8
Fun outdoor exercises for easy to understand mathematics Today’s researchers agree that outdoor activities boost our feeling of wellbeing. Not only does it make us healthier, less stressed, more alert and creative – it is fun! And, the core of all motivation and learning is enjoyment. SLU (the Swedish University of Agricultural Sciences) Partnership Alnarp Landscape and Öland Association of Local Authorities support the initial phase of a project focusing on the development of outdoor pedagogy to assist in the teaching of mathematics. The project is led by Mr Torsten Kellander, Horticultural Technician and Outdoor Pedagogue at Torslunda Experimental Station, SLU on the isle of Öland. GRÖNA FAKTA 1/2008 Gröna Fakta is jointly produced by ‘Utemiljö’ (publication) and ‘Movium’ (Centre for the Urban Public Space at the Swedish University of Agricultural Sciences). Photo: Torsten Kellander

Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

Embed Size (px)

Citation preview

Page 1: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

Fun outdoor exercises for easyto understand mathematics

Today’s researchers agree that outdoor activities boost our feeling of wellbeing. Not only does it make us healthier, less stressed, morealert and creative – it is fun! And, the core of all motivation and learning is enjoyment. SLU (the Swedish University of Agricultural

Sciences) Partnership Alnarp Landscape and Öland Association of Local Authorities support the initial phase of a project focusing on thedevelopment of outdoor pedagogy to assist in the teaching of mathematics.

The project is led by Mr Torsten Kellander, Horticultural Technician and Outdoor Pedagogue at Torslunda Experimental Station, SLU on the isle of Öland.

GRÖNA FAKTA 1/2008Gröna Fakta is jointly produced by ‘Utemiljö’ (publication) and ‘Movium’ (Centre for the Urban Public Space at the Swedish University of Agricultural Sciences).

Photo: Torsten Kellander

Page 2: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

When the participants arrive toTorsten Kellander’s course in out-door mathematics, they always startoff with a fun exercise that allowsthem to be silly, run around andhave fun. They begin to warm upand shyness gives way to the reali-sation that it is all right to play andhave fun.

“Not having fun is not productive,” expla-ins Torsten Kellander.

Halfway through the exercise, the partici-pants sit down for a moment of rest. It isnot possible to be productive for eighthours a day. Everyone needs a break nowand then.

“I am very aware of the stress anddemands that the teachers face at schooland I want to support them in makingdemands on their employers. Ultimately, itis about how we respond to and supportthe children.”

Tangible and enjoyable pedagogic exerci-ses are alternated with meditative experien-ces. The participants crawl through thedamson orchard and listen to Arvo Pärt’smeditative music in the Orbit House. Atthe end of the day, it is all about mathe-matics which in this case is based on theambience of the place.

However, the project run by TorstenKellander in the outdoor pedagogic envi-ronment of Torslunda ExperimentalStation on the isle of Öland is more thanjust mathematics. Torsten encourages theparticipants to come away with personalexperiences.

“I want to introduce the participants to

situations that will affect them in variousways. Based on this, I then ask them toreflect upon their personal experiences andin what direction they would like to pro-gress their teaching. At the end of thecourse, the participants should go homewith at least two main targets! Additionaltargets can be set for a period of five years.If they don’t, then I have failed,” saysTorsten Kellander.

The concept of Torsten Kellander’s flex-ible maths workshop works in any out-door environment. The basic idea is thatpupils and pedagogues shall use their par-ticular maths tools in outdoor exercises forthe purpose of discovering the world ofmathematics in their own time.

Children who are allowed to run aroundand learn about the concept of mathemat-ics through play apply all their senses andwill understand the concept of mathemat-ics throughout life. This has been recogni-sed by the outdoor pedagogue TorstenKellander.

After ten years working with schoollandscape planning with focus on cultiva-tion and mathematics and the OrbitHouse at Torslunda Experimental Station,Torsten Kellander began exploring thepossibility of using the pedagogic outdoorenvironment to make maths lessons moreenjoyable and comprehensible.

