The obligation of Hinuch (education) requires parents to train their children in Misva observance. While children are themselves not under any obligation to observe Misvot, the Sages enacted that parents must see to it that their children perform Misvot to prepare them for a life of religious commitment.
The question arises whether a youngster, who has yet to reach the age of Misva obligation, may recite a required blessing – such as Birkot Ha'Torah – on behalf of an adult. For example, if a man feels unwell, and prefers listening to Birkot Ha'Torah rather than reciting it himself, can he ask his son – who has yet to reach the age of Bar-Misva – to recite the Beracha on his behalf?
According to some opinions, as we have seen in earlier installments, the recitation of Birkot Ha'Torah constitutes a Torah obligation. It is clear that this view would not allow a youngster – whose Misva obligation was instituted by the Rabbis – to recite the Beracha on behalf of an adult. There is a well-established Halachic principle that a person cannot fulfill an obligation by listening to somebody with a lower level of obligation, and therefore, if reciting Birkot Ha'Torah is required on the level of Torah law, it goes without saying that listening to a youngster's recitation does not satisfy one's obligation.
In truth, however, this is the Halacha even according to the other view, that the obligation of Birkot Ha'Torah – like the recitation of virtually all other Berachot – was instituted by the Sages. Normally, one who is obligated Mi'de'rabbanan (by force of Rabbinic enactment) is allowed to fulfill the obligation on behalf of somebody on the same level of obligation. The case of a minor, however, is one of "Tereh De'rabbanan" – meaning, where two Rabbinic obligations are at play. The obligation of Birkot Ha'Torah to begin with is Mi'de'rabbanan (according to some opinions, as mentioned), and, as a minor, the child is required to recite these blessings only by virtue of his father's rabbinic obligation to train him in Misva observance. This makes the child's requirement a lower-level obligation than the adult's direct obligation to recite Birkot Ha'Torah, and so an adult cannot fulfill this requirement by listening to a child's recitation of Birkot Ha'Torah.
Summary: Although youngsters below the age of Bar-Misva must be trained to recite Birkot Ha'Torah due to the obligation of Hinuch (training in Misva observance), an adult cannot fulfill his obligation of Birkot Ha'Torah by listening to a minor's recitation of these blessings.