Example #40 Patterns and Wonder
What if learning about flowers led to wonder?
Alison wanted her students to not only master the details in her science class but also experience moments of wonder at how it all fits together and ask big questions about why.
"This is one of my favourite lessons! It never fails to stun the students and bring out those real ‘wow’ moments that we all long for when a light gets switched on in a pupil’s understanding.
"I asked the students to bring in some flowers (I checked for allergies first!) but provided some myself for those who forgot or had little access to flowers. We then collected data, counting the number of sepals, petals, stamens, stigmas and seeds. Their table of results is usually made up almost exclusively of the numbers 1, 2, 3, 5 and 8.
"Then, I introduce the Fibonacci sequence of numbers (discovered by Indian mathmaticians and made known in the West by a 13th Century Italian). When I give them this string of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34 … ), I get them to circle any in the sequence which also appeared on their results table. The students/pupils quickly recognise that their results are numbers from the Fibonacci sequence. That always puzzles them! Then we look at who Fibonacci was and his work, and students try to work out how the sequence works (each number in the sequence is the sum of the previous two numbers).
"The next section of the lesson is deliberately very slow and reflective. We look very closely at a dried sunflower seed head because this is what sparked Fibonacci off to discover his sequence of numbers. (A close up online photo works if a seed head isn’t available.) What did Fibonacci see that was so special? We spend a long time looking at it, at the patterns that the seeds make. Eventually someone will spot that the seeds are in a spiral pattern or rather two sets spiralling in different directions (clockwise and anticlockwise).
"The Fibonacci numbers related to the seedhead are amazing – If you could count the total number of seeds it is a Fibonacci number, the number of clockwise spirals is a Fibonacci number, the number of anticlockwise spirals is the next Fibonacci number, the number of seeds in each spiral, etc. This realisation is usually a very special moment. It inevitably leads to questions about ‘how did that happen?’ and ‘why?’. We reflect together that Fibonacci must have asked the same questions many centuries earlier. What did he conclude? Is it just an accident or does it suggest, as Fibonacci believed, that there is a creator with a plan and purpose for everything, even something as small as a seed? Students then go away to see what they can find by looking closely at a pine cone or a pineapple."
What's going on here?
Alison saw her science lesson as a way of highlighting the unity of knowledge, making space for attentiveness, wonder and praise, and stimulating her students' curiosity in relation to big questions.
She engaged learners in reflection through progressive discoveries and in approaching the world attentively, making connections, experiencing wonder and asking big questions of life, faith and values (Fibonacci numbers and spirals in biology, stimulating questions).
She reshaped her practice by planning the timing of the various stages of discovery and the pace of each phase of the lesson and using natural objects, creating opportunities for insight and reflection (use of images/real seedheads, slow observation).
How do I do this myself? (Primary) How do I do this myself? (Secondary)
What does this have to do with faith, hope and love?
Christians put their faith in a God the Creator. They believe that God created the world and all that is in it, though they may differ in how this was achieved. This single source of creation provides an underlying unity to knowledge. It also means that the created world can reflect something of its creator in its design. The love of God for his world is reflected in the beauty and complexity of creation, and that includes the beauty of the mathmatical structure of much of creation.
What difference does it make?
This science lesson brought in an element of wonder by linking maths and science. Other combinations can bring wonder, for example maths and art and the 'golden proportion'.
Where could we go from here?
This topic of study can be extended more deeply to look at the occurrence of spirals in nature. It can also be broadened to make connections with patterns in other elements in the science curriculum. Looking at this ‘bigger picture’ raises questions about a creator God, and students often reflect that it takes more faith to believe that such things as patterns in nature occur randomly, by accident, than to believe they result from the work of a creator.
The Bible opens with the words, 'In the beginning God created the heavens and the earth' (Genesis 1:1). It ends with 'behold I make all things new' (Revelation 21:5). God is creator first and last and inbetween he sustains all that is (Psalm 65:9-13). For Christians, creation reflects the wisdom of God in its complexity and design (Psalm 104:24-25) and the universe responds in wonder and praise (Psalm 96:1).
Although beautiful and complex, the universe is not now as God created it. It is spoiled by sin, as God gave people the freedom to choose between right and wrong. However, the universe is still able to tell of a wise creator. It may be marred but it is not completely disfigured.
If the universe is so bad, how on earth did human beings ever come to attribute it to the activity of a wise and good Creator? C. S. Lewis
For the Christian – and many others – the universe points to a creator or designer in some form.
“I’m not an atheist. The problem involved is too vast for our limited minds. We are in the position of a little child entering a huge library filled with books in many languages. The child knows someone must have written those books. It does not know how. It does not understand the languages in which they are written. The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God. We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws.” Albert Einstein (First published as What Life Means to Einstein, Saturday Evening Post, October 26, 1929. Quoted in Walter Isaacson, Einstein: His Life and Universe; New York: Simon & Schuster, 2007, p. 386.)
Explore similar examples:
What if growing cress helped students see the interconnectedness of the world?
