Early Numeracy in the Transition from Kindergarten to Primary School – Supporting Children’s Development in Mathematics by Individual Learning Plans Meike Grüßing University of Oldenburg, Germany 17th EECERA Annual Conference, Exploring Vygotsky’s Ideas Prague, 29th August – 1st September 2007

Background Results of longitudinal studies (e.g. Krajewski, 2003) show that knowledge about quantities and numbers can be seen as an important pre-competency for mathematical learning The findings suggest that it is possible to predict and minimize potential mathematical learning difficulties of ‘children at risk’ prior to them starting school

based on mathematical situations in everyday life and play individual assistance children potentially at risk in learning mathematics gifted children / children with special interests in mathematics Mathematics Learning in Early Childhood Education

Aims of the Study The study seeks to investigate young children‘s mathematical understanding in the transition from Kindergarten to primary school to evaluate appropriate assessment instruments to explore how young children can be supported effectively in terms of their number concept development in early childhood education. Sample: in 2005/2006: 850 Kindergarten children (five-year-olds)

The Study Effects of early interventions for pre- schoolers at risk in learning mathematics – A three year longitudinal study (funded by the EWE-Foundation) Year 1: Kindergarten Year 2: Grade 1 Year 3: Grade 2 Tests and interviews (Sept/Oct 05) Early intervention program (Jan – June 06) Tests and interviews (June 06) Tests and interviews (June 07) Tests and interviews (June 08)

 OTZ / Utrecht Early Numeracy Test  Culture Fair Intelligence Test (CFT 1)  German test of mathematical abilities for the 1st grade (DEMAT 1+)  German test of mathematical abilities for the 2nd grade (DEMAT 2+) Instruments standardized not standardized Tasks on visual perception  Elementarmathematisches Basisinterview (EMBI) (basis interview on elementary mathematics)

Instruments The data collection in kindergarten is based on two different instruments: OTZ / Utrecht Early Numeracy Test (van Luit, van de Rijt & Hasemann, 2001): –a standardized test aiming to measure children‘s development of number concept

Instruments EMBI (ElementarMathematisches Basis- Interview) including a preschoolers’ interview –A task-based one-on-one interview which allows children to articulate their developing mathematical understanding through the use of specific materials provided for each task –This interview is based on the ENRP-Interview developed by the research team of the Australian Early Numeracy Research Project (e.g. see Clarke, 2001)

P1: Simpler Counting Tasks – More or Less – Conservation Place a pile of 20 teddies in front of the child in a scattered pattern, made up exactly by 4 yellow teddies, 5 red teddies, 3 green teddies, and 8 blue ones Please put the yellow teddies together. How many yellow teddies are there? Put a group of 3 green teddies together near the 4 yellow teddies (giving two different small groups) Are there more green or more yellow teddies? Push the yellow and green teddies aside. Please get five blue teddies... Now put them in a line. (If the child has already put them in a line, ask the child to “move them together now“.) … Tell me how many blue teddies there are.

P3: Subitizing – Matching Numerals to Dots I‘m going to show you some cards quite quickly. Tell me how many dots you see. Show each flashcard for 2 seconds only, in the following order and orientation. Now put the dot cards all down in the order shown here. Spread out the 0 – 9 cards randomly, face up, in front of the child, between the child and the dot cards. Find the number to match the dots. (If the child seems puzzled that there are more numeral cards than sets of dots, explain that “you won’t need to use all the numbers.”)

Results of the OTZ (September/October 2005)

Results of the EMBI Preschoolers’ Interview (Sept/Oct 2005)

Results of the EMBI Preschoolers’ Interview (September/October 2005)

Findings Based on interviews with 850 kindergarten children (five-year-olds), a range of number skills that most pre-schoolers demonstrated especially in the material based interviews, were identified. However, around 10 % of the children clearly struggled with certain areas relevant to the development of number concept such as seriation, part-whole-relationships, ordering numbers and counting small collections. They were identified as ‘children at risk’ with respect to their later school mathematics learning.

Intervention Program  Group 1: individual intervention program conducted by preservice teachers during weekly individual sessions  Group 2: Intervention program conducted by the kindergarten teachers within their groups (supported by the researchers)  Group 3: no further support

Intervention Program  Group 1: individual intervention program conducted by preservice teachers during weekly individual sessions  Group 2: Intervention program conducted by the kindergarten teachers within their groups (supported by the researchers)  Group 3: no further support

... should focus on important mathematical ideas ... should be connected to children‘s everyday life and play ... should be based on lots of experiences with all senses ... should be based on appropriate assessment Early Mathematics Learning

A questionable example: Personified numbers

Mathematics and Play Which number do you need to win?

Mathematics learning with all senses Can you jump in steps of two?

Role of the teacher In order to support children in their mathematics development, teachers need to be able to identify children‘s current individual knowledge and skills They need to have knowledge about certain “milestones” or growth points with respect to the mathematics development This knowledge is needed to be able to lead children into their “zone of proximal development”

Finn5 Y 8 M (–)(–)  Development of individual learning plans  (–)(–)

Example: Individual learning plan for Finn FocusContents and activitiesMaterial One-to-one correspondence Co-ordinating number words with the objects to be counted One-to-one correspondence Teddies, pencils, wooden cubes, etc. Counting activities Counting collections Making sets Reading numbers Subitizing Ordinal numbers Various materials Dice “Mice race“ Cards with numerals and dots “Number road” Games: Bingo, Memory, Domino Comparison and seriation Comparison of sets Ordering objects Teddies, pictures, pencils Mathematical language Language of locationTeddies “Number road”

„Mice Race“ „Numbers Road“

Finn writes numbers Finn builds a juice factory

Results of the EMBI Preschoolers’ Interview

Evaluation of the Enhancement Program: First Results EMBI

Finn5 Y 8 M (–)(–)  Results of the Second Interview  (–)(–) 6 Y 4 M Finn   ()()()() (–)(–)(–)(–)(–)(–) 

First Results of the DEMAT 1+ Finn‘s score: 23

First Results of the DEMAT 1+ Identified as „Children at Risk“ Finn‘s score: 23

Findings and implications Especially the results of the EMBI-Interview provide the teachers with valuable information about the mathematical thinking of children and they are useful to develop learning plans. The children who took part in the intervention program generally made progress in their mathematics learning There is evidence to suggest that it is possible to minimize potential mathematical learning difficulties of ‘children at risk’ prior to them starting school Further data analysis is needed! (study in progress)