Mathematics in the Primary School

Mathematics in the Primary School Innumerate school children cost the taxpayer up to  £2.4bn a year. In 2007, Sir Peter Williams the then chair of the Advisory Committee on Mathematics Education (ACME), was commissioned to consider and make his recommendations in response to the teaching of mathematics in early years settings and primary schools, with a view to assessing and improving upon the current practices of mathematics teaching in early years settings (EYS) and primary schools (Adonis 2007). By examining the available evidence, drawing from the best practice nationally and internationally and by working closely with the teaching profession, the Williams final report was published in June 2008. By means of 10 recommendations the report identifies methods by which children in primary schools and early years settings can acquire a greater understanding of mathematics, and a greater appreciation of its importantance with relation to a successful progression through life during and after their school career is over. Through a high-quality curriculum and excellent teaching (Williams, 2008, p61), children should have confidence and feel comfortable with the concept of Mathematics within their day to day lives. In the following, I will explore the implications of the ten recommendations outlined in the Williams Report and will conclude with some reflection on the value of the report and the likely impact it will have on me as a trainee teacher. Recommendation 1 Considers the entry requirements necessary for Initial Teacher Training (ITT). GCSE Grade C mathematics continues to be the mandatory minimum requirement level. However the report argues that grade B in GCSE maths is desirable with the long-term ambition of the government initiative the Training and Development Agency for Schools(TDA), being for all Qualified Teacher Status (QTS) graduates to have reached Masters-level accreditation. However, this is currently deemed inadvisable given the possible risk of falling enrolment of trainee teachers A higher priority is given to teaching experience through teaching placements to increase the students pedagogical knowledge, Williams (2008, p7) states that, a combination of deep subject knowledge and pedagogical skill is required to promote effective learning, a view supported by the research body Mathematical Knowledge in Teaching (2007/2008). The evidence of good grounding in these two fundamental attributes shows; taken together they constitute a necessary condition to progress learning for all children up to the end of Key Stage 2, which prepares them well for Key Stage 3 ((Williams, 2008, p10). The only currently acceptable route to raising mathematical understanding is through properly funded and rewarded continuing professional development (ibid p 12) Q14, Q15, Q19, Q25a,b,c,d Recommendation 2 Local Authorities (LAs) are to continue to up-skill and increase the numbers of their Mathematic Consultants. A continued extensive budget is to be set aside by the Government for local LAs to implement this following the recommendations made by the Primary National Strategy (PNS) (via the National Numeracy Strategy (NNS)), and in partnership with the National Centre for Excellence in the Teaching of Mathematics (NCETM). This funding to be used to develop and track refresher Continued Professional Development (CPD) courses for all LA consultants, evidence being that since the introduction of the NNS, a transformation in the way mathematics is taught can be strongly correlated with the increase in the attainment levels of primary school children (ibid p 16). Q14, Q15, Q18, Q19, Q20, Q25a,b,c,d Recommendation 3 Every school should have at least one mathematics specialist present (or have access to one), whose initial objective is to raise standards and narrow attainment gaps. By utilising the highly-trained (circa) 400 LA Mathematic Consultants to their fullest, a phased proposal is given to have a Mathematical Specialist present in every school which will re-enforce the importance of mathematics within schools and enhance and allow flexibility for CPD provisions available to all teaching and support staff. Small and rural schools benefitting from pooled resources wherever possible. Many of these specialists could be sourced from Newly Qualified Teachers (NQTs) trained to a higher mathematical level through their ITT providers, and all specialists to be monitored by their respective head teacher. Q14, Q15, Q19, Q20, Q25a,b,c,d Recommendation 4 The Department for Children, Schools and Families (DCSF) is to commission a set of materials which will help early years practitioners understand the effect of childrens development as shown through their mathematical mark-making. The resulting report supports the introduction of childrens mathematical graphics (Worthington, M/ Carruthers, E, 2003), at the Early Years Foundation Stage (EYFS). The EYFS adheres to the principles of the central importance of creativity and critical thinking in early learning and development (Mark Making Matters, 2008, p2). By giving practitioners the tools to support and challenge a childs thought process through encouragement and understanding of the young childs mark-making, along-side open ended discussion (sustained shared thinking (Williams, 2008, p34)), the children will become confident and competent communicators, both orally and on paper, in all six areas of learning and development. (Mark Making Matters, 2008, p2) In relationship to mathematics, by encouraging a child to mark-make from a very early age, when children realise that marks can be used symbolically to carry meaning [] they begin to make marks as tools to make their thinking visible (ibid p3). Through drawing the child may develop their concepts in relationship to problem solving, reasoning and numeracy. The importance of the Early Years Practitioners taking the time to observe, listen and analyse childrens mark making in order to understand, praise and enrich the childs achievements (ibid p3), is affirmed. However, I must agree with the importance of a young childs mathematical understanding being developed through imaginative play and effective mathematical learning for children in this age group needs to be predominantly social in nature (Williams, 2008, p36). Q15, Q18, Q19, Q20 Recommendation 5 The forthcoming review of the EYSF in 2010 is to consider the inclusion of time and capacity which Williams feel were omitted when the statutory early learning goals set out in the Statutory Framework for EYFS: Learning and Development Requirements (DCSF 2006) were first developed. By using these two extra concepts along with those