This document is an assignment on research in mathematics education. It discusses the nature of research in mathematics education compared to mathematics. It notes that while mathematics uses proofs, research in mathematics education uses various forms of evidence to build understanding. It outlines the main purposes of research in mathematics education as understanding mathematical thinking and learning as well as improving instruction. It also discusses standards for evaluating theories and models in mathematics education research, including descriptive power, explanatory power, scope, predictive power, rigor, falsifiability, replicability, and using multiple sources of evidence. The document concludes by emphasizing that mathematics education research is still a young field with progress being made to build robust theory and methods.
HCI Research as Problem-Solving [CHI'16, presentation slides] Aalto University
Slides from a talk delivered at CHI 2016, San Jose.
Authors: Antti Oulasvirta (Aalto University) and Kasper Hornbaek (University of Copenhagen).
Link to paper: http://users.comnet.aalto.fi/oulasvir/pubs/hci-research-as-problem-solving-chi2016.pdf
Overview: This talk discusses a meta-scientific account of human-computer interaction (HCI) research as problem-solving. We build on the philosophy of Larry Laudan, who develops problem and solution as the foundational concepts of science. We argue that most HCI research is about three main types of problem: empirical, conceptual, and constructive. We elaborate upon Laudan’s concept of problem-solving capacity as a universal criterion for determining the progress of solutions (outcomes): Instead of asking whether research is ‘valid’ or follows the ‘right’ approach, it urges us to ask how its solutions advance our capacity to solve important problems in human use of computers. This offers a rich, generative, and ‘discipline-free’ view of HCI and resolves some existing debates about what HCI is or should be. It may also help unify efforts across nominally disparate traditions in empirical research, theory, design, and engineering.
HCI Research as Problem-Solving [CHI'16, presentation slides] Aalto University
Slides from a talk delivered at CHI 2016, San Jose.
Authors: Antti Oulasvirta (Aalto University) and Kasper Hornbaek (University of Copenhagen).
Link to paper: http://users.comnet.aalto.fi/oulasvir/pubs/hci-research-as-problem-solving-chi2016.pdf
Overview: This talk discusses a meta-scientific account of human-computer interaction (HCI) research as problem-solving. We build on the philosophy of Larry Laudan, who develops problem and solution as the foundational concepts of science. We argue that most HCI research is about three main types of problem: empirical, conceptual, and constructive. We elaborate upon Laudan’s concept of problem-solving capacity as a universal criterion for determining the progress of solutions (outcomes): Instead of asking whether research is ‘valid’ or follows the ‘right’ approach, it urges us to ask how its solutions advance our capacity to solve important problems in human use of computers. This offers a rich, generative, and ‘discipline-free’ view of HCI and resolves some existing debates about what HCI is or should be. It may also help unify efforts across nominally disparate traditions in empirical research, theory, design, and engineering.
Research Paradigm/framework
Research Paradigm/ Framework
Described as the abstract, logical structure or meaning that guide the development of the study.
All frameworks are based on the identification of key concepts and the relationships among those concepts.
Concepts
Abstractly describes and names an object or phenomenon, thus providing it with a separate identity and meaning.
An intellectual representation of some aspects of reality that is derived from observations made from phenomena.
Conceptual Framework
Conceptual Framework
This consists of concepts that are placed within a logical and sequential design.
Represents less formal structure and used for studies in which existing theory is inapplicable or insufficient.
Based on specific concepts and propositions, derived from empirical observation and intuition.
May deduce theories from a conceptual framework.
Purposes of Conceptual Framework
To clarify concepts and propose relationships among the concepts in a study.
To provide a context for interpreting the study findings.
To explain observations
To encourage theory development that is useful to practice.
Theoretical Framework
Theoretical Framework
The theory provides a point of focus for attacking the unknown in a specific area.
If a relationship is found between two or more variables a theory should be formulated to explain why the relationship exists.
Theories are purposely created and formulated, never discovered; they can be tested but never proven.
Purposes of Theoretical Framework
To test theories
To make research findings meaningful and generalizable
To establish orderly connections between observations and facts.
