after LM

i have went to casino in Singapore, start gambling at 3 am....
went to kuala selangor, sekinchan 
went to bangkok with relatives....

preparing myself for graduation.....
i really cant believe i m graduated!!!
i still looked very childish in the convo photo...

a change occur with a call on the day b4 convo....
tutors was needed...
i tell parents, get their approval, arrange place to stay...(the old place) 
and start a next journey....
actually i cant stay those questions anymore(what are you doing? what do you plan to do.....)

and all my friends pursuit me to try another more challenging job....
with a doubt, i sent in a terrible resume....
and went for interview....and i get the post as an assisstant teacher and mandarin teacher at a very young international school....
i cant really believe it....!!!!
i think it is really my luck that they desperately need teacher....
so i work as a tutor on tuesday, thursday &ｆｒｉｄａｙ．．．．　7-7 and get 250 that week....
attnent cousin convo....
and start another journey....

working as an assistant teacher, is quite fun, challenging and little bit stress...
cos i lack of the experience and confidence....
too worried if the pupils (rich ppl children) dun like me or the parents/teacher dun believe me....
nevertheless....i wnat the experience!!!!

we went to FRIM togehter....though they just 7-10 yrs old, they manage to conquer the climbing....
they are able to carry themselves.....even though they maybe just 4 yrs old, they would vomit or pee in class....
but we cant physicall punish them...
everyday must start fresh, expect it will be a good day....
and though everyday will very tired....
everyday....so tired that want to go to bed on 11....have to wake up at 530....even mum was surprise....but seems it is good for my skin....and seems lost some weight....

one children extract teeth....
3 going to leaves....
they like mental math....
vey talkative....
need to give numbers to calm them down,....
they know my weakness....i m too kind to them....
are they not respecting me????
dun know....

seems like i m going to move to another stage.....
now got the offer to further study master in UM....
just resign.....(a memorable day....beind receptionist, get to know new friends)

attend a grand wedding....thanks to my cousin for helping me to do my hair....
now....got back old habit....spending all time watching drama....

should i help my mum clean the house???
should i study????

why i m so lazy......

cHanGe of rOlE

i m nervous
i must say
i need to transform from a students to a teacher in 1 month time....
i had been a students for 19 years....
i m a good students...
i pay attention in class...
i do score in exam
(though i m not excellent in my social skills)

now i need to become a teacher....
after seeing, observing, listening, interacting with teachers my whole life....
could i play the role of teacher well???
could i make or HELP students to learn?
will they like me?
will they listen to me?
could i achieve the expectation of
the students?
the teachers?
the headmasters/mistress?
the evaluator?
will i succeed?

could i cope with a new life?
in a new place?
new school?
probably new town?
new house?

what kind of schools will i get?
what kind of students will i meet?

would i able to plan interactive activities?
interesting activities?
do i have the time to carry out the activities?

what shall i do after this?
after i finish my practical?
after the graduation?

i m nervous....
i can only wait and react.....
and be calm...
as the Chinese saying: 'the ship will become straight when it reaches the harbour'
i wish the 1st 2 weeks in the school will be exam week,
so that i can be more prepared....

i must admit....
i m not an excellent teacher....
cos i m not yet prepared....

so, i must be optimistic
i must be ready to take challenge...
i must do my best.....

final class notes

each of us get a free MEP magazines, yahoo!!!!!!

why we learn /have our own theories
so that we understand students

it all depends on situation

in a magazines: can for ppl with different intelligence....
some visual, some lingustic

a problem might have more than 1 solution
critical thinking

to prepare a presentation: each have different presentation way...different intelligence....
exam: to test in written form....

constructivism and learning mathematics
ppl vary considerably in the innate levels of math intelligence they are borm with
Nature vs Nurture: helen keller

brain has great plasticity
a lot of brain growth after a person is born
the brain continues to grow new neurons and new connecions among neurins throughout lifes
some drugs can damage brain cells
a certain amount of math knowledge and skill is innate-genetic in origin
the great majority of a person's math knowledge and skills comes form learning, use parts of brain to learn to do math,
math is a cumulative, vertically structured discipline (constructivism)
one learns math by building on the math that one has previously learned

why teach addition 1st: simple, more example

a constructive approach
ppl are born with an innate ability to deal with small integer (1, 2, 3, 4) and to make comparative estimates of larger numbers (the number of st in this class is more than that class)
human brain has component that can adapt to learning and using math
humans vary considerably in their innate math abilities and intelligences
environment vary tremendously
thus, when we combine nature and nurture, by the time children enter school, they have tremendouly varying level of knowledge, skills and interests
altough we offer standard curr, the actual curr, instruction, assessment, engagement of instrinsic and extrinsic, and so on varies considerably
appropriate use of constructivist teaching and learning principles

constructive environment includes

• journaling or diary (keep track)
• project-based learning (PBL)
• problem based learning

transfer of learning and learning mathematics
transfer of learning (use wat ever learnt to apply / address problem encountered later):

