The importance of counting in early number development

The importance of counting in early number development Counting is the action of finding the number of elements of a finite set of objects by continually increasing a counter by a unit for every element in the set, in some order. Counting is used by children to demonstrate knowledge of the number names and number system. Archaeological evidence suggests that humans have been counting for at least 50,000 years, and in ancient cultures counting was used to keep track of early economic data. Learning to count is considered a very important educational and developmental milestone in most cultures of the world. Learning to count is a childs first step into mathematics, and constitutes the most fundamental idea of mathematics. The present essay will attempt to illustrate the importance of counting for the development of number-related skills from an early age (Eves, 1990). The use of numbers is a skill developed from an early age. In mathematics, there is the term number sense, a relatively new construct that refers to a well organized conceptual framework of number information that enables a person to understand numbers and numbers relationships, and to solve mathematical problems that are not bound by traditional algorithms. Number sense includes some component skills such as number meaning, number relationships, number magnitude, operations involving numbers and referents for numbers and quantities. These skills contribute to general intuitions about numbers and pave the way for more advanced skills (Bobis, 1996). Studies have shown that this number sense begins at a very early age. Even before they are able to count properly, children of around two years of age can indentify one, two or three objects. Theorists as early as Piaget noticed this ability to instantaneously recognize the number of objects in a small group. Piaget called in subitizing. Later, as the childs mental powers develop, around the age of four, groups of up to four objects can be recognized without counting. Adults have and continue to use the same ability of subitizing, although even they cannot use it beyond a maximum of five objects, unless the objects are arranged in a particular way or practice that aids memorization. Subitizing refers to the minds ability to form stable mental images of patterns and then associate them with a fixed number. In a familiar arrangement, such as six dots arranged into two rows of three (such as in dice or playing cards) six can be instantly recognized when presented this way (Gelman Galli stel, 1978). Yet, with the exception of familiar arrangements such as the examples above, when people are presented with groups numbering more than five objects, they must resort to other mental strategies. Groups can be broken up into sub-groups to facilitate the process. A group of six objects, for example, can be broken up into two sub-groups of three, which are recognized instantly and then unconsciously combined into six, the number of the bigger group. This strategy does not use any actual counting, but a part-part-whole relationship which is assisted by rapid mental addition. Therefore, there is an understanding that a number can be composed of smaller parts, along with the knowledge of how these parts add up. This kind of thinking has already begun by the time children begin school, around six or seven years of age. It should be nurtured and allowed to develop, as it is thinking of this sort that lays the foundation for understanding operations and developing mental calculation strategies (Bobis, 1996). Skills such as the ability to perceive subgroups, need to be developed alongside counting in order to provide a firm foundation for number sense. Although there is no denying that counting is crucial for the development of numbers, these other skills play an important part as well. Skills and alternative strategies for counting can be developed more effectively by the use of teaching strategies. Children can be shown flashcards with objects in different arrangements (sometimes six in a cluster of four and a pair, or sometimes in three pairs) as these different arrangements will tend to prompt different strategies. Furthermore, if the flashcards are shown for only a few seconds, the mind is challenged to act faster and develop strategies other than counting to make the necessary calculations (Way, 1996). Yet, despite the importance of alternative strategies, a considerable amount of evidence supports the idea that counting is the most important mechanism used by young children in estimating numbers of all sizes, perhaps only with the exception of 1 or 2. Subitizing and grouping, as described above, are used as mediators for the ability to understand small numbers, but it seems that even these skills are developed after children have learned to estimate numbers by counting. Moreover, counting is the basic mechanism used when children learn to add and subtract. At least the initial stages of adding and subtracting, before the child masters the processes, involve counting. For example adding 8 and 3 might be achieved by first counting to 8 and then proceeding to 11 (Gelman Gallistel, 1978). A surge of interest in counting was triggered by Gelman and Gallistels (1978) book, which claimed that preschoolers learning to count was inexplicable unless they had innate predispositions to learn counting. So, is counting innate or not? Butterworth et al. (2005) believe that the human ability to count is innate and is not reliant on numbers or language to express it. They based their study on the fact that the children of Australian Aborigines were able to count even though their languages do not have words for numbers. An extreme form of linguistic determinism has been developed recently, which claims that counting words are needed for children to develop concepts of numbers above three. In contrast, the teams study of aboriginal children suggests that humans have an innate system for recognizing and representing numerosities, the number of objects in a set, and that the lack of a number vocabulary does not prevent them from doing numerical tasks that do not require number words. On the other hand, other cross-cultural studies support the opposite conclusion: counting is not innate. Although it seems to come naturally, counting may be cultural rather than innate. Many hunter-gatherer societies such as the Australian Aborigines or various different peoples in South America have no words in their languages for counting or at best only words for up to the number five. This could be because those societies do not have the culturally supported contexts where exact numbers need to be encoded. To investigate the issue, one study (Hyde et al., in press) examined a population of deaf Nicaraguans who do not speak Spanish and never had the opportunity to learn conventional sign language. These people live in a numerate culture that uses exact counting and large numbers, but because they were