Analyst

Analogical reasoning and mathematical reasoning, is found in both play activities and in more structured learning experiences.  A need to address the frequency of analogical discourse and the contexts in which it occurs is obvious.  This is important for mathematical problem solving and the use of concrete representations.  The ability to detect patterns and relationships is fundamental to both reasoning forms.  This informal learning context is applicable to pre-school years.  Children's increasing cognitive maturity, their learning experiences and informal activities, all contribute to the development of reasoning abilities.

Fostering children's mathematical reasoning was evident in Australian and  American classrooms.  Research has shown that an emphasis needs to be put on identifying patterns and relationships.  Counters and other materials represent numbers.  (Clements, Sarama & DuiBiase, 2003' Ginsburg, Balfanz & Greens, 2000, Ginsburg et al' 2001; Greenes, 1999):    Clements states that learning experiences should be not only enjoyable and meaningful.  They should direct and focus children's thinking on mathematical ways and develop these ideas in an in-depth way. Coloured counters, miscellaneous "junk" items, patterning materials, blocks of various colours, shapes, sizes, linking cubes and base 10 blocks, all contribute to children's cognitive and mathematical reasoning processes.

Taken from Video Streaming in the Workshop of 23.10.14.two two-to-three year old boys are playing together.  They are both adept at counting blocks up to the number of ten.  The boys are respectful of each other and affirm their skills at being able to count up to this number.   The boy's learning has been enjoyable and they acknowledge each other's achievement.   It is probable that both of the boys did know the base numbers up to ten, as they did include three blocks that had been set aside for a time.  These were added to make up the complete number.  Affirming the boy's achievement, it is possible for an educator to further encourage them in numeracy skills.  Spatial awareness can be further learned, with the the opportunity to further contribute in group work, experimenting with heights and length measurements. A good educator can show children how to use relevant mathematically-related materials to create shapes of different types.
With patience, much co-operative learning can be experienced by young children.  Undoubtedly, they retain their learned skills in a much more cohesive manner, when learning is socially-constructed.  Learning can be enjoyable and educational at the same time.


In the video shown on 6.11.14 during the Thursday Workshop, a boy is attempting to build a block of stairs with pieces of wood.  His educator is encouraging him and helps him with his growth of spatial awareness.  She offers suggestions as to room availability for his hands, suggestions for placing the blocks higher than the one before.   Ultimately, the boy's play ends when he has no further blocks available to use.  A puppet is involved in the boy's play and a game of the puppet being able to further and further climb the tower of stairs constructed by the boy, is paramount to his building task.   At one stage,  the boy balances the blocks with his hand, yet this is a short-lived experience.  He becomes aware that he needs to replace it with something else, in order to balance the tower of blocks.  Mathematical learning is taking place here, as the boy learns to think critically  in relation to the vertical tower that he is creating.  Algebraic reasoning takes place as the boy places the blocks in position so that they do not collapse.  He learns patterning also, when shaping the block of stairs, vertically.  Repetition is a good teacher in the continual  stair-making task.    Mathematical concepts that the boy has learned include tipping points (that is - at which point the blocks will fall, if not set out evenly.)  Engineering and science, counter-weight management - this applied when the educator offered the use of her fingers to balance the blocks at certain intervals and fractions were self-taught by the boy as he moved the blocks.  Whole/part fractions were included in his staircase building task.  In order to further foster the boy's learning (individual for him - at this point in time; the educator could ask open-ended questions, affirm his completed achievement using his critical thinking skills, his learning and experience aiding his self-confidence and esteem.  The educator had used intentional teaching by supporting the blocks, as the boy worked towards building his staircase.  Further learning could have occurred if there had been more blocks available for the boy to work with.  I feel that it is very important to not place intentional teaching outcomes over experiments.

In  further experiments, two young toddlers of between one to two years of age are playing alongside of each other.  They are also block-building; one of the boys keen to keep the red blocks to one side, with which to build his tower.  When he uses a yellow block also to complete his work, this boy expresses his pleasure at having performed this challenging task.   The boy was persistent in his task, experimenting with different shaped blocks during his construction efforts.  He has used fine motor skills whilst working on stacking the blocks.  Although this boy was alongside of another boy, he repeatedly worked at his self-given task, physically ascertaining his right and desire to complete his construction, when disrupted by the other boy alongside of him.   An educator could encourage the boy to learn to share, showing him further strategies with which to reach his goal.  Other blocks, possibly of other colours, could be provided by the educator.  This may then have also motivated the other boy to have participated in block-building also.  Learning outcomes such as the weight of blocks, cause/effect, spatial and shape awareness and balance were learned and experienced by the boy.   The educator could also motivate and encourage experiment, question his thought-patterns and doings in his block-tower building.  He/she could emphasis the vertical mathematical concepts of the tower built.  There was obvious enjoyment found in the blocks falling over, the boy's task having been successfully completed.

The Early Years Learning Framework for Australia points out that it is very important for children to feel safe, secure and supported.   They  develop their emerging autonomy, inter-dependence, resilience and sense of agency, when challenged with and able to exercise their critical thinking skills positively.  Children also develop knowledgeable and confident self identities, learning to interact in relation to others with care, empathy and respect.   These factors are paramount to the success of children's individual learning skills and analysing and being competently able to carry out learning prospects in a fair and even manner, fosters their development instrumentally and successfully.  As educators work with and alongside of children in their play , one of the opportunities that they have to further enhance this fair play, is in  helping to instruct children's fairness of respectful and equal relations, when one child or  two or more, dominates in the use of resources.    Further analysis can be given by communicating with children on the ways in which texts construct a limited range of identities and stereotypes.  Drawing children's attention to unfair behaviour patterns when they occur, in relation to observing texts of similar nature,  on a level which children can observe and understand will also help.