SENA 1 Report Age: 5 years, 8 monthsYear: Kindergarten | |||||

Aspect to be developed | Where are they now? | Where to next? | Outcomes and indicators | How? | 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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) |