There are numerous resources available, both in print and online, that could help one enhance their writing mechanics. Websites like Grammarly and Hemingway can correct your grammar mistakes and improve your writing style. For a more focused approach, there are books like "The Elements of Style" and "Eats, Shoots, and Leaves," proving useful in teaching the art of efficient writing.

On the other hand, developing a writing style is a more personal journey. It is about finding your voice – your unique way of expressing your thoughts and perspective. Reading well-written pieces from various authors can be an effective strategy. Learning how to write concisely yet adequately detailing your point is another skill to master.

Encourage your child to write regularly. Just like any other skill, writing improves with consistent practice. Provide various opportunities for writing exercises. This could be in the form of journaling daily events, writing grocery lists, composing emails or letters to family members, or crafting creative stories.

These writing prompts also help students learn the art of persuasion meticulously. They should understand and harness the power of 'rhetoric,' the knack of convincing people through effective communication. Thus, they learn how to sculpt a compelling introductory hook, use concrete particulars to substantiate their ideas, and ingeniously wrap up their writing with, say, a thought-provoking question or a summative statement.

Lastly, online writing tools and software aid in honing the writing skills of homeschoolers. These readily available resources can assist in teaching children sentence structure, grammar, and overall writing composition. They can also be used to provide instant, dynamic feedback, enabling students to learn from their mistakes and progress at their speed.

The transformative concept of gamification of the learning process further contributes to this advancement. Transforming reading and writing exercises into games enables children to learn without realizing they are studying. Such practices allow for a more enjoyable, stimulating, and effective way of capturing the child’s interest, bolstering their interaction, and ultimately, their comprehension and retention.

Both mechanics and style provide significant impacts on the audience’s comprehension. Excellent writing mechanics guarantee the ease of reading and understanding of your composition. A distinctive style, however, can capture the reader's attention, evoke emotions, and make your work truly memorable. Together, they form an integral part of effective writing that not only convey thoughts but also create meaningful and robust connections.

Feedback plays a crucial role in the writing process. Be sure to give your child constructive criticism, pointing out their strengths as well as areas needing improvement. This will not only help them correct their mistakes but also motivate them to keep improving. Remember to keep your feedback encouraging, supportive, and balanced.

Observationally, it is revealed that the potency of persuasive writing stems from the comprehension and opinion of the student about the topic. For instance, in prompts about school uniforms or the importance of sports in the curriculum, students are encouraged to analyze their viewpoints substantively and reflectively. They learn to express their thoughts coherently, thus bolstering their confidence in argumentative discourse.

By the completion of summer in 2015, tangible progress was noticeable in the skill level of most participating students. Around 70% of students displayed substantial improvement in reading comprehension and vocabulary retention. Similarly, nearly 65% of students showcased enhanced writing skills across a range of styles.

"Reading Rocks" used an engaging approach, incorporating popular literature adjusted to various reading levels and integrating fun reading activities. Conversely, "Write Away!" focused on nurturing a students' writing potential by encouraging creative thinking through storytelling, poetry, and essay writing.

These revolutionary advancements undeniably make this era an exciting time for struggling readers. While these resources significantly cater to individual learning needs, they also foster a love for reading. The potent combination of personalized instruction, high-tech tools, and engaging methods are ensuring that the challenges faced by struggling readers are swiftly turning into opportunities for growth and empowerment.

The programs ran for eight weeks each summer, serving over 300 students across the district. The students enrolled in these programs were primarily from low-income families who couldn’t otherwise afford additional educational resources during the summer months.

Additionally, the prompts stimulate an understanding of counterarguments, aiding students to anticipate potential oppositions and address them effectively in their write-ups. Empirical data suggests that this promotes cognitive flexibility in students, allowing them to appreciate the variability of perspectives in their environment and improve their acceptance towards different viewpoints.