Transcript ETP420 Grade 3CF Applying developmental principals to practice

ETP420
Grade 3CF
Applying developmental principles
to practice
Sandra Murphy S219648
ETP420
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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.
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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 intersubjectivityarriving at shared understanding and and scaffolding opportunitiesbreaking 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
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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.
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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)
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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
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Using mathematics
Seeing the potential of
maths in the real world
and within itself and;
Making use of it in this
way.
Pratt (2006)
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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)
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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.
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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.
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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”.
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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)
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References
Perso, T. 2009. 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 1st 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 8th ed.
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