“We used to calculate the weight of thepumpkin harvest and measure the vege-

GRÖNA FAKTA 1/2008

II

Shyness gives way to fun and easy m

You can learn maths anywhere, as long as you have a few simple tools. Here, students from theUniversity of Kalmar complete a grid exercise on the grass at Torsten Kellander’s maths workshopat Torslunda Experimental Station. Photo: Torsten Kellander

Torsten Kellander is an outdoor pedagogue at Torslunda. Experi -men tal Station, the Swedish University of Agricultural Sciences onthe isle of Öland where he has created a centre for outdoor peda-gogy based on his work with school landscape planning and theOrbit House. During the past four years, Torsten Kellander has deve-loped his school landscape and outdoor pedagogy format into mat-hematical teaching methods. Torsten Kellander qualified as aHorticultural Technician in Alnarp and started working at the experi-mental agricultural estate on Öland in 1972. In 2006 and 2007,Torsten Kellander completed a course in Mathematics didactics atthe Blekinge Institute of Techno logy. In the autumn of 2007, ‘Allatiders teknik’ (Technology of all times) published the book ‘Leka ochlära matematik ute – förskolan’ (Play and learn mathematics out-

doors – the nursery school) which TorstenKellander co-wrote. See www.websitefolder.net/allatidersteknikTorslunda Experimental Station is linked to the faculty of landscape planning, hor-ticulture and agriculture at the SwedishUniver sity of Agricultural Sciences inAlnarp. The experimental station on theisle of Öland offers courses in outdoor peda-gogy and school landscape planning forpedagogues working in a childcare or school environment. For more information, visit www.ltj.slu.se

Outdoor pedagogy and mathematics

Torsten Kellanderworks with outdoorpedagogy on Öland.Photo: MarianneÅkesson Skörd

Page 3: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

table garden but I thought about comple-menting and expanding these exerciseswith a simple and portable maths works-hop.”

Spontaneous outdoor mathsAfter many years working with localschools and not to forget, the teachers andpupils at Torslunda School on Öland,Torsten Kellander realised that a lot ofpedagogues would prefer to teach mathsoutdoors. However, the problem was thatthey did not always have an inspiringnatural environment in close proximity totheir school and hence, spontaneous les-sons were not always practical.

“I wanted to provide the pupils and tea-chers with the necessary tools for learningabout mathematics outdoors in a simplebut playful and active way and wheneverthey wanted to.”

The initial source of inspiration was Mr

Gunnar Lindqvist, a teacher at the EliasFries School in Hyltebruk who taughtmaths with the help of wooden boards.

“Gunnar gave me permission to copy theidea and I have progressed from there.”

In 2005, Torsten Kellander applied for agrant for the development of the mathsproject in a pedagogic outdoor environ-ment. The following year, SLUPartnership Alnarp Landscape and ÖlandAssociation of Local Authorities decided tofinance the initial phase of the projectwith the intention of developing the met-hod over a period of three years for thebenefit of nursery school children to year6 pupils.

Since then, pedagogues from nurseryschools and schools all over the countryhave visited Torslunda ExperimentalStation to learn how to best apply the con-cept of Torsten Kellander’s maths works-hop. With local nursery and primary

schools bringing along their pupils toshare the experience, a gradual develop-ment of the method is taking place. As aresult of the collaboration with theUniversity of Kalmar in addition to peda-gogues and pupils throughout Swedenapplying the concept of the maths works-hop, other ideas and teaching methodshave developed since the start of the pro-ject. Torsten Kellander truly believes thathe is on the right path and can tell ofmany instances that verifies this.

“As, for example, when a pupil describedthe moment of understanding as “a flurryin my stomach and pounding of myheart” and “brilliant getting the answerright with the dice!”.

Feel good outdoors Today’s researchers agree that outdoor acti-vities help boost our feeling of wellbeing.The fresh air and open space, daylight andexciting natural materials to experimentwith - the outdoor environment is full ofthings that make us feel good in body andsoul. Not only does it make us healthier,less stressed and more alert and creative,but it is fun to be outdoors! And, whenthe lesson move outdoors, many unexpec-ted things can happen.

