The Bible teaches us the Trinity: Three persons (The Father, the Son, and the Holy Spirit) are contained within one God (monotheism). This post includes tables of Scriptures and the attributes and the works of the Trinity.
Let’s begin.
I. Introduction
A. Basic teaching
This post is about God in himself. The doctrine of the Trinity teaches that one God exists in three persons who fully and equally have the same essence or being.
Three statements
1.. There is one God.
2.. Three persons (Father, Son, and Holy Spirit)
3.. Each person is God. (Williams, vol. 1, pp. 83-90)
Explanation:
1.. The Scriptures clearly teach that God is one. Even Jesus says this (Mark 12:29).
2.. Many Scriptures affirm the existence of the Father, the Son, and the Holy Spirit.
3.. The Scriptures teach that the three persons are equally and fully deity or God
See Section III and IV, for their attributes and roles to support the third statement. We will show the Son’s deity and humanity more fully in the section on Christology (doctrine of Christ), and the Holy Spirit’s deity in the section Pneumatology (doctrine of the Spirit).
God exists in the distinct persons of the Father, the Son, and the Holy Spirit, but they equally have the same fully divine, undivided essence or being, such as uncreatedness, eternality, simplicity (pure spirit, non-composite or indivisible), immutability (unchangeableness), omniscience (all-knowing), omnipotence (all-powerful), goodness, mercy, holiness, will and freedom, and so on.
B. Attributes possessed fully by the three persons
In God, the attributes of his essence are fully possessed by three persons, making each person fully God.
For God, essence and existence are identical; his attributes are essential to his existence (Evangelical Dictionary of Theology, p. 344).
In contrast, we humans exist and express certain attributes, but to be ignorant of something does make us less human. We are not omniscient. But in God, his attributes are perfect, never lacking, never accidental, never uneven, and never inconsistent. God would not be God if he were ignorant even to the slightest degree.
Reformed theologian Louis Berkoff:
The divine essence is not divided among the three persons, but is wholly with all its perfection in each one of the persons, so that they have numerical unity of essence (p. 88).
The three persons wholly possess the same essence, the same “Godness.” That is, the Father and Son and Holy Spirit share the same attributes. The Father, the Son, and the Holy Spirit are equally wise and merciful and holy; one is not more wise or merciful or holy than the other. In that quotation, “numerical” means only one.
Simplest definition of all: Three persons are contained in One God—Triunity. We will look at an illustration, below (one triangle within one circle).
Once again, see the two addenda at the very bottom, for the attributes and roles of the triune God.
C. The three persons are distinct.
They are separated in this way: The Father is neither the Son nor the Holy Spirit; the Son is neither the Father nor the Holy Spirit; and the Holy Spirit is neither the Father nor the Son. The difference is in their personhood or subsistence (Father, Son, and Holy Spirit). Only the Father begets and is not begotten. God does this by necessity. It is not optional. It is in his nature. And his begetting is eternal, since it is in his essence to beget or generate. So the the property that belongs to the Father is generation.
Only the Son is begotten and does not beget. He receives his personhood (Sonship) eternally. This property is called filiation. To simplify “begottenness,” just think of a divine, eternal Father-Son relationship. This relationship existed for eternity, never beginning and never ending.
Only the Spirit proceeds or spirates from the Father and the Son. The Spirit does not do the works that the Father and Son do (begets or is begotten). And this spiration is eternal, since it comes from the essence of of the Father and the Son. And his procession is always occurring and will never end because it is in the essential nature of God to spirate. Therefore the property belonging to the Spirit is spiration or spirated.
Thus it is important to keep the three persons distinct. If they never were distinct, then there would be no difference in how the three persons interrelate. In other words, without these distinctions their personhoods would blur and fuse together (“con-fusion”). But each person is fully God and has all the attributes of God.
And we will see their distinctiveness in their roles in creation and redemption.
D. Summary: God’s oneness in essence, in three distinct persons.
The three persons (Father, Son, and Holy Spirit) are equally of the exact same essence of one God. But this one God revealed himself throughout Scripture as three distinct persons—Father, Son. and Holy Spirit—who are never fused together.
In understanding the basics, it is crucial keep persons and essence clear. There are three persons who are fully of the one essence of one God.