To predict and control situations
To stimulate research
DEVELOPING APPROPRIATE CONCEPTUAL AND THEORETICAL FRAMEWORKTANKO AHMED fwc
Conceptual and theoretical framework is developed for the purpose of clarification and guidance in study or research. This paper explains the meaning of conceptual and theoretical framework in policy research and discusses its usefulness and application. The discussion is systematically corresponded to the basics of research for better understanding of the process. A case study on the Western Sahara Crisis provides exercises on real world adaptation of conceptual and theoretical framework. Workshop participants from the Ministry of Foreign Affairs are exposed to challenges of creating and applying conceptual and theoretical framework to add value to policy inputs in policy research
A description of the analytical tools developed in Physics Education Research for understanding students use of and difficulties with mathematics as used in science.
Research Paradigm/framework
Research Paradigm/ Framework
Described as the abstract, logical structure or meaning that guide the development of the study.
All frameworks are based on the identification of key concepts and the relationships among those concepts.
Concepts
Abstractly describes and names an object or phenomenon, thus providing it with a separate identity and meaning.
An intellectual representation of some aspects of reality that is derived from observations made from phenomena.
Conceptual Framework
Conceptual Framework
This consists of concepts that are placed within a logical and sequential design.
Represents less formal structure and used for studies in which existing theory is inapplicable or insufficient.
Based on specific concepts and propositions, derived from empirical observation and intuition.
May deduce theories from a conceptual framework.
Purposes of Conceptual Framework
To clarify concepts and propose relationships among the concepts in a study.
To provide a context for interpreting the study findings.
To explain observations
To encourage theory development that is useful to practice.
Theoretical Framework
Theoretical Framework
The theory provides a point of focus for attacking the unknown in a specific area.
If a relationship is found between two or more variables a theory should be formulated to explain why the relationship exists.
Theories are purposely created and formulated, never discovered; they can be tested but never proven.
Purposes of Theoretical Framework
To test theories
To make research findings meaningful and generalizable
To establish orderly connections between observations and facts.
To predict and control situations
To stimulate research
DEVELOPING APPROPRIATE CONCEPTUAL AND THEORETICAL FRAMEWORKTANKO AHMED fwc
Conceptual and theoretical framework is developed for the purpose of clarification and guidance in study or research. This paper explains the meaning of conceptual and theoretical framework in policy research and discusses its usefulness and application. The discussion is systematically corresponded to the basics of research for better understanding of the process. A case study on the Western Sahara Crisis provides exercises on real world adaptation of conceptual and theoretical framework. Workshop participants from the Ministry of Foreign Affairs are exposed to challenges of creating and applying conceptual and theoretical framework to add value to policy inputs in policy research
A description of the analytical tools developed in Physics Education Research for understanding students use of and difficulties with mathematics as used in science.
A Qualitative Study on Reframing the Problem-solving Paradigm of Management Science.
Neither Qualitative nor Quantitative methods, as they are currently constituted, adequately resolve the problems of representation and legitimation in the management sciences. This project seeks to resolve contradictions in the ontological and epistemological foundations of social science in order to overcome shortcomings in the two major paradigms that are used in research, where different views of the same phenomena emerge and multiple realities appear to exist.
CBSE Class 10 Mathematics Set theory Topic
Set theory Topics discussed in this document:
Introduction
Sets and their representations
Two methods of representing a set:
Roster form
Set-builder form
The empty set
Finite and infinite sets
Consider some examples
Equal sets
Subsets
Subsets of set of real numbers:
Intervals as subsets of R
Power set
Universal Set
Venn Diagrams
More Topics under Class 10th Set theory (CBSE):
Introduction to sets
Operations on sets
Visit Edvie.com for more topics
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBERijfls
In this paper, a new form of fuzzy number named as Hexadecagonal Fuzzy Number is introduced as it is not
possible to restrict the membership function to any specific form. The cut of Hexadecagonal fuzzy number is defined and basic arithmetic operations are performed using interval arithmetic of cut and illustrated with numerical examples.