never educated in it, they lacked conventional language for themselves. Still, these individuals did not spontaneously develop representations of numbers over three. They use gestur es to communicate about numbers but do not consistently produce gestures that accurately represent the cardinal values of sets containing more than three items. This is in contrast to native speakers of the American Sign Language, who, raised and immersed in a language that uses counting, were just as good as speakers of Spanish and English at counting. Therefore, deafness was not the factor that made the difference. The overall point, though, is that whether innate or not, there can be little doubt that counting is crucial for early number development. People belonging to those cultures without words for numbers larger than five can subitize up to a point but are handicapped when the need arises to deal with larger quantities (Butterworth et al., 2008). Activities that involve counting have been shown to to be very effective for helping young children understand the concept of number. Young children and prepared to engage in and benefit from preschool exposure to counting before they are taught arithmetic in an organized manner. Children form many necessary language associations at a very early age, and even at the early age of three, certain counting principles are already in place. Children can make effective use of guided experiences that help them build developmentally appropriate pre-formal mathematics understandings. Counting can be used to reinforce and extend childrens natural learning. The highly influential book of Gelman and Gallistel (1978) proposes a set of counting principles, and counting exercises based on these principles contribute greatly to childrens pre-formal understanding and progress toward formal understanding. Gelman and Gallistels principles do not refute Piagets classic, ground-breaking findings on the processes of development, but rather extend them. Some of these principles are attainable by age three and all of them by age five. Many counting exercises that emphasize these principles also employ the logical activities recommended by Piaget, such as classification, seriation, matching and comparison (Aubrey, 1993). The one-to-one principle shows that, when counting, only one number word in assigned to each object. This refers to both the verbal and mental act of counting. The stable order principle shows that, when counting, number words are always assigned in the same order. Although the tie of number to language is important, exercises that employ stable order are most useful when they simultaneously employ the previous, one-to-one principle. The cardinal principle shows that the number of objects in the set is the last number word counted. The cardinal principle is similar to the co ncept of cardinality, of which children gain implicit understanding long before they understand numerical quantity. The order irrelevance principle shows that when counting the number of objects in a set, the order in which they are counted is not important, but rather simply that all objects are counted. In other words, a set of objects may be properly counted by starting with any object and going in any order. Finally, the abstraction principle shows that when counting any unique set of objects, all the above principles apply as well as they do to any other unique set. Researchers as early as Beckmann (1924) analyzed the way in which children arrived at an accurate estimate of the number of items, in order to establish the importance of counting. Depending on their behaviour during a counting task and their explanation of how they reached the answer, Bechmann divided the children into counters or subitizers. In general, it was found that the younger the child, the greater the tendency to count for all numbers, while the larger the number, the greater the tendency for all children to count. These results together showed that children estimate a number by counting before they can subitize the same number. Similar effects were observed by Brownwell (1928) and McLaughlin (1935). By asking children to identify the number of elements in arrays of 3 to 10 objects, Brownwell noticed that young children almost always counted and rarely took advantage of the patterns in the display. McLaughlin similarly observed that 3- to 6-year-olds typically counted in or der to determine the number of objects in an array, even when the number of objects was small. As the number of items a child could count increased, so did the ability to estimate numbers. Gelman (1972) notes that when the performance of children in experiments where they have counted is compared with that in experiments where they did not count, the resulting discrepancy adds support to the hypothesis that young children initially estimate by counting. Buckingham and MacLatchys (1930) study on estimation showed children a random throw of objects, and the subjects were not prevented from counting. In contrast, in Douglas (1925) study where three similar number tasks were used, children were discouraged from counting. If the groups of 6-year-olds in these and other studies that accordingly encourage or discourage counting are compared, a large discrepancy can be observed. In the first case, the percentage of children who accurately estimated non-linear arrays of around 10 items on at least one trial varied from 54% to 70%, while in the latter case only 8% of the children successfully estimated the numerosity of 10-element arrays. Although the studies differed in a varie ty of ways, the similarity of the tasks, the selection of the same age group and the use or absence of counting suggest that at least some part of this impressively large discrepancy in successful estimation scores can be attributed to the presence of absence of counting. Overall, the role of counting on early number development is not entirely clear and there are many different, often conflicting, opinions on how these processes occur. The most striking example is whether counting is innate or not, with some researchers claiming that humans are born with the ability to see the world numerically in the same way that they are born with the ability to see the world in colour, and others insisting that it is a cultural, not an innate ability which will not develop outside of a cultural setting that reinforces it. Different opinions also exist in the matter of the importance of counting and the importance of other skills such as subitizing. Subitizing and other similar skills that assist in estimations are crucial, but they only seem to be so when used together with counting. Counting develops first and produces much better results in estimates and numerical tasks in general. It is the first mechanism used in estimation, the most effective one, and also e qually crucial when developing other, more complicated numerical skills such as adding and subtracting. It truly seems to be the basis of early number development.

