Learning in mathematics and science

Rationale

A cross curricular resource box designed to develop children’s understanding of scientific and mathematical concepts, through ‘The Rainbow Fish’ theme has been produced. The box contains activities for Reception children exploring counting in Mathematics and material and properties in Science.

This rationale explains how activities based from the rainbow fish provide conceptual learning in Maths and Science.

Counting is important in providing a foundation for Mathematics. Children will always experience situations where counting skills are vital. The National Curriculum states, counting helps develop skills applicable in everyday life and context. Using the Primary Numeracy Strategy (2006, online) ‘using mathematical methods and ideas to solve practical problems’ and ‘identifying numbers that are one more or less than a given number’ are mentioned in EYFS (2007,online) and developed throughout children’s schooling experience (5B,4B,2B,1E)

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Anghileri (2001, p.6) says counting is learnt suddenly. Children may spontaneously learn counting because they should be experiencing counting in different contexts: cross curricular, play etc. Anghileri (2001) assumes the above occurs because children are making links through context. Yet this is a generalisation, children are different and may need reinforcement or interaction, to firstly understand how they are learning, which then allows making links.

Both Askew and Wiliam (1995, p.5) declare learning to count as mechanical. Askew and Wiliam’s proposition lacks clarity as to how and why counting is mechanical and what the implications are towards children’s learning. One cannot say children feel and experience this.

From experience, I applied Anghileri’s theory. Counting was placed into contexts: songs and games etc, allowing activities to be seen informal. Children’s understanding of counting developed because principles and understanding came naturally.

Science creates opportunities for children to understand the world through play and exploration, using their senses. Although it is classified as Knowledge and Understanding of the World, skills (questions, describing, predicting, sorting, investigating) and attitudes develop (Ward 2005, p.9). Identifying and understanding properties of different materials encourages children to question and become aware of their surroundings.

Through EYFS requirements “Investigate materials through use of appropriate senses,” materials encourages children to develop a simple KS1 level of understanding SC1 2a,b,e,f,g,i,j,  SC3: 1a,b,c, 2a” (QCA 1999, online).

An implication of scientific learning is that of misconceptions, such as distinguishing between materials, to the object made from the material. Guest (2003,pp.2-6) argues that children may develop Paiget’s (2005) constructivist approach towards scientific learning (Smith 2005, p.459). Children may construct their own understanding through their own experiences. Henceforth there are no set principles towards teaching material, other than creating strategies to elicit children’s understanding and misconceptions to then extend.

Below explains how the box could be used (see appendix too).

Activity one allows mixed ability pairs of children to play a board game, using a 1-6 dice. Instructions should be read with children. Children add or remove scales(Extension: +/-3) from their fish, depending on the position landed on the board. The child with the most scales left at the end of the game wins. This develops their counting skills to ten. Number scales and plastic fish can be used as an aid for counting

Activity two involves children using a fishing rod to catch fish, therefore developing their hand eye co-ordination. The fish contain single numbers from 1-10. Children keep the fish if they correctly answer questions from the teacher: “What is one more than 6, one less than 3etc?” If incorrect, the answer is modelled, and the fish go back into the pond. Teachers can change the questions around for children who need extension such as, “What is 3 more or less than 5……?  

Activity three helps children identify and describe properties of material (plastic, paper, wood, velvet, playdough and wool). Children independently group these using sorting rings. Questions can be asked: “Why have you put velvet and plastic here.”….Children then group the materials into five properties. I chose transparency, stretchiness, squishiness, softness and hardness. Explain and allow children to test out materials and their properties before grouping. “Can we see through plastic…?

As an investigative game with the teacher, in turn children (mixed ability groups4) are to feel fish in a feely box, made from material used in the previous activity. A child feels a fish(using sight and touch senses) and responds to questions other children ask(based on first- hand experience activity) to conclude what material the fish are made from- ” The material is soft…” As an aid to investigate what material the fishes are made from, raw material would be displayed for visualisation and for children to test when they receive responses to their questions.

Principles must be considered when teaching and learning about counting and materials.

For Maths, in more or less counting, consideration has to be given to “one-one,” where children need to understand that each items has a name and is counted once. Then “stable order,” where children need to understand that the order of numbers must stay consistent when counting, followed by the third principle, “cardinal” where children state the total number of items. The fourth principle is, “abstraction” where children need to understand that all items are counted despite their different properties. The fifth principle, “order irrelevance” demonstrates that items can be counted in any order (Thompson, 1997, p.35-37). Teaching the concepts for counting and materials can now be used.

Relating counting (one more or less) to addition and subtraction, and materials and their properties to scientific inquiry, may reflect EYFS principles. The activities provide children the opportunity to make connections through using practical apparatus (e.g. material fish/fish with numbers). HMI emphasise that “learning depends on one’s ability to recognise relationships between concepts” (Koshy 1999, p.17).

As activity one should allow children to make connections independently, as it is student led. Yet it is difficult to say whether children could make links between concepts as there is no guidance or questioning to stimulate thinking and association. William reports (2008) in child led activities, children need time and space to discover mathematical ideas and concepts. If time and independent exploration is provided, links may eventually be made (Williams 2008, p.60).

In activity two and first part of three, Harlen (1993) concludes, questions should enable response and inquiry from children, “How can we work out what two more than eight is? “Why have you grouped the wood with plastic…?” Such responses may enable misconceptions to surface, which should structure initial starting points to build concepts, (1993, p.83) as interaction and formative assessment are demonstrated (Black and Wiliam2001, pp.2-14).  Class ethos may develop, as assessment for learning is undertaken directly with children, allowing more time for interaction and observation rather than typical assessment requirements, e.g. collecting work.

