2. 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.
3. 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.
4. 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
5. 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.
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 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.
7. 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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and%20partitioning&f=false.