Creating a Robot to Make Toast with Lego Mindstorm :: Robotics

Toast-O-Bot Abstract: A robot that uses a toaster to make toast, butters it with spray butter and makes a CD player play the song "Yeah Toast" would be both useful and entertaining. Using the Lego Mindstorms and MAC NQC to program them such a robot could be possible. Using the suggested design and programs for the Roboarm in the Definitive Guide to Lego Mindstorms as a starting point I built the robot and modified it for the toaster. During testing of the motors, it was discovered that Toast-O-Bot is not strong enough to press the button on the toaster. Even after toaster modification it was still unable to press the button. The Toast-O-Bot only moves the bread from location to location, so a user is required to press the button on the toaster. Background/Purpose: People with disabilities use many devices today to ease their lives and help with every day tasks. This may include simplified processes, service animals or small machines or robots that perform small tasks for any user; young, old, disabled, or able bodied. There are devices to change TV channels, open doors, turn lights on and off, and now a robot to make toast for them. Ever since the discovery of toast man has looked for a way to make toasting easier, beginning with the primitive toaster, and progressing to the modern pop toaster. The primitive toaster was made of iron and placed in hot coals. In 1909, G.E. introduced and patented the electric toaster. The pop toaster, introduced in 1919, has been modified by many people to develop the modern pop toaster. Toaster ovens, though not as common, are also used to make toast. The hope is to further ease the work that goes into the making of toast by creating a robot that can use a toaster to make toast. The robot will have a claw arm to pick up the bread and place it in the toaster. It will also have an arm to press the button on the toaster and on the spray butter. There will be a touch sensor at the bottom of the button track and when it equals zero the robot will remove the toast to butter it. After buttering the toast, it will then place it on a plate for the user to enjoy. It may also press play on something to play the 'Yeah Toast' song from the Bob and Tom Show. Materials: à ½ LEGO pieces need for the Roboarm from page 313 in the Definitive Guide to Lego Mindstorms à ½ Various decorative things à ½ A way to raise the base to the height of the toaster

Cost Accounting Is A Process That Aims To Capture A Companys Production Accounting Essay

