 # Following is the report for an individualised maths assessment schedule used for an Early Stage 1 student. This was conducted for a mathematics assignment, where a student was interviewed using the Schedule for Early Number Assessment (SENA) then a report written on the results, and 3 lesson plans written for further learning. Following the report below, is the outline of the three proposed lessons. This evidence highlights how important it is that assessment is used to monitor student’s progress, and then used to plan and implement further instruction.

SENA 1 Report Assessment 23rd September, 2007

Age/Year: 5/Kindergarten

Aspect to be developed

Where are they now?

Where to next?

Outcomes and indicators

How?

Why?

Numeral identification

Level 3: 1-100

Recognised all numbers to 100 easily and quickly. When extended to SENA 2 number recognition of numerals beyond 100 was difficult, but did recognise 1000. At one point 90 was confused for 19, but this was self-corrected.

Level 4: 1-1000

Recognises numbers numerals 1-1000.

NS 1.1 Counts, orders, reads and represents two- and three- digit numbers

- Can name and write the write the numeral for a given three digit number

- Can represent a three digit number with various objects, and for these larger numbers systematically group in tens and hundreds

Using activities that require the identification and naming of numerals from 100-1000.

Teaching Point: These larger numbers need to be introduced to the classroom, possibly through posters or flash cards.

Consolidation: These posters should make connections between the numeral and word names.

Basic numeral recognition is vital at all stages of mathematics, and therefore developing these skills is fundamental to all other strands of the syllabus. (Board of Studies, 2006, p.40). In order to progress to larger addition and subtraction problems, the student must be able to recognise and name the larger numbers.

Forward number word sequence

Facile (100): Level 5

Knew all number sequences to 100, and then a bit beyond. Paused occasionally changing decades- 69-70. Confidently gave the number after for all.

Facile (1000)

Can count beyond 100, and give the number after for a three digit number.

NS 1.1 Counts, orders, reads and represents two- and three- digit numbers

- Counts forward by ones from a given three digit number, and then starts counting on in  twos, fives and tens

- Can identify the number after a given three digit number

Activities that promote FNWS 100-1000.

Teaching Point: These larger numbers need to be familiarised in sequence.

Consolidation: Number line activities, such as placing numbers in sequence with pegs along a string. Having a poster number pattern running around the room.

It is a vital consideration for all mathematics learning that students can have an understanding of FNWS, in order to have an develop the idea of place value and the positioning of numbers in relation to one another.

Backward number word sequence

Facile (100): Level 5

Knew all number sequences, even though was a little tentative at trying to count back from 103. I t was interesting to note that when continued beyond the set number, there was a little bit of confusion; 91-80 and then after 14, started ascending again from 10. Gave the number before for all easily. Counted on from 60, to get the number before 70.

Facile (1000)

Can count backward from 1000 and give the number before any three digit figure.

NS 1.1 Counts, orders, reads and represents two and three digit numbers

- Counts backwards by ones from a given three digit number

- Identifies the number that comes before a given three digit number

Activities that show BNWS for three digit numbers.

Teaching Point: Students need to be made aware the importance of learning the numbers both before and after three digit numbers.

Consolidation: Again the use of number lines is helpful in demonstrating the sequencing of numbers, and the alternate direction of counting.

BNWS is a skill required to assist with subtraction and other basic strategies such as ordering and the concept of greater and less than. Continuing the idea of interrelationships between different parts of number is the connection to division, meaning that the basics must be learnt in order for more complicated ideas to be introduced.

Subitising

Conceptual (Level 2)

The dots were easily recognised as two separate groups, that when added together formed a whole. The child was able to identify that the dot patterns were irregular and drew how they would usually appear on a dice. The whole number was found through counting on, with the assistance of fingers.

The student needs to consolidate this knowledge to recognise number combinations that add up numbers such as ten. In this way the student can develop an efficient and quick way of knowing the total, without counting on.

NS 1.1 Counts, orders, reads and represents 2 and 3 digit numbers.

- Can recognise dot patterns instantly for numbers up to 12

- Can make and recognise different visual arrangements for the same number

Subitising activities would be useful at this stage to further the child’s knowledge, and in particular those of common number combinations. Subitising with larger number should also be encouraged.

Teaching Point: Larger numbers need to be incorporated into subitising activities, and an assortment of number facts introduced. An important consideration is the development of an understanding of a group and then a whole.

Consolidation: Dot patterns of larger numbers should be made familiar throughout the room, and in problems. Such could be achieved through the use of dominoes.

Subitising helps form children’s understandings of addition and subtraction. It forms an essential pre-requisite for establishing part-part-whole number knowledge for the learning of particular number combinations that make another; eg 7- can be seen as 5+2, 6+1 or 4+3 (State of Victoria Department of Education, 2006). It further helps make evident particular number combinations. Subitising can help children with number recognition as it put s a model (the dot pattern) to a number and hence creates a symbolic representation.