What if there were moments of wonder in chemistry?
What if music made children think about where creativity came from?
1In the beginning God created the heavens and the earth. 2The earth was barren, with no form of life; it was under a roaring ocean covered with darkness. But the Spirit of God was moving over the water. 3God said, I command light to shine! And light started shining. 4God looked at the light and saw that it was good. He separated light from darkness 5and named the light Day and the darkness Night. Evening came and then morningthat was the first day. 6God said, I command a dome to separate the water above it from the water below it. 7And that's what happened. God made the dome 8and named it Sky. Evening came and then morningthat was the second day. 9God said, I command the water under the sky to come together in one place, so there will be dry ground. And that's what happened. 10God named the dry ground Land, and he named the water Sea. God looked at what he had done and saw that it was good. 11God said, I command the earth to produce all kinds of plants, including fruit trees and grain. And that's what happened. 12The earth produced all kinds of vegetation. God looked at what he had done, and it was good. 13Evening came and then morningthat was the third day. 14God said, I command lights to appear in the sky and to separate day from night and to show the time for seasons, special days, and years. 15I command them to shine on the earth. And that's what happened. 16God made two powerful lights, the brighter one to rule the day and the other to rule the night. He also made the stars. 17Then God put these lights in the sky to shine on the earth, 18to rule day and night, and to separate light from darkness. God looked at what he had done, and it was good. 19Evening came and then morningthat was the fourth day. 20God said, I command the sea to be full of living creatures, and I command birds to fly above the earth. 21So God made the giant sea monsters and all the living creatures that swim in the sea. He also made every kind of bird. God looked at what he had done, and it was good. 22Then he gave the living creatures his blessinghe told the sea creatures to live everywhere in the sea and the birds to live everywhere on earth. 23Evening came and then morningthat was the fifth day. 24God said, I command the earth to give life to all kinds of tame animals, wild animals, and reptiles. And that's what happened. 25God made every one of them. Then he looked at what he had done, and it was good. 26God said, Now we will make humans, and they will be like us. We will let them rule the fish, the birds, and all other living creatures. 27So God created humans to be like himself; he made men and women. 28God gave them his blessing and said: Have a lot of children! Fill the earth with people and bring it under your control. Rule over the fish in the sea, the birds in the sky, and every animal on the earth. 29I have provided all kinds of fruit and grain for you to eat. 30And I have given the green plants as food for everything else that breathes. These will be food for animals, both wild and tame, and for birds. 31God looked at what he had done. All of it was very good! Evening came and then morningthat was the sixth day.
1I saw a new heaven and a new earth. The first heaven and the first earth had disappeared, and so had the sea. 2Then I saw New Jerusalem, that holy city, coming down from God in heaven. It was like a bride dressed in her wedding gown and ready to meet her husband. 3I heard a loud voice shout from the throne: God's home is now with his people. He will live with them, and they will be his own. Yes, God will make his home among his people. 4He will wipe all tears from their eyes, and there will be no more death, suffering, crying, or pain. These things of the past are gone for ever. 5Then the one sitting on the throne said: I am making everything new. Write down what I have said. My words are true and can be trusted. 6Everything is finished! I am Alpha and Omega, the beginning and the end. I will freely give water from the life-giving fountain to everyone who is thirsty. 7All who win the victory will be given these blessings. I will be their God, and they will be my people. 8But I will tell you what will happen to cowards and to everyone who is unfaithful or dirty-minded or who murders or is sexually immoral or uses witchcraft or worships idols or tells lies. They will be thrown into that lake of fire and burning sulphur. This is the second death. 9I saw one of the seven angels who had the bowls filled with the seven last terrible troubles. The angel came to me and said, Come on! I will show you the one who will be the bride and wife of the Lamb. 10Then with the help of the Spirit, he took me to the top of a very high mountain. There he showed me the holy city of Jerusalem coming down from God in heaven. 11The glory of God made the city bright. It was dazzling and crystal clear like a precious jasper stone. 12The city had a high and thick wall with twelve gates, and each one of them was guarded by an angel. On each of the gates was written the name of one of the twelve tribes of Israel. 13Three of these gates were on the east, three were on the north, three more were on the south, and the other three were on the west. 14The city was built on twelve foundation stones. On each of the stones was written the name of one of the Lamb's twelve apostles. 15The angel who spoke to me had a gold measuring stick to measure the city and its gates and its walls. 16The city was shaped like a cube, because it was just as high as it was wide. When the angel measured the city, it was about two thousand four hundred kilometres high and two thousand four hundred kilometres wide. 17Then the angel measured the wall, and by our measurements it was about sixty metres high. 18The wall was built of jasper, and the city was made of pure gold, clear as crystal. 19Each of the twelve foundations was a precious stone. The first was jasper, the second was sapphire, the third was agate, the fourth was emerald, 20the fifth was onyx, the sixth was carnelian, the seventh was chrysolite, the eighth was beryl, the ninth was topaz, the tenth was chrysoprase, the eleventh was jacinth, and the twelfth was amethyst. 21Each of the twelve gates was a solid pearl. The streets of the city were made of pure gold, clear as crystal. 22I did not see a temple there. The Lord God All-Powerful and the Lamb were its temple. 23And the city did not need the sun or the moon. The glory of God was shining on it, and the Lamb was its light. 24Nations will walk by the light of that city, and kings will bring their riches there. 25Its gates are always open during the day, and night never comes. 26The glorious treasures of nations will be brought into the city. 27But nothing unworthy will be allowed to enter. No one who is dirty-minded or who tells lies will be there. Only those whose names are written in the Lamb's book of life will be in the city.
