To determine the independent variable in the given research problem, we must first understand the role of independent and dependent variables in research:

• Independent Variable: This is the variable that is manipulated or varied by the researcher to observe its effect on the dependent variable. It is the cause or input in the relationship being studied.
• Dependent Variable: This is the outcome or effect that is observed as a result of changes in the independent variable. It is the result or output in the relationship being studied.

Now, consider the research problem: "studying the effect of Teaching Methods on the Scholastic Achievement of boys and girls in terms of their socio-economic background". We need to identify which component is being manipulated to observe its effect:

1. Teaching Methods: These are the techniques or strategies used to instruct students. In this research problem, different teaching methods are the input or variable that are being studied to observe their impact on scholastic achievement.
2. Scholastic Achievement: This refers to the students' performance or success in academic activities, which is the observed outcome or effect being measured in the study.
3. Gender: This is a categorical attribute of the students, which is part of the demographic information and not the primary focus of manipulation in this study.
4. Socio-economic Background: This refers to the socio-economic status of the students, which could act as a moderating variable but is not the primary variable being tested.

Based on the above analysis, the independent variable in this research problem is Teaching Methods. This is because the study aims to examine how different teaching methods affect the scholastic achievement of students, distinguishing them based on gender and socio-economic background as secondary considerations.

Conclusion: The correct answer is Teaching Methods.