already required i.e., shape, space, measures along with the use of correct mathematical language, it would enable the child to apply their mathematical knowledge in practical and active ways (Williams, 2008, p36), whilst also enhancing the childs understanding of problem solving. The responsibilities of effective pedagogy for this remit falling to local authorities, leaders, managers and head-teachers. Q14, Q15, Q19, Q20, Q25a,b,c,d Recommendation 6 The DCSF is to continue to increase the amount of graduate practitioners going into Early Years Settings (EYS). The Childrens Workforce Development Council (CWDC) (2010), states High quality early years provision can have a significant impact on childrens development, performance at school and their future life chances (CWDC, 2010, Areas of Work- Early Years) and the early years workforce must be well qualified. (ibid) With reference to the Effective Provision of Pre-School Education (EPPE, 2004), the Millennium Cohort Study (MCS, 2005) and the evaluation of the Neighbourhood Nursery Initiative (NNI, 2000), it recognises the importance of having a good proportion of trained teachers on the staff. The recommendation being for one graduate early years professional per setting by 2010 and with provision for two graduates per setting in disadvantaged areas. A member of staff having Qualified Teacher Status (QTS) and a Graduate Early Years Practitioner who has a specialism in working with early years children could have the most benefit to most childrens development and learning. Standards could also be raised with additional funding given to implementing CPD within the Early Years Workforce where mathematics is given essential priority. It should however be noted that EYFS provisions are currently very erratic throughout the UK. Q14, Q15, Q18, Q19, Q20, Q25a,b,c,d Recommendation 7 Engaging the full understanding and commitment of participating children and their parents/carers before the onset of intervention, paying special attention to the integration of intervention in the class room and in a home-school partnership through official home-learning activities. Where research is undertaken, it is proven that the inclusion and understanding of parents/carers before the onset of intervention is paramount in guaranteeing programme success, and parents/carers could support their childs learning progress through official home-learning activities. Equally, children who understand exactly the nature of the programme show genuine delight in their progress and the importance of this factor should not be under estimated for a successful programme (Williams, 2008, p55). In terms of the integration of intervention, the DCSF National Strategy Standards (PNS) (1998) cites; Intervention is not just about additional out-of-class provision. It also includes reviewing what happens in class to make sure it is appropriately tailored to the needs of the children. Q14, Q15, Q18, Q19, Q20 Recommendation 8 The Wave 3 Intervention programme from The Every Child Counts (2008) initiative; a partnership between government, businesses and the charity Every Child a Chance (2007) aims to enhance achievement for approximately 5%-10% of children nationally who are failing to master the basics of numeracy (Adonis, 2007). Adonis (2007) states; there is no single cause of under-attainment and therefore no single answer'(ibid) It is best to summarise the implications, logistics and recommendations of wave 3 intervention in Year 2 as follows:- Intervention should be led by a qualified teacher on a 1: 1 teacher pupil ratio. The benefits of working in pairs or small groups should also be explored. The childs class teacher should be given responsibility to decide whether intervention is necessary. Investigation into of the efficacy of using video tapes for assessment and training should be undertaken. Diagnostic tools should be developed to aid teachers with assessment before intervention and monitor progress after leaving the programme, using for example, Assessing Pupils Progress (APP) and the Early Years Foundation Stage Profile (EYFSP). Intervention should ideally last for one term and be completed by the end of Key Stage 1. Where it is deemed that a child is in need of intervention for both literacy and mathematics, it is imperative that mathematics be given equal standing to literacy. A wide range of (potentially costly) multi-sensory resources should be made available, for example, Numicom and the interactive whiteboard, to enable the teacher and child to select the appropriate aid to their specific issue. CCD programmes should be developed for the teacher as intervention specialist and for LA intervention specialists. Currently there is only a small cohort of intervention specialists available. Combining the roles of intervention specialist and mathematics specialist should be considered through the pooling of resources wherever possible to limit cost implications. Teaching Assistants could be further trained to lead less intensive wave 2 and 3 interventions. A longitudinal study is to be carried out over the next 10-15 years to assess the success of the programme. Q14, Q15, Q18, Q19, Q20, Q25a,b,c,d Recommendation 9 and 10 Refer to the importance of continued building on the currently solid curriculum, with more prominence being given to use and application (Williams, 2008, p60) of Mathematics across all subjects and to give renewed focus to oral and mental mathematics. Q14, Q15, Q18, Q19, Q20, Q25a,b,c,d Conclusion In conclusion, the above discussion has demonstrated the key features of the Williams Report and has reflected on the implications of the report for EYP, strategies for intervention and the roles of the curriculum, training, accreditation, head-teachers and the family. I have demonstrated how the Williams Report has both drawn on existing regulations, recommendations, policies and practice but crucially, identified the weaknesses in existing legislation. For me the key strengths of the report lie in its emphasis on the role of teacher pedagogy and practice and the shared responsibility of the LAs with schools, in particular the head-teacher, and with the parent/carer. A key recommendation is being pro-active and understanding that every child matters. I feel the weaknesses of the report relate to its over-emphasis on high-levels of formal accreditation, which do not reflect an individuals natural gift to teach and which may jeopardise future recruitment. Of course, the question remains what the effect of recent government changes and the very real and imminent threat of public sector cuts will mean for the practical implementation of the Williams report recommendations.