Once again, the best single word to describe God is Tri-unity or three persons in one essence or Godness.
II. Illustrations
A. Love
Nothing is more relatable to us humans than love.
Augustine (354-430 AD) comes up with this deep analogy: the lover, the beloved, and love. At the baptism of Jesus, the Father says that he loves the Son, and at that very moment, the Spirit descends and rests on Jesus (Matt. 3:16-17). Augustine seems to say that the Father loves the Son, who receives his love and returns it, for example, in his willingness to obey the Father and die on the cross, while the Spirit communicates the love between them.
This image of a triad of love expresses how the Father, the Son, and the Holy Spirit existed before the creation of time and the universe, and how the three persons will forever exist. It is into this love that the Trinity welcomes all believers and all who have received the love of God, through Christ and by the power of the Holy Spirit. (The Trinity Books VIII.14; IX.2, and XV.10)
The verses “God is love” (1 John 4:8 and 16) now take on a much, much deeper meaning.
In contrast, the strict unity of God seen in Islam or Judaism, for example, does not make sense in terms of the love of God, because divine love amounts to self-love. This is deficient.
Back to Augustine. His analogy is profound, because we have all experienced love from a lover, and we have returned the same love. All illustrations are inadequate, and this one still does not explain how, in detail, the one God shares this divine attribute of love and the other three persons. Our human love is but a poor reflection of divine love.
B. Sunlight
Athanasius (c. 296-373 A.D.) uses the radiance of the sun to express the Son being co-equal with the Father. The sun = the Father. The Son = the radiance or light. The Spirit = the heat or warmth.
The sun cannot help but radiate light–radiating light is in the sun’s nature. So the sun and light have the same essence or nature. Light proceeds from the sun. Likewise, the Father and Son have the same essence or nature, and the Son proceeds from the Father. So Athanasius described Jesus as Light (the Son) from Light (the Father)
Now what about the Spirit and the metaphor of Light? Athanasius did not deal with this topic (in his surviving writings that I’m aware of). But let’s try. It is also in the nature of the sun and its radiance to be hot. Heat proceeds from the sun and light. Heat has a different role, but it cannot exist apart from the sun and its light. Heat proceeds from the sun and the radiating light.
Here the analogy breaks down a little–as all analogies do–but the main point is clear. The sun and light and heat–three things–go together as one, though they have different roles. All three elements co-exist as co-equals; one cannot properly exist without the other two, by the nature of the one thing.
You can try this illustration with your children and newcomers. But as usual, let’s not push illustrations or metaphors too far.
C. Images to illustrate the Triunity
1.. Three persons in One God (Grudem, p. 321):
ONE GOD IN THREE PERSONS
Note how the three persons Father (F), Son (S), and Holy Spirit (HS) are located in one circle—God. The dotted lines merely indicate their personal relationship, not a division in God. They interpenetrate each other yet maintain their distinctive persons.
2.. Here is an ancient representation of the Trinity (Moody p. 207).
This image has existed for centuries. You may need to study it for a while.
Note that God and the three persons are within the triangle, which symbolizes their unity. God is in the center, which symbolizes their one essence. It says the Father is not the Son, and the Son is not the Spirit, and the Spirit is not the Father, and so on. But all three persons are one God in the center.
3.. Geisler suggests a simple triangle (p. 551).
It possesses a simultaneous threeness in its oneness. I expand on this idea, next.
The circle represents one God or unity or monotheism. The triangle symbolizes three persons: Father Son, and Holy Spirit: plurality or threeness.
Circle = One God = Unity = Monotheism
Three Sides of Triangle = Three Persons (Father, Son, Holy Spirit)
= Plurality or Threeness
Here is the triangle within the circle, representing:
ONE GOD IN THREE PERSONS
Note how the three persons of the Father, the Son, and the Spirit are all contained within one God and share the same space (or nature) within the circle. All three persons have the same “Godness” or deity within the circle (one God).
Placing a triangle within a circle is not a contradiction or even odd. It does not damage either geometric shape.
So this is Trinitarian (plurality) monotheism (unity).
III. Three Persons in the New Testament
A. Brief intro
The Trinity is found in the Old Testament. Please see this article:
The Trinity: What Does the Old Testament Say?
