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Evidence 1

SENA 1 Report     Age: 5 years, 8 monthsYear: Kindergarten
Aspect to be developedWhere are they now?Where to next?Outcomes and indicatorsHow?Why?
Numeral identification     

Level 2: 1-20 

Can recognise most numbers from 1 to 20. 12 was recognised as 20, and 23 was recognised as 13, indicating some confusion between teens and tens.

Level 3: 1-100 

Moving onto Level 3 with focus on the recognition of teens and tens, consolidating the recognition of numbers 10-20 from Level 2.  

NS1.1

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

Indicators:

Recognises and names  2 and 3 digit numbers   

To consolidate Level 2 Activities/Consolidation -Counting and bundling groups of 11 to 19 items.-Using ten frames to represent numbers 11-19.

Teaching point -Highlight that the oral language pattern of numbers 11 to 19 is the reverse of the usual pattern of “tens first and then ones”. At the same time encourage the student to describe the teen numbers as “ten and one” (11), “ten and two” (12), and so on, to ensure that they understand the meaning of the number. 

Advancing to Level 3 Activities - Use activities that focus on place value

Teaching point - Describe the number 35, for example, as 3 tens and five ones before introducing the term “thirty-five”. At the same time, emphasise that a digit has a fixed face value, but that its place value depends on its position in the numeral.

Consolidation -Use place value charts and blocks to count forwards and backwards by ones between 20 and 100-Use of number expanders to demonstrate the relationship between place values and digits in numbers

Students need to recognise and identify numerals in order to accurately record their mathematics (Department of Education and Training, 2002, p.45), and to interpret and manipulate written mathematical problems. Understanding the difference between tens and ones, in terms of place value, will help students in using strategies other than counting by ones to solve problems (Department of Education and Training, 2002, p.153).  Furthermore, without any understanding of place value, numbers above 9 will have little mathematical significance, and be no more than a symbolic representation of a verbal label.
Forward number word sequence 

Level 4: Facile (30) 

Can count to 30 and give number after. The student was able to identify some numbers directly after numbers greater than 30, and could count on from 96 to 100. In being unable to identify the number after 69, but able to identify numbers after 27, 46 and 80, it is likely that counting over the decade may be a problem.

Level 5: Facile (100)

 Counting on from numbers between 30 and 100, ensuring the ability to both count on between a range of numbers, and give the number after. Focus may be needed on counting over the decade.

NS1.1

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

Indicators:

Counts forward by ones from a given 2 or 3 digit number. 

Identifies the number after a given 2 or 3 digit number

Activities - Use activities that require counting on from a given two digit number up to 100, as well as those that require identification of numbers just after a given multiple of ten.

Teaching point -Revisit place value and identify the same forward number pattern in the ones column for each multiple of ten. Introduction of counting by tens from a given number may help to consolidate this concept (for example, 36, 46, 56, etc)

Consolidation-Use number lines to count on from a given number by ones and tens-Peg numerals in order on a clothesline with focus on “the number after”-Use of a 100’s chart to identify patterns-Circle counting-Fence posts (putting numbered paddle pop sticks in sequential order) 

Students need to be proficient in forward number word counting in order to move to counting-on strategies and solving addition problems (Department of Education and Training, 2002, p.31).  If students are able to automatically name the number after a given number they will not have to rely on counting from one in order to solve problems (Department of Education and Training, 2002, p.99).
Backward number word sequence 

Level 3: Facile (10)

Can count backward from 10 and give number before without the need to count from one. The student was able to count backward from 103 to 101, however, was not able to count backward from 23. It is assumed that this is because of the vocal emphasis on the “3” in 103, in comparison to 23, and the consequential recognition of being able to use the same counting pattern as for numbers less than 10.

Level 4: Facile (30) 

Counting backward from numbers up to 30. Focus should be on recognition of the same backward number sequence in the ones column, regardless of the tens.

NS1.1

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

Indicators:

Counts backward by ones from a given 2 or 3 digit number.

Identifies the number before a given 2 or 3 digit number

Activities-Use activities that require counting backward from a given two digit number up to 30, as well as those that require identification of numbers just before a given number up to 30.

Teaching point- Exposure to backward number sequencing is not as common as forward number sequencing and, as such, the student will find it more difficult (as is evident in this SENA assessment). It may be necessary to discuss with the student to clarify the meaning of “before”.

Consolidation-Use of a number line to count backward from numbers up to 30.-Pegging numerals up to 30 in order on a clothesline with focus on “the number before”. -Circle counting 

Students need to know the correct backward counting sequence in order to count down from a number to solve subtraction problems (Department of Education and Training, 2002, p.79). If students are able to automatically name the number before a given number, they will not have to rely on counting from one.
Subitising                                   

Level 2: Conceptual 

Student is able to see the eight-dot & nine-dot domino pattern as both two groups and “as a whole”. There was not instant recognition of the above mentioned patterns. In identifying the eight-dot and nine-dot patterns the student was able to recognise two groups. However, she used her fingers to represent the dots in each group to come up with the total, indicating use of perceptual strategies.

