Week 1 Reading - Helping Children Learn Mathematics With Understanding (17-45) PDF

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Week 1 Reading Notes - Pages 17-45...

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Week 1

Helping Children Learn Mathematics With Understanding (17-45) ECM3260 - Early Childhood Mathematics 2 Introduction (18) • Need to know their students • Lesson planning • The learning environment • Engagement of students How Can We Support The Diverse Learners In Our Classrooms (18,19) • Variety of sociocultural situations • Gender • Special learning needs • Disabilities • Setting • Culture • Family structure • Experiences • Interest • Styles of learning Creating A Positive Learning Environment (19) • Maximise students learning potential • Awareness of student needs • Value the active engagement in mathematics • Safe • Comfortable • Room arrangement is suited to its purpose (Round tables for small group experiences = Collaboration) • Encourage academic risk taking • Help students understand that everyone learns things at different rates • Reward critical thinking and creative problem solving Avoiding Negative Experiences That Increase Anxiety (20-22) • Be aware of own attitude = Communicate to the students • Active engagement • Connect maths to the real world • Provide elements of choice • Give clear expectations • Emphasise meaning and understanding > Memorisation • Model problem solving strategies • Encourage students to explain their feelings about mathematics • Avoid competition • Avoid learning at a pace that is too fast Establishing Clear Expectations (22) • Respect and value students ideas • Students should respect and value each other • Reflection • Questioning • Ask students to explain their thinking Treating All Students As Equally Likely To Have Aptitude For Mathematics (22,23) • Expect all students to succeed • Convey the message that mathematics is for everyone 1

Week 1 • All students need to be equally challenged • Identify and build on the child’s strengths • Current causes of failure: Ability, effort, luck, difficulty, age, grade, context, prior knowledge • Dispel myths/ Stereotypes • High high expectations for all students • Encourage equal participation • Make connections between mathematics and the students life • Awareness to role models/ Career opportunities • Communicate the importance of encouragement • Assessment Current Problems In The Classroom • Male failure = Lack of motivation • Female failure = Lack of talent/ Ability • Feelings of learned helplessness: Low competence, self esteem and motivation Helping Students To Improve Their Ability To Retain Mathematical Knowledge And Skills (23,24) • Retention: Degree students can hold on to what they have learnt • Build new concepts off previous understandings • if not used regularly = Forgotten • Problem solving strategies - Take longer to develop, Retained longer • Meaningful learning - Connect to prior understanding • Awareness of the procedure used - Knowledge from exploration = More likely to be retained • Establish connections - Relate ideas, Relate mathematics to the real world • Review ideas = Spiral curriculum - Reinforce/ Refresh knowledge Meaningful Connections Between Procedural And Conceptual Knowledge (24-26) • Need to “give rise to efficient and meaningful methods, whilst also gaining the correct answers” (26) • Develops an appreciation for mathematics ACARA 4 Proficiency Strands 1. Conceptual understanding 2. Procedural fluency 3. Problem solving 4. Reasoning Procedural Knowledge/ Fluency • Skilful use of rules/ Algorithms • Compete a process/ Sequence of actions • Difficulty applying knowledge/ Knowing when to use it Conceptual Knowledge • Awareness of mathematical concepts • Link ideas in networks by connect meanings + New information = See relationships • Construct experiences that help build connections between ideas • Focus on getting the right answer, not the process= No motivation How Do Children Learn Mathematics (26,27) • Learning through the environment, play and social experiences • Record learning in visual representations • Becomes more abstract • Learning from experience and and active involvement • Importance of meaningful experiences Piaget - Constructivism • Interpretation of information • “Actively building new knowledge from their person al experiences and prior knowledge” (27) • Shared responsibility between the teacher and student • Integrate ideas and experiences with prior knowledge Behaviourism 2