In this section let’s cite passages that formulate the Father, Son, and Holy Spirit. Verses that discuss Christ’s and the Spirit’s full deity will be covered in posts about Christ and the Spirit
B. Table of Trinitarian verses
This table has verses where God (the Father), the Son (Jesus Christ) and the Spirit appear in the same verses. This proves that the Trinity is a true doctrine. We can never give it up. It is a sure thing that I left many verses back in the Bible.
|
Trinitarian Verses The Father (God), the Son (Jesus Christ), and the Holy Spirit Are Mentioned |
|
| 1 | As soon as Jesus came up out of the water, “he saw the Spirit [Spirit] of God [Father] descending like a dove and lighting on him. And a voice from heaven said, ‘This is my Son, whom I love and with him I am well pleased’” (Matt. 3:16-17). |
| 2 | But if it is by the Spirit of God that I [Jesus] drive out demons, then the kingdom of God [Father] has come upon you. (Matt. 12:28) |
| 3 | All authority in heaven and on earth has been given to me. Therefore, go and make disciples of all nations, baptizing them in the name of the Father, the Son, and the Holy Spirit […] (Matt 28:18-19) |
| 4 | At that time Jesus, full of joy through the Holy Spirit, said, “I praise you, Father, Lord of heaven and earth, because you have hidden these things from the wise and learned, and revealed them to little children. Yes, Father, for this is what you were pleased to do. (Luke 10:21) |
| 5 | Jesus answered, “Very truly I tell you, no one can enter the kingdom of God [Father] unless they are born of water and the Spirit. (John 3:5) |
| 6 | For the one [Jesus] whom God [Father] has sent speaks the words of God [Father], for God [Father] gives the Spirit without limit. (John 3:24) |
| 7 | But the Advocate, the Holy Spirit, whom the Father will send in my [Jesus’s] name, will teach you all things and will remind you of everything I have said to you. (John 14:26) |
| 8 | “When the Advocate comes, whom I [Jesus] will send to you from the Father—the Spirit of truth who goes out from the Father—he will testify about me [Jesus]. (John 15:26) |
| 9 | All that belongs to the Father is mine [Jesus] That is why I said the Spirit will receive from me what he will make known to you.” (John 16:15) |
| 10 | Again Jesus said, “Peace be with you! As the Father has sent me, I am sending you.” 22 And with that he breathed on them and said, “Receive the Holy Spirit. (John 20:21-22) |
| 11 | On one occasion, while he [Jesus] was eating with them, he gave them this command: “Do not leave Jerusalem, but wait for the gift my Father promised, which you have heard me speak about. 5 For John baptized with water, but in a few days you will be baptized with the Holy Spirit.” (Acts 1:4-5) |
| 12 | He [Jesus] said to them: “It is not for you to know the times or dates the Father has set by his own authority. 8 But you will receive power when the Holy Spirit comes on you; and you will be my [Jesus’s] witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth.” (Acts 1:7-9) |
| 13 | God [Father] has raised this Jesus to life, and we are all witnesses of it. 33 Exalted to the right hand of God, he has received from the Father the promised Holy Spirit and has poured out what you now see and hear. (Acts 3:32-33) |
| 14 | Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. 39 The promise is for you and your children and for all who are far off—for all whom the Lord our God [Father] will call.” (Acts 2:38-39) |
| 15 | God [Father] exalted him to his own right hand as Prince and Savior that he might bring Israel to repentance and forgive their sins. 32 We are witnesses of these things, and so is the Holy Spirit, whom God has given to those who obey him.” |
| 16 | […] how God [Father] anointed Jesus of Nazareth with the Holy Spirit and power, and how he went around doing good and healing all who were under the power of the devil, because God was with him. (Acts 10:38) |
| 17 | […] the gospel he [Father] promised beforehand through his prophets in the Holy Scriptures 3 regarding his Son, who as to his earthly life was a descendant of David, 4 and who through the Spirit of holiness was appointed the Son of God in power by his resurrection from the dead: Jesus Christ our Lord. (Rom. 1:2-4) |
