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4Teaching Algebraic Expressions in a Meaningful Way
"... QUITE OFTEN, algebraic expressions are introduced by stating that theyinvolve variables and that "a variable is a letter that stands for one or more numbers. " Such formal definitions may be adequate for mathematics teachers but they often fail to provide meaning for the beginning student. ..."
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QUITE OFTEN, algebraic expressions are introduced by stating that theyinvolve variables and that "a variable is a letter that stands for one or more numbers. " Such formal definitions may be adequate for mathematics teachers but they often fail to provide meaning for the beginning student. The construction of meaning for algebraic expressions by novices necessitates finding in their background a cognitive basis on which to build. Helping students create meaning on the basis of their existing knowledge has been our prime objective. To achieve it, we designed an innovative teaching outline. The teaching outline introduces algebraic expressions as answers to problems. The problems chosen involve previously learned concepts such as the number of dots in a rectangular array, the length of a line segment, and the area of a rectangle. The advantage of these types of problems is that they have an easy visual representation. The use of letters is introduced cautiously by first letting them represent hidden quantities and only afterwards using them to stand for specific unknown quantities. This geometric approach is used systematically to help students construct meaning for expressions involving one unknown and one operation to expressions with several unknowns and multiple operations. Not only are the students learning to use algebraic expressions as answers to problems, but they are also encouraged to reverse the process—that is, they are asked to generate problems corresponding to given expressions. Our teaching outline, which covers three lessons, has been tested by teaching six students individually. This teaching experiment was intended to determine the accessibility of our new presentation as well as to uncover any new cognitive problems we may have inadvertently introduced. Individual
Connecting the Dots of the Academic Triangle: Combining Teaching, Research, and Service in Meaningful Ways
"... This paper examines the opportunities of combining teaching, research, and service and highlights the inherent challenges of such an approach. By offering evidence on how professors at small liberal arts colleges can combine their research, teaching, and service responsibilities in ways that enrich ..."
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This paper examines the opportunities of combining teaching, research, and service and highlights the inherent challenges of such an approach. By offering evidence on how professors at small liberal arts colleges can combine their research, teaching, and service responsibilities in ways that enrich
Writing Autobiographies: A Meaningful Way to Sensitize Trainee Teachers
"... This article discusses the final results from a research work which aimed to identify the pedagogical processes that emerge from the autobiographies that modern languages trainee teachers at the University of Caldas write. These autobiographies become a starting point to develop their teaching pract ..."
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to childhood memories, teacher`s influence, and affective factors. The authors conclude that auto biographies become a meaningful instrument to raise trainees awareness about their own performance as future teachers.
Development Outcomes: The Search for a Meaningful Way to Inform Institutional Practice and Policy
"... Using a typological schema derived from freshman survey data and other empirical measures, this study examines the link between students ’ traits upon entry to college and their college academic performance and skill development in various areas as measured at the exit point. The findings indicate t ..."
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and student interests and aptitudes on the other: How well do various aspects of our programs meet the distinctive needs of diverse students? Whom do we serve well, and whom less well, and in what ways?
Sequence Logos: A New Way to Display Consensus Sequences
 Nucleic Acids Res
, 1990
"... INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. ..."
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Cited by 638 (27 self)
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INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. National Cancer Institute, Frederick Cancer Research and Development Center, Laboratory of Mathematical Biology, P. O. Box B, Frederick, MD 21701. Internet addresses: toms@ncifcrf.gov and stephens@ncifcrf.gov. y corresponding author 1 2. The order of predominance of the residues at every position. 3. The relative frequencies of every residue at every position. 4. The amount of information present at every position in the sequence, measured in bits. 5. An initiation point, cut point, or other significant location (if appropriate) . Any aligned set of DNA, RNA or protein sequences can be represented using this technique. CREATION OF BINDING S
When Is "Nearest Neighbor" Meaningful?
 In Int. Conf. on Database Theory
, 1999
"... . We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance ..."
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Cited by 402 (1 self)
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meaningful; we illustrate this point by identifying some highdimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate highdimensional indexing techniques is flawed, and should
The SPLASH2 programs: Characterization and methodological considerations
 INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE
, 1995
"... The SPLASH2 suite of parallel applications has recently been released to facilitate the study of centralized and distributed sharedaddressspace multiprocessors. In this context, this paper has two goals. One is to quantitatively characterize the SPLASH2 programs in terms of fundamental propertie ..."
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Cited by 1399 (12 self)
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scale with problem size and the number of processors. The other, related goal is methodological: to assist people who will use the programs in architectural evaluations to prune the space of application and machine parameters in an informed and meaningful way. For example, by characterizing the working
Labeling Images with a Computer Game
, 2004
"... We introduce a new interactive system: a game that is fun and can be used to create valuable output. When people play the game they help determine the contents of images by providing meaningful labels for them. If the game is played as much as popular online games, we estimate that most images on ..."
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Cited by 763 (11 self)
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We introduce a new interactive system: a game that is fun and can be used to create valuable output. When people play the game they help determine the contents of images by providing meaningful labels for them. If the game is played as much as popular online games, we estimate that most images
Distance Metric Learning, With Application To Clustering With SideInformation
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 15
, 2003
"... Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as Kmeans initially fails to find one that is meaningful to a user, the only recourse may be for the us ..."
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Cited by 799 (14 self)
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Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as Kmeans initially fails to find one that is meaningful to a user, the only recourse may
LOF: Identifying DensityBased Local Outliers
 PROCEEDINGS OF THE 2000 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 2000
"... For many KDD applications, such as detecting criminal activities in Ecommerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for m ..."
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Cited by 499 (14 self)
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that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This degree is called the local outlier factor (LOF) of an object. It is local in that the degree depends on how isolated the object is with respect to the surrounding neighborhood. We give a detailed formal
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