• teaching for transfer is one of the seldom-specified but most important goals in edu
• to gain knowledge and skills st can use in & outside school now& future
• deals with transfering one knowledfe i skill in problem solving situation
• teaching for transfert often happen without conscious thought.....(making milo compare with making a tea)
• occurs at subconscious level, perhaps aided with a little conscious thought
• many transfer of learning situations that are far more difficult

situated learning
learning normally occurs is a fx of the activity, context and culture in which it occurs
learners become more active and engaged within the culture (social interaction)

super genius / gifted students & multiple intelligences

http://dawnlikechickenrice.blogspot.com/2011/04/super-prodigy.html

What if.....Why.......they will always ask this....contrast with slow learners (seldom ask)
they learn a language very fast
intellectual playfulness= very creative, eg: some computer games can be very intellectual

assessment: require more from this group of students, dont satisfy easily, see whether they can go higher; ask st to explain

textbook: enriched, include concepts beyond the basics

have multiple resources to help students
flexible: eg: more than 1 methods to solve a problem....

talk to the parents, let them participate in contest: math olypmpic, new south wales

have career talk where the ppl have opportunity to know them
group activity: create free thinking....

let the children mix with other with the same ability, professor, they will be able to give feedback

they lack of experience in concrete activities

calcultors: exploring tools
computer: have many advantages

24 Game: suitable to them
Sudoku.....kakuro
to make it simpler....start form 2X2.......

http://www.educationoasis.com/resources/Articles/teaching_gifted_math.htm

can give normal students 1-2 level higher problem (as enrichment activity)....maybe 1-2 studens can do it...indirectly help the st learn a bit than what they can....

mep: the magazine towards english proficency
http://mepedu.com/


Multiple intelligence-Howard Gardner: a feel good theory

http://www.thomasarmstrong.com/multiple_intelligences.php

coach: strategy good...

spatial-visual: they need to see the thing..

can have more than 1 intelligences.....

they are outstanding in their field...

some of the st have different learning style from others....

Carl Rogers

1st of all, i must say that i really think his name sound like

& i wound be happy if they have some connection........

back to the topic, who is carl rogers (beside he have the same family name with kenny)?

Carl Rogers (1902–1987)

American psychologisthistory
contributed to fields of education, counseling, psychotherapy, peace, and conflict resolution
one of  founder of humanistic psychology
focused on demonstrating the psychological conditions for allowing open communication and empowering individuals to achieve their full potential.

Since we focus on humanistic theories, let see what is meant by it...

Humanism is a philosophical movement that emphasises the personal worth of the individual and the centrality of human values.  The focus of the humanistic perspective is on the self, which translates into "YOU", and "your" perception of "your" experiences. The Humanistic approach rests on the complex philosophical foundations of existentialism, and emphasizes the creative, spontaneous and active nature of human beings. This veiw argues that you are free to choose your own behavior, rather than reacting to environmental stimuli and reinforcers. This approach is  very optimistic and focusses on noble human capacity to overcome hardship and despair. Issues dealing with self-esteem, self-fulfillment, and needs are paramount. The major focus is to facilitate personal development. Two major theorists associated with this view are Carl Rogers and Abraham Maslow.

Carl Rogers feels that each person operates from a unique frame of reference in terms of buliding Self Regard or their self concept. Self Concept is one's own belief about themselves. These beliefs stem, in part, from the notion of Unconditional Postive Regard and Conditional Positive Regard. Unconditional positive regard occurs when individuals, especially parents, demonstrate unconditional love. Conditioned positive regard is when that love seems to only come when certain condtions are met. Rogers theory states that psychologically healthy people enjoy life to the fullest, hence, they are seen as fully functioning people.

Abraham Maslow feels that indivduals have certain needs that must be met in an hierarchical fashion, from the lowest to highest. These include basic needs, safety needs, love and belonging needs, achievement needs, and ultimately, Self-Actualization.
According to Maslow's Hierarchy of Needs, the needs must be achieved in order. For instance, one would be unable to fulfill their safety needs if their physiological needs have not been met.

based on:
http://wilderdom.com/personality/L10-2Humanistic.html
http://www.mesacc.edu/dept/d46/psy/dev/Fall98/Theories/humanistic.html

more about humanistic theory by carl rogers: http://facultyfp.salisbury.edu/iewhite/The%20Humanistic%20Theories%20of%20Carl%20Rogers.htm


Carl Rogers' Quates (that i like):

The only person who cannot be helped is that person who blames others


“The good life is a process, not a state of being. It is a direction not a destination.”