| 18 | For what the law was powerless to do because it was weakened by the flesh, God [Father] did by sending his own Son in the likeness of sinful flesh to be a sin offering. And so he condemned sin in the flesh, 4 in order that the righteous requirement of the law might be fully met in us, who do not live according to the flesh but according to the Spirit. (Rom. 8:3-4) |
| 19 | 12 And again, Isaiah says,
“The Root of Jesse [Jesus] will spring up, 13 May the God [Father] of hope fill you with all joy and peace as you trust in him [Jesus], so that you may overflow with hope by the power of the Holy Spirit. (Rom. 15:12-13) |
| 20 | And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God [Father]. (1 Cor. 6:11) |
| 21 | Therefore I want you to know that no one who is speaking by the Spirit of God [Father] says, “Jesus be cursed,” and no one can say, “Jesus is Lord,” except by the Holy Spirit. (1 Cor. 12:3) |
| 22 | 4 There are different kinds of gifts, but the same Spirit distributes them.5 There are different kinds of service, but the same Lord [Jesus]. 6 There are different kinds of working, but in all of them and in everyone it is the same God [Father] at work. (1 Cor. 12:4-6) |
| 23 | […] to be a minister of Christ Jesus to the Gentiles. He gave me the priestly duty of proclaiming the gospel of God [Father], so that the Gentiles might become an offering acceptable to God, sanctified by the Holy Spirit. (Rom. 15:15-17) |
| 24 | […] by the power of signs and wonders, through the power of the Spirit of God [Father]. So from Jerusalem all the way around to Illyricum, I have fully proclaimed the gospel of Christ. (Rom. 15:19) |
| 25 | “May the grace of the Lord Jesus, and the love of God [Father], and the fellowship of the Holy Spirit be with you all” (2 Cor. 13:14). |
| 26 | But when the set time had fully come, God [Father] sent his Son, born of a woman, born under the law, 5 to redeem those under the law, that we might receive adoption to sonship. 6 Because you are his sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, “Abba, Father.” (Gal. 4:4-6) |
| 27 | For through him [Jesus] we both have access to the Father by one Spirit. (Eph. 2:18) |
| 28 | But when the kindness and love of God [Father] our Savior appeared, 5 he saved us, not because of righteous things we had done, but because of his mercy. He saved us through the washing of rebirth and renewal by the Holy Spirit, 6 whom he poured out on us generously through Jesus Christ our Savior, (Titus 3:4-6) |
| 29 | It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, 5 who have tasted the goodness of the word of God [Father] and the powers of the coming age 6 and who have fallen away, to be brought back to repentance. To their loss they are crucifying the Son of God all over again and subjecting him to public disgrace. (Heb. 6:4-6) |
| 30 | […] have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, for obedience to Jesus Christ and sprinkling by his blood (1 Peter 1:2) |
| 31 | But you, dear friends, by building yourselves up in your most holy faith and praying in the Holy Spirit, 21 keep yourselves in God’s [Father’s] love as you wait for the mercy of our Lord Jesus Christ to bring you to eternal life. (Jude 20-21) |
| 32 | And this is his command: to believe in the name of his Son, Jesus Christ, and to love one another as he commanded us. 24 The one who keeps God’s [Father’s] commands lives in him, and he in them. And this is how we know that he lives in us: We know it by the Spirit he gave us. (1 John 3:23-24) |
| 33 | 21 To the one who is victorious, I [Jesus] will give the right to sit with me on my throne, just as I was victorious and sat down with my Father on his throne. 22 Whoever has ears, let them hear what the Spirit says to the churches. (Rev. 3:21-22) |
| 34 | This calls for patient endurance on the part of the people of God [Father] who keep his commands and remain faithful to Jesus. 13 Then I heard a voice from heaven say, “Write this: Blessed are the dead who die in the Lord from now on.” “Yes,” says the Spirit, “they will rest from their labor, for their deeds will follow them.” (Rev.14:12-13) |
| I got this idea from Harwood, pp. 147-49, but expanded on it. | |
C. Summary
The readers should also look up these verses: John 1:1-4, 14:26, 15:26, 16:13-14, 20:25-27; Acts 10:38 in connection with Romans 9:5, 15:13; 1 Corinthians 12:4-6; Colossians 2:9; Hebrews 1:3, 1:8, 1:10; Titus 2:13; 2 Peter 1:1; Jude 20-21.
