A research proposal provides a road-map to the study and normally consists of five parts (based on UTM format)

1. Title of research (working title)

2. Introduction

3. Review of the literature

4. Methodology of research

5. Expexted findings and summary

How many pages (10-30 or 40-70 or 70-100 pages or more ?)

When to present ? 2nd sem (master) or 3 sem (PhD) or ??) - full time or part - time

Introduction :

- providing the background (issues/arguments/phenomena) and the context of the problem to be dealt with (including objectives, significance and scope of research)

- formulating/conceptualized the statement of the problem

(problem well-defined is half-solved!!!)

Review of the literature :

- expand upon the context and background of the study and further define the problem/a key concept (concepts)

- review relevant research, unanswered questions (gap), untried method, findings of others you are challenging or extending

- develop theoretical framework of the study

- provide a basis for rationale of the study and the formulation of hypotheses.

Methodology of research :

- describing the methods, design and procedures of the study

- quantitative or qualitative or mixed methods ( instrumentation, sampling, data collection and analysis)

- Gantt chart/plan/schedule of tasks in the research

Expected findings and summary :

- brief descriptions of the findings

# Mathematics Education/Pendidikan Matematik

A synergy of mathematics,education, psychology, curriculum, pedagogy, assessment and management.

## Sunday, September 6, 2015

## Monday, March 2, 2015

### kemahiran berfikir aras tinggi dlm matematik - ketibaan makna

DRP highlight teaching and learning activities in the field of education the knowledge whatsoever about what to do when there is a meaning to arrival (the arrival of meaning) about something (eg a concept) kedlm soul / conscience man.

Similarly in mathematics that involves various concepts DRP easy KPD hard and complex. somebody told students understand the meaning kedlm when they reached him.

Apa buktinya?

Various data can work with them antaranya pelajar dapat menerangkan dgn jelas makna sesuatu konsep itu dan dpt menggunakan konsep dan kemahiran yg berkaitannya dlm proses penyelesaian masalah.

Discuss dgn contoh contoh yg sesuai mengenai pernyataan diatas.

Similarly in mathematics that involves various concepts DRP easy KPD hard and complex. somebody told students understand the meaning kedlm when they reached him.

Apa buktinya?

Various data can work with them antaranya pelajar dapat menerangkan dgn jelas makna sesuatu konsep itu dan dpt menggunakan konsep dan kemahiran yg berkaitannya dlm proses penyelesaian masalah.

Discuss dgn contoh contoh yg sesuai mengenai pernyataan diatas.

## Saturday, February 8, 2014

Synopsis :

This course aims at exploring critically issues and trends related to four main aspects namely curriculum, teaching and learning, assessment and research in mathematics education from both local and international perspectives. It focuses on the concepts and philosophies underlying the implementation of curriculum, teaching and learning and assessment in mathematics education. Students are expected to do a lot of independent and critical reading from local and international mathematics education research journals.

Assessment methods :

1. Review of selected research articles and presentation (individual) - 30%

2. Project - analysis of secondary school mathematics textbook (group of 2/3) - 30 %

3. Final exam (comprehensive) - 40 %

## Monday, December 9, 2013

### PROBLEM POSING, PROBLEM SOLVING AND PEDAGOGY

Assumption (epistemologically) - mathematics as result of human problem posing and solving

- mathematics as a mental construction (creation, invention or

discovery)

In term of learning, social constructivism identifies all learners of mathematics as creators of mathematics involving problem posing and solving.

Therefore as a consequences of problem posing and solving pedagogy :

1. School maths for all should be centrally concerned with mathematical problem posing and solving

(reduce content- oriented mathematics curriculum)

2. Inquiry, investigation, problem posing or formulation should occupy a central place in the school

maths curriculum and precedes problem solving

3. The pedagogy (teaching, learning and assessment) should be process and inquiry(or investigation)

focused (vs product)

4. learner-centered view of investigation as a learner directed activities (new questions posed, new

situations are generated and explored- promotes active learning)

5. Increase learner autonomy and self- regulation ( develop reflective and meta-cognitive skills)

Mathematical problem posing (formulation, investigation etc) is divergent (creative thinking and higher order thinking) as the process of mathematical problem solving (critical thinking and higher order thinking - eg by using Polya method)) is convergent.

- mathematics as a mental construction (creation, invention or

discovery)

In term of learning, social constructivism identifies all learners of mathematics as creators of mathematics involving problem posing and solving.

Therefore as a consequences of problem posing and solving pedagogy :

1. School maths for all should be centrally concerned with mathematical problem posing and solving

(reduce content- oriented mathematics curriculum)

2. Inquiry, investigation, problem posing or formulation should occupy a central place in the school

maths curriculum and precedes problem solving

3. The pedagogy (teaching, learning and assessment) should be process and inquiry(or investigation)

focused (vs product)

4. learner-centered view of investigation as a learner directed activities (new questions posed, new

situations are generated and explored- promotes active learning)

5. Increase learner autonomy and self- regulation ( develop reflective and meta-cognitive skills)

Mathematical problem posing (formulation, investigation etc) is divergent (creative thinking and higher order thinking) as the process of mathematical problem solving (critical thinking and higher order thinking - eg by using Polya method)) is convergent.

## Tuesday, December 3, 2013

### PROBLEM-BASED LEARNING(PBL) IN MATHEMATICS

Paradigm shift from traditional teaching model (content-based, teacher directed and student as knowledge recipient) to problem- based learning model( problem motivated, teacher as facilitator and student as problem solver).

