The solution to reduce the number of students in a classroom

Going Green in the Classroom Going Green in the classroom, using technology to reduce waste, help collaborationand help the environment. Teaching is a profession that comes with a lot of stuff. I realized this one year when I had to move from one room to another.

The solution to reduce the number of students in a classroom

Russell Gersten and David J. Chard Abstract We describe the concept of number sense, an analog as important to mathematics learning as phonemic awareness has been to the reading research field.

Understanding the concept of number sense and relevant research from cognitive science can help the research community pull together fragmented pieces of earlier knowledge to yield a much richer, more subtle, and more effective means of improving instructional practice.

More than three decades have passed since Kirk and Bateman proposed that auditory processing was one of the psycholinguistic process deficits underlying specific learning disabilities.

Although subsequent psychometric studies identified the flaws in their conceptualization, our current understanding of the importance of phonological processing and its contribution to reading development suggests that Kirk and Bateman were at least partly accurate in their analysis.

More specifically, important advances have been realized in the prevention e. These advances are primarily the result of the growing knowledge base on phonemic awareness and its importance to the development of strong reading skills.

We believe that there may be an analog as important to mathematics learning as phonemic awareness has been to the development of reading. Our goal in this article is to introduce this analog. To accomplish our goal, we briefly review the concept of phonemic awareness and its crucial role in helping students with learning disabilities to learn to read.

Then, we demonstrate how this concept helps the research community pull together fragmented pieces of earlier knowledge and yield a much richer, more subtle, and more effective means for improving instructional practice than earlier conceptions e.

We demonstrate how the number sense concept can inform and significantly enhance the quality of mathematics interventions for students with learning disabilities, just as the concept of phonemic awareness has informed the field of reading. The number sense concept acts as a lens to reveal reasons for relative successes and failures of past attempts at innovations.

The solution to reduce the number of students in a classroom

In particular, we review the research of Hasselbring, Goin, and Bransford and Pellegrino and Goldman from a contemporary perspective. We conclude with a model of understanding specific learning disabilities adapted from Kolligian and Sternbergand Geary, We demonstrate how this can he a useful framework for conceptualizing interventions.

Our model indicates how the number sense concept provides a sensible middle ground in what is becoming an increasingly heated controversy about how to teach mathematics. In this conceptualization, mathematical learning occurs as students a learn the conventions, language, and logic of a discipline such as mathematics from adults with expertise: We believe that cognitive insights can, and should have a profound impact on how math is taught to special education students and can help radically reform the mundane drill and practice typical of special education mathematics instruction.

In this article, we draw analogies between phonological awareness and number sense. We also draw analogies between earlier research on ways to remediate mathematical disabilities and earlier research on reading disabilities.

The goal here is to provide a brief overview of phonological awareness concepts and number sense before introducing the concept of number sense, rather than to attempt to provide a comprehensive review of either topic. Overview of phonological awareness In the reading field in the s, based on insights gained from cognitive psychologists such as Perfettithe consensus was largely that fluent, virtually automatic decoding was essential for comprehension.

As a consequence, sustained efforts were critical to transform students with learning disabilities into fluent readers. Typically, there were two components: There was, perhaps, an underlying sense that merely teaching phonics was insufficient for helping students with disabilities to learn to read.

Yet, there were some findings that could not be explained by this view. Kavale for example, found that correlations between auditory skills and reading were consistently positive and consistently replicated. Similarly, Gersten and Carnine noted that, in particular, the skill of auditory blending was highly correlated with reading measures.

Adams synthesized the body of research on early reading and popularized the concept of phonemic awareness. Adams noted that measures of phonemic awareness were the best predictors of early reading performance, that is, better than IQ, readiness test scores, or socioeconomic level.

Phonemic awareness is the insight that words are composed of sounds. Phonemic awareness is not always easy for children to obtain. As Williams noted, Phonemes are abstract units, and when one pronounces a word one does not produce a series of discrete phonemes; rather phonemes are folded into one another and are pronounced as a blend: Although most young children have no difficulty segmenting words into syllables, many find it very difficult to segment at the phoneme level.

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Nevertheless, an emerging base of empirical evidence suggests that more intense interventions at the kindergarten level, as well as longitudinal interventions may provide necessary benefit for those children.

Current thinking about special education reading instruction, both remedial and preventive, now invariably notes the importance of explicit instruction in phonemic awareness skills. For example, we have learned from research that explicit training in sound blending is useful to students.

However, students are helped even more if they are provided with instruction not only in how to blend phonemes together, but also in how to "pull apart" or segment words into phonemes Smith et al: The concept of phonemic awareness has helped connect the pieces of the puzzle of reading acquisition.

Phonemic awareness provides greater precision and helps to inform instruction in a way that earlier concepts of phonics instruction, which rarely included instruction in either blending or segmentation, did not.

It is extremely important to note that the findings regarding phonemic awareness and its importance to reading acquisition do not diminish the importance of automaticity of decoding for strong reading comprehension.Should teaching be a popularity contest?

Probably not.

The solution to reduce the number of students in a classroom

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