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.