“Set routines and rigid roles start tobreak down. Pupils not doing themselvesjustice in the classroom often find a rene-wed confidence during the practical out-door exercises,” explains Torsten Kellander.

The teamwork between the pupils andtheir pedagogue through playful, tangibleand lively exercises in addition to a changeof environment often result in a desire todiscover and sporadic questions. By focu-sing on simple exercises that everyone canmanage with a clear link to the everydaylife of the child, mathematics becomeunderstandable.

Children and adults learn from eachother, grasp the connection, get a directresponse and have fun together.Discovering mathematics becomes anenjoyable and satisfying experience.

Naturally, the appearance of the environ-ment where the exercises are carried out isimportant. The best possible exercise envi-ronment includes a variety of componentssuch as a tarmacked or grassy surface, agravelled path, different types of trees inc-luding fruit trees, interesting hedging

GRÖNA FAKTA 1/2008

III

athematics

What is six minus six dots? Our senses are stimulated by the outdoors and maths takes on a newangle when you are allowed to use your body unhindered. Photo: Torsten Kellander

Page 4: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

plants and bushes, boulders, rock faces andother gradients, flowers, soft fruit plants, avegetable patch and if possible, a wild gro-wing area. Natural ‘materials’ such as lea-ves, fruits, home grown vegetables, chest-nuts, pine nuts, sticks and small stones arealso good to have although these can ofcourse be collected during an outing andbrought back to the workshop.

“Although the basic idea behind mymaths workshop is that it should work justas well in a garden as in a park, forest orbarren city school yard,” explains TorstenKellander.

Portable workshop The maths workshop does not need totake up a very large area of the school yardand since the material is portable, nothingstops it from being moved to another loca-tion.

Usually, it does not take long for nurseryschool teachers to see how they can trans-fer the material used in the maths labora-tory to other diverse natural environments.For example, grids can be drawn in sand,painted on snow or built with sticks in thewoods.

However, the maths workshop describedin this article does require small grassedand tarmacked areas to achieve the opti-mum result.

It is also beneficial to create a couple ofattractive and slightly secluded school yard

meeting places where the children - eithertwo by two or in a group – can meet toreflect and discuss an activity.

The idea behind the maths materialdeveloped by Torsten Kellander for useoutdoors by children, pupils and pedago-gues is primarily to promote both sponta-neous and planned maths exercises. Still,the most important aspect of the materialused in the ‘maths lab’ (as described in thenext article), e.g. wooden boards, vests,grids, dice and rope stumps is that they areeasy and inexpensive to make.

“Nursery and primary school childrenwho are involved in the making of themaths lab material together with theirpedagogues will take responsibility and feelpart of the process. Making the mathstools together will also give everyone aninsight into the mathematical world,” saysTorsten.

For example, spraying a grid on the grassillustrates quite clearly how large a 0.5 by0.5 m square is ‘in reality’. And if you haveto measure the length of a wooden boardmade up of five sections with each sectionmeasuring one metre, you soon becomefamiliar with the metric system.

By using a folding rule and a measuringtape, the children really get to understandthe different measurements.

The material used in the maths works-hop should of course appeal to as many ofour senses as possible and consequently, alot of colours are a must. In addition, the

material should be hard-wearing to with-stand outdoor storage, perhaps in a shedor under a roof. In this way, all mathstools are easily accessible for spontaneousoutdoor lessons.

The subject of the maths lab can of cour-se be varied endlessly and children ofteninvent completely new or a combinationof old exercises. At the same time as themethod is modified to the requirements ofthe school, new ‘tools’ may be invented toadd to the existing workshop supply.

“If everyone is allowed to partake in andtake responsibility for the planning, inven-tion and making of new tools, then themaths laboratory becomes a project thatfollows the progress of the pupils anddevelops from year to year,” says TorstenKellander.

Preparation and reflection Torsten Kellander repeatedly reiterates theimportance of time. And, he is not just tal-king about the time it takes to do thepractical exercises outdoors and encourageteamwork.

“It is essentially about children and adultexplorers having the time to collectivelyand calmly reflect on what they havefound and how, i.e. not to rush the processand instead do fewer exercises to gain adeeper understanding.”

