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- 1. EDME145 Primary Mathematics 1: Numeracy Semester 2 Julie Papps 220076557
- 2. INTRODUCTION:After viewing the video clip of the young boy Mark completing a Schedule for EarlyNumber Assessment (SENA 2) this paper will discuss the mathematical areas thatmark could and couldn’t answer within the areas of numeral identification, countingby 10’s and 100’s, addition and subtraction, combining and partitioning, place valueand multiplication and division. This paper will also illustrate what parts of thenumeracy continuum and the New South Wales (NSW) K-6 syllabus the student fullyand partly satisfies. This paper will also reveal goals and skills that could be set forthe student to develop his skills further and the reasons for moving the student on toa new level, as well as what tools could be used to assist the student from hiscurrent level onwards.NUMERAL IDENTIFICATION:Mark fulfils the requirements of the numeral identification part of the assessmentalmost perfectly. Mark could recognise and name the numerals written on 9 out of 10cards that were shown to him. The cards ranged in numbers from 59 to 4237. Thestudent’s responses were instant without any hesitation. Mark fully satisfies thenumeral identification code NS1.1 as the student could instantly recognise andcommunicate all eight numbers between 1 and 1000. Mark partially meets numeralidentification code NS2.1 as he was able to instantly say one of two numbersbetween 1001 and 10000.The only numeral card that Mark could not recognise was the number 3060, whichfalls into the numeracy continuum code NS2.1.The skills and understandings that Mark should work towards include being able tounderstand the place value of digits including zero in four digit numbers. Forexample in the number 3426, the 3 represents 3000 (Board of Studies 2002:44).Mark almost fulfils the requirements of NS2.1 so if the student is moved on to workon the above goals he will gain greater understanding and will meet the terms ofstage two and can then start working on the basics of stage three.The tools the teacher should work on with Mark is to continue to show him more andmore cards with 4 digit numerals written on them to practice saying the four digitnumbers.COUNTING BY 10’S AND 100’SThe student demonstrated that he can count forwards off the decade in incrementsof 10. He can also count backwards in 10’s on the decade from 110, and countbackwards from 924 off the decade in increments of 100. The skills show that Markcan clearly meet the recommendations of the numeracy continuum code NS1.1 ashe can count both forwards and backwards by 10’s and 100’s both on and off thedecade and 100.
- 3. The student could not count forwards from 367 in increments of 10; instead hecounted in 100’s. This seemed to occur due to the assessment going from anexercise counting in 10’s to an exercise counting in 100’s then coming back tocounting in 10’s. This means that Mark doesn’t quite fulfil the requirements of thenumeracy continuum code NS2.1.Board of Studies (2002: 44) illustrates Mark should continue to practice countingforwards and backwards by 10’s and 100’s alternatively so that the skill becomessecond nature. Mark can then start working on counting forwards and backwards by10’s and 100’s with four digit numbers. The student will then meet the requirementsof NS2.1.The reason for moving the student on from where he is now is to assist him inmeeting the requirements of NS2.1. This will form the basis of all further mathematicskills.The tools the teacher could use with Mark is to get Mark to continue counting withsmall blocks and arranging them into units of ten and hundreds.ADDITION AND SUBTRACTIONMark successfully subtracted two digit numbers arriving at the correct answer. Hecame up with the answer by using his fingers and counting in his head. Mark fulfilsthe perceptual counting strategy (NES1.2) completely as he can count visible itemsto find the total count, build and subtract numbers by using materials or fingers torepresent each number and Mark’s fingers remain constantly in view while counting(Numeracy Continuum ???????). The student also performs some of the figurativecounting strategy (NS1.2) as he can visualise concealed items and tries to determinethe total by counting from one. Mark can also complete parts of the counting on andback strategy (NS1.2) as he can count on rather than start from one to solve additiontasks (Board of Studies 2002: 46).When Mark was asked to add 25 dots onto the 48 covered up dots he had previouslyadded together. He was on the right track with the calculation but came up with theincorrect answer. All dots were then covered and he was asked how many dots hewould need to make 100, again he had the right idea with the counting but just gotthe subtraction slightly incorrect.Mark was also asked two addition questions. Mark came up with the incorrectanswers but when asked by the teacher how he got the answer he actually explainedthe process correctly.The goals Mark should work towards completing the figurative counting strategy bypracticing visualising concealed items and determining their totals. This will helpMark fulfil NS1.2.