I believe that the testing of the student's achievements in order to see if he meets some criterion held by the teacher, is directly contrary to the implications of therapy for significant learning.

The curious paradox is that when I accept myself just as I am, then I can change

The good life is a process, not a state of being. It is a direction not a destination 

The facts are always friendly, every bit of evidence one can acquire, in any area, leads one that much closer to what is true.

In my early professionals years I was asking the question: How can I treat, or cure, or change this person? Now I would phrase the question in this way: How can I provide a relationship which this person may use for his own personal growth?

"The very essence of the creative is its novelty, and hence we have no standard by which to judge it."

"Experience is, for me, the highest authority. The touchstone of validity is my own experience. No other person's ideas, and none of my own ideas, are as authoritative as my experience. It is to experience that I must return again and again, to discover a closer approximation to truth as it is in the process of becoming in me. Neither the Bible nor the prophets -- neither Freud nor research --neither the revelations of God nor man -- can take precedence over my own direct experience. My experience is not authoritative because it is infallible. It is the basis of authority because it can always be checked in new primary ways. In this way its frequent error or fallibility is always open to correction."


"A second characteristic of the process which for me is the good life, is that it involves an increasingly tendency to live fully in each moment. I believe it would be evident that for the person who was fully open to his new experience, completely without defensiveness, each moment would be new."

With the price of life these days, you've got to get everything for free you can.

week 13 psiko math

on wednesday, we will have substitute class.....
today....show each other blog.....

the most important is to learn how to learn...
Carl Rogers....

oraganizers: a map or steps of procedures....; colours, arrows....factor tree....

what we learn, we apply....
we aware of it, and do something....
if not work. go on & try another way....

my 1st Prezi

1st time using Prezi, a free presentation tool...
at 1st, it is complicated, but after 2 days, it become enjoyable...

i use Prezi to prepare presentation for Sej Fals Pendi Math assignmetn, GeoGebra & Graphs of function...

this is not the best Prezi ever, but i hope u will like it...
https://prezi.com/secure/41197525b524d4c312082af54b0734572b93f06d/

or can directly use the file below (i hope it works)



i try to embedded GeoGebra here, but fail.....
so use this link below go to the the GeoGebra files...
http://www.geogebra.org/en/upload/files/yzy887/4_type_of_graphs.html

it is really interesting playing with 2 new software..

Week 12 Presentation Mathematics Slow Learners

Week12 Math Psychology slide

View more presentations from yzy887.

Grammer error in the slides:
Slide 6: "Constanly reference" to Constrantly refer to
Slide24: "How much he lose" to "How much did he lose?"


They want to learn, and we want to help them.

There is no proof that any particular method is beat and it is probable that, as in the teaching of slow learners, the 2 factors most conducive to learning are the skills and enthusiasm of the teacher and a blend of methods to suit the situation.

The best activities are those arise out of the normal day's activities.

Effective teacher provide frequent and numerous opportunities for students to makes discoveries and explorations on their own. Certainly it is easier to just tell facts to students, but learning is far more effective, exciting, and pleasurable if the students is able to make these discoveries on his own.

Mathematical recreations ( tricks, games, or puzzles) provide an excellent means of stimulating the interest of slow learners. Teacher can have 'puzzle of the week' on the bulletin board to capture the attention and interest of students.

week 11 class notes

Learning to Teach math from other learning theories
Ausubel: verbal meaning learning
Brunner: discovery learning
Skemp: Mathematicak Understanding (relational vs instrumental learning)
Dienes: mathematical fun (game) learning

ausubel: metapgrs, cognitive structure, heirarchy, subsumption, organizers, retention, (vs) forgetting
mnemonic is 1 of the advance organizers: "kuda baca to"
wat works for a group of stu may not work for other....

humanistic: relate math to human activities: math is in real life; socialcultural perspective (sosial interection) involved st learning in classroom , in a group
integrated approach: put all this together

http://kasut-biru.blogspot.com/2011/03/11th-week-presentation.html

humanistic perspective: the development of the child's self-concept
if st feel he is good, it is a good start for his learning....he believe he can go it
eg: if we want to teach addition....if he can answer the question correctly, he will feel good;
if he could not, teacher give guidance (so he would feel better)....repeat the question, make the question simple & small part...relate it to their pass or experience...
teacher use activities


http://en.wikipedia.org/wiki/Carl_Rogers (find one or 2 cotation from him about humanistic)
& maslow http://en.wikipedia.org/wiki/Abraham_Maslow

