Outdoor Education: A Reason Why Ten-YearOlds Excel in Mathematics

Anne CookUniversity Elementary School, BIoomington, Indiana

Ten-year olds excel if and when they want to. Likewise, ten-yearolds learn if, what, and when they want to. The problem then becomesone of deciding what is important for them to learn, how importantit is to you as the teacher for them to learn it, and how you are goingto achieve these goals for them and yourself.Knowing that most children this age should still be children con-

cerned more with playing and having a good time than they are withacademic excellence per se, it then becomes the task of the teacher toblend the two.My goal can be simply stated as trying to achieve a classroom full

of children with inquiring minds who think learning is fun. This paperdoes not purport to be the total answer: just one approach.Each spring the fifth grades of University School�approximately

100 in number�go to Bradford Woods for a week of Outdoor Educa-tion. Obviously, all of the skills necessary to the most advantageousutilization of this time can not be achieved in one week. We plan fromthe first day of school in September to get ready to enjoy to the ut-most, both academically and emotionally, this experience; therefore,this approach to mathematics.

This involves first, a close scrutiny of the curriculum to determinethe areas for study. Then we face the problem of how we learn towork cooperatively in groups to explore these areas. The next problemfor consideration is which ones can be related to real problems�notjust textbook problems? This is where we identify the skills we musthave: such as a facility with the various combinations of sets, the con-cept of accurate estimating as opposed to accurate solution. Fromsimple fractions and their equivalents we move into proportion withease since we have already acquired the necessary facility with multi-plication and have compared similar triangles. To be specific this isone activity: knowing the height of the flag pole, we measure thelength of the shadow it casts. Then working in pairs, the length ofeach child’s shadow is measured. He can then figure his height bysolving for the unknown number, and looking at the results to seewhether he has a reasonable answer. This is then checked by actualmeasurement. This activity permits getting outside on a pretty day,being free to work, talking together in an orderly manner and bydoing to really understand the problem and solution.We also ask the man from the soil conservation district to help us

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with the use of the transit in outdoor contour mapping. The childrenhold different colored flags as they are placed at different levels on asmall watershed. The children having already paced off 100 feet to getthe length of the pace, then pace off the intervening distances. Thesedimensions are recorded and from these and the use of contour mapswe construct a scale model of the area. This can be used to show vari-ous phases of science�water control, erosion, suggested plantings, etc.These drawings show other types of problems which can be done by

children out-of-doors.

MEASURING HEIGHT AND SLOPE OF HILLS WITHTHE CARPENTERS LEVEL (ALIDADE)

1. Set the base of the alidade at the bottom of the hill to be measured.2. By leveling the alidade and sighting along the top edge, mark a spot on the

hill where your line of sight strikes the hill.3. If the alidade (h) is 5’ tall, this point will be 5’ above the base of the alidade.4. Move the base of the alidade up to the point sighted on the hill and repeat

the above process.5. To find the slope of the hill from the base of the alidade to the point of inter-

section where your line of sight intersected the hill, divide the number offeet between the two points just mentioned (j) into the height of the alidade(h). This will give you percentage of slope.

ESTIMATING HEIGHTUSING THE ISOSCELES RIGHT TRIANGLE TO

ESTIMATE THE HEIGHT OF OBJECTS1. Hold the ^j so that one of the sides (b) is level and so one can sight along

the hypotenuse.2. Sighting along the hypotenuse (a) align the top of the object with the line of

vision along (a).

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3. From the point where these are in line, pace the distance to the base of theobject (d).

4. Add the distance from the ground to the observers eye (g) to the distancepaced to the object being measured (J). This sum will be the height of theobject (ZQ.

ESTIMATING DISTANCES WHICH ARE HARD TO MEASURE

1. Sight an object (a) close to the point you want to measure.2. From (6), go at a bangle to the line of vision with the object ten-to-thirty

paces to point (c).3. Continue on from this point one half of the first distance to a point (d).

^4. At point (d), go at a right angle until you can line point (c) and the objectbeing measured to (a) up.

5. The distance from the starting point (b) to the point to which you are esti-mating is twice the distance paced from (d) to (e).

USE OF THE PROTRACTOR TO ESTIMATEUNMEASURABLE HEIGHTS

1. Sight along the base of the protractor, aligning the edge with the top of theobject to be measured.

2. At the point where the plumb-bob string strikes the protractor at 45°, pacethe distance to the base of the object being measured (J).

3. To this distance (d), add height (c) which is the eye height from the groundand the sum will be the height of the object (k).

This is not the total math program, only the extra special partwhich seems to help children want to learn the skills necessary foractive participation�and they all participate. This is not enrichmentfor the gifted. It would seem that 10 year olds, and I suspect others atany age, learn best what they see a need for and what they enjoy.