Cost accounting is a procedure that aims to capture a companys production, to measure the input cost of each production. Cost accounting is frequently used in the company to assist the direction with determination devising. Cost comptrollers are a good as a tool for direction in budgeting and in puting up cost control which improves the net borders of the company in future. Cost comptrollers in traditional fabrication companies would normally do usage of machines that automate certain operations. Production activity is measured in machine hours. Traditional fabrication is besides labour intensive where there are high labor costs and low operating expenses. Traditional fabrication allocates the companies ‘ indirect cost to the points produced in order of their volume, figure of units produced, direct labor hours and machine hours. The usage of machine hours implies that machine hours are cause footing of the mill operating expense, this deduction is done when merely machine hour s are used to apportion the fabricating operating expense to merchandises. Cost comptrollers in traditional fabrication companies use a individual caput pool, this method of apportioning indirect costs normally consequences in the wrong cost of informations. Merchandises with high volumes have high labor costs likewise merchandises with lower volumes would normally be understated and be ignored. Traditional fabrication companies cost comptrollers are needed to assist in the managing of costs which is normally non an easy undertaking to make, but the cost comptrollers have found a manner of pull offing them. Modern fabrication was developed to work out the complexnesss of running a immense concern. Modern fabrication companies make use computing machines and robotics ; they control the whole production/manufacturing procedure. Cost comptrollers would normally necessitate modern fabrication companies because they have an built-in flexibleness to supply particular studies and assist direction with determination doing sing cost activities undertaken. Modern fabrication houses are normally non forced to stay by the fiscal coverage demands. Modern fabrication companies would normally delegate costs to activities and merchandises based on how the costs and resources are consumed by the procedure or merchandise. Cost comptrollers are needed in the modern fabrication companies because it gives them a clearer image of cost of procedure and the profitableness of clients and merchandises. They are besides needed because it would assist them with budgeting techniques for the truth of fiscal prognosi s and besides increasing the comprehension of the directors. Cost comptrollers are needed in the modern fabrication companies because modern fabrication houses use computing machines and robotics this helps in the quick and accurate production of fiscal programs to assist the comptrollers in wise determination devising. Productivity is truly improved in modern fabrication companies because there is a wider set of related component here, which is computing machines and robotics. Absorption costing is no longer for modern auto manufacturer such as BMW discuss. Your reply should include suggestions of other bing methods that are more relevant for a modern auto manufacturer and supply your accounts. Absorption costing is absorbing all the fabrication through units produced. It absorbs all the direct labor, direct stuffs, with all the variable and fixed costs. It is By and large Accepted Accounting Principles which means it is used for external coverage. Absorption costing because it absorbs all the cost is non suited for modern fabrication houses, because with this bing pricing is lesser extent than it appears to be in the instance. Cost is calculated to make up one's mind how much net income you have made, and so the monetary value while be set. Because absorbs all the costs, that establishes the fact that it does non recognize the importance fixed costs. This makes it difficult to distinguish between fixed and variable costs. The variableness of net incomes besides causes confusion because the gross revenues and stock alteration. Absorption bing recognises the importance of fixed costs in production by including them in the production procedure. It is used to fix fiscal histories. When production remains changeless while gross revenues rise and autumn irregularly in figure this method will demo a less fluctuation in net net income. Absorption costing is non suited for the modern auto makers like BMW because it is non so utile to t he direction to do wise determinations, to be after and command that is it does non assist directors to develop the company ‘s mission and aims to be the decisive factor in carry throughing them and non set uping public presentation criterions, mensurating and describing existent public presentation and comparing them to take a disciplinary action as necessary. This truly shows that it is non suited fabricating companies like BMW because they need to utilize the cost information for good determination devising intents and budgeting. But instead modern fabrication houses like BMW need to utilize Activity Based Costing because is the method of bing that assigns costs to their activities based on the resources instead than merchandises or services. Other costs and resources are equally distributed to the merchandises and services they use. This method does non extinguish any costs ; it gives more information and takes into history how costs are consumed. This method is suited for BMW because BMW is involved process betterment and reduction costs. Activity Based Costing assigns all the single activities involved in the fabrication procedure are accurately costed, that is it makes seeable waste and non value added. Therefore doing it easier to place the cost of each procedure. It uses unit cost instead entire cost. It facilitates benchmarking which means there is a standard mention against which things can be compared and assessed. It provides a better apprehension of operating expenses and it is easy understood by everyone because since companies like BMW discloses their fiscal studies to the populace they can understand why things are the manner they are. Activity Based Costing helps with future merchandise planning because for illustration all the activities associated with BMW can be accurately determined before it is launched. This can besides assist to find the monetary value and other outgos. Question 3 Cost?Material X & A ; Y working 1 4,000 Material which can be used in another machine 6,000 Labour – Department A ( working 2 ) -Department B ( working 3 ) 12,800 3,600 Sale of machine 5,000 Alteration work 2,000 Entire 33,400 Entire = ? 33,400 + ?125, 000 = ? 158, 400 Working 1 5000 – 1000 = 4000 Working 2 Department A 200 ten 2 ten 4 ten 8 = ?12,800 Working3 Department B 150 ten 4 ten 6 = ?3,600 Working 4 = ? 33, 400 = 125, 000 = ? 158, 400 ten 10 % = ? 174, 240 The minimal monetary value that should be quoted to the new purchaser is ?174, 240 ( working 4 ) . This is because this monetary value includes all the alteration work costs. MM should accept the offer made by the new purchaser because it more than the sum willing to be paid by the first purchaser. MM should besides disregard the ?2000 sedimentation made by the original purchaser because it is a historical cost that is it is a cost that has already occurred therefore doing it an irrelevant cost. I would besides advice MM to go on with alterations asked for by the new purchaser as would convey him more net income than of the original purchaser. The net incomes made would besides assist him to cover the costs he incurred when doing the alterations. Cost?Material X & A ; Y working 1 4,000 Material which can be used in another machine 6,000 Labour – Department A ( working 2 ) -Department B ( working 3 ) 12,800 1,500 Sale of machine 5,000 Alteration work 2,000 Entire 31, 300 Working 1 5000 – 1000 = 4000 Working 2 Department A Mach Dept B = ?150 x 5 tens 2 = ?1, 500 Working3 Department B 150 ten 4 ten 6 = ?3,600

Is Addiction to Pornography a Brain Disease - 1027 Words

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