First of all, the pedagogue should careful-ly prepare for and think about why she/hehas chosen a specific exercise. What is thepurpose with the exercise? What do I wantthe pupils to learn and understand? Whichmathematical concepts and keywords willthe pupils come across and do they under-stand what these mean?

”By practising indoors, the pedagoguecan see whether the children have actuallygrasped the difference between variousmeasurements – or the outdoor exercisewill not be constructive,” says TorstenKellander.

At one school, the classroom childrenwere asked to think of different mathema-tical concepts relating to the measuring ofa length. What is longer? Seventy centi-metres, seven decimetres or a metre?

One way is to measure the length of thefloor using a ruler, folding ruler or a stringwhile another is to guess the answer, argueone’s viewpoint and consider the opinionsof other classmates.

However, to begin with, it would behelpful to explain the concept of length byasking the pupils to line up according toheight and then describe and explain theexercises that the pupils will be doing out-

GRÖNA FAKTA1/2008

IV

Hmm, now what is six dots minus two dots? Mathematics becomes more comprehensible whenusing dice and a maths board. Photo: Torsten Kellander

Page 5: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

side. The pupils can also form groups andtry to come up with new exercises for theirschool friends.

When doing the outdoor exercises, thepupils must be given time to find alterna-tive solutions to a maths problem and tosee and understand how a friend managedto solve a problem, discuss the methodused and agree on an answer.

“In this way, everyone can see that thereis more than one explanation and solutionto a problem.”

Process and understandThe solutions found by the pupils andpedagogues are then processed. Perhapsnot everyone has had the time to see howa friend managed to solve a specific pro-blem or to understand the implication ofone’s own conclusions. It is important toassess whether the exercises have helpedthe children to better understand thewords, concepts and keywords discussedprior to the exercises and to link theirnewfound knowledge to certain mathema-tical concepts, understand patterns and asknew questions that will lead to other areas.What did you do and why? Could youhave done it in any other way?

“In this way, children as young as six willbecome familiar with mathematical wordsand terminology and manage to link aword to a mathematical concept,” saysTorsten Kellander.

The processing, outdoor exercises and

preparatory work should of course beadapted to the individual needs and age ofa child. Small children do not have the sta-mina of older children and lose their con-centration after about fifteen minutes. Ashort break with a lively and simple mathsgame is then welcome.

Naturally, it is important for the adult tobe flexible and responsive at all times,especially in the company of older pupils,and to reassess the situation when a groupof pupils is unable to keep up. TorstenKellander remembers when a group ofrestless Year 7 pupils was asked to do someexercises relating to time.

“It did not quite work according to plan,so I thought that they probably needed toget rid of some energy.”

Every pupil was asked to run a distanceof thirty metres while a friend clocked thetime on his/her mobile telephone!

The final result varied with precisetimings from 4.1 to around 5 seconds.After that, the pupils had to figure out inwhich square in the grid on the lawn thatshe/he should stand with her/his time. Afairly advanced exercise in the art of roun-ding off that the pupils solved indepen-dently without a problem.

In order to do the exercise, the pupilsneeded to put their thinking caps on and

discuss the activity. Torsten Kellanderbelieves that these outdoor exercises andthe maths workshop do not only create agreater understanding of mathematicalconcepts.

“By using all senses in a stimulating out-door environment and trying differentways in which to solve a problem, childrenand adults are given the opportunity offinding the method of learning that bestsuits them. We are all different!”

Over time, Torsten Kellander would liketo see the outdoor teaching method beingused by a growing number of pedagogues,regardless of whether it is his own methodor that of someone else. What is mostimportant is that the pedagogues give thepupils a chance to become familiar withdifferent and other ways of learning aboutmathematics.

“All pedagogues should have the oppor-tunity to study and develop outdoor peda-gogic skills, not least in mathematics.”

Perhaps Torsten Kellander’s vision for thefuture is about to become reality when thenew partnership with the mathematicaldidactics at Växjö University starts in2008, giving the teachers of the future anopportunity of teaching mathematics out-doors to pupils from Year 6 to Year 9 aswell as sixth-formers.

