I can't guarantee you that if you garden with your children they will become gardeners. But I can assure you that if you do expose your children to gardening that the gardening gene within specific children will be awakened. My gardening gene was awakened by my dear aunt. So anyone can awaken that gene in a child, parents, grandparents, friends, teachers.
Each year I taught young children, I would pull out the planting cups, children would decorate, fill with soil, push their little finger down and plunk in a seed or two. Some years we did vegetables, some flowers. It was difficult to get a nice looking plant years ago because we did not have plant lights in the classroom. No matter how weak some of them looked, we wrapped tissue around the cups, made beautiful Mothers Day Cards and wondered if they would ever survive the bus ride home. It wasn't just a gift for their Mother, it was a gift of knowledge for that child. They learned the basics of plant growth (soil, water, light) and the responsibility of taking care of what they had decided to grow.
When I began working with children and gardens , we planted in outside gardens, digging through rock-like clay my first year. Needless to say, the vegetables did not flourish. The plastic pool seemed like a great idea until we arrived to see it tipped over and our plants strewn all over the playground. We pulled ourselves up and moved on to the soil berm (couldn't be tipped over), however, the plants could be pulled out and they were!
We really did get very modern through the years, graduating to a double tiered planting greenhouse with lights, a root vue garden (where we could see the roots forming on radishes, carrots, onions) and a raised garden bed outside (behind the school) with our own child-sized shovels and garden gloves.
Gardening at home with my own children seemed to produce less than the desired results. It was all excitement in the beginning, picking out the seeds, planting them and giving them that first drink of water. It was a lot like getting the new puppy and guess who ends up taking care of him! I put in a lot of time caring for my children's gardens over the years and crossed it off as a lost cause. But, lo and behold, as adults, they are both avid gardeners!
So, I didn't write about plants today, it's all about the "gardeners" of tomorrow!
Check out http://www.gardenrant.com/ and their article Caitlin Flanagan Demonstrates What A Deficient Education Will Do (In Defense Of School Gardens)