8
More Components: Knowledge, Literature, Intellectual Projects
Keywords
action; critical evaluation; instrumentalism; intellectual projects; knowledge; literature; policy; practice; reflexive action; research; theory; understanding; value stances
In the last two chapters, we first introduced the idea of a mental map for navigating the literature plus the tools for thinking that represent the key to this map. We then looked at the first map component: the two dimensions of variation amongst knowledge claims. Here we complete our introduction to the mental map by describing its other three components:
three
kinds of knowledge
that are generated by reflecting on, investigating and taking action in the social world;
four
types of literature
that inform understanding and practice;
five
sorts of intellectual project
that generate literature about the social world.
Figure 8.1 Tools for thinking and the creation of three kinds of knowledge about the social world
Three kinds of knowledge
The three kinds of knowledge that we distinguish are
theoretical
,
research
and
practice
. We describe each below and show how they relate to the set of tools for thinking summarized in
Chapter 6
.
Figure 8.1
represents that relationship, showing that the tools for thinking play a central role. They are employed both to generate and to question the three kinds of knowledge.
What is theoretical knowledge?
The tools for thinking are most obviously reflected in
theoretical knowledge
– you cannot have a theory without a set of connected concepts. We define theoretical knowledge as deriving from the creation or use of theory, in the following way. On the basis of a theory about the social world, we make claims to knowledge about what the social world is like. The theory itself may or may not be our own and will have been developed on the basis of patterns discerned in that social world, whether through general observation (armchair theorizing), through specific investigations (empirically based theorizing) or a mixture of the two.
For example, in order to provide warranting for the claim that all children should be given the chance to learn a foreign language before the age of eight, an author might offer as evidence the theoretical knowledge that there is a ‘critical period’ for language acquisition. The theory upon which the author is drawing for this knowledge has been built up over the years by various theorists (beginning with Eric Lenneberg). The theorists have used both general observation about what happens when people of different ages learn a language and a range of empirical studies that have sought to establish what the critical age and determining factors are. Bundled up in the theory are potential claims about roles for biology, environment and motivation. The author would need to unpack these roles if the fundamental claim were to be developed into an empirical research study (to see how well it worked to offer foreign langua ...
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AUTHOR YIN CHAPTER 1Chapter 1 Plan· Identify the relev.docxcelenarouzie
AUTHOR: YIN
CHAPTER 1
Chapter 1: Plan
· Identify the relevant situation for doing a case study, compared with other research methods
· Understand the twofold definition of a case study inquiry
· Address the traditional concerns over case study research
· Decide whether to do a case study
Abstract
You want to study something relevant but also exciting—and you want to use an acceptable if not esteemed social science method. Doing a “case study” strikes your fancy, but how you might do a good one remains a challenge, compared with doing an experiment, survey, history, or archival analysis (as in economic or statistical modeling). You are intrigued and want to learn more about doing a case study.
This chapter suggests that you might favor choosing case study research, compared with the others, when (1) your main research questions are “how” or “why” questions, (2) you have little or no control over behavioral events, and (3) your focus of study is a contemporary (as opposed to entirely historical) phenomenon—a “case.” The chapter then offers a common definition to be applied to the ensuing case study. Among the variations in case studies, yours can include single or multiple cases, can even be limited to quantitative evidence if desired, and can be part of a mixed-methods study.
Properly doing a case study means addressing five traditional concerns—conducting the research rigorously, avoiding confusion with nonresearch case studies (i.e., popular case studies, teaching-practice case studies, and case records), arriving at generalized conclusions if desired, carefully managing your level of effort, and understanding the comparative advantage of case study research. The overall challenge makes case study research “hard,” although it has classically been considered a “soft” form of research.
Being Ready For The Challenge, And Setting High Expectations
Doing case study research remains one of the most challenging of all social science endeavors. This book will help you—whether an experienced or emerging social scientist—to deal with the challenge. Your goal is to design good case studies and to collect, present, and analyze data fairly. A further goal is to bring your case study to closure by composing a compelling article, report, book, or oral presentation.