GRÖNA FAKTA 1/2008

V

Nothing compares with inciting the need for and love of knowledge or you would only create packing mules.

Michel de Montaigne

The concept of maths can also be taught using home grownvegetables. A little fun can do no harm! Photo: Torsten Kellander

Page 6: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

GRÖNA FAKTA 1/2008

VI

The maths lesson starts with thepedagogues and pupils togethermaking the maths tools.Involvement increases the feeling ofcommitment and responsibility.Colourful wooden boards, dice andreflective vests stimulate the senses.These simple teaching materialshave endless uses.

All maths tools should be kept close athand to facilitate easy access whenever nee-ded. After all, the idea is that nursery andprimary schools situated far from natureshall be able to teach mathematics in theschool yard whenever they want to.However, it would be an advantage if thenursery or primary school yard had grassy,gravelly and tarmacked areas.

If there are no natural materials close athand (e.g. pine cones, pebbles and sticks),then these should be collected as mathe-matics is not just about counting and lear-ning figures. It is also about volume, posi-tioning, sorting, comparing and making anassessment based on various criteria in

addition to colour, shape, weight and size.Filling the maths workshop with approp-

riate materials is a process that should beallowed to take time. When nursery andprimary school children make the mathsworkshop tools together with their pedago-gues, an exciting joint discovery of theworld of mathematics occurs.

The exercises described below can bevaried to infinity and are only limited by alack of imagination. However, it is alwaysimportant to prepare the pupils for theexercises. What do you want to achieveand make easier to understand? It is parti-cularly important to go through and putinto practice different concepts and key-words that may crop up during the exerci-se. Does everyone understand the metricsystem, e.g. seven decimetres being shorterthan one metre? How can this be betterexplained?

It is also important to think about anddiscuss how the children used the boards,vests and grid. The children’s own thoughtsdo not only shed light on what they havelearnt and what method of learning theyprefer. They often induce ‘Aha!’ momentsamong the other participants.

Most importantly, the children learn torealise that a problem can be solved inmore than one way, using a number ofstrategies – none better or more accuratethan the other!

Wooden boardsPlaned wooden boards can be bought fromthe nearest builder merchant at a standardlength of 3.6 metres. The boards are reaso-nably easy to handle and using a markerpen, the surface of the wooden board canbe divided into ten equally large sectionswith a number in each square, e.g. from 1to 10, from 11 to 20 and so forth.

The numbers can also be replaced withsymbols (dots, stars, etc.) with one dot inthe first square, two dots in the secondsquare, etc., similar to the dots on a dice.Position the boards alongside each other toreveal the actual number and correspon-ding amount of dots.

Exercises using a number scale and ‘10-friends’Using the wooden board with numbersfrom 1 to 10, ask the smaller children tostep into each of the squares while callingout the number of the squares. Then see ifthe children can figure out what numberthey would get to if adding 1 to 2 and tostep into the correct number or symbolsquare.

The older children (from five years) canbe divided into groups of two with eachpair being given a note with 2 + 3 or 1 + 1and so on with the total sum not excee-ding 10. Then ask each pair to add up thenumbers on their note and step into thesquare that corresponds to their sum total.

For the ‘10-friends’ exercise, put thechildren into pairs. One child steps onto anumber square while the other figures outwhich square he/she should step into tomake up the number 10 together withhis/her friend.

The strategies applied by the children tofind the correct answer usually varies.Some pace the board, others do a mentalcalculation while others still count on theirfingers.

Reflective vestsMost nursery and primary schools have asupply of reflective vests. By writing diffe-

The meeting place is where everyone can take a break, think about what they have achieved andput words to their experiences. Photo: Torsten Kellander

Making your maths tools generates re

Page 7: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

rent numbers on the vests, they can thenbe used for different exercises. SeeExercises with a number scale and ‘10-fri-ends’ above.

As an example, ask the children to lineup in numerical order. The vests can alsobe used for practising the concepts ofbehind, in front and beside.

