ETP420 Grade 3CF Applying developmental principles to practice Sandra Murphy S ETP4201

Links to development Piaget Concrete operational cognitive stage (7-11) Formulation of ideas and construction of meaning-through accommodation and assimilation-construction of schemas Logico-mathematical knowledge- understanding of how number concepts develop in children Constructive learning- cognitive learning of mathematics-actively building and constructing knowledge Future construction of learning must be facilitated Discovery learning opportunities to allow a rich variety of stimulating activities to cater for a wide variety of understanding. To be sensitive to children’s readiness to learn new concepts and language. Explicit adult instruction provided with knowledge of concepts to be taught. Sandra Murphy S ETP4202

Links to development Vygotsky Socio-cultural way of learning and the use of language and inner speech in performing cognitive processes. Provide learning opportunities in the zone of proximal development to construct growth and to provide challenging activities that can be modelled and instructed through explicit instruction. To promote cognitive development through intersubjectivity- arriving at shared understanding and and scaffolding opportunities- breaking down the task into manageable units through instruction and withdrawing support as knowledge increases. Using cognitive strategies in questioning, summarizing, clarifying and predicting. Providing cooperative learning opportunities for peer collaboration Sandra Murphy S ETP4203

Links to development Case (1998) “many understandings appear in specific situations at different times rather than being mastered all at once”. Sieglers model of strategy choice “Strategy variability is vital for devising new more adaptive ways of thinking, which evolve through extensive experience solving problems”. Memory, Retreival, Reconstruction, Adapting attention and planning Metacognition Children construct theories and coherent understandings which are revised through new experiences, reflections. Sandra Murphy S ETP4204

Constructivism and teaching maths in primary school Rather than being passively received, knowledge is actively constructed by students. Mathematical knowledge is constructed by students as they reflect on their physical and mental actions. By observing relationships, identifying patterns and making abstractions and generalisations, students come to integrate new knowledge into their existing mathematical schemas. Learning mathematics is a social process where, through dialogue and interaction, students come to construct more refined mathematical knowledge. Through engaging in the physical and social aspects of mathematics, students come to construct more robust understandings of mathematical concepts and processes through processes of negotiation, explanation and justification. (Zevenbergen, Dole and Wright, 2004) Sandra Murphy S ETP4205

Learning mathematics involves Doing mathematics Engaging in mathematical activity Developing processes and procedures, and a sense of the subject Knowing mathematics Developing mathematical knowledge and understanding Using mathematics Seeing the potential of maths in the real world and within itself and; Making use of it in this way. Pratt (2006) Sandra Murphy S ETP4206

The abilities required to perform and work mathematically: Read and comprehend a problem; Identify that “maths can help here”; Work out what needs to be done; Make some choices about how they might do it; and Decide whether the solution they have arrived at makes sense in the context. (Perso, 2009) Sandra Murphy S ETP4207

Reflection of Development Number line strategies Following on from place value I have aimed to develop a working model of children’s prior knowledge through profiling the learner and their number knowledge. This lesson aims at constructing on place value knowledge and developing strategies to extend the concept of number into number line strategies and addition. A strong number sense is established form jump strategies modelled and then applied on the empty number line. Children are encourage to split numbers to 10. Through various assessment strategies children have acknowledged the place value of items and then through modelling, instruction and rehearsal have attempted number lines to represent counting on from place values to model addition problems. To accommodate the range of abilities, the number line strategies used will cater for all students, students will less ability are given small numbers with counting on from 1 to 2 strategies on the number line. Capable children are looking at decades on the number lines and counting on by 10’s and then either 1 or 2 on the number line. As number sense increases children are then able to ascertain place value more certainly and work with more difficult number situations. Instructional tools such as the empty number line assist us in the process of teaching and learning mental computational strategies. It visually assists students to record and share their strategies. Student progress should be monitored to ensure that their use of the strategy becomes progressively more sophisticated. The empty number line is a representational tool that not only scaffolds students’ thinking along the path to a more abstract level, but also allows that thinking to become visible. This tool enables scaffolding of mental strategies as it represents what has been calculated and what has not, this could help in reducing the cognitive load of children learning mental strategies. Seeing strategies visibly will also help to acknowledge and assess the strategies that children are using and further instruction can then be matched to develop understanding. Sandra Murphy S ETP4208

Reflection on Development Mathematical language The use of mathematical language, reading and comprehension skills in regards to mathematical problems needs to taught explicitly if children are able to solve numeracy problems. Teaching mathematical language will help the cognitive development of children in numeracy. Mathematical terms were modelled with open questioning from the NAPLAN test. We then progressed to brainstorming other words for maths terms like equals, add etc. Children were shown a maths dictionary and where to source information and we looked up a few terms. An explanation of the addition test was then given and children were given the role of the teacher to find the incorrect answers. We looked at answering the first question and the children set to task. Upon completion children then wrote their own mathematical problem in their maths book using some of the language we had just worked with ie. sum, equals, altogether, tally. Assessment of learning takes place as an ongoing process via formative assessment. Questioning and listening to responses takes place as group to ascertain knowledge and brainstorming of ideas gives an indication to what knowledge the children have ascertained about maths terms like “equals”. Sandra Murphy S ETP4209

Mathematical language cont’d Summative assessment occurred at the end of the lesson from the addition test to ascertain the knowledge of mathematical language. Questions were worded using various maths terms and children ascertained their meaning ie. tally, altogether, sum total Newman, N.A (1977) looked at the cognitive errors students made in solving worded mathematical problems. He found that 35% of the errors made occurred before students even attempted to apply mathematical skills and knowledge. The language based errors occurred during the reading, comprehension, and transformation stages. Being numerate requires a certain degree of literacy skill as well as being able to perform the mathematics. (Newman, 1977) Sandra Murphy S ETP42010

References Perso, T Cracking the NAPLAN code:Numeracy and Literacy demands APMC 14 (3). Newman, N.A (1977) An analysis of sixth-grade pupils errors on written mathematical tasks. Paper presented at the 1 st conference of the Mathematics Education Research Group of Australia. Melbourne MERGA. Pratt, N. (2006) Interactive maths teaching in Primary School. Paul Chapman Publishing, London. Berk, L. (2009) Child Development Pearson Education/Allyn & Bacon 8 th ed. Sandra Murphy S ETP42011