social personal developmetn: let st do presentation & praise them (the reward) , reduce punishment
make them feel good

performance-oreinted, still have to test them.....
keep in mind of their level.......ask question of their level....provide oppurtunity for success

math has more than one way of computation....let them do it their way.....respect st aspiration

right to self-determination: bagi peluang bina keazaman

open classroom....mesti use certain strategy.....mesti siap sekian-sekian masa...
learning style....lets st learn in his way.....teacher be flexible
co-operative learning...in group learning....everyone try to be better and best to help others

social cultural perspective: emphasized the influence of culture, peers and adults on the developing child
zone of proximal devekpment

cultural tools
computer....some cultural use computer better in learning......eg US and Japan is fast in helping them to learn

Integrated approach perspective
old math, teach in new way
3 main components: numbers, shapes and relations

ameriaca & singaopre learn math using themes...in themes have number, shape relation

integration of math as problem solving, communication, reasoning, connections representation

in the process of problem solving, they learn about the concept, the learn what is circle, circumferences.....
communication....able to reading (st collect data adn think) , listenint (st respons to questions and think to solve it),
reasoning....basic for understaning and solvinf problem...st preject answer by using concrete materials
(A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p > 1 that has no positive integer divisors other than 1 and p itself. (Source)

1 certainly does not meet that criteria since 1 is not greater than 1. ) st can reasons why, even using definition

connection...inter & intra
representation...symbol, chart, graph

6 principles
Equity
curriculum....math is integrated, not separate pieces
teaching...t understand how st learn & select methods for teaching
learning....when to teach and learn math
assessment
technology

teaching and learning as an integrated approach....make connection....so that the undestanding together
balance between understanding of concepts and mastering of skills
apply mathematical skills in real problem solving situations

encourage st to use calculator to check the answers.....
when teach problem solving, should also teach to check the asnwer....
so that they will remember to chech their answer

humanistics mathematics: attenmpt to explore the human side of mathematical thought and to guide st to discover this beauty of mathematics (nature, environment)

goals: gain appreciates for mathe as a creative, collaborative and move away from thinking of math as a boring subject
looking at problems and concepts in different ways; developing visual techniques for delving deeper into particular topic

strategies: use visual imagery and art to introduce math idea....to illustrate abstract ideas and make them more concrete
use history and cultural perspective to help st understand math as a human endeavor.....to enliven enthusiasm in the manner in which math is developed

use collaborative
humanistic math creates a learning environment that is productive, meaningful and enjoyable for st

 social.....math knowledge is build socially and real
math is part of human culture....a human identity....

history to excite the students toward the subject
values such as efficientcy, confudent level and systematic thinking must be applied throughout this subject
(give them different level of question, so that they are encourage with the small little success)
study group can help st to applu social skilss and cooperative behaviors

relationship: relate knowledge of conceptual and procedure....and to other subject
st have to participate activily
discusssion

Integration approcaced...Kaiser Messer

dimensions of aims....4 goals....

week 10 class note

Ausubel

meaningful learning: understand rather than memorize it
mnemonic is one type of advance organizer (but still a rote learnin), unless can relate

memorize multipllication table is rote learning, unless u relate to ....

expositiory--- triangles....show example &non-exaple.....ask to clasify nd give defi od triangles
comparison tye...symbol of abselon with e

phase two....presentation must be meaningful to the students

http://www.scribd.com/doc/27043905/Ausubel-Theory
http://www.scribd.com/doc/27846629/Bruner-Theory-of-Learning
http://www.lifecircles-inc.com/Learningtheories/constructivism/bruner.html
http://tip.psychology.org/bruner.html

jerome bruner....related and trying to make constructivism more understandable

notation....the dot for multiplication and decimal must be written correctly

contrast and variation.....intersection set with ''and'' set....differentiate with integration
connectivity...dydx to graph increase or devrease

richard skemp: talk about math understanding

intrumental vs relational UNDERSTANDING

http://www.scribd.com/doc/46489435/Skemp-Theories
http://www.scribd.com/doc/50402712/Shemp-Teories

math as reasoning...use vein diagram

encourahe balance between computational skills (KNOW HOW) and reasoning skilss (KNOW WHY)

http://www.davidairey.com/how-not-to-use-powerpoint/

Zoltan ....CONCRETE EXAMPLE....propose using games in teaching math

free play: example try and error...play without giving any rules....no rules!!!
games...have rules that st have to follow to play....start seeing the pattern
while playing games....they look for sommunalities like differences.....eg....suduko have rules that each number can appear in .....
representation/.....draw diagram
symbolisation.....formula....