Do not underestimate the extent of the challenge. Although you may be ready to design and do case study research, others may espouse and advocate other modes of social science inquiry. Similarly, prevailing federal or other research funds may favor methods other than case studies. As a result, you may need to have ready responses to some inevitable questions and set high expectations for yourself.
Following a clear methodological path.
First and foremost, you should explain how you are devoting yourself to following a clear methodological path. For instance, a conventional starting place would be to review literature and define your case study’s research questions. Alternatively, however, you.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
3. Research in Mathematics
3
Education
“Bertrand Russel has defined mathematics as the science in which we
never know what we are talking about or whether what we are saying is
true. Mathematics has been shown to apply widely in many other scientific
fields. Hence, most other scientists do not know what they are talking about
or whether what they are saying is true.”
Joel Cohen,”On the nature of mathematical proof”
“There are no proofs in mathematical education”
Hentry Pollark
The first quotation above is humorous; the second serious.
Both, however, serve to highlight some of the major differences
between mathematics and mathematics education—differences that
must be understood if one is to understand the nature of methods and
results in mathematics education. The Cohen quotation does point to
some serious aspects of mathematics. In describing various
geometries, for example, we start with undefined terms. Then, following
the rules of logic, we prove that if certain things are true, other results
must follow. On the one hand, the terms are undefined; i.e., “we never
know what we are talking about.” On the other hand, the results are
definitive. As Gertrude Stein might have said, a proof is a proof is a
proof. Other disciplines work in other ways. Pollak’s statement was not
meant as a dismissal of mathematics education, but as a pointer to the
fact that the nature of evidence and argument in mathematics education
is quite unlike the nature of evidence and argument in mathematics.
Indeed, the kinds of questions one can ask (and expect to be able to
answer) in educational research are not the kinds of questions that
mathematicians might expect. Beyond that, mathematicians and
education researchers tend to have different views of the purposes and
goals of research in mathematics education.
4. 4
Purposes
Research in mathematics education has two main purposes, one pure and
one applied:
• Pure (Basic Science):
To understand the nature of mathematical thinking, teaching, and
learning;
• Applied (Engineering):
To use such understandings to improve mathematics instruction. These
are deeply intertwined, with the first at least as important as the second.
The reason is simple: without a deep understanding of thinking, teaching,
and learning, no sustained progress on the “applied front” is possible. A
useful analogy is the relationship between medical research and practice.
There is a wide range of medical research.
Some is done urgently, with potential applications in the immediate future.
Some is done with the goal of understanding basic physiologica
mechanisms. Over the long run the two kinds of work live in synergy.This
is because basic knowledge is of intrinsic interest and because it
establishes and strengthens the foundations upon which applied work is
based. These dual purposes must be understood. They contrast rather
strongly with the single purpose of research in mathematics education, as
seen from the perspective of many mathematicians: “Tell me what works
in the classroom.”Saying this does not imply that mathematicians are not
interested at some abstract level in basic research in mathematics
education, but that their primary expectation is usefulness in rather direct
and practical terms. Of course, the educational community must provide
useful results—indeed, usefulness motivates the vast majority of
educational work—but it is a mistake to think that direct applications
(curriculum development, “proof” that instructional treatments work, etc.)
are the primary business of research in mathematics education.
Some of the fundamental contributions from research
in mathematics education are the following:
5. • Theoretical perspectives for understanding thinking, learning, and
teaching;
• Descriptions of aspects of cognition (e.g., thinking mathematically;
student understandings and misunderstandings of the concepts of
function, limit, etc.);
• Existence proofs (evidence of cases in which students can learn
problem solving, induction, group theory; evidence of the viability of
various kinds of instruction);
• Descriptions of (positive and negative) consequences of various forms
of instruction.
5
.
Standards for Judging Theories, Models,
and Results
There is a wide range of results and methods in mathematics education.
