How God Matures Us Through Trials
James 1:2-4 (ESV)
Count it all joy, my brothers, when you meet trials of various kinds,  for you know that the testing of your faith produces steadfastness.  And let steadfastness have its full effect, that you may be perfect and complete, lacking in nothing.
In light of this text, the reason why we are to rejoice in the midst of trial is because we know that trials produce steadfastness, and steadfastness - when it has its full effect - produces spiritual maturity. So, one of the questions we asked was, "in what specific ways do trials produce spiritual maturity?" The discussion which followed was rich and helpful. Several things that members of our group suggested (and at least one I've thought of since) are the following:
1. Trust and hope in God
Romans 5:2-5 (ESV)
Through him we have also obtained access by faith into this grace in which we stand, and we rejoice in hope of the glory of God.  More than that, we rejoice in our sufferings, knowing that suffering produces endurance,  and endurance produces character, and character produces hope,  and hope does not put us to shame, because God's love has been poured into our hearts through the Holy Spirit who has been given to us.
Psalm 56:3-4 (ESV)
When I am afraid, I put my trust in you.  In God, whose word I praise, in God I trust; I shall not be afraid. What can flesh do to me?
2. Compassion for Others
2 Cor. 1:3-7 (ESV)
Blessed be the God and Father of our Lord Jesus Christ, the Father of mercies and God of all comfort,  who comforts us in all our affliction, so that we may be able to comfort those who are in any affliction, with the comfort with which we ourselves are comforted by God.  For as we share abundantly in Christ's sufferings, so through Christ we share abundantly in comfort too.  If we are afflicted, it is for your comfort and salvation; and if we are comforted, it is for your comfort, which you experience when you patiently endure the same sufferings that we suffer.  Our hope for you is unshaken, for we know that as you share in our sufferings, you will also share in our comfort.
3. An Eternal Perspective
2 Cor. 4:7-18 (ESV)
But we have this treasure in jars of clay, to show that the surpassing power belongs to God and not to us.  We are afflicted in every way, but not crushed; perplexed, but not driven to despair;  persecuted, but not forsaken; struck down, but not destroyed;  always carrying in the body the death of Jesus, so that the life of Jesus may also be manifested in our bodies.  For we who live are always being given over to death for Jesus' sake, so that the life of Jesus also may be manifested in our mortal flesh.  So death is at work in us, but life in you.  Since we have the same spirit of faith according to what has been written, "I believed, and so I spoke," we also believe, and so we also speak,  knowing that he who raised the Lord Jesus will raise us also with Jesus and bring us with you into his presence.  For it is all for your sake, so that as grace extends to more and more people it may increase thanksgiving, to the glory of God.  So we do not lose heart. Though our outer nature is wasting away, our inner nature is being renewed day by day.  For this slight momentary affliction is preparing for us an eternal weight of glory beyond all comparison,  as we look not to the things that are seen but to the things that are unseen. For the things that are seen are transient, but the things that are unseen are eternal.
James 1:5 (ESV)
If any of you lacks wisdom, let him ask God, who gives generously to all without reproach, and it will be given him.
Wisdom is a fruit of trials, when in the trials we seek the Lord from it from an unwavering heart. That James probably intends this is evident because of the verbal link between "lacking in nothing" in verse 4 (part of James' description of a the mature - "perfect and complete" - person) and "lacks wisdom" in verse 5. So, wisdom comes through suffering.
5. Understanding of Scripture
Psalm 119:50 (ESV)
This is my comfort in my affliction, that your promise gives me life.
Psalm 119:67 (ESV)
Before I was afflicted I went astray, but now I keep your word.
Psalm 119:71 (ESV)
It is good for me that I was afflicted, that I might learn your statutes.
As Martin Luther said: ""I want you to know how to study theology in the right way. I have practiced this method myself ... Here you will find three rules. They are frequently proposed throughout Psalm  and run thus: Oration, meditatio, tentatio (Prayer, meditation, trial) (see note 56). And trials (Anfechtungen) he called the "touchstone." "[They] teach you not only to know and understand but also to experience how right, how true, how sweet, how lovely, how mighty, how comforting God's word is: it is wisdom supreme". . . . He proved the value of trials over and over again in his own experience. "For as soon as God's Word becomes known through you," he says, "the devil will afflict you will make a real doctor of you, nd will teach you by his temptations to seek and to love God's Word. For I myself ... owe my papists many thanks for so beating, pressing, and frightening me through the devil's raging that they have turned me into a fairly good theologian, driving me to a goal I should never have reached." (Quotations from John Piper's biographical lecture on Martin Luther.)
Hebrews 12:5-11 (ESV)
And have you forgotten the exhortation that addresses you as sons? "My son, do not regard lightly the discipline of the Lord, nor be weary when reproved by him.  For the Lord disciplines the one he loves, and chastises every son whom he receives."  It is for discipline that you have to endure. God is treating you as sons. For what son is there whom his father does not discipline?  If you are left without discipline, in which all have participated, then you are illegitimate children and not sons.  Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live?  For they disciplined us for a short time as it seemed best to them, but he disciplines us for our good, that we may share his holiness.  For the moment all discipline seems painful rather than pleasant, but later it yields the peaceful fruit of righteousness to those who have been trained by it.
What good God does in our lives through suffering! This is an exhortation to all of us to not wish our trials away.