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

Get Started. It's Free
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

2.1.1.1. Pictures

2.1.1.1.1. graphical representation

2.1.1.1.2. diagram

2.1.1.1.3. tables

2.1.1.1.4. lines

2.1.1.2. Words

2.1.1.2.1. equation

2.1.1.2.2. expression

2.1.1.2.3. number and symbol

2.1.1.2.4. theorems

2.1.1.2.5. notation

2.1.1.2.6. symbolic expressions

2.1.1.2.7. formula

2.1.1.2.8. figures

### 2.2. interaction

2.2.1. allow to change parameters

2.2.1.1. 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

2.4.2.1. no decoration

2.4.3. divide the related concepts into different sections

### 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

### 2.9. importan concept

2.9.2. colour change (optional)

## 3. Content (Algebra)

### 3.1. procedural knowledge

3.1.1. fact

3.1.1.1. values and numbers

3.1.2. symbol

3.1.2.1. identification between different parts

3.1.2.1.1. delta

3.1.2.1.2. symbols for root

3.1.3. principle

3.1.3.1. component in the theory

3.1.3.1.1. theory for solving quadratic equations

3.1.3.1.2. formula for delta

3.1.3.1.3. nautre of roots

3.1.4. rules

3.1.4.1. arithmetic

3.1.4.2. indices

3.1.5. graphical representation

3.1.5.1. its nature

3.1.6. procedure

3.1.6.1. Multiplying and Dividing Monomials’

3.1.6.2. factorization

3.1.7. equations

3.1.7.1. Polynomials

3.1.7.2. different look of quadratic equation

3.1.7.2.1. (ax+b)^2=c

3.1.7.2.2. (ax+b)^2-c=0

3.1.7.2.3. ax^2+bx+c=0

3.1.8. functions

3.1.8.1. 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

3.2.1.1. identify the most appropriate strategy to solve quadratic equation

3.2.1.2. further exploration on properties of quadatic graphs

3.2.1.3. identify the best formula to solve the mathematical problems

3.2.1.4. identify the best method to solve the real life problems

3.2.1.5. explore the effects of transformation on the functions from tabular, symbolic and graphical perspectives

3.2.1.6. visualize the effect of transformation on the graphs of functions when giving symbolic relations

3.2.2. conceptual in conceptual knowledge

## 4. Its importance

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

4.4.1. existing supporting learning material

4.4.1.1. low opinion from teachers on the existing supporting learning material

4.4.1.2. low rate of usage of the existing supporting learning material

4.4.2. handling the variable items

4.4.3.1. focus on distributive peoperty

4.4.3.2. focus on manipulative skills

4.4.3.3. cognitive obstacles and differences in levels

4.4.3.4. rich in content and skill-based

4.4.3.5. teacher-centred

4.4.3.5.1. directed students' thought processes

4.4.3.5.2. narrow the focus of the discussion

4.4.3.6. Transmission approach

4.4.3.7. examination-oriented

4.4.4. difficulties students faced

4.4.4.1. weaknesses in algebratic thinking

4.4.4.1.1. alarming in HK mathematical issue

4.4.4.2. misunderstanding: treating letters as as genealized numbers of variables

4.4.4.3. difficulty in producing relational and extended abstract responses

4.4.4.3.1. demonstrated a coherent argument and capacity of hypothetical thinking

4.4.4.4. student has little or no opportunity for students have the need of the development of conceputal understanding

4.4.5. text book

4.4.5.1.1. emphasis on learning computational skills

4.4.5.2. 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

5.2.1.1. approach 1

5.2.1.1.1. presentation object

5.2.1.1.2. information object

5.2.1.1.3. simulation object

5.2.1.1.4. practice object

5.2.1.1.5. contextual representation

5.2.1.2. approach 2

5.2.1.2.1. self learning with CM

5.2.1.2.2. practice object

5.2.1.2.3. contextual representation

## 7. Background (the construction of mathematical concepts)

### 7.1. traditional teaching

7.1.1. symbolic reconstructive approach

7.1.1.1. tranmission

7.1.1.1.1. listening

7.1.1.1.2. 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