A major question thenis the following: How much faith should one have
in any particular result? What constitutes solid reason, what constitutes
“proof beyond a reasonable doubt”? The following list puts forth a set of
criteria that can be used for evaluating models and theories (and more
generally any empirical or theoretical work) in mathematics education:
• Descriptive power
• Explanatory power
• Scope
• Predictive power
• Rigor and specificity
• Falsifiability
• Replicability
• Multiple sources of evidence (“triangulation”)
Descriptive Power
The capacity of a theory to capture “what counts” in ways that seem
faithful to the phenomena being described. Theories of mind, problem
solving, or teaching should include relevant and important aspects of
thinking, problem solving, and teaching respectively. At a very broad
level, fair questions to ask are: Is anything missing? Do the elements of
the
6. theory correspond to things that seem reasonable? For example, say a
problem-solving session, an interview, or a classroom lesson was
videotaped .Would a person who read the analysis and saw the
videotape reasonably be surprised by things that were missing from the
analysis?
Explanatory Power
By explanatory power providing explanations of how and why things
work. It is one thing to say that people will or will not be able to do used
those techniques did poorly on the test, largely because they ran out of
time.
Scope
By scope mean the range of phenomena covered by the theory. A theory
of equations is not very impressive if it deals only with linear equations.
Likewise, a theory of teaching is not very impressive if it covers only
straight lectures!
Predictive Power
The role of prediction is obvious: one test of any theory is whether it can
specify some results in advance of their taking place. Again, it is good to
keep things like the theory of evolution in mind as a model. . About half
of the time they were then able to predict the incorrect answer that the
student would obtain to a new problem before the student worked the
problem! Such fine-grained and consistent predictions on the basis of
something as simple as a diagnostic test are extremely rare of course.
For example, no theory of teaching can predict precisely what a teacher
will do in various circumstances; human behavior is just not that
predictable. However, a theory of teaching can work in ways analogous
to the theory of evolution. It can suggest constraints and even suggest
likely events. Making predictions is a very powerful tool in theory
refinement. When something is claimed to
be impossible and it happens, or when a theory makes repeated claims
that something is very likely and it does not occur, then the theory has
problems! Thus, engaging in such predictions is an important
methodological tool, even when it is understood that precise prediction is
impossible.
6
Rigor and Specificity
7. Constructing a theory or a model involves the specification of a set of
objects and relationships among them. This set of abstract objects and
relationships supposedly corresponds to some set of objects and
relationships in the “real world.
Falsifiability
The need for falsifiability—for making non tautological claims or
predictions whose accuracy can be tested empirically—should be clear
at this point. It
is a concomitant of the discussion in the previous two subsections. A
field makes progress (and guards against tautologies) by putting its ideas
on the line.
Replicability
The issue of replicability is also intimately tied to that of rigor and
specificity. There are two related sets of issues: (1) Will the same thing
happen if the circumstances are repeated? (2) Will others, once
appropriately trained, see the same things in the data? In both cases
answering these questions depends on having well-defined procedures
and
constructs.
Multiple Sources of Evidence (“Triangulation”)
Here we find one of the major differences between mathematics and the
social sciences. In mathematics one compelling line of argument (a
proof)
is enough: validity is established. In education and the social sciences
we are generally in the business of looking for compelling evidence. The
fact is,evidence can be misleading: what we think is general may in fact
be an artifact or a function of circumstances rather than a general
phenomenon.
7
Lessons From Research
Decades of research indicate that students can and should
solve problems before they have mastered procedures or algorithms
traditionally used to solve these problems (National counsil of teachers of
mathematics,2000). If they are given opportunities to do so, their
conceptual understanding and ability to transfer knowledge is increased.
8. Indeed some of the most consistently successful of the reform curricula
have been programs that
Build directly on students strategies
Provide opportunities for both invention and practice.
Have children analyse multiple strategies.
Ask for explanations.
Research evaluations of these programs show that these curricula
facilitate conceptual growth without sacrificing skills and also help
students learn concepts and skills while problem solving.
Reaserch provides several recommendations for meeting the needs of
all students in mathematical education.
Keep expectations reasonable, but not low.