ZOLTAN for children to actually play with concrete things, easy for them to grasp the concept
Dienes blocks....helps st to learn numbers
cuisenaire rods...to teach fraction


http://www.zoltandienes.com/?page_id=226
http://www.zoltandienes.com/wp-content/uploads/2010/05/Six_stages_integers.pdf
http://google-chrome-browser.com/prevent-google-chrome-closing-when-you-close-last-tab

Bruner.....encourage socratic learning
4 major principles, a perchant (motivated) toward learning
how a body of knowledge is able to be constructed best to be understood by the leaner
effective manners or sequence for the teacher to present said material to the learner
the natural pacing rewards as well as punishment

good method for stucturing knowledge shoulf result in simpllifying, generatin gnew propositions, and incresing th emanipulation of info

bruner is passionate about language and how this affects cognition withiun this theory of llearning development
if language skills is not develop, cannot communicate....with others and within the mind
teacher should be given the languages skills too....example when PSMPI is introduced....

when a questions is big to be undertan, break it into 2, and the merge them togehther


Ausubel theory is not particularly in vogue today, perhaps because he seems to advocate a fairly passive role for the learner, who receives mainly (active recepting learning) verbal instruction that has been arranged so as to require a minimal amount of 'struggle'.
streesed on meaming ful learning is betterh than discovery learnin
ask them a lot of question...

summarize 1 paraghaph...4-5 sentense about any one of the theory

Wednesday class notes

final questions do not come directly from notes n class material,
Q is not going to be what the theory say, nut how does it effect the teaching and learning, its; IMPLICATION
will based on reading
do not memorize all the sentences...but the content
the theories are related, and based on other

1 of the problem is we dun read a lot....mayb bcos the level of eng is so high....
we need to memorize who say who
but make the theories related to teaching
to feel that it is a new way of looking at teaching...

constructivist teaching is not well defined, rather it contradicts, philosophically, the meaning of constructivism
(if st build their knowledge, then how we teach them)

in fact constructivism is not about teaching, it is about knowledge & learning...

CONSTRUCTIVIST VIEW OF LEARNING: how they view learning

it is about the teaching which results from such a view of learning.


The constructivist view involves two principles: (http://www.grout.demon.co.uk/Barbara/chreods.htm)

1. Knowledge is actively constructed by the learner, not passively received from the environment.

2. Coming to know is a process of adaptation based on and constantly modified by a learner's experience of the world.

children get shock in exam bcos the exam paper is not made completely same as what they learn in the class

RELATE.....only when relate to daily life, it is meaningful to them...

what is in the computer games have that make it so excited  (audio visual colourful, level after another level, reward, competition with computer or friends, something they dun see in normal live, challenges (u have do 5 Qs, not we are going to solve 2 more Qs)
how can we make it in to our teaching....
http://www.squarecirclez.com/blog/review-how-computer-games-help-children-learn/1338

only think, we can retain the memory longer.....

we learn it so that we can use it in our live later on....

b4 MI, there is only IQ test....;later then found out that intelligence can grow, by educating urself
there4, there is not only 1 way of teaching.......ENDLESS....
eg teaching math using song....for those with MUSIC

when st having discussion, t should actively help them to develop the ideas,

over the years, knowledge has grow.....wat is true now is not going to b true forever

radical cons: knowledge is constructed rather than constricted (knowledge expand)

http://www.networkworld.com/community/blog/most-kids-want-educational-video-games-school

Most kids want educational video games in school, survey shows. ... So?

use games when necessary....when u r tired....computer lab...or 1 computer with projector....(which group handle it the best....fun...other group give points)

why u stressed n u make other ppl stressed?????
punishing them.........why????
yr 1,,,,they not understand school life.....punish them make them hate coming to school....

http://www.papert.org/

Week 9 (ops...) class draff

Difference between constructivism and Constuctionism

http://www.slideshare.net/guest2ec2f4/constructivsm-vs-constructionism-presentation

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.132.4253&rep=rep1&type=pdf

In education, Piaget described Constructivism as being the process whereby students constructed their own unique systems of knowing, in consequence of which the teacher should focus on this individual process of internal construction rather than standing at the front and spouting their own models.

Seymour Papert, a student of Piaget, expanded on this to describe Constructionism in terms of helping the student produce constructions that others can see and critique.

In this educational frame, then, Constructivism is more cognitive and Constructionism more physical.

Constructionist learning is inspired by the constructivist theory that individual learners construct mental models to understand the world around them. However, constructionism holds that learning can happen most effectively when people are also active in making tangible objects in the real world. In this sense, constructionism is connected with experiential learning and builds on some of the ideas of Jean Piaget.

