GRAND SCENARIO. 1. Problem Identification. 2. Problem Formulation. 3. The Review of Literature. 4. Designing the Research Study ...
RESEARCHING MATHEMATICS EDUCATION: A PERSONAL REFLECTION BASED ON CURRENT PRACTICES IN MATHEMATICS TEACHER EDUCATION IN INDONESIA
Abdur Rahman As’ari Dosen Universitas Negeri Malang To be Presented at Studium General at Universitas PGRI Adibuana Surabaya 10 Mei 2018
GRAND SCENARIO 1. Problem Identification 2. Problem Formulation 3. The Review of Literature 4. Designing the Research Study
TWO CHOICES THEORETICAL
PRACTICAL
Produce New Theory
Create New Products
Complement the Existing Theory
Having a Solution
DEFINITION OF A THEORY A theory is a set of interrelated constructs (concepts), definitions, and propositions that present a systematic view of phenomena by specifying relations among variables, with the purpose of explaning and predicting the phenomena
A theory is a set of concepts and relationship statements that enables one to understand, describe, explain, evaluate, predict, and control things (phenomena).
MATH ED THEORIES (PARTS) Student Centered Learning • RME • CTL • Guided Discovery
methods
conditions
Teacher Centered Learning • Expository • Q &A
Students Background • Sosec • Psychological • Cultural Environment Timing Class Size Formal/In/Non Formal
Goals
Learning/Academic
Knowledge
Working/Vocational
vs
Skills vs
Attitudes
TO PRODUCE NEW THEORY
Know the State of D’arts
Raise Questions that Cannot Be Answered
Consider its Significance and Worthiness
Choose and Focus on One Topic
Deeper Study the Literature
Choose Paradigm (QUANT VS QUAL) and Lens
Develop your Research Design
TO COMPLEMENT THEORY
Choose a Theory
Observe the Application of the Theory in the Field
Identify a Phenomenon
Design a Case Study
TO CREATE NEW PRODUCTS
Study the weakness of existing and circulating products
Design a new Product and Develop a prototype
Evaluate the validity, practicality, effectiveness of the prototype
Disseminate the New Product
TO HAVE A SOLUTION
Reflect on the weaknesses of your own practices
Choose macro, meso, or micro focus type of CAR
Develop a hypothetic al plan of actions
Execute, Observe, and Record the actions
Evaluate, and Reflect
Develop a new and better plan of actions
IDENTIFYING STATE OF D’ARTS 1. Get access to internet 2. Open the journal article provider(s), such as: google scholar, researchgate.net, or eric.ed.gov, pnri.go.id and others (University may subscribe institutionally international journals) 3. Pick a research topic and download as many as journal articles related to the topic 4. Study its abstracts and identify what is studied, how it was studied, and what are the results 5. Classify all of your study results
QUESTIONING STATE OF D’ARTS EXAMPLE OF STATE OF D’ARTS ON CRITICAL THINKING 1. Critical thinker students needs a longer time in solving mathematical problems 2. Once critical thinker studenta are abled to solve the problems, the solutions is perfect 3. Critical thinkers tend to have field independent cognitive style 4. There is no correlation between critical thinking skills and culture 5. Critical thinking skills are strongly influenced by learning motivation 6. The use of Socratic Questioning in Mathematics Teaching improve students’ critical thinking dispositions
EXAMPLE OF A CASE As’ari, a critical thinker, answer a following problem: Find the value of 𝐴 and 𝐵 such that
1 𝑥 2 −1
=
𝐴 𝐵 + 𝑥−1 𝑥+1
as the following : 1. 1 = 𝐴 𝑥 + 1 + 𝐵(𝑥 − 1) .......Multiply each side by 𝑥 2 − 1 2. Substitute 𝑥 = 1 into the equation 1 3. Hence 1 = 2𝐴 , and 𝐴 =
1 2
4. Substitute 𝑥 = −1 into the equation 1 5. Hence 1 = −2𝐵, and 𝐵 = −
1 2
6. So, the value𝑠 𝑜𝑓 𝐴 and 𝐵 consecutively are
1 2
1 2
and − .
CAR: MACRO, MESO, AND MICRO Macro : How to Improve Students Achievement Meso : How to Use RME To Improve Students Achievement Micro : How to Manage Observation Activity in Scientific Approach to Improve Students Questioning Skills
RESEARCH & DEVELOPMENT 1. Many Choices: BORG & GALL, ADDIE, 4Ds, PLOMP etc. 2. Important Notes: R & D Should Be Implemented If There is No Way for ADOPTING Or ADAPTING any Innovative Works 3. Four Main Processes Of R&D: Preliminary Study (To Ensure The Needs), Prototyping (Developing The Draft And Reviewing Its Progress Through Formative Assessment), Evaluating (Assessing Its Practicality And Its Effectiveness), Disseminating (Send The Product To The Needed) 4. The study is applied to both processes and product
Any Questions?