Though appealing, Harlen (1993 p.83) and Westwood (2000,p.51) suggest language used in questions could affect children’s understanding. Language may produce open/closed questions, which creates false observation and assessment, because the way questions are constructed determines whether children are asked “how can we find two more than eight..?”, or “we solve it by…’ As there is a strong relationship between the importance of language in learning, one could portray Harlen and Westwood’s view as an opinion, as neither provide statistics and further evidence to prove how language use in questions demotes learning.

From experience, my questions helped children reflect and achieve objectives, but I didn’t consider whether the language I used in my questions easily allowed children to achieve objectives, as I may have given them the answer through my questions “to figure this out, we need to add…” Drawing upon Harlen and Westwood’s principles, a reflective and evaluative approach to questioning should be adopted. Practioneer can identify and evaluate how their language is used within questions, and consider improvements needed to allow children to think through an approach, highlighting Brunel’s (1976) child led approach towards constructive thinking and learning (Smith 2003, p.405).

Williams and Vygotsky (1962,p.405) deem discussion as encouragement towards children’s  conceptual learning. Activity one allows children to work together as they are in charge of the situation. Exploratory talk develops children’s teambuilding and communication skills as children rephrase and correct each other. Positive relationships form and children learn together. A point to consider is that Williams and Vygotsky may be biased, they are using words (rephrase/correct) that favour children working together. Children are unique some may be shy or do not like helping each other, therefore won’t rephrase or correct each other. The gap in this evidence could make us question the reliability of Williams and Vygotsky view, as one could question what is happening to children who are not getting help from peers.

Barnes (1976,pp.31) believes in activity one, children working independently may not do the activity due to lack of authority figures. Not all children get ‘off task’, thus a balance of when to leave and when to refocus children on the game must be considered, here children not receiving help, would.

Williams states “learning should be developed through children’s experiences of games and play” (Williams 2008, p.36).

An aspect of teaching in foundation settings is to encourage children’s learning through exploratory play. The second part of activity three should stimulate and promote understanding as children are clarifying, extending and reinforcing ideas (Oliver 2006,p.144). “If she can stretch this…it will not be wood…” Oliver’s (2006) view is achieved through children conversing, especially to those in need of encouragement.

Both Williams and Oliver’s view overcome inclusion barriers, as all children are involved in the game and are helping one another reach learning outcomes, allowing Vygotsky’s ZPD (2003, p.497) where peer-scaffolding can develop children’s ability to do a task. Children experience Froebel’s (1906,p.229) theory of successful learning because learning is influenced through play than rote learning approaches.

As a result, supporting Waite (2006,p.12), play may allow children to ‘fit into class’ and may explain the importance of personal and social learning (Wood 2001,p.12) rather than support towards self-actualisation (Maslow 1987,p.12).

Far from just learning, activity three allows children to have fun and embrace ECM (2009,online) ‘enjoy and achieve through games’ and EYFS ‘build concepts and skills through play’ outcomes (2007,online).

Scott’s (1985) physics games study reflects Williams and Oliver’s argument, as games provided opportunities for discussion and negotiation amongst girls and boys (Bentley 1989, p.127). One could query whether this condition took into consideration the communication amongst diverse children and the barriers to communication. Regarding secondary physics, questions could surface as to whether the results would apply for primary children, as from experience, secondary students like working co-operatively and many primary children like working independently.

Investigations are used throughout the activities. Investigations in activity two and second part of three relate to problem solving, in that they are focused by a problem which requires children’s questions and explanations. Both VESP (1992,p.48) and Aksis (1998,pp.4-6) evaluate thinking and responding allows children to engage themselves within the activity and acquire interpreting, questioning, predicting and hypothesising skills to propose explanations and solutions. Yet VESP and Aksis falsely assume that all children acquire these skills. Both researchers’ views can be convincing if investigations create open learning situations rather than common didactic teaching methods (Bentley1989, p.82). However ASE (1998 p.6) attack the views of both researchers, as skills to be acquired through open learning situations are ignored, because emphasis is on planning and carrying out an investigations rather than evaluating the investigative process “how did we come to our conclusion…” This could be due to difficulties in achieving timely involvement for pupils. ASE concluded ‘Primary schools ask only half the class to carry out investigations‘. One could argue that we maybe going against ECM and EYFS principles of equal opportunities and participation for children.

From experience, supporting ASE, children not involved in investigations have their inherent capabilities disregarded. Activity two and three is not didactic, allows all children to participate regardless to class timing as every child has the right to learn. If not, we are removing children’s potential learning style and forcing them to do work which they may struggle with, but would not if they did the investigation.

The activities may produce errors like, counting same spaces twice on the board, difficulty identifying random numbers and counting to/from a number. However Hansen (2005) and Smith (1997) state, these are common errors children make when learning to count. In future, reinforcement must be given to counting principles (Bruce 2005, pp.25).

To conclude, I have given explanations to how and why these activities can be carried out, with consideration to issues one should be aware too. Stating how these issues maybe overcome are potential starters. I have realised that interaction and discussion are key to children’s learning, and must be in daily lessons. Children will engage in the activities as they are fun, motivating and creative. Children would share and take turns in throwing the dice and catching fish, as well as talk and share with each other what material the fish are made from. By interaction and observation with children, one can identify children’s understanding of material and counting. As Vygotsky states, children think and learn socially through experience, interaction and support (Smith et al, 2003, p.493). The activities enable children to experiment, make decisions, errors and correct themselves (Bruce 2005, p.64).

References

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