Number/Calculation in primary schools 4

TEACHINGNUMBER/CALCULATION IN PRIMARY SCHOOLS

Cityand State

Number/CalculationTeaching in Primary Schools

Notonly is teaching of number/calculation in primary schools veryimportant as it gives pupils the ability to calculate, but also it isan essential tool for managing everyday occurrences and demands ofthe society. Mathematically confident and mathematically literatesociety forms the basis for economic, technological, engineering, andscience foundation (Christos, 2012). Furthermore, Goulding (2006)argues that of all the subjects, mathematics makes the most wellorganized and most natural type of art. The national mathematicscurriculum need to put into consideration and put more emphasis onareas of mathematical knowledge, mental arithmetic, confidence ofmathematics confidence, best strategies, ICT in mathematics, as wellas languages used to teach mathematics in primary schools (Clements*etal*.,2014). This research was aimed at investigating the main issues thatrelate to mathematic teaching and learning, as well as identifyingvarious areas that need improvement. A literature research ofmathematic instructions and observation studies from 2003 to 2015will be identified with the purpose of discussing various issues andareas for improvement that have been identified in relation to theteaching of number/calculation in primary schools. Also, review ofmore than fifty studies focusing on number and calculation in primaryschools will be conducted. The extent to which the new mathematicsNational Curriculum is likely to address these issues In England isalso discussed (Boonen *etal*.,2014).

Issuesrelated to number/Calculation teaching

Thereare many issues that surround the topic of number and calculation inprimary schools. Compared to earlier research on teaching ofnumber/calculation in primary schools, recent research produce aconsiderable amount of evidence of improved use of successfulinstructional practices by teachers in respective areas. According toa research that was conducted by the Department for Children,Schools, and Families (DCSF) in 2007,between nineteen ninety sevenand two thousand and six, the percentage of students that were ableto reach level five before the final part of key stage two increasedfrom sixteen to thirty two percent in English at the same level .Also, in mathematics the proportion increased from eighteen to thirtythree percent in the same years. Moreover, the report says thatalthough children get equal access and despite everyone’s optimalattempts, they do not advance the same. It is very hard for pupilswho perform well at key stage one to carry on with the sameperformance at key stage two (DCSF, 2007). Firstly, a review that wasconducted by DCSF (2008) concluded that both the family and theteacher influence the performance of a young learner. Abreu and Cline(2005) suggest that parents should be given support both on how tolearn how mathematics is taught and on various strategies that fillsthe gap between school and home work. However, the teacher has moreinfluence in determining the learning results in mathematics (Wright*etal.*,2015). Also, the review states that teaching mathematics hasundergone a substantial change ever since most parents opted for ownschooling (DCSF, 2008). This review found out that many schoolsengaged in exceptional teaching although Mathematics seemed to be achallenge and a very demanding subject for most primary levelteachers. Zhang and Yuren (2003) suggest that overcoming thesechallenges and becoming excellent mathematics teachers, agility andconfidence should be a priority to teachers.

MathematicalConfidence

Thequestion is how teachers can acquire mathematical confidence. Variousstudies suggest that confidence comes from intense pedagogicalknowledge and an understanding of mathematical subject (Mix *etal.*,2008).Therefore, it is important to probe the convenient provision inmathematics throughout education and Initial Teacher Training (ITT)(DCSF, 2008).

“High-qualityteaching secures pupils’ understanding of structure andrelationships in number, for instance place value and the effect ofmultiplying or dividing by 10, and progress in developingincreasingly sophisticated mental and written methods” (Ofsted,2011:6).

Importantly, a research that was conducted by Ofsted (2008) produceda comprehensive report that entailed analysis and evidence fromvarious inspections of mathematic teaching. The report suggested thatthe standards that govern mathematic learning have risen in the pastdecade. Additionally, these improvements have happened to students atall levels of education. The report recommends that there should bemore students attaining GSE grades that are higher than what they gettoday (Ofsted, 2009). Strategies that focus on improving examinationperformance and test improvement, as well as those teaching methodsthat focus on qualification preparation are not good for the futureof pupils. Therefore, it is important to invest on methods that giveattention to the mathematical understanding of the pupils rather thanthose that only focus on disparate skills of pupils (Handley, 2012).

