participating and eventually absorbing information that will believe they would not get from "normal" show-me - tell-me methods. The single most important benefit is that although it requires a great deal of preparation time, once a system is developed, hands-on teaching makes teaching fun. If the kids are learning and having fun doing it, then the teacher having fun at job, and a happier person overall.
2. The Activity Will Be Stored In Their Memory For Useful Retrieval
Students in a hands-on mathematics program will remember the material better, feel a sense of accomplishment when the task is completed, and be able to transfer that experience easier to other learning situations. When more than one method of learning is accessed as in hands-on learning, the information has a better chance of being stored in the memory for useful retrieval. Students who have difficulty in the learning arena for reasons of auditory deficiencies, or behavioural interference can be found to be on task more often because they are part of the learning process and not just spectators. Justifying why we would use hands-on mathematics is based on all the research and methods studies that are current. They support the notion of multi-faceted bombardment of information and experiences so that the retention level is improved.
3. To Develop Pupils Critical Thinking Skills
Students who are involved in labs and activities are empowered in their own learning process.
Developer Thoughts
• I hear and I forget

• I see and I remember

• I do and I understand
- Chinese Proverb
Although these words may not be the exact translation, they underscore the need for a hands-on approach to science teaching. Without this approach students must rely on memory and abstract thought, two methods which restrict learning in most students. By actually doing and experiencing mathematics, students develop their critical thinking skills as well as discover mathematics concepts. This self discovery stays with students throughout their lifetimes while memory fades.
4. Pupils Become Independent Learners
If they conduct the experiments, it encourages questioning of the observed events and the resulting data. When students carry out their own experiments, they become very familiar with the events and the variables involved. It also promotes cause and effect thinking. It will reduce dependence upon authority. Practical experiences in generating hypotheses and planning experiments will make the students more independent later when they no longer have authorities standing by at every turn of their lives. The importance of providing children with direct experiences with materials, objects, and phenomena is supported by experience and understanding of how learning takes place. While information can be remembered if taught through books and lectures, true understanding and the ability to use knowledge in new situations requires learning in which children study concepts in-depth, and over time and learning that is founded in direct experience. Therefore, the justification for hands-on learning is that it allows students to build understanding that is functional and to develop the ability to inquire themselves, in other words, to become independent learners.

(ii) Two weaknesses

1. Hard to Understand The Language Or Terms In English
Experience has shown that the concept “Fraction” is abstract and difficult to conceive, especially among pupils or students who speak English as a second language. Fractions and any part of a whole are perceived as equal. They are more got the picture if the teacher use bilingual to make them understand the activity. If not they will not get what are the teacher trying to tell them. They also cannot follow the instruction if they cannot understand the language and the teacher will not achieve the objectives of the lesson. They also cannot understand the terms of mathematics that teacher use during teaching and learning session.
2. Pupils Face Problems In Visualisation During Teaching Session
Some of the pupils still cannot understand the visualisation that the teacher uses during teaching and learning session. Especially when the teacher draws and asks pupils to shade the part of the fractions, example ½, ¼ and ¾. They also cannot apply what they have see on the blackboard into their books. Some of them will write like a reflection from a mirror on their book. This will make teacher cannot understand what they have learnt and see on the blackboard. Every time teacher gives any exercise on what they have learnt, they will write like a reflection from a mirror on their books. Some of them also can understand what to write in numerator place and also denominator.