- 4. The student should be moved on from where he is in order for Mark to fullyunderstand addition and subtraction. He has the basic counting concepts but justneeds to build on these skills.One of the tools that could be used to help Mark understand these new skills is bygiving Mark two dice to roll. He can start by adding together the two numbers rolledand once Mark has the basic addition skills he can keep adding the dice togethereach roll he completes (Department of Education & Training: 2002: 163)COMBINING AND PARTITIONINGWhen asked to find two numbers that add up to 10, Mark was able to come up withthree examples that were correct. When Mark was asked to come up with examplesthat add up to 19, he was able to find two correct examples. He came up with all ofthe examples off the top of his head, but it did take a little time to find the answers,therefore this would put Mark at the NES 1.1 level.Although mark knows the answers when asked to find number combinations, hetakes a fair amount of time to find the answers, therefore he is not quite at the stageof being able to come up with the answers instantly.The goals Mark should work towards are becoming more autonomous when comingup with two number that can be added together to make another number.Mark should move on from where he is now to become more autonomous with theskills he already possesses. This will also assist with his future mathematics.One exercise that a teacher could participate in with Mark is for the teacher to callout a number starting with single digits, and Mark has to call out two number that addup to the number the teacher has called out. Once Mark is proficient with singledigits they can start working with two and three digit numbers (Wright, Stanger &Stafford. 2006: 71).PLACE VALUEMark was able to add up strips of single dots and groups of 10 dots, and continuedto do this in his head even when the previous dots had been covered up. He alsounderstood when the teacher explained to him that each row of dots equalled ten.Mark also seemed to find it quite easy to count on from the middle of the decade aseach new group of numbers was uncovered up until the number 48. This shows thatMark can successfully fulfil the requirements of the numeracy continuum level NS.1.2.The teacher covered all the dots up at the end of the exercise and asked the studenthow many dots were needed to make 100 dots. Mark found it quite difficult once all
- 5. the dots were covered up to work out how many more dots were needed to reach100.The goals and understandings Mark should be working towards is being able tosolve addition and subtraction problems mentally by separating the tens from theones and adding or subtracting separately before combining. This involves learningthe jump strategy eg. 23+35; 23+30=53, 53+5=58 and the split strategy eg. 23+35;20+30+3+5=58. This will assist Mark to work towards NS. 2.2.The reason for moving Mark on compared to where he is now is so he can learnseveral ways of completing addition and subtraction problems, which in turn willassist him in the future when learning multiplication and division.The tools that will help Mark achieve the above goals is by using the number line orthe hundred chart. Both of these tools will show Mark visually how to work theproblems out and also assist him to learn to work things out in his head (ORIGIOEducation 2007:166).MULTIPLICATION AND DIVISIONMark could easily group random counters into three equal groups or four counters.When six circles each with 3 dots inside were hidden under a sheet of paper, Markcounted by three’s to find the correct answer. When prompted, Mark also found itquite easy to count by 4’s, eg. 4, 8, 12, 16. This shows the student can accomplishmost parts of the numeracy continuum level NES1.3.When asked a theoretical question about dividing 27 cakes between boxes with eachbox holding a maximum of 6 cakes, Mark was able to work out that five boxes wouldbe needed and that one box would not be full. The teacher could see how Markworked it out as he was counting backwards out loud and using his fingers to countthe groups. This shows that Mark is starting to comprehend the numeracy continuumlevel NS1.3.During another hypothetical question about dividing twelve biscuits between children,which each child receiving two biscuits each Mark could not answer this questionand did not seem to understand what the teacher was asking of him.Mark was then shown a card with a grid of dots. The majority of the dots on the cardwere covered, only showing the top horizontal row and the first vertical row. Markwas asked how many dots were on the card altogether he gave an incorrect answeras he had just counted the uncovered dots.Mark also did not know what eight multiplied by four was, but did know to group thenumerals into groups of four and only missed the answer by one digit.
- 6. The skills Mark should develop now are skip counting of other numbers such as six,seven, eight and nine.The reason for moving Mark on to learning skip counting of the other single digitnumbers is he is proficient in skip counting one’s, two’s, three’s, four’s, fives andtens. Once he can fill in the gaps by learning the other numbers he will be able tocomplete multiplication and division quite easily.The tools that will help mark achieve the above goals include counting by six, seven,eight and nine using rhythmic or skip counting. Another tool to assist mark is bymodelling division by sharing a collection of objects equally among different groups,or in equal rows and using arrays and calculating the total number of items in eacharray (Board of Studies. 2002: 53).CONCLUSIONIn conclusion, after completion of the SENA 2 assessment Mark is almost totallycompetent with the requirements of Stage one of the NSW Board of Studies K-6Syllabus. He has also started to work towards the requirements set out in stage twoof the NSW syllabus.
- 7. REFERENCE LISTNSW Board of Studies. (2006). K-6 NSW mathematics syllabus. Retrieved from http://k6.boardofstudies.nsw.edu.au/go/mathematicsNSW Board of Studies. (2002). Numeracy Continuum. Retrieved from http://moodle.une.edu.au/mod/resource/view.php?id=113572.NSW Department of Education and Training. (2002). Count Me In Too Curriculum K-12 Directorate. Retrieved from NSW Board of Studies. (2006) K-6 NSW mathematics syllabus. Retrieved from http://k6.boardofstudies.nsw.edu.au/go/mathematicsORIGIO Education. (2007). The ORIGIO Handbook. Queensland, Australia. ORIGIO Education.HAYLOCK, D. (2010). Mathematics Explained for primary teachers. 4th Ed. London, UK. SAGE PublicationsWright, R., Stanger, A., Stafford, J. (2006). Teaching Number in the Classroom with 4 – 8 year olds. Pp. 71. Retrieved from http://books.google.com.au/books?id=ZyIKdh1N31UC&pg=PA64&lpg=PA64&dq=co mbining+and+partitioning&source=bl&ots=rkOyr92M0n&sig=Q- GquZEh4_orvFr9oczplyvz5N8&hl=en&ei=OQVqTpLfB4fPiAKkmtHFDg&sa=X&oi=bo ok_result&ct=result&resnum=1&ved=0CCgQ6AEwAA#v=onepage&q=combining%20 and%20partitioning&f=false.

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