The Working Girls

Women are entering the labor market in greater numbers and are staying in it longer and for a larger proportion of their work lives (Looking 1996). When asked what they want, women respond in survey after survey† â€Å"pay equity,† â€Å"better wages,† or â€Å"more money† (Looking 1996). In other words, women believe they are not being paid what they are worth (Looking 1996). This is a common response up-and down the income spectrum, â€Å"women from the executive suite to the factory floor, from the office to the washroom,† all feel that they are underpaid (Looking 1996). During the 1970's, women earned 59 percent of what men earned, and today they generally earn approximately 72 percent of what men earn (Looking 1996). However, although women's earnings have risen, about 3/5 of the narrowing of the gap is due to the fall in men's real earnings (Looking 1996). Moreover, the wage gap grows as women and men age, the gap is relatively small for young women and men, but thereafter men's wages increase sharply while women's do not (Looking 1996). In fact, the average woman in her working prime, in her early forties, makes only about the same as a man in his late twenties (Looking 1996). About fifteen years ago, it all seemed possible, to â€Å"bring home the bacon, fry it up in a pan, split the second shift with some sensitive New Age man,† however slowly the upbeat work-life rhythm has changed for professional women (Wallis 2004). Although many countries have given women the right to maternity leave and, sometimes, generous subsidies for child care, and some have even initiated a 35-hour workweek, however, the norm for most executives is still 50 hours a week for women (Wallis 2004). According to Catalyst, a U. S. esearch and consulting group, the average number for executives in the U. S. is roughly 70 hours a week (Wallis 2004). And for dual-career couples with children, the combined work hours have grown from 81 hours a week in 1977 to 91 hours per week in 2002, according to the Families and Work Institute (Wallis 2004). The U. S. Census data reveal an increase in stay-at-home moms who hold graduate or professional degrees, these are the very women who seemed destined to blast through the glass ceiling, yet 22 percent of them are home with their children (Wallis 2004). A study by Catalyst found that one in three women with M. B. A. s are not working full-time, compared to one in twenty of their male peers (Wallis 2004). Sylvia Ann Hewlett, economist and author at Columbia University in New York City, who sees a brain drain throughout the top 10 percent of America's labor force, says â€Å"What we have discovered in looking at this group over the last five years is that many women who have any kind of choice are opting out† (Wallis 2004). According to a new study released in March 2006 by Accenture, a global management consulting company, women executives around the world still face an uphill battle in workplace equality, despite significant gains during the past ten years (Most 2006). The study, entitled â€Å"The Anatomy of the Glass Ceiling: Barriers to Women's Professional Advancement,† is based on a survey of 1,200 male and female executives in eight countries (Most 2006). The respondents were asked to score factors they believed influenced their career success across three dimension: individual (career planning, competence, assertiveness, etc. , company (supportive supervisors, transparent promotion processes, etc. ), and society (equal rights, government support of parental leave, etc. ) (Most 2006). The differences between male and female respondents' answers were sued to calculate the current â€Å"thickness† of the glass ceiling, a term used to describe an unacknowledged barrier that prevents women and other minorities from achieving positions of power or responsibility in their professions (Most 2006). According to the study, 30 percent of women executives and 43 percent of male executives believe that women have the same opportunities as men do in the workplace, thus supporting the existence of a glass ceiling (Most 2006). Although there has been some progress in shattering the glass ceiling over the past twenty years, organizations and societies need to understand how important it is to capitalize and build upon the skills of women (Most 2006). In the Bem Sex Role Inventory, researcher Pamela Butler focused questions on real problems women face in changing stereotypical perceptions (Merrick 2000). According to Butler, there is intense pressure for professional women to conform to stereotypical roles such as â€Å"cheerfulness,† â€Å"tenderness,† and even â€Å"gullibility† (Merrick 2000). As women move into management in increasing numbers, it has become more apparent that these stereotypical beliefs ten to limit their advancement (Merrick 2000). The ‘Catch 22' is that when women try strategies of gender-reversal and adopt the so-called male characteristics, they often find that they face another set of problems, that of alienation and hostility, because as Butler points out, becoming one of the boys is harder than it looks (Merrick 2000). According to Butler, it takes cooperation from peers on the job to make strategies work, because research shows that attitudes held by those around a woman, even herself, hinder working relationships between women and men, and these attitudes ultimately are realized in losses of productivity and of real dollars to organizations (Merrick 2000). The purpose of Butler's research was to explore the ethics of perpetuating gender stereotypes in management, and to investigate how the woman manager operates under the system with feminine traits that are perpetuated by socialization and, vice versa, as well as how she operates under the system when she adopts masculine traits that break gender roles (Merrick 2000). The choices of leadership styles pose ethical dilemmas for women, because to get along, the new-age woman manager often finds that she has to act one way on the outside while being driven by a very much different psyche on the inside (Merrick 2000). Moreover, she may discover that in the same way, her male colleagues act toward her one way on the outside yet feel very much differently about her on the job (Merrick 2000). The new-age woman manager also might find herself playing a cruel double game in which she is utilized to show the organization has non-discriminatory hiring practices, â€Å"and at the same time she find she has to handle covert hostility from her colleagues in the workplace, who feel they have been forced to work with her to avoid trouble with the powers that be† (Merrick 2000). Data collected by L. K. Brown reveals that 5 percent of the total worldwide managers in 1947 were women, while only 6 percent of all managers in 1978 were women (Merrick 2000). In the United States, the figures were 14 percent in 1947, compared to 22 percent thirty years later (Merrick 2000). However, most of the managerial positions held by women are in the fields of health administration, building supervision and restaurant management, meaning there are more women managers in fields that have traditionally been perceived women's work (Merrick 2000). A survey carried out by Fortune, found that only ten of 6,400 people who worked at managerial positions in 1,300 of the nation's largest companies were women (Merrick 2000). Moreover, according to Brown, only 3 percent of women managers in the United States earn more than $25,000 annually (Merrick 2000). Brown concludes that larger companies are not promoting women on a large scale, and that women seeking top management posts may prefer smaller companies instead of large male-dominated companies (Merrick 2000). According to a Canadian survey, 55 percent believe that it is easier for men to advance in the workplace than women, and 42 percent of female executives who were surveyed believe that gender-based discrimination will never completely disappear from the workplace (Pollara 2000).

A Brief Note On Sociological Factors On Clients - 1666 Words

CHCDEV002 ANALYSE IMPACTS OF SOCIOLOGICAL FACTORS ON CLIENTS IN COMMUNITY WORK AND SERVICES ASSESSMENT A – ARGUMENTATIVE ESSAY ~ Australia’s social inclusion policy and its failure to support all minorities, specifically same-sex couples King (cited in Australian Marriage Equality, 2015) stated â€Å"When any society says that I cannot marry a certain person, that society has cut off a segment of my freedom†. This quote from Martin Luther King Jr is as applicable today to legalising same-sex marriage as it was to the civil rights movement and inter-racial marriage over half a century ago. Marriage is a right that most Australians take for granted. Studies have shown that having the freedom of choice to marry, regardless of sexual orientation, enriches the lives of those couples and that marriage enhances their health and wellbeing. The following essay will outline an argument in support of same-sex marriage by discussing some of the advantages from the standpoint of a couple and from the perspective of children being raised in that family dynamic, it will also outline an argument in support of gay marriage in Australia. The argument posed will be based on human rights and social inclusion policies. In the view of Triggs (2013) the spirit of Australia’s social inclusion policy, is the value placed on the human rights of individuals and minority groups. He further asserts that it encompasses the â€Å"fundamental values of equity, equality, social justice, and humanShow MoreRelatedHnc Social Care Essay4439 Words   |  18 Pagesa full reference in an end list attached to the back of your work. Please visit the power point on the moodle for further information as to the correct technique to use. In addition lecturers and library staff will help you with this. 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Business Law Case - 1391 Words

Having in regard all the information that is given in the Case Study, what is, in your opinion, the best Investor/Partner choice for NatuRi Corporation? Is it the Angel Investor, the Strategic Investor, Waltham Partners or Westlake Partners? Please justify your answers. In order to make a comprehensive review, we will discuss each investor/partner choice separately on its positive and negative aspects. Angel Investor The angel investor is a wealthy individual who is willing to make a personal investment in their venture. An advantage of this investor is that Kartik is familiar with him, as he has done some consulting work for him. The individual investor is willing to put up $1,000,000. A disadvantage of this angel investor is that, as†¦show more content†¦This is not preferable for NatuRi as there can be negative consequences for them. For example, if NatuRi flourishes in the next couple of months, its value will increase significantly. 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