When I studied verbs implying remembrance and recall, I learned that there are some differences. So I will write down what I know.
Remembering something learnt
Consider something you learned. It can be 2 minutes ago or 2 years ago, it does not matter. When you learn something it gets inside you for the rest of your life. What happens when we want to use the things we learned? We try to remember them.
In these situations you use 覚{おぼ}える.
だって皆{みな}、昨{き}日{のう}習{なら}った事{こと}をまだ覚{おぼ}えているのか。 => So everyone, do you remember the things we learned yesterday?
昨{き}日{のう}は急{きゅう}に故{ふる}郷{さと}の帰{かえ}り道{みち}を覚{おぼ}えたんだよ! => Yesterday, suddenly, I remembered the way back home in my birthplace.
Recalling something
Consider something you saw or heard some days ago. Consider some old memory or memento of yours. When it comes to memories, to things you saw and memorized inside of your mind/spirit/heart you should use 思{おも}い出{だ}す.
Of course this implies learning, but it is different. We learn things that will turn useful in our life. When it comes to memories, they are just things we store inside of us. They are not really useful (practically speaking).
ええ、無{む}理{り}ですよ!その人{ひと}は子{こ}どもの時{とき}に会{あ}った人{ひと}だからさ、名{な}前{まえ}が思{おも}い出{だ}せないよ! =>
What? This is impossible! That man is someone I met when i was a kid so, I cannot recall him!
クリスマスの時{とき}にくれたプレゼントを思{おも}い出{だ}せなくて、ごめんね〜 =>
I am not recalling the present you gave me, I am sorry...
Furthermore consider that 思{おも}い出{で} means memory or reminiscence.