St learn by constructing or making, it provide experience and satisfactory of achieve something, an artifact, proof tha learning has taken place….meaningful learning

Each ppl should learn extra 3-4 languages

The introduction of calculators aims to

o    achieve a better balance between emphasis on computational skills and problem solving skills in teaching and learning and in assessment ;

o    Widen the repertoire of teaching and learning approaches to facilitate the use of investigations  and problems in authentic situations (provide more teaching methods, eg: use calculator to check answer); and

o    Help students, particularly those with difficulty learning mathematics, develop greater confidence in doing mathematics.

The use of calculators created a computational advantage and more often resulted in the selection of a proper approach to a solution in problem solving. Students in elementary schools who used

ü  calculators possessed better attitudes and had

ü  better self-concepts in mathematics .

ü  There were significant differences in problem solving , computation , and conceptual understanding , favouring students who used calculators to those who did not.

Literature Review

Based on Towards a Constructivist Pedagogy for Year 12 Mathematics by Ian Sheppard.

Write a summary of the article in not more than 500 words;

This article was written by Ian Sheppard, an Australian teacher who has taught mathematics for 30 years. In 2004, he started working in a new school where he focused on the Year 12 (age 16-17) mathematics courses. He used constructivist and inquiry based approaches to handle his class.

Sheppard worked at Australian Science and Mathematics School (ASMS), with support and encouragement from the mathematics staff. ASMS caters final 3 years of schooling before entry into higher education, designed for highly collaborative, interactive and student-directed teaching and learning. Majority of students comes from local area with wide variety of abilities and aspirations. The school provides strong emphasis on the disciplines of science and mathematics, lifelong learning,  relevance of science and mathematics to the world’s future, interconnectedness of knowledge and  importance of human communication in all its forms.

Sheppard’s student majority were from MAT (Mathematics and Abstract Thinking) course, had learnt mathematics using constructivist and inquiry-based approach in their Year 10 and 11. Though Year 12 mathematics course is exam-based, Sheppard decide to let the students continue learning under the same approach. The learner is responsible for their own learning. He desire to teach for understanding, rather than for algorithmic proficiency. He rejected to teach using textbook approach. Sheppard want more students to enjoy what they were doing, not just gain a sense of achievement in being able to do mathematics.

The course was centered on core investigations. The worksheets presented problems embedded in conversation or story line. They covered key ideas outlined in the curriculum statement, extensions for further investigations was provided for interested students or who aspiring to an ‘A’. The materials were written in such a way that students can work by themselves, anytime and anywhere. In scheduled class, students usually worked in groups with teacher support.

After complete the core investigation, students make an entry in their notebook, creating their own text book which was permitted in all tests.

Communication of mathematics is promoted by presentation and sharing of findings, through Unseen Orals and Public Presentation Pieces (PPP). The audience consisted of teacher and other groups who had concentrated on different problems. Students demonstrated high level of engagement. A quiz will be conducted each week to allow students to check their understanding and ability to apply the concepts.

During the course, teacher acts more as a facilitator rather than a broadcaster of knowledge.  Teacher spends very little time talking to whole group, but to individual or small group, responding to the students’ concern.  Most of the students were able to learn well. Some were largely independent, using peer support to clarify and develop understanding while others relied more extensively in staff for directional and support. The classroom atmosphere was collaborative and informal.

Through this course, students increasingly learn independently. Learning occurs as part of a process of constructing knowledge; learners communicate their questions, intuitions, conjectures, reasons, explanation and ideas. Moreover, learning involves developing knowledge, skills and dispositions to think and act in ways which determined by individual effort, the setting of personal goals and self awareness.

Discuss, in not more than 500 words,

(i)    how the learning theory shapes your understanding of how students learn mathematics;

(ii)   if there are, in your understanding, learning theories that are especially relevant to the teaching and learning of math?

Though many teachers doubt constructivist approach is efficient enough in covering a set syllabus, but with much effort, we will manage to do it.

It is important that students enjoy learning mathematic and make it their responsibility. This will encourage the development of lifelong learners. Teacher should allow space for individual approaches to learning, as different students learn at different ways and rates. Teacher should be flexible to develop a cooperative classroom culture.

In a conducive and encouraging environment, most students are able to learn effectively, though some might relied on facilitator for direction and support. Many students may not fully understand at first time, as it takes time for them to modify existing schema. Hence they should be allowed time to use multiple approaches for understanding. Drill and practice is rather meaningless if students cannot understand what there was doing.

Students construct their own understanding; teacher cannot feed them with information. It is essential for students to understand key ideas; the rest will follows much more easily.

Students can learn mathematics as part of a process of constructing knowledge. By solving problem where the mathematics is presented implicitly, students develop their understanding of the mathematics. By solving problem students reflect upon what they had learned. Also, students will be able to direct their learning according to their interest, capability, goals and current workload.

