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SENA 1 Report     Age/Year: Kindergarten
Aspect to be developedWhere are they now?Where to next?Outcomes and indicatorsHow?Why?
Numeral identification     Level 3: 1-100Can confidently identify numerals up to 100 most of the time. The student could not say the number 101 out loud, but has shown in later tasks that she is aware of these numbers.Level 4: 1-1000The student can identify numerals up to 100 and should progress to numerals up to 1000. However some consolidation should be considered before moving on to the next level to ensure that the student is confident in recognising numerals from 1-100. NS1.1 Counts, orders, reads and represents two- and three-digit numbers·  Recognises and identifies two and three digit numbers·  Say and write two and three digit numbersUse activities that are stimulating for the child and assist them in identifying numbers 1-1000.Teaching input: Teacher should introduce new numbers by talking and writing about them. Exploration of these numbers should also be included with resources such as a number chart and flash cards.Consolidation: Activities such as bingo can assist students in recognising a numeral to a spoken number. Numeration is the foundation for many other procedures in mathematics, with naming numbers the most fundamental concept needed in numeration (Booker, Bond, Briggs & Davey, 1997, p. 54-55). The ability to interpret numbers is also seen by Turkel and Newman (1988) as a characteristic of those with number sense, which is important in ensuring a student’s ability to do mathematics. Without knowledge of numbers, students will not be able to develop further mathematical knowledge or skills.
Forward number word sequence Level 5: Facile (100)Can count forwards confidently from varying numerals particularly with numerals under 50. The student could count past 100 however stopped at 109 and did not know what came next. The student also hesitates a little before jumping to the following decade. In identifying the number after, the student often counted on from the nearest decade to arrive at the answer with numerals after 20.Level 5: Facile (100)The student needs consolidation in counting forwards with concentration on numerals greater than 50 and with the jumps between decades.NS1.1 Counts, orders, reads and represents two- and three-digit numbers·  Counts forwards by ones from a given two-digit number·  States the number after a given two-digit numberBuild confidence through various activities in recognising the number after a number stated and FNWSTeaching input: Reinforcement of counting sequences using number charts and calculator activities to count forwards by ones. Also emphasise the jumps from decades and introduce larger numbers.Consolidation: Activities such as filling in the blanks on a number chart can reinforce the student’s ability to count forwards and develop a forward number word sequence. Bingo can also be adapted to covering the number after the number that has been called out. Effective teaching of forward number word sequences can assist in the development of counting on strategies. These counting on strategies will then in turn assist the child in developing addition skills. These sequences will also assist students in seeing the relation of one number to another and establish place value. The use of calculators assists children to establish efficient and accurate counting skills. It also assists them in further developing their concept of number (Lindquist, Reys & Suydam, 1984, p.67).
Backward number word sequence Level 5: Facile (100)Can count backwards with numbers up to 100, however in task 32 skipped 100 and went straight to 99. The student was not confident in counting backwards from numbers greater than 10 and often counted forward first in their head to then count backwards. Level 5: Facile (100)Although the student can count backwards, it is important to consolidate this level, as the student often counts forward from the closest decade before counting backwards.NS1.1 Counts, orders, reads and represents two- and three-digit numbers·  counts backwards from a given two digit number·  does not rely on counting forwards first before counting backwards Build confidence through various activities in recognising the number before a number stated and BNWS, particularly with numbers greater than 20.Teaching input: Similar to FNWS and help student gain confidence between the jumps between decades.Consolidation: Filling in the blanks activities can help student gain confidence in knowledge of BNWS. Counting backwards should be practiced as much as forwards as it also helps to establish sequences but relates each number to another in a different way (Lindquist, Reys & Suydam, 1984, p.66). Backward number word sequences are also a good way to introduce zero, which should be included in numeral recognition. Backward number word sequences are also linked to counting backwards, which will assist developing subtraction.
Subitising                                   Level 2: ConceptualCan recognise the eight dot and nine dot patterns. Student saw these patterns as two separate groups and counted on to make them whole.Level 2: ConceptualAs the student has already reached the highest level of subitising, emphasis can be placed on building the student’s efficiency and confidence in recognising dot patterns and ability to combine separate groups as a whole.NS1.1 Counts, orders, reads and represents two- and three-digit numbers·  can recognise dot patterns extending beyond the number 6·  can combine two dot patterns representing 1-6 and recognises them as part of two groups and a wholeActivities using ten frames to develop knowledge of patterns and number facts beyond 6Teaching input: Reinforce the idea that two separate groups can form a whole group. Use ten frames to explore the different combinations of smaller groups to form a whole group.Consolidation: Using two dice to reinforce the idea of two separate dot patterns can form a whole. These dice could be used in a game of bingo, where students take turns rolling two dice and call out the number as a whole for bingo.The skill of subitising is useful for early number work and assists simple mental addition and subtraction. It is also essential for the development of concepts of number (von Glasersfeld, 1982, cited in Dole, Wright & Zevenbergen, 2004, p.131). Using counters to facilitate subitising will allow for more effective counting and operation strategies (Dole,, 2004, p.131), which is one of the key aspects in the Learning Framework in Number (1999).
Early arithmetic strategies Stage 4: FacileStudent largely uses counting on strategies to solve problems. However the student has shown evidence of skip counting and knowledge of doubles. SENA 2 task 17 was carried out and student was able to state that 5+5=10Stage 4: FacileDespite showing evidence of more sophisticated strategies, the student requires consolidation in solving problems without concrete materials. The student should also develop more confidence in utilising counting on and backwards strategies and to solve problems.NS1.2 Uses a range of mental strategies and informal recording methods for addition and subtraction involving one- and two digit numbers·  counts on from the larger number to find the total of two numbers·  counts on or back to find the difference between two numbersUse activities which encourage students to count on and back.Teaching input: Emphasise that it is more effective to count on from the larger number, rather than starting back at one.Consolidation: Activities where students are not provided with concrete materials to solve problems, and instead utilise knowledge of counting on and backwards to solve problems.The integration of mental computational skills in early years enables the development of robust number fact knowledge and informal, non-standard algorithms based on number sense (Bobis, Mulligan & Lowrie, 2004, p. 160).  Utilising arithmetic strategies such as counting-on also allows for more efficient methods of solving problems.
Multiplication and division Level 1: Perceptual counting by ones (Forming equal groups)Can form three groups of four with ease, but counted out each four by ones. When asked to comment on how many altogether, the student counted on from eight, showing awareness of doubles.Level 2:  Perceptual counting in multiplesUses groups or multiples in perceptual counting and sharing. Eg. Skip-counting and one-many dealing.NS1.3 Uses a range of mental strategies and concrete materials for multiplication and division·  counts by ones, twos, fives or tens·  uses counting strategies to find the total number of objects eg rhythmic counting, repeated additionProvide activities which will introduce skip counting, repeated addition and the idea of multiples. Teaching input: Ensure that students understand the idea of equal grouping and that counting doesn’t have to involve counting by ones.Consolidation: Group activities which involve counting loudly and softly to emphasise multiples. Activities which involve sharing concrete materials between groups.Skip counting forwards and backwards is an important learning experience as they are precursors for multiplication and division (Dole, 2004, pp. 130-131).
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