1Our God, you deserve praise in Zion, where we keep our promises to you. 2Everyone will come to you because you answer prayer. 3Our terrible sins get us down, but you forgive us. 4You bless your chosen ones, and you invite them to live near you in your temple. We will enjoy your house, the sacred temple. 5Our God, you save us, and your fearsome deeds answer our prayers for justice! You give hope to people everywhere on earth, even those across the sea. 6You are strong, and your mighty power put the mountains in place. 7You silence the roaring waves and the noisy shouts of the nations. 8People far away marvel at your fearsome deeds, and all who live under the sun celebrate and sing because of you. 9You take care of the earth and send rain to help the soil grow all kinds of crops. Your rivers never run dry, and you prepare the earth to produce much grain. 10You water all its fields and level the lumpy ground. You send showers of rain to soften the soil and help the plants sprout. 11Wherever your footsteps touch the earth, a rich harvest is gathered. 12Desert pastures blossom, and mountains celebrate. 13Meadows are filled with sheep and goats; valleys overflow with grain and echo with joyful songs. (A song and a psalm for the music leader.) Shout praises to God
1I praise you, Lord God, with all my heart. You are glorious and majestic, dressed in royal robes 2and surrounded by light. You spread out the sky like a tent, 3and you built your home over the mighty ocean. The clouds are your chariot with the wind as its wings. 4The winds are your messengers, and flames of fire are your servants. 5You built foundations for the earth, and it will never be shaken. 6You covered the earth with the ocean that rose above the mountains. 7Then your voice thundered! And the water flowed 8down the mountains and through the valleys to the place you prepared. 9Now you have set boundaries, so that the water will never flood the earth again. 10You provide streams of water in the hills and valleys, 11so that the donkeys and other wild animals can satisfy their thirst. 12Birds build their nests nearby and sing in the trees. 13From your home above you send rain on the hills and water the earth. 14You let the earth produce grass for cattle, plants for our food, 15wine to cheer us up, olive oil for our skin, and grain for our health. 16Our Lord , your trees always have water, and so do the cedars you planted in Lebanon. 17Birds nest in those trees, and storks make their home in the fir trees. 18Wild goats find a home in the tall mountains, and small animals can hide between the rocks. 19You created the moon to tell us the seasons. The sun knows when to set, 20and you made the darkness, so the animals in the forest could come out at night. 21Lions roar as they hunt for the food you provide. 22But when morning comes, they return to their dens, 23then we go out to work until the end of day. 24Our Lord , by your wisdom you made so many things; the whole earth is covered with your living creatures. 25But what about the ocean so big and wide? It is alive with creatures, large and small. 26And there are the ships, as well as Leviathan, the monster you created to splash in the sea. 27All of these depend on you to provide them with food, 28and you feed each one with your own hand, until they are full. 29But when you turn away, they are terrified; when you end their life, they die and rot. 30You created all of them by your Spirit, and you give new life to the earth. 31Our Lord , we pray that your glory will last for ever and that you will be pleased with what you have done. 32You look at the earth, and it trembles. You touch the mountains, and smoke goes up. 33As long as I live, I will sing and praise you, the Lord God. 34I hope my thoughts will please you, because you are the one who makes me glad. 35Destroy all wicked sinners from the earth once and for all. With all my heart I praise you, Lord ! I praise you! The Lord can be trusted
1Sing a new song to the Lord ! Everyone on this earth, sing praises to the Lord , 2sing and praise his name. Day after day announce, The Lord has saved us! 3Tell every nation on earth, The Lord is wonderful and does marvellous things! 4The Lord is great and deserves our greatest praise! He is the only God worthy of our worship. 5Other nations worship idols, but the Lord created the heavens. 6Give honour and praise to the Lord , whose power and beauty fill his holy temple. 7Tell everyone of every nation, Praise the glorious power of the Lord . 8He is wonderful! Praise him and bring an offering into his temple. 9Everyone on earth, now tremble and worship the Lord , majestic and holy. 10Announce to the nations, The Lord is King! The world stands firm, never to be shaken, and he will judge its people with fairness. 11Tell the heavens and the earth to be glad and celebrate! Command the ocean to roar with all its creatures 12and the fields to rejoice with all their crops. Then every tree in the forest will sing joyful songs 13to the Lord . He is coming to judge all people on earth with fairness and truth. The Lord brings justice