b) The approaches that I would choose to teach fractions in the classroom is the fractions circle set. It is because the teacher is using concrete resources in her teaching and learning activities. In these middle years of primary schooling, the teaching of common fractions frequently involves written activities which use abstract representations of numbers, symbols and images. Many students, however, still need the benefit of concrete materials and sensory motor experiences to enhance their understanding of the concepts associated with common fractions. Sowell (1989) and von Glasersfeld (2002) have argued for the continuing engagement of students with concrete materials. They claim this builds deeper understanding of mathematical concepts. Bastick (1993) has also argued strongly for the need to develop deeper understandings in this transition phase of learning.
The fractions circle set is the applets used most often by teachers. The ways teachers used the virtual manipulatives most frequently focused on investigation and skill solidification. It was common for teachers to use the virtual manipulatives alone or to use physical manipulatives first, followed by virtual manipulatives.
Virtual manipulatives provide that additional tool for helping students at all levels of ability "to develop their relational thinking and to generalize mathematical ideas" (Moyer-Packenham, Salkind, & Bolyard, 2008, p. 204). All students learn in different ways. For some, mathematics is just too abstract. Most learn best when teachers use multiple instructional strategies that combine "see-hear-do" activities. Most benefit from a combination of visual (i.e., pictures and 2D/3D moveable objects) and verbal representations (i.e., numbers, letters, words) of concepts, which is possible with virtual manipulatives. The ability to combine multiple representations in a virtual environment allows students to manipulate and change the representations, thus increasing exploration possibilities to develop concepts and test hypotheses.
This study focused on using manipulatives while teaching fraction concepts including addition and subtraction, simplifying and equivalent fractions. The students experienced the use of manipulatives while being introduced to fraction concepts and were able to use them while working on problems. Along with the use of manipulatives, students were taught math vocabulary that helped them understand fraction concepts, thereby, helping them work with fractions.
Teaching mathematics through the use of workbooks, drills, and memorization has proven to be ineffective and outdated. Current research shows that children cannot think, or stay on task, when they sit silently. The worksheet must be replaced with an environment that offers the opportunity for children to think as they manipulate objects.
Second, when we use paper it is also save our budget. The important things is, the teacher knows that the resources that they use is suitable with the teaching and learning activities and also can help the teacher to achieve the objectives and the pupils can use the resources and easily can help them to understand the concept of fractions.
Third are the pupils will get the benefits from this active learning. "Active Learning" is, in short, anything that students do in a classroom other than merely passively listening to an instructor's lecture. This includes everything from listening practices which help the students to absorb what they hear, to short writing exercises in which students react to lecture material, to complex group exercises in which students apply course material to "real life" situations and or to new problems. The term "cooperative learning" covers the subset of active learning activities which students do as groups of three or more, rather than alone or in pairs; generally, cooperative learning techniques employ more formally structured groups of students assigned complex tasks, such as multiple-step exercises, research projects, or presentations. Cooperative learning is to be distinguished from another now well-defined term of art, "collaborative learning", which refers to those classroom strategies which have the instructor and the students placed on an equal footing working together in, for example, designing assignments, choosing texts, and presenting material to the class. Clearly, collaborative learning is a more radical departure from tradition than merely utilizing techniques aimed at enhancing student retention of material presented by the instructor; we will limit our examples to the "less radical" active and cooperative learning techniques. "Techniques of active learning", then, are those activities which an instructor incorporates into the classroom to foster active learning.

QUESTION 2
Teaching and Learning Activity to Divide Units of Time in Hour and Minutes
Learning Outcomes: Pupils will be able to:
iv) Divide units of time in:
a) Hours; and
b) Minutes.
Prior Knowledge Understand the relationship between units of time.
i) Use units of time and know the relationship between
a. Minute and seconds;
b. Week and days; and
c. Year and months.
ii) Convert weeks to days and vice versa.
Teaching Aids: i) Telling Time Song
ii) Power Point slide show
iii) Worksheets (Evaluation)
iv) A4 paper
v) Number Puzzle
Procedure:
PHASE CONTENTS TEACHING AND LEARNING ACTIVITY REMARKS
Introduction
(10 minutes)
Telling Time Song.
Teacher plays the song of “Telling Time Song”

Teacher asks pupils to sing along. Resources:
1) Telling Time Song

PHASE CONTENTS TEACHING AND LEARNING ACTIVITY REMARKS
Step 1
(20 minutes)

Introducing division of times (hours and minutes)

Teacher shows a Microsoft Power Point slide show on introducing how to divide units of time in hours and minutes in long division.

Teacher gives a few questions and asks pupils to do on the paper.
Eg:
46 hours
5 230 hours
-20
30
30
00

Teacher guides pupils to write the question in long division and find the answers of the questions.

Teacher proceeds with other questions. Pupils try to solve the questions in long division on the blackboard.

Teacher checks the answers with Microsoft Power Point slide show.

Resources:
1) Power Point slide show
2) A4 Paper

Moral Value:
1) Be patient
vi) Power Point slide sho

PHASE CONTENTS TEACHING AND LEARNING ACTIVITY REMARKS
Step 2
(15 minutes)
NUMBER PUZZLE
Teacher asks pupils to work in pairs.

Teacher gives a worksheet to each pair of pupils.

Teacher asks pupils to count and fill in the number puzzle within 15 minutes.

Pupils that can give the correct answers will be the winner.

Teacher can shows the answer on the screen.
Resources:
1) Number puzzle
2) A4 paper (to do the culcalation)

Step 3
(15 minutes)
SURF THE INTERNET

Teacher asks pupils to work in pairs. Teacher give the website address that they have to surf.

Pupils have to surf the internet and find the information about times.

Then, they have to print the worksheets and do it. They have to change the “dividend maximum number” to 1000. Resources:
1) http://www.softschools.com/math/worksheets/division_worksheets.jsp
2) http://www.teachingtime.co.uk/draggames/sthec3.html

PHASE CONTENTS TEACHING AND LEARNING ACTIVITY REMARKS
Closure
(10 minutes)
Fast Test
(Worksheets)

Teacher gives each pupils a worksheet.

Pupils have to answer the questions as many as they can within 10 minutes.

After 10 minutes, teacher will collect all the worksheets to evaluate the pupils.
Resources:
1) Worksheets

Reflection: _________________________________________________________

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