GOOD PROBLEM 1. Clear and Focused 2. Based on Prior Research or Theory 3. Important to Answer 4. Has Intuitive Appeal 5. Empirical (not intuitive) Nature Nuance
PROBLEM FORMULATION SEVERAL CHOICES 1. Exploratory 2. Descriptive 3. Explanatory
EXPLORATORY TYPE 1. 2. 3. 4.
Clarifying Questions Clarifying Populations Clarifying Ideas Open-ended
DESCRIPTION TYPE 1. Obtaining specific facts 2. Obtaining facts to describe issue 3. Summarizing population characteristics 4. Examining non-causal relationships
EXPLANATORY TYPE 1. Examines causal relationships 2. Tests causal hypotheses 3. Explains relationships 4. Builds theories 𝐷𝑜𝑒𝑠 𝑡ℎ𝑒 𝑢𝑠𝑒 𝑜𝑓 𝑃𝑗𝐵𝐿 𝑖𝑚𝑝𝑟𝑜𝑣𝑒 𝐽𝐻𝑆 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 ′ 𝑚𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑎𝑙 𝑎𝑛𝑓 𝑠𝑐𝑖𝑒𝑛𝑐𝑒 𝑙𝑖𝑡𝑒𝑟𝑎𝑐𝑦? Is there any relationship between students’ thinking Style and their mathematics achievement?
Any Questions?
REVIEW THE LITERATURE 1. To present the state of d’arts of the research topic 2. To inspire the Hypotheses for Quantitative Type of Research – confirmatory approach 3. To provide insights of how the data to be collected, interpreted and analyzed in Qualitative Type of Reseach – exploratory approach
REVIEWING THE LITERATURE LOGICAL Consider the following title The impact of reviewing illogical mathematical problems toward students’ critical thinking disposition? 1. The focus is on STUDENTS’ CRITICAL THINKING DISPOSITION 2. The intervention activity is REVIEWING ILLOGICAL MATHEMATICAL PROBLEMS
PROPOSED RL 1. Critical Thinking 2. Critical Thinking Disposition 3. Factors That Influence Critical Thinking Disposition 4. Mathematical Problem Solving 5. Critical Thinkers In Solving Mathematical Problems 6. The Role Of Illogical Problems For Critical Thinking Disposition Development
Any Questions?
RESEARCH DESIGN 1. Considered as one among research quality indicators – through the validity of its conclusion 2. It refers to: the plan, structure, and strategy of research--the blueprint that will guide the research process. 3. Many options: qualitative, quantitative, mixed method
TO GENERALIZE? The research design can be choosen from: 1. Quantitative -- all types of design that using Inferential Statistics Technique of Data Analysis 2. Qualitative – Grounded Theory (only?)
QUANT DESCRIPTIVE RESEARCH
EXPERIMENTAL RESEARCH 1. PRE EXPERIMENTAL DESIGN • One-Shot Design • One-Group Pretest-Posttest Design • Static Group Design
2. TRUE/QUASI EXPERIMENTAL DESIGN • • • • •
Pretest – Posttest Control Group Design Postest Olny Control Group Design Solomon Four Group Design Completely Randomly Group Design Factorial Design
QUALITATIVE STUDY 1. Ethnography – Lead to Ethnomathematics 2. Phenomenology – Lead to Case Study 3. Grounded Theory 4. Historical Research – Very rare in Math ED
CLASSROOM ACTION RESEARCH Practical Based Research – Practitioner Not intended for Generalization Types: Macro, Meso, Micro Research Question type: HOW Data ; Main (Teacher), Supporting (Students, or others) 6. Type of Data: Macro and Meso (T: Nominal), Micro (T: Qualitative), 1. 2. 3. 4. 5.
WRITING THE RESEARCH PROPOSAL 1. Proposal is written to convince stakeholders that the study is important and is needed 2. Content of the proposal: (a) Rationale, (b) Review of the Literature, and (c) Research Design 3. Rationale should consists of: (a) the research problem, (b) state of d’arts related to the study, (c) deficiencies of the existing studies, (d) the significance of the proposed study, and (5) purposes of the study
1.
2.
3.
Review of the literature is a must for quantitative study. It serves as a means for developing a research hypothesis. But, in qualitative study, review of the literature is tentative in nature. Research Design – should be clear – dont just use sentences like: “using quantitative or qualitative approach”. Subject, sampling, instruments (its development process, its characteristics etc), collecting data methods, techniques of data analysis should be made explicit and clear
REFERENCES 1. Refering your point to journal articles is better than refering to books 2. Try to use last 10 years articles 3. Use Reference Management Softwares such as: Mendeley, Zotero etc
Any Questions?
FINALLY
