From my own experience as a pupil, teaching purely formal systems with no help in building the intuition of why the formal rules are what they are is a recipe for disaster. It invites thinking of mathematics as a game, and when you forget the rules, you tend to invent new ones.
My belief is that is exactly how you end up with students doing fraction addition as a/b + c/d = (a+c)/(b+d); or the infamous shepherd's age problem[0] - they forgot the actual rules, and picked a different rule that makes just as much sense to them.
And regarding analogies, I think that the best approach is to pick a real-world problem, and translate that into math, as a starting step for explaining the formal rules and building this intuition. Doing thing the other way around is much more likely to lead to contrived examples. But math rules have good intuitive reasons for existing, and explaining these as you introduce the rules is likely to help rather than hinder.
Of course, I wouldn't advocate for having students go back to the analogy while solving more advanced exercises with the rules that they have internalized. But having lots of exercises initially that try to drive home the intuition behind the rules is going to be very helpful in my opinion.
[0] "A shepherd has 25 goats and 53 sheep. How old is the shepherd?" A lot of kids will give you an answer: if they do, they will probably say that it's 25+53 or 53-25, since they may apply some common-sense reasoning after they "do the math", but at the wrong end of the problem.
My belief is that is exactly how you end up with students doing fraction addition as a/b + c/d = (a+c)/(b+d); or the infamous shepherd's age problem[0] - they forgot the actual rules, and picked a different rule that makes just as much sense to them.
And regarding analogies, I think that the best approach is to pick a real-world problem, and translate that into math, as a starting step for explaining the formal rules and building this intuition. Doing thing the other way around is much more likely to lead to contrived examples. But math rules have good intuitive reasons for existing, and explaining these as you introduce the rules is likely to help rather than hinder.
Of course, I wouldn't advocate for having students go back to the analogy while solving more advanced exercises with the rules that they have internalized. But having lots of exercises initially that try to drive home the intuition behind the rules is going to be very helpful in my opinion.
[0] "A shepherd has 25 goats and 53 sheep. How old is the shepherd?" A lot of kids will give you an answer: if they do, they will probably say that it's 25+53 or 53-25, since they may apply some common-sense reasoning after they "do the math", but at the wrong end of the problem.