Hi. According to Piaget et al. is it better to follow the process near to development stages of the learner. Constructivism say something similar. You can check Steve Krahen theory about language acquisition to bring support about this idea.
The language window in a new born is open till 3 months. Then it is worth exposing the newborn to many languages. We who use two languages every day, we expose children to at least two from the day they are born. In Europe you can use five languages without problems. Already from the 5th mo. in the womb the fetus hear and you can also choose the kind of music you want your children to enjoy. I used to breastfeed to opera music:)
I think within the first 15 years exists no really phase of better learning, it is clear that preschool learning has much advantages, not so few children are bilingual educated by the parents, escpecially in academic circles or in the situation of immigration in another country. This model-learning is quite effective but you need much time for this, and the reference person should not change. The cognitive development is in the beginning school age qute higher, so that systematic learning is possible, which is time-saving. But still the most valid results you will get with the well-known procedure of staying in another country where the foreign language is arousing your mental capacities 24 hours a day.
...." the important window specifically for language acquisition begins to shut down by the age of 5. Children can learn many languages simply by being exposed to them during the language window of opportunity, and they can learn those languages simultaneously. However, if your child is introduced to and acquires a new language at the onset of adolescence, then that language will be spoken with a foreign accent because your child did not track that language during the optimal window for language acquisition."
Dr. Gail Gross Human Behavior, Parenting, and Education Expert, Speaker, Author. Ph.D., Ed.D., M.Ed.
You ask the follwing: What is the appropriate age to learn foreign language based on researches? I may be wrong, but I think that you want to know what is the appropriate age to begin to learn a foreign language. According to Piaget and his constructivist assumptions, in order to learn a language, be it his/her mother tongue or a foreign language, the child has to acquire first what Piaget and his collaborators called symbolic function, that is, one's ability to understand that a "signifier" (e.g., a word, an object) can be used to signify or mean something different (i.e., referent) from the "signifier". For example, that the word mother can be applied to or means his/her real mother or another's mother or that a ball can be used to pretend that it is a cat. According to Piaget's theory of stages of cognitive developmental, the symbolic function appears roughly at the end of his sensori-motor stage, that is, around 2/3 years . Accordingly, this age seems to be a suitable age for a child to begin to learn a foreign language. Before this age, the child is at what developmentalists such as Piaget and Yygotsky called a pre-lingustic phase. Needless to say, the more a new-born or even a foetus is exposed to a certain language, the more s/he is likely to learn the language at hand. Note that there was a time at which it was thought that babies were only capable of, say, eating and sleeping. There is now accumulated evidence that shows that babies are highly competent creatures.
Well, there is no consensus on this issue, still Critical Age Hypothesis CAH has a big role and can interpret some crucial reasons behind early age as more effective than older age in learning a foreign language. For details, you can refer to CAH or this research