Every child has derived traits from each respective parent. This is pretty well known and accepted regarding DNA and genetics, but I am not as certain it is known for the characteristics of each parent as well. Perhaps it is passively considered, but not actively factored. I may be wrong, but I am not sure if the majority of parents explicitly factor how these traits are passed down and demonstrated, so I will simply write my views on the matter and leave to the reader to confirm or adjust.
The first step in recognizing derived traits in your children is knowing your own characteristics and respective strengths and weaknesses. This first step applies to both parents, and spans all facets of life – socially, intellectually, physically, mentally, emotionally and spiritually. Ideally these trace to elementary, middle and high school so you can relate to the child as they are growing up. However, many people are not reflective of their upbringing to that extent, and I am not sure what percentage of people actually know their true self and the respective maturation from childhood to adulthood. If either or both parents are not aware of who they are then it immediately becomes difficult to recognize those traits in their children as they grow up.
Assuming the above is known – by both parents, truthfully and honestly, at a minimum as adults if not as a youth - the next level is which attributes apply to each child, and in what combination. This has a macro and micro view – in general who has the predominance of the attributes (macro), then across the different facets of life (i.e. social, academic, athletic/activities) what are the unique characteristics of each parent in each child. The depth and breadth of living makes this an evolving and dynamic exercise, particularly at the micro level.
If this is difficult to grasp, allow me to give a personal example. My oldest daughter, at the macro level, has a majority of my traits. Because of this we naturally connected, so when I spoke to her, she easily picked up what I was putting down. I also had keen insights into how she thought about school when she struggled, and why she was stressed in sports. At the micro-level (academically and athletically), it was clear to my wife and I that she had my characteristics, my strengths and my weaknesses. At the same time, we knew in some form or fashion, my wife’s attributes were there. It wasn’t until she was a teenager and started dating that the unique characteristics of my wife started to show. It was associated with her view of boys and how relationships work. It was during a ride home and my oldest daughter was complaining about how her pseudo-boyfriend was demanding more time from her, but she had school and sports that did not allow it. My wife and I looked at each other as she was complaining and both recognized the attribute. It was little concerning in that the characteristic was derived from a grown, married woman (in several respects), but the social similarities were noticeable nonetheless.
This just reflects how varied derived traits can be based on circumstances and facets of living; on the parental traits passed down and on the diversity of derived traits in the kids. But if personality traits are not factored, it becomes difficult to tailor parenting.