This Education Dive article provides a brief overview of a new report from Georgia Tech that considers five initiatives to address the higher education needs of students in The author notes other reports and writers who have addressed one or more of these topics.
The second and third schemata are commonly called partitive and quotitive division, respectively, and the problems are to find f 1 and x, respectively, given a and b.
The fourth schema is referred to as the rule of three problems, in which the problem is to find x given a, b, and cwhere x can appear in anyone of the four positions.
In Vergnaud's formulation, multiplication and division problems appear as special cases of direct proportion problems. Ohlsson criticizes these lists because they are not exhaustive and they include things that should not be included.
Ohlsson goes on to criticize his own earlier attempt to address the range of interpretations of the rational number concept, an attempt in which he considered rational numbers from the perspective of a semantic field. The idea is to assign a structure to the field that explains the meanings of concepts in the field and brings out the semantic relationships between them.
In his analysis, Ohlsson began by considering an ordered pair of integers and placing constraints on the domain of referents for these integers. Because each pairing of constraints would lead to a potential interpretation of rational number, it was hoped that this approach would limit and exhaust the possible interpretations.
Since both components of the pair are integers that can be interpreted as quantities or as parameters for operations that is, the number of times it can be repeatedthere would be four potential interpretations of fractions.
While Ohlsson considered this analysis an advancement over previous ones, he found serious weaknesses and attempted yet another approach. In the new approach, he attempted to substantially advance the construct theory of rational numbers; because of this we give a more extensive overview of his analysis.
The development proceeds by considering both a mathematical theory for each of these four constructs and corresponding applications of the mathematical theory.
In the first and third applications, x and y represent a quantity and a parameter, respectively, and in the second and fourth both represent quantities. A difficulty with the first and third applications in terms of their definitions is that the concept of quotient does not seem to be well defined by operands of two different types, quantity and parameter.
Here the fraction application does not seem different from the usual pan-whole notion of fractional part and, as defined, the measure application does not relate to the measure concept of rational number in the sense of Kieren or Behr, et al.
Moreover, as defined, it is very close to the part-whole concept of fractions and is limited to the use of standard units of measure.
These interpretations seem not to add anything new to our understanding of rational numbers because they are redundant with concepts described by earlier analyses or, as with his concept of intensive quantity, they are too limited in scope.
It would appear, then, that five subconstructs of rational number-part-whole, quotient, ratio number, operator, and measure-which have to some extent stood the test of time, still suffice to clarify the meaning of rational number.
A major thrust of this chapter is to apply the concepts of mathematics of quantity to the five subconstructs to provide a deeper semantic understanding of them. This analysis is given in section 2, "Rational Number Construct Theory: Toward a Semantic Analysis," of this chapter.
Questions such as how rational number knowledge is acquired and organized were recently addressed by Kieren and Pirie Resnick addressed mathematical knowledge from a more global perspective with emphasis on intuitive mathematical knowledge.
Their contributions are summarized here. Acquisition of Rational Number Knowledge Kieren presents a theoretical model of mathematical knowledge-building and relates it specifically to rational number knowledge.
One aspect of his theory is the notion of an ideal network of personal rational number knowledge.We would like to show you a description here but the site won’t allow us.
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Preparing a Qualitative Research-Based Dissertation: Lessons Learned Glenn A. Bowen Western Carolina University, Cullowhee, North Carolina In this article, a newly minted Ph.D. shares seven lessons learned during the process of preparing a dissertation based on qualitative research methods.
Link to College of Arts and Letters Programs Anthropology. Undergraduate Courses/link to graduate courses Cultural Difference in a Globalized Society (ANT .
In this article, a newly minted Ph.D. shares seven lessons learned during the process of preparing a dissertation based on qualitative research methods.
While most of the lessons may be applicable to any kind of research, the writer focuses on the special challenges of employing a qualitative methodology.
Preparing a Qualitative Research-Based Dissertation: Lessons Abstract. Abstract. In this article, a newly minted Ph.D. shares seven lessons learned during the process of preparing a dissertation based on qualitative research methods.