Primary School KS2 (Key Stage 2) Maths - Number Patterns and Sequences - Ages 7-11 eBook
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Primary School ‘KS2 (Key Stage 2) - Maths – Number Patterns and Sequences - Ages 7-11’ eBook
We'll publish them on our site once we've reviewed them. Continue shopping. Item s unavailable for purchase. Please review your cart. Both formative and summative assessment of these skills is recorded in each child's Early Learning Profile. Early years practitioners are encouraged to use play as part of the child's learning activities and the focus is on providing the basic skills necessary to make the transitions into KS1. At all stages there is a general attainment target for using and applying mathematics. However this does not have detailed standards and is included to ensure that teachers instruct students about the connections between different areas of mathematical knowledge National Curriculum for England Mathematics, , p.
The skills measured at KS1 come under two broad sections called number and shape, and space and measures. Under each section the curriculum outlines a number of standards that set out detailed targets. This includes patterns of multiples of 2, 5, and 10, sequences of odd and even numbers and the relationship between halving and doubling National Curriculum for England Mathematics, , p. At KS1, academic performance is assessed via individual teacher assessment against the National Curriculum Attainment Targets rather than by examination and pupils is expected to achieve KS1 level 2.
At KS2 the skills measured are number; shape, space, and measures, handling data, and mental arithmetic.
Again each section has standards with associated targets. Pupils at KS2 have formal assessments in the final year of primary school and this provides information about the children's math performance before they move onto secondary schooling and KS 3 and 4.
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Pupils are expected to reach a KS2 Level 4 standard in mathematics and schools were set a target to ensure 60 per cent of pupils achieve this standard DfES, The skills measured at KS3 come under the same broad topic headings as at KS2. As expected, the level of difficulty and range of skills required increases. For example, within the handing data topic children are expected to move up to a level of understanding where they can use statistical calculations and begin to use probability.
Similar to KS1, pupils are assessed through teacher assessment and pupils are expected to reach either KS3 Level 5 or 6 in mathematics National Curriculum for England Mathematics, , p. In contrast to the English system, the mathematics curriculum in the US has been largely up to individual states before introduction of the new curriculum ; there was no common curriculum.
In , a nationally representative sample of , children from 21 urban districts of the US were assessed on five content areas: number properties and operations e. Thus it appears that the number of children with difficulties increases as they progress through the curriculum.
Although it is not possible to compare performance between the English and US children because the measures of assessment differ considerably, as well as the ages of the children, it is clear that a significant number of children in both countries are not achieving attainment targets in mathematics. Educators in the US and elsewhere have found it necessary to redefine what students should be able to understand and do when learning mathematics.
They defined common core standards, while recognizing that the assumption that what is learnt before should determine what is learnt at a later stage is unwarranted, given the current state of the science. At the moment, indeed, only partial models of learning pathways to mathematical concepts and skills can be obtained from scientific and education research, with very few exceptions see e. The criteria for the standards were developed from academic research; analyses of which skills are required of students entering college and workforce training programs and by looking at standards from high achieving nations and data from the TIMSS in collaboration with some of the teaching bodies within the US.
For the purpose of this review, which concentrates on children up to age 11, we will report the four key domains: Operations and Algebraic Thinking; Number and Operations in Base 10; Measurement and Data; Geometry. In addition Counting and Cardinality is included for Kindergarten and Number and Operations is included for Grades 3 and 5. Within each domain, there are several standards, clustered into related standards.
The first assessments of this new curriculum are due to begin in the — school year. Specifically assessing mathematical understanding means assessing: 1 the ability to generalize knowledge to novel situations, 2 the ability to explain the underlying meaning of procedures. Difficulty with math is not only defined by an inability to follow the procedure but may unveil a deeper problem i.
To assess learning, we needn't focus exclusively on achievement: apparently normal achievement at one stage, may still lead to later difficulties with numbers, if it is exclusively driven by procedural learning. Difficulties may appear at a later stage due to lack of proper understanding at earlier stages; a child who shows MD at Grade 7 may not have understood concepts from Grade 5 and 6 despite normal achievement.
Both the current English and new US curricula provide clear and detailed targets for arithmetic development and how children will build up an understanding of this complex discipline, and there are many commonalities between them.
For example, they both have a strong focus on counting and place value within the early years and use this skill as a basis for progression onto calculations. Calculations are conducted first with single digit and then multi-digit numbers. They both also have a focus on shapes, space, and measurement that begins in early years and is included at all levels of the curriculum.
However there are also differences that may impact on the selection of MD children. The US curriculum is much more strongly focused on number and operations within the early grades and purposely does not introduce additional topics until later schooling The Hunt Institute, The idea behind this was to achieve an intricate grounding in these skills which can then be taken forward to new skills later in the trajectory. There is also more emphasis on conceptual understanding than rote procedural learning.
The English curriculum does introduce these other topics. For example it has a strong emphasis on patterns. Another contrast is that the English curriculum outlines the use of mental models for calculation. The target is to develop rapid recall of number facts and procedures; a target which calls directly on memory processes.
In the remainder of this article we will provide an overview of one of the mathematical development models that, in our opinion, looks promising for the identification of potential causes and areas of intervention in MD. These can occur at any stage of primary schooling when there is a decoupling between the general expectation and an individual's actual developmental trajectory.
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Although our knowledge on mathematical learning and cognition has enormously expanded in the last few decades, there is no consensus or comprehensive developmental trajectory for mathematical skills, let alone a consensus model on MD. Grade placements for specific topics are therefore suggested on the basis of national and international comparisons, educators' collective experience, and researchers' and mathematicians' professional judgment. By establishing a standard set of principles and objectives on such basis, the initiative opens to the possibility of improving the process on a large scale as research on learning and effectiveness progresses.