Remembering to forget

I have been challenged lately to notice how often God says, "Remember..." in the Old Testament. Actually that word is in the NT as well. It was the "not remembering" that turned the children of Israel away from God. They forgot God's faithfulness to them.
Many times I find it easy to remember the things I should forget and forget the things I should remember. Often we are commanded in scripture to forget or lay aside sinful things, including the wrongs done to us.
I wonder what would happen to me during trials if I was better at remembering God's faithfulness in the past? What would that do to me in the present? How would this change my response to trials?
How would it change the way I even shared my testimony? Instead of setting up my regrets from the past as a shrine, perhaps my focus in my testimony would turn towards God's faithfulness to me?
Perhaps my trials of today would be overshadowed by God's faithfulness in the past? Maybe a focus on God's faithfulness would make today's worries seem like only momentary bumps in the roads.