Each passage affirms the person and function of the Father, the Son, and the Holy Spirit, and sometimes just the Father and the Son.
IV. Attributes and Works of the Trinity
A. Attributes
Here is a table of attributes for further study:
|
ATTRIBUTES OF THE TRIUNE GOD |
|||
| Attribute | Father | Son | Holy Spirit |
| Life | Jos. 3:10 | John 1:4 | Rom. 8:2 |
| Omniscience | Ps. 139:1-6 | John 4:17-18 | 1 Cor. 2:10-12 |
| Omnipotence | Gen. 1:1 | John 1:3 | Job. 33:4 |
| Omnipresence | Jer. 23:23-24 | Matt. 28:20 | Ps. 139:7-10 |
| Eternity | Ps. 90:2 | John 1:1 | Heb. 9:4 |
| Holiness | Lev. 11:44 | Acts 3:14 | Matt. 12:32 |
| Love | 1 John 4:8 | Rom. 8:37-39 | Gal. 5:22 |
| Truth | John 3:33 | John 14:6 | John 14:17 |
| Glory | Ex. 16:7 | 1 Cor. 2:8 | 1 Pet. 4:14 |
| Wisdom | Job 9:4 | Col. 2:2b-3 | Eph. 1:17 |
| Graciousness | Is. 30:18 | Eph. 2:4-9 | Heb. 10:29 |
| Peacefulness | Rom. 15:13 | Eph. 2:14 | Rom. 6:6 |
| Goodness | Exod. 33:19 | John 10:11, 14 | Gal. 5:22-23 |
| Patience | Rom. 2:4 | 1 Tim. 1:16 | Gal. 5:22-23 |
| Faithfulness | 1 Cor. 1:9 | Rev. 19:11 | Gal. 5:22-23 |
| Righteousness | Rom. 3:21-26 | Acts 7:52 | Rom. 14:17 |
| Joy | Neh. 8:10 | John 17:13 | Rom. 14:17 |
In the right column, Galatians 5:22-23 speaks of the fruit of the Spirit. The main point is that if the Spirit produces those fruits, then he must have them in his person. (Towns, p. 100).
B. Work of the three persons
Elmer Towns came up with this table too, which shows all three persons doing works that only God can:
|
THE WORK OF THE HOLY TRINITY |
|||
| Work | Father | Son | Holy Spirit |
| Creation of World | Ps 102:25 | John 1:3 | Gen 1:2 |
| Creation of Man | Gen 2:7 | Col. 1:16 | Job 33:4 |
| Death of Christ | Is 53:10 | John 10:18 | Heb 9:14 |
| Resurrection of Christ | Acts 2:32 | John 2:19 | 1 Pet 3:18 |
| Inspiration | Heb 1:1-2 | 1 Pet 1:10-11 | 2 Pet 1:21 |
| Indwelling of Believers | Eph 4:6 | Col 1:7 | 1 Cor 6:19 |
| Authority of Ministry | 2 Cor 3:4-6 | 1 Tim 1:12 | Acts 20:28 |
| Security of Believer | John 10:29 | Phil 1:6 | Eph 1:13-14 |
| This shows the unity of the Trinity. Each person of the Trinity contributed to each of these wonderful works, to God’s glory and for our salvation and redemption (Towns p. 100) | |||
V. Reflections
A. Practical application for the the laity and on Sunday morning.
The Trinity has practical application, especially for your Sunday morning service.
1. Your deeper relationship with God
The more deeply your know God, the more you can develop a relationship with God in a deeper way. The doctrine of the Trinity is the fullest revelation of the living and personal and relational God. The one God exists in three persons, Father, Son, and Holy Spirit. You can now relate to each person.
God is your Father; you are his daughter or son—his child. Jesus is your elder redeemer brother, and he comes alongside and assists you. The Spirit actually lives in your awakened, reborn spirit and comforts, guides, advocates for, and communicates the Father and the Son to you. He also inspires Scripture to your spirit and mind, so you can understand it.
We have a fullest relationship with him thanks to his initiation through his grace.
2. Unity of God → Unity of people
The arrow means “leads to.”