Additionally,according to several research findings the teachers should come upwith effective ways of developing the mathematical understanding. Thereports from these findings endorse various imperative ingredients ofpowerful mathematics teaching. These ingredients are knowledge of thesubject, as well as understanding the manner in which pupils’master mathematics (Haylock *etal.*,2003). The report from Ofsted (2009) calls this process subjectexpertise. How to use this expertise in the classroom is equallyimportant. According to the Department for Education and Skills(2007), the best teaching method is not only knowledgeable andenthusiastic, but also it focuses on improving and developing theunderstanding of pupils on essential concepts. Moreover, when goodassessment is used across each lesson, the teachers are able to spotthe thinking capacity of pupils and they accordingly adjust tolearning and teaching strategies that are effective (Haylock *etal.*,2003). Consequently, the pupils become mathematically independent,making them well equipped for successful results in examinations andover. These research findings not only indicate good methods ofmathematic teaching, but also mention weaker practices (Mooney *etal*.,2011).

MentalArithmetic

Anotherissue that relates to the teaching of number and calculation inprimary schools is mental arithmetic. Thompson (2010:152) suggeststhat “mental arithmetic includes recall of facts and figuring”.He gives a precise recount of research findings that focuses onsubtracting and adding numerals to a hundred. Additionally, he givesan advanced model that gives guidance on mental calculation and abrief explanation of known fact and quick calculation. Children whouse their own methods tend to make fewer errors in calculation(Lester, 2007). Therefore, Thompson (2010) concludes that mentalarithmetic is much more effective in teaching number and calculationthan “teaching by rule” and points out that “errors” arechildren methods and he reasons that mental methods of childrenoperate in a different way than algorithms of standard paper. Thatbeing the case, these methods do not affect one another in any way.Several suggestions and illustrations of informal non-standardalgorithms of children are presented well and explored, andemphasizes on written methods and how they shape mental methods ofchildren (Thompson, 2010).

PrimarySchool Trainees

Theneeds and capabilities of pupils are very important when it comes tolearning number/calculation in primary schools. Equally, it is veryimportant to address the needs of primary school apprentice on allcurriculums of Initial Teacher Training (ITT). In such courses, thetrainees are expected to demonstrate a good understanding of thesubject knowledge as well competence in applying this piece ofknowledge in teaching (Cockburn *etal*.,2008). For a trainee to qualify for the award of Qualified TeacherStatus (QTS), mathematical subject knowledge is a paramountrequirement. Attention should also be directed to Newly QualifiedTeachers (NQTS) and all education professionals dealing withmathematics. Professional standards for QTS suggest that for ateacher to teach effectively, he or she should be well equipped withsecure understanding and knowledge of his or her curriculum orsubject areas (Osborne, 2015).

“Oneof the best ways for children to learn and understand much of themathematics in the primary school curriculum is for a teacher whounderstands it to explain it to them” (Haylock *etal.*,2014:99).

School’sNational Curriculum

Anothermain issue that was found in many studies is concerned withinformation about national curriculum programs. This is about thetype of mathematics that schools are supposed to follow until a newcurriculum is put in place. In the UK and various parts of England,the Early Years Foundation Stage is concerned with building aflexible and coherent approach to learning and care. In it, severalguidance and statutory materials are listed to guide all people onhow to deal with young children. Children leave EYFS when they turnfive years in the end of the academic year, which means that childrenare supposed to follow EYFS until their reception year is over. In UKand England, the National Curriculum is designed in key stages, suchas key stage one that deals with children of five to seven years, keystage two that is concerned with pupils of seven to eleven years(Mooney *etal.,*2011). Each key stage is made up of components like programs ofstudy, which outlines the type of mathematics that pupils shouldlearn. The second component is attainment targets, which outlines theskills, understanding, as well as mathematical knowledge that pupilsshould achieve. The third component is known as level descriptions,which gives an illustration of the range and types of performancethat pupils working at a specific level should emulate or reflectafter each achievement in each key stage. Mathematics has been aminimum statutory requirement in most country’s nationalcurriculum. Also, since its inception in nineteen eighty nine,mathematic in the national curriculum has undergone three revisions.There are several current programs of study for mathematics in UK andEngland that includes handling data, applying and using mathematics,algebra and number, measures, space, and shape (Boonen *etal*.,2014).

Informationand Communication Technology (ICT)

Undeniably,the society today has become aware of ICT.

“Computershave been commonplace in primary schools for a number of years now,and this is also becoming the case with other forms of ICT such asdigital projectors and interactive whiteboards” (English, 2006:1).

