EDME145 Primary Mathematics 1: Numeracy

Semester 2

Julie Papps

220076557

INTRODUCTION:

After viewing the video clip of the young boy Mark completing a Schedule for Early

Number Assessment (SENA 2) this paper will discuss the mathematical areas that

mark could and couldn’t answer within the areas of numeral identification, counting

by 10’s and 100’s, addition and subtraction, combining and partitioning, place value

and multiplication and division. This paper will also illustrate what parts of the

numeracy continuum and the New South Wales (NSW) K-6 syllabus the student fully

and partly satisfies. This paper will also reveal goals and skills that could be set for

the student to develop his skills further and the reasons for moving the student on to

a new level, as well as what tools could be used to assist the student from his

current level onwards.

NUMERAL IDENTIFICATION:

Mark fulfils the requirements of the numeral identification part of the assessment

almost perfectly. Mark could recognise and name the numerals written on 9 out of 10

cards that were shown to him. The cards ranged in numbers from 59 to 4237. The

student’s responses were instant without any hesitation. Mark fully satisfies the

numeral identification code NS1.1 as the student could instantly recognise and

communicate all eight numbers between 1 and 1000. Mark partially meets numeral

identification code NS2.1 as he was able to instantly say one of two numbers

between 1001 and 10000.

The only numeral card that Mark could not recognise was the number 3060, which

falls into the numeracy continuum code NS2.1.

The skills and understandings that Mark should work towards include being able to

understand the place value of digits including zero in four digit numbers. For

example 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 work

on the above goals he will gain greater understanding and will meet the terms of

stage 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 and

more cards with 4 digit numerals written on them to practice saying the four digit

numbers.

COUNTING BY 10’S AND 100’S

The student demonstrated that he can count forwards off the decade in increments

of 10. He can also count backwards in 10’s on the decade from 110, and count

backwards from 924 off the decade in increments of 100. The skills show that Mark

can clearly meet the recommendations of the numeracy continuum code NS1.1 as

he can count both forwards and backwards by 10’s and 100’s both on and off the

decade and 100.

The student could not count forwards from 367 in increments of 10; instead he

counted in 100’s. This seemed to occur due to the assessment going from an

exercise counting in 10’s to an exercise counting in 100’s then coming back to

counting in 10’s. This means that Mark doesn’t quite fulfil the requirements of the

numeracy continuum code NS2.1.

Board of Studies (2002: 44) illustrates Mark should continue to practice counting

forwards and backwards by 10’s and 100’s alternatively so that the skill becomes

second nature. Mark can then start working on counting forwards and backwards by

10’s and 100’s with four digit numbers. The student will then meet the requirements

of NS2.1.

The reason for moving the student on from where he is now is to assist him in

meeting the requirements of NS2.1. This will form the basis of all further mathematic

skills.

The tools the teacher could use with Mark is to get Mark to continue counting with

small blocks and arranging them into units of ten and hundreds.

ADDITION AND SUBTRACTION

Mark successfully subtracted two digit numbers arriving at the correct answer. He

came up with the answer by using his fingers and counting in his head. Mark fulfils

the perceptual counting strategy (NES1.2) completely as he can count visible items

to find the total count, build and subtract numbers by using materials or fingers to

represent each number and Mark’s fingers remain constantly in view while counting

(Numeracy Continuum ???????). The student also performs some of the figurative

counting strategy (NS1.2) as he can visualise concealed items and tries to determine

the total by counting from one. Mark can also complete parts of the counting on and

back strategy (NS1.2) as he can count on rather than start from one to solve addition

tasks (Board of Studies 2002: 46).

When Mark was asked to add 25 dots onto the 48 covered up dots he had previously

added together. He was on the right track with the calculation but came up with the

incorrect answer. All dots were then covered and he was asked how many dots he

would need to make 100, again he had the right idea with the counting but just got

the subtraction slightly incorrect.

Mark was also asked two addition questions. Mark came up with the incorrect

answers but when asked by the teacher how he got the answer he actually explained

the process correctly.