Teacher understands students more than the curriculum or textbook do. So, curriculum documents and textbook just provide the guidance for designing materials and learning opportunities. Teacher should arrange curriculum according to the development of students.

Creating note book help students to reflect on mathematics and focus on the underlying principles.

Students should learn in group, as it can contribute to the collaborative climate of the classes. The collaborative climate can be further enhanced by the team teaching approach. The extensive use of group work encourages collaboration and the communication of questions, intuitions, conjectures, reasons, explanations and ideas. The learning is refined as students freely discuss their ideas and argue a case until they come to a shared understanding.

Students enjoy working with teacher rather than working for the teaching. In the shared classroom, teacher should act as a facilitator instead of a transmitter of understanding. Before students able to work independently, teacher should stay beside them to model their learning.

important principles that guide the work of a CONSTRUCTIVIST teacher

·         encourage and accept student autonomy and initiative.

Encourage students to be responsible on their learning.

Allow student responses to drive lessons, shift instructional strategies, and alter content.

Tailor their teaching strategies to student responses, create the learning experience that is open to new directions depending upon the needs of the student as the learning progresses

·         inquire about students' understandings of concepts before start activity

new knowledge must be built on previous knowledge and experience

guided students from basic to deeper levels of understanding through questions and encouragement  so that they can learn from the incorporation of their experiences

—  Provide learning environments such as real-world settings or case-based learning instead of predetermined sequences of instruction.

Learning must start with the issues around which students are actively trying to construct meaning. Example, in teaching volume and area, we must show the object. When teaching probability, we must let students explore where it will be used.

Avoid oversimplification and should represent the complexity of the real world.

Use raw data and primary sources along with manipulative, interactive, and physical materials. For example, when teaching statistics, can collect students information rather than use tables created from nowhere.

—  encourage students to engage in dialogue both with the teacher and with one another.

Example: Discussion, research project, field trip, group activity. Each member of class should be able to share their opinion with other.

Create a discourse of comfort wherein all ideas can be considered and understood and the students then feel safe about challenging other hypotheses, defending their own, and supporting real-world situations with abstract supporting data

—  encourage student inquiry by asking thoughtful, open-ended questions and encouraging students to ask questions of each other.

Instead of telling, the teacher must begin asking. Instead of answering questions that only align with their curriculum, teacher must make it so that the student comes to the conclusions on their own instead of being told. Teachers must challenge the student by making them effective critical thinkers and not being merely a "teacher" but also a mentor, a consultant, and a coach.

Open-ended questions and critical thinking encourage students to seek more than just a simple response or basic facts and incorporate the justification and defense of their organized thoughts. For example, question like ‘Define a triangle’ should be asked instead of ‘How many sides does a triangle has?’

Socratic learning is suggested as the best method of communication in this theoretical framework, as it allows the teacher to actively note any study skills the learner verbalizes, their progression, their frustrations, and form a rubric of their current learning state based on the dialogue. Any teacher lesson plans, teacher worksheets, or resources should in fact be constantly building the learner's knowledge in a spiral manner.

—  Support collaborative construction of knowledge through social negotiation, not competition among learners for recognition.

Students should support each other in learning for the sake of knowing, not learning to get grades or recognition.

—  seek elaboration of students' initial responses.

The first is discovering and maintaining an individual's intellectual identity. This forces students to support their own theories, in essence taking responsibility for their words and respecting those of others

students are encouraged to think and explain their reasoning instead of memorizing and reciting facts.

—  engage students in experiences that might engender contradictions to their initial hypotheses and then encourage discussion.

Example, let students to explore whether median is  equal or not equal to mod or mean and the reason.

—  provide a waiting time after posing questions and for students to construct relationships and create metaphors.

Time is needed to process and reflect the question, also to analyze the requirement and choose the best response, if possible along with explanation.

—  nurture students' natural curiosity

Though curiosity may kill a cat, without it, one cannot learn well. Curiousity  create the spirit of learning. For example, let students why the shortest distance between two points on Earth surface is using Great Circle.

Young children and scientists have much in common.  Both are interested in a wide variety of objects and events in the world around them.  Both are interested in, and attempt to make sense of, how and why things behave as they do.  (Osborne & Freyberg 1985, p.1)

Some strategies for teacher include having students working together and aiding to answer one another's questions. Another strategy includes designating one student as the "expert" on a subject and having them teach the class. Finally, allowing students to work in groups or pairs and research controversial topics which they must then present to the class.