Main characteristic of PBL approach is that,

**the problem (real-world problem : unstructured and authentic (vs simulated) is the starting point of learning.**(discuss its implications to the current maths curriculum).

eg (solve the following problems)

1. The costs for two different kinds of heating systems for a three- bedroom home are given below

solar system - cost to install rm 29700 and operating cost/year is rm 150

electric system - cost to install rm 5000 and operating cost/year is rm 1100

After how many years will total costs for solar heating and electric heating be the same?

What will be the total costs for both systems at that time?

2. Two ordinary six-sided dice are rolled, what is the probability of getting a sum of 8?

3. Working together, Ahmad and Ali can complete a job in 4 hours. Working alone, Ahmad requires

6 hrs more than Ali to do the job. How many hrs does it take Ali to do the job if he works alone?

Benefits of PBL:

1. creating meaningful learning(content/topic/concept) through inquiry (emphasis on critical, logical creative thinking, deep reasoning and metacognition))

2. encourage the development broad -based mathematical problem solving strategies (heuristics)

rather than content learning in a limited sense.

3. development of self-directed/regulated/independent learners - students assume major responsibility

for the acquisition of knowledge.

## Sunday, December 1, 2013

### Broad- based mathematical problem solving strategies

...in USA (cont..)

NCTM (National Council of Teachers of Mathematics) - focus on concept development and problem solving.

By learning and acquiring a variety of broad-based ( general ) mathematical problem-solving

strategies (heuristics) students are equip to be a better problem solvers across the topics in mathematics or transferring those skills to a variety of problems. Some of the general problem solving strategies are :

1. Characterize the problem : What is given? What is needed?What is missing? etc

2. Have you seen this before? : or different form ?

3. Look for pattern : eg Gauss recognized a pattern 1+2...+100 = ?

1+100=2+99=...101 (50 pairs)

50 @ 101 = 5050

4. Simplification/reduction : can the problem be broken up into smaller or manageable

sub-problems?

5. Work backwards : when trying to prove a theorem, it may begin from the conclusion and back track logically

6. Modeling/simulation : a mathematical model may be developed that simplify some complicated process/phenomena in the real word (representing/translating into a mathematical forms eg table, diagram, chart, graph, equation, relationship, function, inequalities, matrices, etc)

7. Logical reasoning/arguments - inductive and deductive reasoning,

8. guess and check/improve - develop a sense of estimation

9. make and test conjectures

10. formulate/pose problems from situations within and outside mathematics

NCTM (National Council of Teachers of Mathematics) - focus on concept development and problem solving.

By learning and acquiring a variety of broad-based ( general ) mathematical problem-solving

strategies (heuristics) students are equip to be a better problem solvers across the topics in mathematics or transferring those skills to a variety of problems. Some of the general problem solving strategies are :

1. Characterize the problem : What is given? What is needed?What is missing? etc

2. Have you seen this before? : or different form ?

3. Look for pattern : eg Gauss recognized a pattern 1+2...+100 = ?

1+100=2+99=...101 (50 pairs)

50 @ 101 = 5050

4. Simplification/reduction : can the problem be broken up into smaller or manageable

sub-problems?

5. Work backwards : when trying to prove a theorem, it may begin from the conclusion and back track logically

6. Modeling/simulation : a mathematical model may be developed that simplify some complicated process/phenomena in the real word (representing/translating into a mathematical forms eg table, diagram, chart, graph, equation, relationship, function, inequalities, matrices, etc)

7. Logical reasoning/arguments - inductive and deductive reasoning,

8. guess and check/improve - develop a sense of estimation

9. make and test conjectures

10. formulate/pose problems from situations within and outside mathematics

## Sunday, November 24, 2013

### TEACHING MATHEMATICAL PROBLEM SOLVING

In USA :

1. Philosophy of mathematics education for the 21 st century :

The goal of teaching mathematics is to help all students develop

ie to produce effective problem solvers and powerful mathematical thinkers.

2. Mathematics must be seen as an integrated whole ( not as a separate and unrelated topics),

as a part of human experience, emerging from everyday experience, interaction with science

and technology and other fields.

3. Spend more time on developing broad- based mathematical problem solving skills

( general problem solving techniques ie heuristics) and less time on perfecting routine

computations.

4. Teaching mathematics as problem solving

- problem solving as a means as well as a goal of instruction

- apply problem solving skills to solve problems in new contexts with emphasis on multi-steps

and non-routine problems.

- recognize and formulate (posing) problems from real word situations/phenomena

- mathematics is problem-centered and application- based

- subject to be investigated, discovered, explored and created

5. Problem solving is seen as the most important means to develop powerful mathematical thinkers.

1. Philosophy of mathematics education for the 21 st century :

The goal of teaching mathematics is to help all students develop

**mathematical power**ie to produce effective problem solvers and powerful mathematical thinkers.

2. Mathematics must be seen as an integrated whole ( not as a separate and unrelated topics),

as a part of human experience, emerging from everyday experience, interaction with science

and technology and other fields.

3. Spend more time on developing broad- based mathematical problem solving skills

( general problem solving techniques ie heuristics) and less time on perfecting routine

computations.

4. Teaching mathematics as problem solving

- problem solving as a means as well as a goal of instruction

- apply problem solving skills to solve problems in new contexts with emphasis on multi-steps

and non-routine problems.

- recognize and formulate (posing) problems from real word situations/phenomena

- mathematics is problem-centered and application- based

- subject to be investigated, discovered, explored and created

5. Problem solving is seen as the most important means to develop powerful mathematical thinkers.

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