Expectations must be raised because “mathematics can
and must be learned by all students” ( NCTM, 2000), Raising standerds
includes increased emphasis on conducting experiments, authentic
problem solving and project learning.
Patiently help students develop conceptual understanding and skill.
Students who have difficulty in maths may need
additional resources to support and consolidate the underlying concepts
and skill being learned. They benifict from the multiple experiences with
models abstract, numerical manipulations.
8
Build on childrens strengths.
This statements often is little more than a trite
pronouncement. But teachers can reinvigorate it when they make a
conscientious it when they make a conscientious effort to buid on what
children know how to do, relying on children’s own strengths to address
their deficits.
Build on childrens informal strategies
Even severely learning disabled children can
invent quite sophisticated counting strategies. Informal strategies provide
a sterting place for developing both concepts and procedures.
Develop skills in a meaningfull and purp[oseful fashion.
Practice is important, but practice at the
problem solving level is preferred whenever possible. Meaningfull
purposefull practice gives the price to one.
Use manipulate wisely
9. Make sure students explain what they are doing
and link their work with manipulates to underlying concepts and formal
skills.
9
Use technology wisely
Computers with voice recognition or voice
creation software can teachers and peers access to the mathematical
idea and arguments developed by students with facilities.
Make connections
Integrate concept and skill help children link
symbols, verbal description and work with manipulatives.
Adjust instructional formats to individual learning styles or specific
learning needs
It includes modeling, demonstration and feedback ,
guiding and teaching strategies, mnemonic strategies for learning
number combinations and peer mediations
Conclusion
The research in (undergraduate) mathematics education is a very
different enterprise from research in mathematics and that an
understanding of the
differences is essential if one is to appreciate (or better yet, contribute to)
work in the field. Findings are rarely definitive; they are usually
suggestive. Evidence is not on the order of proof, but is cumulative,
moving towards conclusions that can be considered to be beyond a
reasonable doubt. A
scientific approach is possible, but one must take care not to be
scientistic—what counts are not the trappings of science, such as the
experimental method, but the use of careful reasoning and standards of
evidence, employing a wide variety of methods appropriate for the tasks
at hand.It is worth remembering how young mathematics education is as
a field. Mathematicians are used to measuring mathematical lineage in
centuries, if not millennia; in contrast, the lineage of research in
mathematics education (especially undergraduate mathematics
education) is measured in decades. The journal Educational Studies in
Mathematics dates to the 1960s. The first issue of Volume 1 of the
Journal for Research in Mathematics Education was published in
January 1970. The series of volumes Research in Collegiate
Mathematics Education—the first set of volumes devoted solely to
10. mathematics education at the college level—began to appear in 1994. It
is no accident that the vast majority of articles cited by Artigue [1] in her
1999 review of research findings were written in the 1990s; there was
little at the undergraduate level before then! There has been an
extraordinary amount of progress in recent years, but the field is still very
young, and there is a very long way to go. Because of the nature of the
field, it is appropriate to adjust one’s stance toward the work and its
utility. Mathematicians approaching this work should be open to a wide
variety of ideas, understanding that the methods and perspectives to
which they are accustomed do not apply to educational research in
straightforward ways. They should not look for definitive answers but for
ideas they can use. At the same time, all consumers and practitioners of
research in (undergraduate) mathematics education should be healthy
skeptics. In particular, because there are no definitive answers, one
should certainly be wary of anyone who offers them. More generally, the
main goal for the decades to come is to continue building a corpus of
theory and methods that will allow research in mathematics education to
become an
ever more robust basic and applied field.
10
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http://:www.ernweb.com/browse-topic/math-ed
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and K. THOMAS, A framework for research and
curriculum development in undergraduate mathematics
education, Research in Collegiate Mathematics
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eds.), vol. II, Conference Board of the Mathematical
Sciences, Washington, DC, pp. 1–32.
D. P. AUSUBEL, Educational Psychology: A Cognitive
View, Holt-Reinhardt-Winston, New York, 1968.
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Cognitive Science 2 (1978), 155–192.
11