Working in groups, learners support each other’s understanding as they articulate their observations, ideas, questions and hypotheses. Working in groups help students learn social interaction skills they will need later in life. Students will learn to value each others input and opinions.

week 8 Pschology mathe class notes

theory is not really important but why we learn it.......
how does it relate to us
thri is not important unless it is useful to us

final exam.....
4 questions..12..12..12..14..answer all.....1-3 ab.....4abc

t greet st b4 start....
share recent things with st.....
create some relationship...
help dr shahul wife is going to be well soon...

the topic is relevant.....how to u make it relavant to
them.....connect of their daily life....
IPT....input.....see, hear, smell, touch,......sight n hearing use
most.....therefor we must adjust our teaching so that we use it the
most n safe....ok.....

bila buat presentation.....must link so that ppl is interested...

constructivism...u construct knowledge wat u already know n new knowledge....
if u not have enuf knowledge, might construct knowledge not
right......might want to test and improve....

shud convince friend that we must noe it now....

children construct knowledge....dun have to tell children how to play....
just give them the toy n observe.....they will be able to
play....though maybe they make a few mistake...
but they will realize....

kita main====explore...

learning can take place anytime....
but active.....st do something....& learn

t just guide....
bcs first st will not learn about it.....we have a time constraint

ex.....give 2 groups same article...when present.... different ideas
and approaches come in.....as long as what they say make sense....this
is what constructivism matter

i would say not all the constructivism is useful in all cases, we need to modify it to fit to our class.....

put st into groups, the more ppl, the more different ideas they will be exposed to must mayb less interaction….something tat t must think about

subtraction is not easy to teach, especially when it involve negative…negative is some number less than zero, something that we lack of, concept of basement, temperature, sea level, dropping level

to teach constructivism, first to let them experience it….; to teach the importance of friends or social interaction, put them into solo camp (like in outbound school), let them experience loneliness, let them explain wat they feel

encourage st to say, dun critic if they are wrong, but GUIDE them to correct route

computer games, st know better, they curious, they have experience than teacher…their previous experience is stronger

teacher must be energetic, enthusiasm…; have st to prepare b4 class if want an effective constructivism class

teacher must be able to identify 3 groups of st ability: low, average, and high, though lesson plan is build for average, must consider the low and high achiever, remedial class for low, extra or challenging problem for hign to be solve

if only school exam….then must have the accountability

must tell students : learning is the resposibility of the learner
i cannot learn for u n sit for the exam for u....
then is the time they play a bigger role in learning...

from time to time u assess ur st...they learn how much they learn n
will work harder.....

constructivism is an approach to teaching and learning based on the premise that cognition (learning) is the result of ''mental
construction''

st learn by fitting new into together with what they already know. learning is affected by the context in which an idea is taught as well as by students' beliefs and attitudes.

for those who belief we learn today, will go back and read more about it
http://www.connectionscharterschool.org/constructivism.htm....12
principles (NI in exam)

not angry too much...big challenge to get them process only what u r telling

it does not mean looking at u or not==listening to u

cannot just focusing on the mind....but is the whole body.....
in the same room is not equal to share the same environment

Constructivism, the cognitive theory, was invented by Jean Piaget. His idea was that knowledge is constructed by the learner. The learner must consciously think about trying to derive meaning, and through that effort, meaning is constructed through the knowledge structures. Piaget liked to emphasize learning through play, but the basic cognitive theory of constructivism certainly supports learning through lecture -- as long as that basic construction of meaning takes place.

Constructionism is more of an educational method which is based on the constructivist learning theory. Constructionism, invented by Seymour Papert who was a student of Piaget's, says that learning occurs "most felicitously" when constructing a public artifact "whether a sand castle on the beach or a theory of the universe.“ Seymour does lean toward the constructivist learning philosophy in his writings, where he talks about the difficulty of conveying a complex concept when the reader is going to construct their own meaning. In general, though, his claim is more about method. He believes that students will be more deeply involved in their learning if they are constructing something that others will see, critique, and perhaps use. Through that construction, students will face complex issues, and they will make the effort to problem-solve and learn because they are motivated by the construction

While I was trying to find out ‘’why teachwe always want to tell everything’’, I suft through this page, ‘’best teacher ever’’, I think I will keep this link so that I can come back and read again in future….http://www.etni.org.il/bestteacherever.htm

A page with quates about teacher: http://www.quotegarden.com/teachers.html

Tips of becoming a teacher: http://www.adprima.com/tipson.htm

But I still cannot find the reasons why teacher tend to explain everything to students (students are able to and should learn by themselves), I will try to figure this by myself.  Actually the first thought was the teacher want to show that he knows everything. Other reasons might be he want to share his knowledge with students (sharing is caring); he do not want the students to lack of single detail; he hope students really understand…