The goals Mark should work towards completing the figurative counting strategy by

practicing visualising concealed items and determining their totals. This will help

Mark fulfil NS1.2.

The student should be moved on from where he is in order for Mark to fully

understand addition and subtraction. He has the basic counting concepts but just

needs to build on these skills.

One of the tools that could be used to help Mark understand these new skills is by

giving Mark two dice to roll. He can start by adding together the two numbers rolled

and once Mark has the basic addition skills he can keep adding the dice together

each roll he completes (Department of Education & Training: 2002: 163)

COMBINING AND PARTITIONING

When asked to find two numbers that add up to 10, Mark was able to come up with three examples that were correct. When Mark was asked to come up with examples that add up to 19, he was able to find two correct examples. He came up with all of the 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, he

takes a fair amount of time to find the answers, therefore he is not quite at the stage

of being able to come up with the answers instantly.

The goals Mark should work towards are becoming more autonomous when coming

up 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 the

skills 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 call

out a number starting with single digits, and Mark has to call out two number that add

up to the number the teacher has called out. Once Mark is proficient with single

digits they can start working with two and three digit numbers (Wright, Stanger &

Stafford. 2006: 71).

PLACE VALUE

Mark was able to add up strips of single dots and groups of 10 dots, and continued

to do this in his head even when the previous dots had been covered up. He also

understood 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 as

each new group of numbers was uncovered up until the number 48. This shows that

Mark 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 student

how many dots were needed to make 100 dots. Mark found it quite difficult once all

the dots were covered up to work out how many more dots were needed to reach

100.

The goals and understandings Mark should be working towards is being able to

solve addition and subtraction problems mentally by separating the tens from the

ones and adding or subtracting separately before combining. This involves learning

the 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 learn

several ways of completing addition and subtraction problems, which in turn will

assist 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 or

the hundred chart. Both of these tools will show Mark visually how to work the

problems out and also assist him to learn to work things out in his head (ORIGIO

Education 2007:166).

MULTIPLICATION AND DIVISION

Mark 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, Mark

counted by three’s to find the correct answer. When prompted, Mark also found it

quite easy to count by 4’s, eg. 4, 8, 12, 16. This shows the student can accomplish

most parts of the numeracy continuum level NES1.3.

When asked a theoretical question about dividing 27 cakes between boxes with each

box holding a maximum of 6 cakes, Mark was able to work out that five boxes would

be needed and that one box would not be full. The teacher could see how Mark

worked it out as he was counting backwards out loud and using his fingers to count

the groups. This shows that Mark is starting to comprehend the numeracy continuum

level NS1.3.

During another hypothetical question about dividing twelve biscuits between children,

which each child receiving two biscuits each Mark could not answer this question

and 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 card

were covered, only showing the top horizontal row and the first vertical row. Mark

was asked how many dots were on the card altogether he gave an incorrect answer

as he had just counted the uncovered dots.

Mark also did not know what eight multiplied by four was, but did know to group the

numerals into groups of four and only missed the answer by one digit.

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 digit

numbers is he is proficient in skip counting one’s, two’s, three’s, four’s, fives and

tens. Once he can fill in the gaps by learning the other numbers he will be able to

complete 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 by

modelling 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 each

array (Board of Studies. 2002: 53).

CONCLUSION

In conclusion, after completion of the SENA 2 assessment Mark is almost totally

competent with the requirements of Stage one of the NSW Board of Studies K-6

Syllabus. He has also started to work towards the requirements set out in stage two

of the NSW syllabus.

REFERENCE LIST

NSW Board of Studies. (2006). K-6 NSW mathematics syllabus. Retrieved from

http://k6.boardofstudies.nsw.edu.au/go/mathematics

NSW 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/mathematics

ORIGIO Education. (2007). The ORIGIO Handbook. Queensland, Australia. ORIGIO

Education.

HAYLOCK, D. (2010). Mathematics Explained for primary teachers. 4th Ed. London, UK.

SAGE Publications

Wright, R., Stanger, A., Stafford, J. (2006). Teaching Number in the Classroom with 4 – 8

year olds. Pp. 71. Retrieved from

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