This question doesn't specify if it is asking for individual teacher strategies or school-wide strategies that increase parental involvement in the education and assessment of students. There isn't a singular strategy that will work best, and different classrooms and schools have unique situations that make it so different strategies will work better in different situations.
Getting parents involved with and knowledgeable of the education and assessment process is a good thing. Anecdotally, I tend to see that students with involved parents perform better in my classes. I wrote my master's thesis on what types of assignments are most beneficial to student learners, and the research shows that assignments that incorporate parental involvement are some of the most beneficial assignments for student learners.
Creating this kind of assignment is one strategy to get parents involved with the education process. In a biology class, this might involve an assignment that has students working on a pedigree chart for an autosomal trait in the family tree, because parents will be able to help fill in information about brothers, sisters, aunts, uncles, grandparents, great-grandparents, and so on. In an English class, the assignment might be writing a short story that takes place during the time when the student's parents were young. In my technology class, I create a stock market game, and I frequently have parents tell me how much fun they had helping their child research and "buy" stocks. At the elementary level, a teacher can send home a weekly newsletter that highlights the week's education topics. Parents are then informed of what is going on, and they can engage their own child with additional questions.
Involving parents in the assessment process is a little more difficult; however, there are some simple and effective tools and strategies that can be used. One such tool is a rubric. The rubric for a project or presentation should be given to students ahead of time, but it can also easily be sent home to families. This would allow parents to know where their child should focus their time and energy in the preparation process.
Another strategy is for the school to publish grades online and give parents the ability to see those online grade books through some kind of "parent portal." If the school chooses to do this, then administrators need to make sure that teachers are frequently updating those grade books. That allows parents to see frequent feedback and scores on assignments.
In general, the key is connection. Find ways to get parents involved, and sometimes it is as simple as inviting parents to awards ceremonies, after-school activities, and parent-teacher conferences.