Week 1 • Focus on observable behaviours • Production of responses to stimuli • Does not consider processes Building Behaviour (27-29) • Thorndike, Skinner, Gagne • External factors and behaviours • Does not consider the child's own thinking • Shaped through reinforcement • Can help children acquire fluency - Proficiency in one skill → Proficiency in the next skill • Stated objectives and goals = Gives direction in planning • Consistent learner engagement • Short term goals → Short term proficiency = Un-meaningful learning • “Making sense of mathematics is a major goal of mathematics learning” (27) Constructing Understanding (29) • Bronwell, Piaget, Bruner, Dienes • System of ideas, principles and processes • Isolated learning is not retained • Mathematics needs to make sense to the learner • “Meaningful learning provides the basis for mathematical connections and is an integral part of the constructivist perspective” (29) • “Students learn mathematics well only when they construct their own mathematical understanding” (29) • Learning is a process that takes time • “Learning is active and internally monitored” (31) • Children process through stages • Concrete → Abstract • Need opportunities to communicate ideas with tigers 3 Tenets Of Constructivism 1. Knowledge is not passively received 2. Students construct new knowledge by reflecting their physical and mental actions 3. Learning is a social process, they engage in dialogue with others as they develop intellectually Vygotsky • Lower limit of knowledge: Concepts and skills already learnt • Upper limit of knowledge: Can successfully complete with scaffolding • ZPD: Where learning will be most successful How Can We Help Children Make Sense Of Mathematics (31) • Concrete → Abstract • Recognise prior experience and knowledge → Actively build new knowledge Recommendation 1: Teach To The Developmental Characteristics Of Students (32) • Present topics in enjoyable and interesting ways • Challenge their thinking • Add new knowledge to existing ones • Cognitive development: Thinking and reasoning : How the child learns new information Physical development: Muscles and motor skills • : Needed for active participation • Social development: Interactions with others : Self concept : Consideration off group dynamics Developmental Characteristics (4-7 Years) (32) Cognitive 3

Week 1 • Preoperational stage - Piaget • Centration: Can only focus on one idea at a time • Irreversibility: Unable to recognise reversibility of change • Understand ideas beyond concrete experiences Physical • Control of large and small muscles • Fine motor skills • Short attention span Social • Egocentric: Focus on the self : Talks at rather than with others • Developing sense of self • May exclude others • Learning self expression • Decision making Children Aged 4-7 Years Implications (32) • Connect maths to everyday life experiences • Break tasks into manageable parts • Encourage exploration • Encourage decision making • Experimentation with concrete materials • Questioning • Use of pictorial and symbolic representations • Short hands on activities • Opportunities for movement • Focus on process rather than product • Encourage friendships skills (Sharing, turn taking, working with others) • Provide support and feedback • Encourage planning • Encourage problem solving Developmental Characteristics (8-11 Years) (33) Cognitive • Operational stage • Decenter: Focus on part and whole • Understands reversibility • Classification • Sequencing • Use of logic • Use of concrete objects • Problem solving Physical • Complete more complex physical tasks Social • Independent • Small groups of friends • Influenced by others • Hard to accept failure and criticism Children Aged 8-11 Years Implications (33) • Link concrete materials to symbols • Classification opportunities • Sequencing opportunities • Explore multiple representations 4

Week 1 • • • • • • •

Encourage students to explain their thinking Promote active, physical involvement in experiences Use of real tools and materials Conduct experiments Problem solving opportunities Group work opportunities Provide support and feedback

Recommendation 2: Actively Involve Students (33,34) • Active → Making sense of what they are doing → Greater understanding • Interactions • Hands on experiences • Concrete materials • Reflection Encouraging Student Exploration And Sense Making (34,35) • Encourage physical involvement • Problem solving • Encourage students to discuss their method/ Process • Connections with previous learning • Student centred exploratory approach → Increased understanding and retention Encouraging Student Reflection And The Use Of Metacognition (36) • Metacognition: Thinking about your own thinking : Beliefs about themselves as a learner : Regulation of behaviour • Striving to make sense of what is learnt • Be explicit in how the problem was solved • Awareness of common ways of problem solving • Awareness of their own strengths and weaknesses • Identify their preferred learning style • Ways to communicate their thinking • Rephrase tasks/ Problems in their own words - Ensures their understand Recommendation 3: Move Learning From Concrete To Abstract (36,37) • Concrete → Pictorial → Abstract • Need to have conceptualisation and meaningful understandings first • Need physical objects → Pictures and other representations → Symbols - Bruner Using Concrete Materials And Models (37,38) • Provides a context for the mathematical concept → Learning best occurs • Draw attention to specific attributes = Learning is enhanced • Multiembodiment: Using many different models : Focus on common attributes : Enables generalisation • Non-examples: Help identify missing attributes : Focus on attributes that are significant Making Formal Representations Follows Conceptualisation (38) • Need multiple concrete experiences first • Express ideas through pictures • Keep concrete objects available for those who need it = Supports thinking Recommendation 4: Use Communication To Encourage Understanding (39) • Opportunities for thinking, talking and listening 5

Week 1 • Deepens understanding • “Talking and writing about mathematics are essential in learning mathematics” (39) Using Oral Communication To Encourage Sense Making (39) Vygotsky • ZPD • Role of language in learning • Learning is a social experience → Interactions = Make sense of ideas • Provide students with opportunities to talk about their thinking → Clarify thoughts • Allow students to learn from each other Using Written Communication To Convey Thinking (40) • Think more deeply • Clarify thoughts • Drawing • Dictating by more capable writers • Reflective writing • Use of conventional symbols to communicate ideas to others • Increases student interest

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