Early number pv workshop
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The document discusses early concepts of number and counting for young children, outlining stages of development like understanding number sequences, one-to-one correspondence, cardinality, and conservation of number; it also examines how children represent mathematics through mark-making, considering samples in relation to key counting and number concepts, and assesses learners' understanding.
Early number pv workshop
- 1. Early Number Concepts
- 2. Learning outcomes At the end of this tutorial and self study you should have: •developed your knowledge of the stages of development towards acquiring mathematical concepts, particularly number •raised your awareness of the mathematics going on in an early years setting •helped you devise and encourage relevant mathematical experiences leading to mathematical ideas for young children •Examined some resources and considered their use in the early years
- 3. Early Years Mathematics Margaret Donaldson Children’s Minds 1978 (Fontana) ‘An adults knowledge of the general nature of the subjects taught to children when they first enter school is apt to be so well established that it blocks the realisation of precisely what the children need to be helped to see.’
- 4. Counting 1 - 19 • I have explored numbers, understanding that they represent quantities and I can use them to count, create sequences and describe order MNU 0-02a
- 5. Early Years Mathematics Counting What does it mean? View video – ‘Twice five plus the wings of a bird’
- 6. Early Years Mathematics Counting and Numbers From the video we can see that a child must • know the sequence of number names. • Be able to match one-to-one words with objects being counted (one-to-one correspondence). • Be able to identify a set to be counted (or a subset) • Understand that the last number name in a count gives the numerical size of the set of objects (ie. the cardinality) of the set. • have conservation of number. • understand the abstract concept of number ie. sets of 4 whatever have the common property of 1, 2, 3, 4. • can start counting a set in a different place and realise the number is the same (advanced conservation). Refer to the concept maps for ‘Number’ and ‘Counting’
- 7. Early Years Mathematics Counting and Numbers Assessment of learners • Activity – Read and discuss ‘Talk 1’ • Activity – Read and discuss ‘Talk 2’
- 8. Early Years Mathematics Children’s Mark Making Children should explore number situations, count, begin to calculate, talk about how they worked things out and record or represent their mathematics in their own ways “Learning involves moving progressively from concrete examples to the use of symbolic representations.” Building the curriculum 2 – Active learning, A guide to developing professional practice, Scottish Government (2010) Consider: 'Children’s Mathematical Graphics: Understanding the Key Concept’ Carruthers and Worthington (2009)
- 9. Early Years Mathematics Children’s Mark Making Task: Consider the sample recordings in relation to the key concepts of number and counting. • knows the sequence of number names. • can match one-to-one words with objects being counted (one-to-one correspondence). • can identify a set to be counted (or a subset) • understands that the last number name in a count gives the numerical size of the set of objects (ie. the cardinality) of the set. • has conservation of number. • understands the abstract concept of number ie. sets of 4 whatever have the common property of 1, 2, 3, 4. • can start counting a set in a different place and realise the number is the same (advanced conservation). What assessments can be made?
- 10. Introducing place value I have investigated how whole numbers are constructed, can understand the importance of zero within the system and can use my knowledge to explain the link between a digit, its place and its value. Responsibility of all MNU 1-02a
- 11. Introducing place value Use unstructured materials to show the number 34 Use semi-structured materials to show 34 Now make 34 using structured materials How is 34 displayed on an abacus? Discuss the difference between each of the materials in terms of helping children develop understanding of place value. Online manipulatives - Chip Abacus Click here for an interactive abacus
- 12. Using Structured Material Activity Use structured material to show these numbers 256 1089
- 13. Using Structured Materia Children should be given practice in investigating different ways of partitioning numbers using blocks:- 234 - 2 hundreds 3 tens 4 units 23 tens 4 units 2 hundreds 43 units 234 units Activity - Investigate six different ways to make 248
- 14. A comparison Activity Discuss the difference between the two types of cards. 3 300 60 6 4 4 What do you think is meant by the ‘quantity value’?
- 15. Place Value Mark-up Play this game. What knowledge and understanding does this activity reinforce?
Editor's Notes
- #7: There should be a variety of counting materials on the tables. Discuss and illustrate each of the principles. Spend some time modelling and talking about activities that could be used. Remind students that there are lots of ideas and resources to be found on BB. Give out the concept maps - 'Number' and 'Counting' and suggest that students work together to identify ideas for the blank activities column.
- #8: There should be a variety of counting materials on the tables. Discuss and illustrate each of the principles.
- #9: Consider: How are you first going to introduce ‘Place value’ (previous input) – bundles of ten, then bundles on PV board, then bundles, board and PV cards, then B,B & digits, towards just digits
- #11: Discuss the important role of Place Value
- #12: Each table should have different unstructured materials Straws Pennies
- #14: Worksheet provided