Let P be a set (called points), Q be a set (called queries) and a function f : P ×Q → [0, ∞) (called cost). For an error parameter > 0, a set S ⊆ P with a weight function w : P → [0, ∞) is an ε-coreset if s∈S w(s)f (s, q) approximates p∈P f (p, q) up to a multiplicative factor of 1 ± ε for every given query q ∈ Q. Coresets are used to solve fundamental problems in machine learning of streaming and distributed data.We construct coresets for the k-means clustering of n input points, both in an arbitrary metric space and d-dimensional Euclidean space. For Euclidean space, we present the first coreset whose size is simultaneously independent of both d and n. In particular, this is the first coreset of size o(n) for a stream of n sparse points in a d ≥ n dimensional space (e.g. adjacency matrices of graphs). We also provide the first generalizations of such coresets for handling outliers. For arbitrary metric spaces, we improve the dependence on k to k log k and present a matching lower bound.For M -estimator clustering (special cases include the well-known k-median and k-means clustering), we introduce a new technique for converting an offline coreset construction to the streaming setting. Our method yields streaming coreset algorithms requiring the storage of O(S + k log n) points, where S is the size of the offline coreset. In comparison, the previous state-of-the-art was the merge-and-reduce technique that required O(S log 2a+1 n) points, where a is the exponent in the offline construction's dependence on −1 . For example, combining our offline and streaming results, we produce a streaming metric k-means coreset algorithm using O( −2 k log k log n) points of storage. The previous state-of-the-art required O( −4 k log k log 6 n) points.

A review of research on deaf students in higher education reveals a significant body of knowledge about the barriers these students face in gaining access to information in the classroom. Much less is known about the potential solutions to these problems. In addition, there is a dearth of research on the effectiveness of such support services as interpreting, note taking, real-time captioning, and tutoring, particularly with regard to their impact on academic achievement. This article summarizes relevant research and suggests directions for educational researchers interested in enhancing academic success and the retention of deaf students in higher education programs.

One hundred and thirty-three mathematics teachers of deaf students from grades 6-12 responded to a survey on mathematics word problem-solving practices. Half the respondents were teachers from center schools and the other half from mainstream programs. The latter group represented both integrated and self-contained classes. The findings clearly show that regardless of instructional setting, deaf students are not being sufficiently engaged in cognitively challenging word problem situations. Overall, teachers were found to focus more on practice exercises than on true problem-solving situations. They also emphasize problem features, possibly related to concerns about language and reading skills of their students, rather than analytical and thinking strategies. Consistent with these emphases, teachers gave more instructional attention to concrete visualizing strategies than to analytical strategies. Based on the results of this study, it appears that in two of the three types of educational settings, the majority of instructors teaching mathematics and word problem solving to deaf students lack adequate preparation and certification in mathematics to teach these skills. The responses of the certified mathematics teachers support the notion that preparation and certification in mathematics makes a difference in the kinds of word problem-solving challenges provided to deaf students.

Six learning style dimensions of the Grasha-Riechmann Student Learning Style Scales (GRSLSS) were examined in this study with 100 deaf college students. In addition, six corresponding scales of teaching emphases were administered to the 16 instructors of these students. Student mean scores were higher for the dependent, participative, collaborative, and independent dimensions than for the competitive and avoidant styles. The participative learning style correlated significantly with course achievement and course interest, which suggests that an emphasis on active learning may be desirable. For instructors, as with students, the mean scores for teaching emphases were found to be higher for the collaborative, dependent, participative, and independent dimensions. the similar patterns of results for students and teachers suggest a correspondence between the learning styles and the teaching emphases.

We designed and administered rating and ranking instruments to examine the perceptions about teaching characteristics held by administrators, academic department chairpersons responsible for evaluating teaching, instructional faculty, and deaf college students. The differences in perceptions found between supervisors and teachers about characteristics of effective teaching indicate a need for ongoing dialogue. In addition, teachers and deaf college students were found to differ in their views of the importance of certain characteristics, and we suggest teachers discuss these perceptions with students. We also recommend additional research on particular characteristics of effective teaching.