Additionally,he states that although the access to technological knowledge and toICT has increased tremendously, it has not been in a par withpedagogical terms. Personal experience with computers is not enoughfor a person to be able to apply it effectively in process oflearning and teaching in the classroom. Therefore, it is veryimportant for trainee teachers and teachers to be empowered with thenecessary skills connected to ICT and practical workable ways.Clausen (2008) Suggest that many computer software have beendeveloped to assist in learning such as Furbles, Cinderella,Geometer’s sketchpad, and Cabri-Geometre. For example, teachersrequire pedagogical training to enable them to become creativetrainers across the course. English (2012) discussed various waysthat an individual can use ICT creatively when teaching mathematics.Promising developments have been realized as now many teachers useinteractive whiteboards to teach. English (2006:9) stated that “allpupils should see and experience ICT in a very positive way, not justin mathematics but in all areas of the curriculum.”

Howcan ICT be incorporated into number/calculation teaching? One, theinclusion of the wireless voting system to the interactive whiteboardhas made learning mathematics to become more effective than before.The wireless voting system is used in key parts of various mathlessons to enhance cooperative learning band discussion (English,2006). Each group of student is given one keypad by the teacher whoencourages them to think as a group and give answers jointly. Thesystem is also used by the teacher to assess pupils. The system isset in a way that it logs individual responses for future analysis.Second, the use of videoconferencing is now used in many primaryschools during math’s lessons. For example, pupils from one schoolcan describe mathematical concepts and models to the other schools.Teachers also benefit from videoconferencing because they can nowshare and collaborate with other teachers in relation to assessment,planning, and teaching. Tablet PCs are other gadgets that have helpedin learning mathematics. They assist pupils to represent data indifferent ways by use of graphs and charts. The intranet has alsoenhanced the quality of math’s learning and teaching because pupilscan access learning materials online, making learning easier forprimary school learners (Carbonneau *etal*.,2013).

ArithmeticKnowledge

Knowledgeof Arithmetic or number has been a key component in ensuring thatpupils in primary schools acquire the prime foundation inmathematics. The society thinks that arithmetic is usually related toan individual’s capacity to compute accurately and quickly.According to ofsted (2011), there is so much in learning mathematicsthan just subtraction, addition, division and multiplication.Additionally, Langley (2013) suggest that a good understanding ofnumbers, their relationships, as well as structures form the basisfor an advancement from reciting numbers in nursery rhymes tocomputing and thinking about all sizes of numbers, to dealing withmeasures, and instituting the key algebraic thinking foundations

“Inorder to achieve the aim of *functionalnumeracy *childrenneed to be able think flexibly and to apply their knowledge to newsituations, to solve practical problems, to experiment withinmathematics itself, to develop the ability to reason mathematicallyand to communicate their reasoning to others” (Mooney, 2011:2).

Towiden the range of mathematical experiences, various modern materialscan be used to enhance learning and teaching mathematics in primaryschools such as

Numicon

Learningof number/ calculation cannot be complete without Numicon (Harris,2013). Thisis a mathematics teaching programme that allows pupils to use Numiconmathematic shapes in variety of teaching activities that requirespractical knowledge. Not only do these shapes give learners knowledgeabout number values, but also they acquire knowledge about hownumbers relate in such a coherent way that written numerals cannotprovide (Harris,2013). Furthermore,Numicon allows learners to construct mental visual images as theycompare and combine several shapes when doing arithmetic during achain of applied activities. Moscardini (2009) suggest that thekinesthetic, auditory, and visual approaches to Numicon apply todivergent learning styles. Learning in this case includes bothfeeling and seeing the connection between these patterns. Theteaching activities that uses Numicon involves early stages primaryschool children who play with the shapes and associate them withspecific numbers, thus enabling them to begin using shapes duringarithmetic activities that require practical application (Tucker,2014)This type of teaching programme gives an illustration of subtraction,addition, multiplication, place value, estimation, doubling, andhalving, therefore making mathematics learning enjoyable to pupilsnot only independently, but also in groups. Teachers also deviceother advanced ways of using Numicon like describing decimals,fractions, and percentages through shapes (Carbonneau *etal., *2013).

Arrays

Theseare pictorial representations that allow pupils to acquire knowledgeabout timetables. In key stage 1, teachers teach pupils the means ofcounting in 2s,5s, as well as in 10s (Back, 2013) until they becomeconfident with it, before teaching them the ways of computing timetables’ problems through the use of arrays. Before using arrays,children are supposed to have the ability to count numbers indifferent steps. Not only are arrays helpful in computation of wordedproblems, but also they help pupils with learning difficulties atthis stage (Moscardini, 2009)

Countersand Dominos

Countersare used in teaching and learning mathematics in various ways. Theyshow patterns, help in keeping track of moves, and model the pupil’sthinking. Dominos on the other hand are a set of resources that areused to solve puzzles and play games. According to a meta-analysisthat was conducted by Carbonneau *etal*.,(2013), use of manipulative gadgets in teaching mathematics inprimary schools has profound positive effect on learning outcomesfrom moderate to large in retention. However, the effects were smallin case of transfer, problem solving, as well as justification(Moscardini, 2009).

