Homeschooling offers a variety of pedagogical approaches, each with its own philosophy and methods. Some popular options include traditional homeschooling, which mirrors a classroom setting, and online or virtual public school, where students learn through digital platforms. Unit studies, focus on a central theme across multiple subjects, while classical education emphasizes grammar, logic, and rhetoric. Waldorf and Montessori methods offer holistic and hands-on learning experiences, respectively. Unschooling, on the other hand, is a learner-led approach, and eclectic homeschooling combines elements from various methods. 

Here's a more detailed overview:

1. Traditional Homeschooling (School-at-Home):
This approach closely resembles a traditional classroom, with structured lessons, textbooks, and workbooks. 
It often follows a similar grade-level progression to public schools. 
Parents may create a designated learning space and utilize a boxed curriculum. 

2. Online/Virtual Public School:
Students are enrolled in a public school but receive their education at home through online platforms. 
This method provides flexibility and access to various digital resources. 
Some programs offer live interaction with teachers and peers, while others are asynchronous. 

3. Unit Studies: 
This method centers learning around a central theme, integrating various subjects.
For example, a unit on the rainforest could incorporate science, geography, and language arts.
It encourages exploration and deeper understanding through thematic learning.

4. Classical Education:
This approach follows a three-stage process: Grammar (learning foundational knowledge), Logic (reasoning and analysis), and Rhetoric (applying knowledge). 
It emphasizes critical thinking and developing strong communication skills. 

5. Waldorf Education: 
This holistic approach focuses on the development of the whole child – body, mind, and spirit.
It emphasizes arts, crafts, music, and nature-based learning.
Formal academics are often delayed, with a focus on play and practical skills.

6. Montessori Education:
This method emphasizes hands-on, self-paced learning in multi-age groups. 
It utilizes specially designed materials that encourage exploration and discovery. 
A Montessori-trained teacher guides the learning process. 

7. Unschooling: 
This approach is child-led and interest-based, with learning emerging from the child's natural curiosity.
Parents act as facilitators, providing resources and support as needed.
It emphasizes learning through real-world experiences and exploration.

8. Eclectic Homeschooling:
This approach combines elements from various homeschooling methods and philosophies. 
Parents tailor the curriculum and learning experiences to suit their child's individual needs and interests. 
It offers flexibility and allows for a personalized learning journey. 

9. Charlotte Mason:
This method emphasizes living books, nature study, narration, and habit training. 
It encourages a love of learning through engaging with quality literature and the natural world. 
Simply Charlotte Mason suggests shorter lessons and incorporating outdoor learning.