Alternatively, ask the children to collectthe same number of pine cones (sticks,pebbles) as the number on their vests andtalk about which number that is greaterand/or smaller than another number.Practise odd and even numbers by askingthe children with odd numbers (or viceversa) to close their eyes. The childrenwith even numbers and their eyes opencan then together try to guide everyoneinto a numerical line-up .

The vests are perfect for active mathema-tical games that involve running around orhugging a ‘10-friend’. The complexity ofthe games should vary according to age.

GridPaint or draw a grid directly onto a grassyor tarmacked surface using white spraypaint, special line marker equipment orchalk. The grid should consist of onehundred or ten by ten half metre squares.You can also make a temporary grid withfood colouring in the snow or by drawinglines in the school yard sand. The grid isperfect for training positional terminologyand the concept of space.

ExercisesThe grid can be used to pace out and cle-arly explain the concept of a bar chart. Forexample, how tall is the chart that has tenstones compared with the one that hasfive?

In addition, the grid can be used forvarious decimal and rounding off exercisessuch as when the Year 7 pupils mentionedabove measured the time in seconds.

DiceReady-made, large dice can be boughtfrom a shop or made in wood. The benefitof using dice is that they can easily becombined with other maths workshopmaterials.

For example, the concept of additionand subtraction can be explained by cove-ring one or a couple of the dots on thedice with your hand (and then removeyour hand).

GRÖNA FAKTA 1/2008

VII

sponsibility and stimulates all senses

“Our first teachers of philosophy are our feet, handsand eyes. To substitute books for them does not teachus to reason, it teaches us to use the reason of othersrather than our own; it teaches us to believe much andknow little.”Jean-Jacques Rousseau

Pupils learning about number tenwith the help of wooden mathsboards. Photo: Torsten Kellander

Page 8: Fun outdoor exercises for easy to understand … outdoor exercises for easy to understand mathematics ... chers with the necessary tools for learning about mathematics outdoors in

Dice and boardsDice and boards can be used to practisesubtraction across all ages.

This exercise was developed by BirgittaAndersson and pupils from Year 1 to 3 atthe Torslunda School on Öland. Theadvantage of mixed age groups is that thechildren will learn from each other.Another advantage is that everyone can beactive together, eliminating any boringwaiting around.

Subtraction exercisesThis exercise requires a maths board num-bered from 0 to 5 and two dice but beforestarting the exercise, it is important to talkabout the highest numbers on the dice.Ask a pupil to throw a dice. The diceshows 2. Then ask another pupil to throwthe other dice. The total of the two dice is4. What is the difference? The correct ans-wer is 2! Mark the correct answer by put-ting a colourful note on the correspondingnumber on the maths board. Continue inthe same way until all numbers are mar-ked. This exercise can also be used as a com-petition between two groups of children.

Other materialThe maths workshop materials can obvio-usly be alternated and supplemented wit-hout end. For example, the three metreslong maths boards can become foldableand portable if replaced by an oilcloth.

Moreover, the outdoor environment isfull of free material that can readily beused for different maths exercises. Pinecones, small or large stones, leaves, twigsand fallen fruit can be counted and/or sor-ted according to colour, shape, weight,length, etc., either individually or in com-bination with the boards, grids and vests.

GRÖNA FAKTA 1/2008

Gröna Fakta is produced by Movium, SLU, Box 54, 230 53 Alnarp. Tel.: +46 (0)40 41 50 00.Editor: Titti Olsson. ISSN 0284-9798. Published in Utemiljö 1/2008.

…was written by Torsten Kellander, Outdoor Pedagogue at Torslunda Experimental Station, the Swedish University of AgriculturalSciences and Eva Selin, Chief Editor for the periodical Familjedaghem, Fortbildning AB Stockholm. Eva Selin is also the author of ‘Rumför utelek’ (Room for outdoor play), Fortbildning AB. Cover: Teachers from the United Kingdom, the Slovak Republic, Italy andGermany have visited the maths workshop at Torslunda Experimental Station.

This ‘Gröna Fakta’...

Pupils from the University of Kalmar practise geometrical shapes using a rope. At the maths workshop, there is usually more than one solution to aproblem and everyone can find the way that suits them the best. Photo: Torsten Kellander