Consolidation at the Conceptual level. 

Work towards instant recognition of grouped domino patterns such as the eight-dot and nine-dot pattern in questions 45 and 46.  

NES1.1

Counts to 30, and orders, reads and represents numbers in the range of 0 to 20 

Indicators-

Can instantly recognise dot patterns greater than 6- Can see dot patterns as two groups and as a whole

Activities- Use activities that require subitising beyond six-dot domino patterns.- Practice recognition of basic addition number facts to enhance instant identification of grouped dot patterns.-Activities that allow for visualisation of number facts.

Teaching point-Ensure students understand the concept of joining two groups to make a whole.- Encourage students to use a variety of terms to describe the joining of groups, eg. put together, add, makes, join.- Use incidental opportunities during the day to draw students’ attention to addition.

Consolidation-Have students make number sentences using dominos- Have students come up with as many different dot patterns as they can to represent the same number, encouraging recognition of different number facts-Use ten frames to consolidate addition facts     

Instant recognition of dot patterns can lead to strong visualisation and mental images for students. This visualisation will assist them in counting and problem solving tasks, recalling number facts and understanding number relations without the use of concrete materials (Department of Education and Training, 2002, p.28-115; Bobis, Mulligan & Lowrie, 2004, p.125).    
Early arithmetic strategies 

Stage 3: Counting On 

Uses larger number and counts on to find the answer. For questions 47, 48 and 49 (counting and addition using concrete materials), the student counted by ones. For questions 50 to 52 (word problems requiring addition), she counted on from the larger number. The student was able to complete question 53 (subtraction word problem) by counting back from the larger number, but could not complete questions 54 or 55 which required subtraction from larger numbers. For these questions, the student attempted to use her fingers and count from one.

Stage 4: Facile 

Uses known facts and other non-count-by-one strategies to solve problems.Developing the strategies of partitioning and using doubles to enable addition and subtraction of larger numbers 

NS1.2

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

Indicators:-

Uses larger number and counts on to find the answer

Uses the strategies of grouping and partitioning - Uses doubles, doubles plus one, and near doubles

Uses a “making a ten” strategy

Activities-Use activities that will allow students to easily apply a range of mental strategies in order to solve simple addition and subtraction problems

Teaching points- Highlight the efficiency of using mental strategies- Encourage the use of a range of different strategies- Have students record the strategies they have used to solve problems- Have students come up with different ways of solving the same problem.

Consolidation- Using base 10 materials to represent number problems- Using open number lines to solve addition and subtraction problems 

The development of non-count-by-one-strategies within the range of 1 to 20 is important. Counting by ones is slow and error-prone, while more advanced strategy use promotes number sense and numerical reasoning, and develops a part-whole conception of numbers, providing a basis for further learning (Wright, 2007).
Multiplication and division 

Level 1: Able to form groups (counting by ones) 

Although the student was able to form equal groups, she was unable to come up with the correct total. She was able to add two groups together by subitising  4 and 4, however, she identified the total number of counters as  9 (instead of 12), by adding 1, as representative of  “one more group”, instead of another  4 from the third group of four. This suggests that more work on whole-part knowledge and composite wholes is required.

Level 2: Perceptual Multiples 

Consolidation of composite wholes is required. Although this student appears to understand that a group or collection of items should be viewed as one (that is, one group of four counters), she has not grasped the concept of counting in multiples.

NS1.3

Uses a range of mental strategies and concrete materials for multiplication and division. Indicators:-Uses skip counting- Can construct arrays to represent multiplication and division

Activities - Use activities that require making equal groups, sharing, and counting collections.

Teaching Points - Do not place any emphasis on the memorisation of multiplication factors, but rather the concept of equal groups being added to give a total- Introduce the use of repeated addition and skip counting- Use activities that link concrete materials and pictorial representations

Consolidation - Constructing arrays- Forming equal groups in games such as “Teddy Bear Restaurant”- Skip counting games (whisper counting, rhythmic counting)- Sharing problems using concrete materials among small groups.

Students need to view a group as one countable item in order to develop multiplication and division concepts (Department of Education and Training, 2002, p.123). The development of counting in multiples supports the understanding of multiplication and division (Department of Education and Training, 2002, p.125). Students need to develop concepts of making and counting equal groups in order to solve multiplication and division problems (Department of Education and Training, 2002, p.131).The ability to divide a collection of objects into equal parts is critical to the logical development of part-whole relationships and the idea of equality and inequality. It may also be important for children’s understanding of other mathematical topics such as measurement and geometry (Lamon, 1996, p.170)
                               
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