Asat various times in education history, so many possible changes haveoccurred not only in mathematics curriculum, but also in thesubject’s requirements. For this reasons, there have beenimprovements in this area of study. For example, in 2010, the UKgovernment amended the Early Years policy that had an immense effecton the Early Years Foundation Stage (English, 2013). Moreover, thethen department of education took an initiative to review the primarynational Curriculum.

Nationalcurriculum in England

Thenew mathematics National Curriculum in England is likely to addressthese issues in the following ways. First, the curriculum recommendsthat pupils should become eloquent in all mathematics elementary.Then, it requires students to think mathematically not only by use ofa line of inquiry and conjecturing generalizations and relationships,but also by argument development and justification through use ofmathematical language (DFE, 2014). Finally, the pupils are requiredto gain the ability to solve problems through application ofmathematical knowledge to a wide range of non-routine and routineproblems (Haylock & Manning, 2014).

Besidesensuring that students get quality understanding of mathematics, thecurriculum addresses the issue of ICT which is very important intoday’s world. It suggests that calculators are important materialsin learning mathematics because they assist key stage 2 pupils innumber investigation and conceptual understanding (Mooney*etal*.,2011). This process can only be achieved if good mental and writtenarithmetic are well established. Therefore, it is the responsibilityof teachers to decide when to use these digital gadgets.Additionally, the school curriculum is a vital issue that theNational Curriculum in England addressed. For pupils in key stagesone and two, the mathematics study programmes follow year by year setup, hence when each key stage ends, schools should have taught theappropriate programme. Allowing this information online is also vitalin ensuring that learning and teaching of number/calculation isimproved in England (Mooney*etal*.,2014).

Whosaid that language is not important when learning mathematics? DCSF(2007:29) recommends that teachers need “greater awareness of theimportance of vocabulary to learning and gaining confidence inmathematics.” The National Curriculum of England indicates thatspoken language allows pupils to develop linguistically, socially,and cognitively. When pupils present mathematical justification orwhen they develop their math’s vocabulary, the quality of thelanguage they speak or hear is of crucial importance (Department foreducation, 2014). This improvement shows that the England NationalCurriculum not only focuses on building pupils’ knowledge andexperience, but also it builds on community, linguistic, family, andcultural backgrounds. By actively introducing mathematical methods,language, and concepts through a wide variety of teaching strategiesand experiences, the curriculum has managed to address main issuesthat relate to mathematics (Department for education, 2014).

Themain areas of mathematics in England’s National Curriculum for keystage 1(years 1 and 2) are number and place value, number (additionand subtraction), multiplication and division, fractions,measurement, geometry (properties of shapes), and geometry (positionand direction). In year two programme of study, statistics as mainarea is added. In lower key stage two (year 3 and 4), the main areasof mathematics aims at ensuring that all pupils become more and morearticulate with numbers that are whole and the main four operations,including the concept of place value and number facts (Department ofeducation, 2014). Accurate calculations and mathematical reasoningwith simple decimal value and fractions are vital at this stage.

Yearthree, four, five programmes of study put emphasis on all the areasmentioned above but involve dealing with more complex mathematicalproblems. For example, in year 4, pupils are expected to gain theknowledge of converting between various units of measure….In yearfive, pupils should be able to read, interpret, and completedifferent table information. In year 6, pupils should be able toorder, read, compare, and write numbers up to ten million and be ableto know each digit’s value. In addition, year 6 includes the areasof ratio and proportion, algebra, and also percentages (DCSF, 2008).

Assessmentreform was made to the National Curriculum in 2014. The levels thatwere used to show the progress and attainment of children wereremoved, not to be replaced again. This act ensures that teaching andlearning of mathematics has some flexibility, which means thatteachers can assess or plan learning in their own ways. Schools arealso allowed to develop their own curriculum as long as it isrelevant to the teachers and pupils (Department of education, 2014).

Conclusion

Insummary, the main issues related to teaching number and calculationinvolves the subject’s understanding, ICT in mathematics, language,the teacher’s knowledge about the subject, the school’scurriculum, as well as manipulative strategies for studyingmathematics. All these areas are meant to make learning and teachingof number/calculation easier and they are subject for improvement andchange from time to time (Department of education, 2014). Themathematics National Curriculum in England addresses most of theseissues, therefore improving how pupils in all key stages solveproblems develop fluency, and how they reason mathematically. Ithink more research should be done on areas that link involvement ofparents with how children learn.

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