Conceptual Models (CM) for Learning Algebra in Hong Kong Secondary School

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Conceptual Models (CM) for Learning Algebra in Hong Kong Secondary School by Mind Map: Conceptual Models (CM) for Learning Algebra in Hong Kong Secondary School

1. Conceptual Learning

1.1. facilitate learning by

1.1.1. interacting

1.1.2. experiencing

1.1.3. exploring

1.1.4. involving

1.1.5. decoding

1.1.6. integrating text and graphics with existing knowledge

1.2. provided an learning environment for

1.2.1. developing multi-modal thinking and reasoning

1.2.2. re-capturing knowledge

1.2.3. re-discoverinfg knowledge

1.2.4. re-developing knowledge

1.2.5. having different knowledge

1.2.6. having different experience

1.2.7. having different interpretation

1.2.8. having mixed knowledge

1.2.9. having holistic knowledge

1.2.10. constructing new knowledge

1.2.11. leaners' reflection

1.3. support higher order thinking

1.3.1. deep understanding

1.3.2. new knowledge

1.3.3. own interpretation and expression

2. Design

2.1. Represention

2.1.1. Visual Pictures graphical representation diagram tables lines Words equation expression number and symbol theorems notation symbolic expressions formula figures

2.2. interaction

2.2.1. allow to change parameters variable

2.2.2. control curve

2.2.3. control table

2.3. consistent

2.3.1. placed navigation element

2.3.2. familiar look

2.4. layout

2.4.1. moderate colour

2.4.2. simple design no decoration

2.4.3. divide the related concepts into different sections

2.5. situative persepctives

2.6. help

2.6.1. explanation for control interface

2.6.2. pre training

2.7. content

2.7.1. no redundant information

2.7.2. suitable amount of concept

2.8. New node

2.9. importan concept

2.9.1. alert (audio)

2.9.2. colour change (optional)

3. Content (Algebra)

3.1. procedural knowledge

3.1.1. fact values and numbers

3.1.2. symbol identification between different parts delta symbols for root

3.1.3. principle component in the theory theory for solving quadratic equations formula for delta nautre of roots

3.1.4. rules arithmetic indices

3.1.5. graphical representation its nature

3.1.6. procedure Multiplying and Dividing Monomials’ factorization

3.1.7. equations Polynomials different look of quadratic equation (ax+b)^2=c (ax+b)^2-c=0 ax^2+bx+c=0

3.1.8. functions idea of input-processing-output to the meaning of dependent and independent variables

3.1.9. mathematical concepts

3.2. conceptual Knowledge (mathematical concept)

3.2.1. relationships between procedural knowledge identify the most appropriate strategy to solve quadratic equation further exploration on properties of quadatic graphs identify the best formula to solve the mathematical problems identify the best method to solve the real life problems explore the effects of transformation on the functions from tabular, symbolic and graphical perspectives visualize the effect of transformation on the graphs of functions when giving symbolic relations

3.2.2. conceptual in conceptual knowledge

3.3. Characteristics

4. Its importance

4.1. support the new learning enviroment

4.2. support meaningful learning

4.3. improve learning and teaching processes

4.4. Learning algebra issue in Hong Kong (age 12 to 18)

4.4.1. existing supporting learning material low opinion from teachers on the existing supporting learning material low rate of usage of the existing supporting learning material

4.4.2. handling the variable items

4.4.3. traditional teaching focus on distributive peoperty focus on manipulative skills cognitive obstacles and differences in levels rich in content and skill-based teacher-centred directed students' thought processes narrow the focus of the discussion lead role Transmission approach examination-oriented

4.4.4. difficulties students faced weaknesses in algebratic thinking alarming in HK mathematical issue misunderstanding: treating letters as as genealized numbers of variables difficulty in producing relational and extended abstract responses demonstrated a coherent argument and capacity of hypothetical thinking student has little or no opportunity for students have the need of the development of conceputal understanding

4.4.5. text book procedural paradigm emphasis on learning computational skills pupil -centred

5. Use of CM for instruction

5.1. Support for aquistion of meaningful learning

5.1.1. Semantic Knowledge

5.1.2. Conceptual knowledge

5.1.3. Schematic knowledge

5.1.4. Prodcedural knowledge

5.1.5. Strategic knowledge

5.1.6. decalarative knowledge

5.2. Design for Task for algebra learning in lesson or self learning(package)

5.2.1. With help of other types of learning object approach 1 presentation object information object simulation object practice object contextual representation approach 2 self learning with CM practice object contextual representation

6. Problems of conceptual Learning

6.1. the conceptual is not well understood

6.2. it is difficult to define Mathematical concepts

7. Background (the construction of mathematical concepts)

7.1. traditional teaching

7.1.1. symbolic reconstructive approach tranmission listening observing

7.1.2. can create obstacles to learning

7.2. conceptual learning

7.2.1. construction of a rich experiential base

7.2.2. perceptuo-motor approach

8. Conceptual Change

8.1. ontological perspective

8.1.1. conceptual change learning model

8.2. mental model

8.3. concept map

9. Types of Learners

9.1. experience learners

9.2. novice learner

10. Number of Conceptual Models