Algebra is introduced in the middle classes. According to Piagets' theory of cognitive development, it is appropriate to introduce algebra at this stage as

Options

A. the child is at formal operational stage and is fully mature to grasp the abstract concepts
B. the child is at sensorimotor stage and can understand with the help of lots of manipulatives
C. the child is at pre-operational stage and can understand abstract concepts
D. the child is at concrete-operational stage and he can understand and conceptualize concrete experiences by creating logical structure

Answer

To determine the appropriate stage for introducing algebra according to Piaget's theory of cognitive development, we need to analyze the stages of cognitive development and their characteristics.

### Step 1: Identify Piaget's Stages of Cognitive Development
Piaget proposed four stages of cognitive development:
1. **Sensorimotor Stage (0-2 years)**: In this stage, children learn through sensory experiences and manipulating objects. They do not yet understand abstract concepts.
2. **Pre-operational Stage (2-7 years)**: Children begin to think symbolically and use language, but they still struggle with logic and understanding the perspective of others. They can understand some abstract concepts but are not fully capable of logical reasoning.
3. **Concrete Operational Stage (7-11 years)**: Children start to think logically about concrete events. They can understand the concept of conservation and can perform operations mentally.
4. **Formal Operational Stage (12 years and up)**: In this stage, individuals develop the ability to think abstractly, logically, and systematically. They can handle hypothetical situations and use deductive reasoning.

### Step 2: Analyze the Options
Now, let's analyze the options provided in the question:
- **Option 1**: The child is at the formal operational stage and is fully mature to break the f-stack concept.
- **Option 2**: The child is at the sensory motor stage and can understand with the help of lots of manipulatives.
- **Option 3**: The child is at the pre-operational stage and can understand abstract concepts.
- **Option 4**: The child is at the pre-operational stage and is fully mature to break the f-stack concept.

### Step 3: Determine the Correct Option
Given that algebra involves abstract reasoning and logical thinking, it is most appropriate to introduce it during the **Formal Operational Stage**. Therefore, **Option 1** is the correct choice.

### Conclusion
Algebra should be introduced when the child is in the **Formal Operational Stage** according to Piaget's theory of cognitive development.