Early arithmetic strategies

Facile (Stage 4)

All these questions were answered with relative ease. The child counted on where appropriate. Question 50 did require a quick second look at one of the groups of counters. The only question that proved slightly difficult was the one about how many counters were taken away, however when extended to the SENA 2, a similar question were answered quickly and correctly. The counting by 10s off the decade, and 100s was a task the child was unfamiliar with.

Non-count by one methods need to be introduced and developed by the student. In particular are off the decade counting by 10’s and 100’s, which will come about as three digit number recognition is fostered. The ability to count backwards to solve a subtraction problem also needs to be developed.

NS 1.2 Uses a range of mental strategies and informal recording methods for addition and subtraction involving 1 and 2 digit numbers

- Counts on or back to find the difference between two numbers

- Knows combinations of numbers to make ten

The strategy of counting on or back to find the difference between two numbers needs to be reiterated. The student should also be introduced to the combination pairs that add together to give ten, for assistance in addition and subtraction sums.

Teaching Point: Provide problems that require the child to count on or back in order to find the difference between two numbers. (eg. If there are x objects left, how many have I taken away.) Provide opportunities for the student to experiment in how many different grouping combinations can be found for the number 10.

Consolidation: Use counters in problems that require the student to determine how many were taken away from an original number, when given the answer. The counters can then be used to show how many grouping combinations can be formed with a total of 10.

Various early arithmetic strategies such as counting on, and then skip counting or counting by 10’s, are vital considerations of young mathematics students. This is because addition, subtraction, multiplication and division knowledge is based fundamentally on the development of counting sequences and arithmetical strategies, as well as partitioning and patterning (Bobis, Mulligan & Lowrie, 2004, p. 133). Further to this are the connections between the various operations, such as seeing multiplication as repeated addition (Haylock, 2005, p.69), making it an essential concern that students master one component before they can move on to the next.

Multiplication and Division

Level 1 Perceptual counting by ones (forming equal groups)

This was an interesting task as the student formed three equal groups 5, although found it quite a difficult task. The student counted on from the first group, however kept counting to 20.

Level 2 Perceptual counting in multiples

Uses groups of multiples in perceptual counting and sharing, eg. rhythmic or skip counting.

NES 1.3 Uses a range of mental strategies and concrete materials for multiplication and division.

- Counts on by ones, twos, fives and tens, using groups or multiples in perceptual counting and sharing.

Understanding could be developed using similar activities of grouping and counting on.

Teaching Point: The idea of groups being recognised as individuals and then coming together to form wholes needs to be enforced.

Consolidation: Various materials should be provided so that the child can reinforce the idea of group making and then the forming of whole groups or composite units.

In order to gain a true understanding of multiplication and division, it is necessary for students to be able to see individual groups and then altogether as a composite unit, ‘a collection or group of individual items that must be viewed as one thing.’ (Bobis et al., 2004, p. 134)

Lesson Ideas

Number 1

This is a lesson that focuses on the consolidation of sharing and grouping strategies, the vital foundation for multiplication and division work. The activity involves a series of stations that require the use of various materials and objects to solve problems posed, by applying grouping and sharing strategies. ‘Using and applying mathematics, must always be at the heart of learning the subject.’ (Haylock, 2005, p. 1) The solutions found are recorded on a worksheet by each child. The problems focus mainly on the creation of equal groups and rows, and the sharing out of materials between each group.

Number 2

This lesson is a whole class lesson that further develops the use of grouping and sharing strategies. While teachers must be careful not to repeat lessons unnecessarily, it is essential that adequate opportunity for revision is provided (Zevenbergen, Dole & Wright, 2004, p. 65). It is done so in a practical way, whereby students select a problem at random on a card and are asked to solve it using their peers. The practical involvement addresses the different learning styles of children as only some learners find it easy to learn through watching and listening, while others need to be actively involved (Groundwater-Smith, Ewing & Le Cornu, 2003, p.68). The lesson works with students arranging their peers into equal groups or rows as posed by the card. Some tasks require materials to be shared out amongst the groups, be it hats or other clothing, or some type of food, eg biscuits. The task also asks students to draw a representation of their problem and solution on the board for all to see. This helps children to form representations of their problem solving skills. This practical form of maths engages children and encourages deep learning at the same time.

Number 3

The final lesson in the series focuses on the challenging of the selected, more advanced child. Providing challenges to children is a vital consideration in their development of more sophisticated and efficient strategies (Bobis et al., 2004, p. 132). It introduces a topic from the Stage 1 Syllabus in Multiplication and Division, as they have achieved all that is required of the Early Stage 1 component. The lesson focuses on rhythmic and skip counting methods, and their use to find totals of individual groups and rows, and then progressing on the finding of the total number. The student is asked to work through a hundreds chart highlighting in different colours, the numbers involved in particular counting strategies. This shows the patterns that exist, and provides an easy way to check the sequencing of the various new counting methods. The final component uses unifix cubes to model numbers, and for the child to find the total number, counting by twos, fives and tens.