God is a united being in one essence, so you must reflect this unity. Humans, especially you, must live in unity with other humans.
3. Recognizing diversity in creation
Knowing that God is diverse in his personality, you can recognize diversity in his creation. God living in diversity of three persons of the Father, the Son, and the Holy Spirit reflects this diversity of humans. Countless numbers of creatures live on this planet, and the highest creature is humankind. You can recognize many peoples as reflecting God’s own being and will.
4. Your redemption
In the bigger picture, the triune God redeems humanity in three persons, Father, Son, and Holy Spirit. God loves you so much that the Father sent his Son into the world to die for your sins. The Father and the Son send the Spirit into your heart to draw you to salvation and then to live in you forever.
5. Your justification
Without the Trinity our salvation goes down the drain. If Christ is not fully God, then how can we trust him to save us in his redemptive act on the cross? As a creature, he would need redemption too. We may as well do all kinds of good works, hoping against hope that we may get invited into heaven when we die, but not knowing for sure that God will let us in. Rather, since Jesus Christ was fully deity in human flesh, his salvation is divinely secure for us. We are justified (declared righteous) by grace through faith.
6. Your sanctification
You are sanctified (growing in holiness) through receiving his Holy Spirit. The Spirit is holy and personal. If he were an impersonal force, we could not relate to him, and he could not relate to us. Blessedly, he is fully God and utterly personal and relational.
7. Your meaningful worship
You can now worship God more fully and meaningfully. We now have a fuller revelation of who God is. Our worship can be full and meaningful, much more so than before we knew about the triune God. Scriptural revelation does that to us.
8. Diversity of gifts
In the bigger church, God distributes a diversity of gifts to his people, who are called to live in unity. Just as the three persons (Father, Son, and Spirit) have different roles, so the church is diverse and enjoys a variety of gifts, but no matter what, we must live in unity, just as the three persons do.
9. Your eternal life or death
Without the full deity of Jesus Christ, God the Son, our salvation or guarantee to get into heaven becomes shaky. Therefore, the doctrine of the Trinity is a matter of eternal life and death. We Christians must hold on to the Trinity, as we experience the Father, the Son, and the Holy Spirit in our daily life and in our creeds.
10. Jesus’s fuller identity
If we diminish Jesus to a mere messiah or an anointed prophet, then our experience with God is lopsided and incomplete. Why not just pray to another saint or biblical prophet instead of Jesus? Worshipping a creature is idolatry and forbidden. Jesus must be fully God if we wish to maintain our biblical worship.
11 The Spirit’s fuller identity
If we diminish the Spirit to an impersonal force or power, then I would not want it dwelling in me. I need to communicate with the Spirit, and I could not do that with an impersonal force or power that I might be able to boss around or who ignores me and cannot talk to me. I won’t pray to the wind!
12. Fuller knowledge of God
It is a blessing, rather, that I can experience the fullness of the three persons of God the Father, God the Son, and God the Spirit in all their deity. I can worship and pray to all three persons of the Trinity and have the fullest experience with God. Wonderful!
B. Summary
Let’s conclude with simple truths.
The Scriptures reveal the Father and the Son and the Holy Spirit, not to give us a headache, but so we can relate to them. We can have a personal relationship with the Father as intimately (and more so) as we have with our own father. And we can relate to the Son as the Messiah and Lord, who has a unique relationship with the Father. The Son reveals the Father. The title Father is more personal and revealing than “God.” The Spirit of the Father and the Son now lives in us so he can empower us to have a relationship with the Father and the Son.
May the grace of the Lord Jesus Christ, and the love of God, and the fellowship of the Holy Spirit be with you all. (2 Cor. 13:14)
In this next verse “him” is Christ. The Spirit gives us access to the Father through his Son. It is lovely Trinitarian verse.
18 For through him [Christ] we both have access to the Father by one Spirit. (Eph. 2:18)
Bottom line: let’s have a relationship with the Father and the Son and the Holy Spirit, since they are revealed in Scripture in those three persons, for our relational benefit.
On Sunday morning, it is best to teach the relationship aspect of the Trinity.
For my reflections, please see Parts Two and Three.
RELATED
Longer Post
BIBLIOGRAPHY
Dr. Jim's Essential Bible Teaching 