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Comparison/ differences of the three frameworks: Lee's seven mathematical categories, Bishop's six mathematical activities and Preschool Numeracy Indicators 

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Comparison/ differences of the three frameworks: Lee's seven mathematical categories, Bishop's six mathematical activities and Preschool Numeracy Indicators 

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There is considerable overlap among the three frameworks, but each provides a unique perspective. Lee's categories focus on observations of children's play behaviours, while Bishop's activities are theoretical, proposing universal mathematical actions. In contrast, the Preschool Numeracy Indicators are pedagogical and designed to guide educators in identifying, planning for, assessing, monitoring, and reporting on each child's learning and growth.

Both Lee's and Bishop's frameworks highlight the importance of counting as a key mathematical activity. The Preschool Numeracy Indicators build on this by emphasising the development of confidence in counting and comprehension of quantities, helping children to make sense of their world through quantification.

Lee's spatial category corresponds with Bishop's "Locating" and the Indicators' statement, 'I explore and understand my place and space in the world.' Both emphasise the significance of comprehending positions and relationships in space.

All three frameworks recognise measurement as a key mathematical concept, emphasising the comparison and quantification of attributes.

The shape category can be compared to Bishop's 'Designing' and numeracy Indicator 'I explore and understand my place and space in the world'.

Lee's 'Pattern' category and the indicators' focus on patterning in the learning processes related to Bishop's concept of "Designing," which involves creating structured arrangements, often incorporating patterns.

Lee's framework includes "Classification," which involves grouping objects based on attributes. It can link to the Indicator's sorting learning processes and Bishop's 'Explaining.'

Problem-solving is essential in the three frameworks as children learn through various trial-and-error strategies.

Play is a vital component of the three frameworks through which children learn mathematical and scientific concepts.

Activities incorporating counting, measuring, spatial awareness, classification, and problem-solving seamlessly connect with scientific exploration. For instance, when children pour sand into various containers, they grasp scientific concepts like mass and volume. Involving children in hands-on, inquiry-driven play promotes both mathematical and scientific reasoning in a relevant and interconnected manner.

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Lee provides analysis of an observational study showing the incidence of early mathematical concepts in children's natural play. The mathematical concepts identified by Lee, were space, number, shape, measurement, pattern, classification and problem solving. These concepts overlap with the universal categories outlined by Bishop.

The importance of quality play opportunities is highlighted, when we consider the strong link between Lee's observation of the presence early mathematical concepts in play and the preschool numeracy indicators.

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Comparing the 3 different forums I find that they are all very similar but with different groupings. The preschool indicators are a lot broader in their use of headings. Bishops groupings are broken down into very specific concepts whereas Lee's are very much play-based concepts. Bishops activity area of playing can be seen throughout all of Lee's categories. All 3 forums use the areas of measurement and number/counting/quantify. One area I find lacking in Bishops activities is the concept of space in regard to the spatial understanding that children, particularly young children, discover and explore at this age. He discusses it slightly in the area of Locating where he discusses the concepts of up/down, left/right and forwards/backwards. However, children's exploration of space around them, manipulating their bodies or objects through, over and under are very important concepts at this age.

Through all 3 forums, science can be easily linked to these concepts. As children involve themselves in learning, discovering, investigating and observing to obtain the required knowledge.

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Compare and contrast Lee categories with Bishop and preschool numeracy indicators

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Compare and contrast Lee categories with Bishop and preschool numeracy indicators

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Lee's 7 identified 7 mathematical categories:

Space - Number - Shape - Measurement - Pattern - Classification - Problem solving

Bishops 6 universal activities: Counting - locating - measuring - designing - playing & explaining

preschool numeracy indicators:

I explore & understand my place and space in the world

I measure & compare my world

I analyse, read & organise data in my world

I quantify my world

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When comparing all three, the concept of change in the state of a measure can be linked to the act of measuring and comparing the world around us. Measurement is emphasized across all three frameworks—Lee’s, Bishop’s, and the Preschool Numeracy Indicators—highlighting its importance in both science and mathematics development. While play is not explicitly mentioned, it is assumed to be integrated into the activities.

I observed that Lee and Bishop’s frameworks provide direct instruction on mathematical categories, whereas the Preschool Numeracy Indicators offer a broader perspective, allowing for flexibility in how and what is taught. The scientific concepts of patterns, form and function, stability and change, scale and measurement, matter and energy, and systems can all be interconnected across these frameworks. Encouraging children's natural dispositions of wonder, curiosity, and excitement through relatable learning experiences fosters deeper engagement with these fundamental concepts.

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The three studies, Lee's, Bishop's, and the Preschool Numeracy Indicator, emphasize measurement as key to understanding change and comparing our world. While Lee and Bishop focus on specific math categories, the preschool Numeracy Indicators offer more flexibility in their teaching approcah.

Science concepts like patterns, change, measurement, and energy can be connected across all frameworks. Play-based learning activities are the main part of the learning activities, as children discover and explore when playing with curiosity.

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All three frameworks, have a significant overlap in their outcomes for learning.

Bishops 6 I found was to be precise and intent based in acknowledging critical structure in mathematical concepts.

Numeracy Indicators, was left open to interpretation and had more room for concepts to develop and for Educators to focus on laying those foundations.

Lee's 7 Mathematical categories is a balance between the two, leaning more into identifying areas of mathematical learning.

All three can be used to link with scientific inquiry based learning, for example in a water based play with scoops and pouring, you can introduce counting, volume terms; like full, half, empty, weight, problem solving if there's holes, using language to help build and solidfy those concepts into the cognitive processes of the childen involved.