Practical exercise from statistics for young scientists (biology) Authors: Dagmar Kubátová, PF UJEP Ústí nad Labem, Czech Republic.

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1 9-11 years Science Content: Statistics Target Concepts/Skills: Gauss distribution curve Target Age group: 9-11 years Duration of activity: 3 hours maximum Summary: The pupils will deduce a statistical rule described by the Gaussian curve on the basis of identifying the value frequencies of selected features in natural materials presented to them. Children are presented with examples from nature: mainly different types of beans and flowers and are invited to identify what they have similar and then to hypothesise how and in what way they think that they vary. They are then invited to test their hypothesis e.g. classifying the beans in different lengths, size of flowers etc. This will lead children to learn that one will find many examples within the average range, but there will be much fewer at the ends of the range e.g. very short or very long beans. Objective: By the end of the activity children should be able to: hypothesise about how certain properties of same beans or flowers can vary; collect data for the purpose of obtaining statistics ; use the data collected to note any particular patterns; identify ranges of a property and the frequency at which they occur; observe and identify the statistical rule described by the Gaussian distribution curve Resources: 100 large bean seeds (preferably the scarlet runner bean (Phaseolus coccineus)) 100 plants or plant parts from the following: 100 blooming plants of oxeye daisy (Leucanthemum ircutianum), or Anemone hepatica (Hepatica nobilis) or barren brome (Bromus sterilis) or other brome spikelets, or other fescue which have large multiflorous spikelets or opium poppy (Papaver somniferum L.)heads, or corn poppy (Papaver rhoeas) heads (fresh or dry, hollow) (Bean seeds, poppy heads or brome or fescue spikelets have the advantage that the teacher can store them when dried, recollect them from the pupils after the lesson and use them again in years to come.) Measure (can be made from paper, and only 100 mm long) Tweezers Paper or plastic cups for small material (beans, brome spikelet, etc.) 7 glass cylinders of a volume of 100 ml or larger, depending on the total number of examined scarlet runner bean seeds (Phaseolus coccineus) during the experiment for the whole class young scientists (biology) Authors: Dagmar Kubátová, PF UJEP Ústí nad Labem, Czech Republic The content of the present document only reflects the author s views and the European Union is not liable for any use that may be made of the information therein.

2 1. Engage (Forming hypotheses) Decide which question to investigate (= the challenge) What do children already know? What are their ideas? (make the question to investigate meaningful for the children) The teacher tells the pupils that this exercise deals with the frequency of certain features or effects and that they may themselves discover a very interesting statistical rule. The teacher asks pupils to observe the plants or parts of plants presented to them. (For the types of the specimens from nature suitable to use for this purpose, see the teachers notes further on. The teacher: formulates problem questions such as: Are all the plants or plant parts of the same type exactly the same? How do they differ? What made you notice? Pupils are ask to notice the obvious - that the seeds of beans, which have been placed in front of them are not all the same size, that the Hepatica flowers do not have the same number of petals, that there is a different number of beams in the target of a poppy, etc. The teacher encourages the pupils to think about which measurable values of a certain feature in a specific product of nature are represented the most and the least, on the basis of which hypothesis the pupils formulate. Possible hypothesis formulations: The formulation can be specific, when the pupil assumes that for example the most Hepatica flowers have 6 petals or the hypothesis can be formulated in general terms, such as that the flowers with the largest and the smallest number of petals are the fewest. 2. Inquiry The teacher encourages the pupils to offer suggestions of how they could verify their hypothesis, and what tools would they need to do this. Expected responses, e.g.: we split the Hepatica flowers into groups according to the number of petals and count and compare the number of individual flowers in these groups; we measure the length of the bean seeds (we will need a measure) and split them into groups according to length, we count and compare the number of individual beans in groups. The pupils supervised by the teacher and using the Worksheet for pupils then carry out the statistical surveys. They classify individual plants or plant parts into groups (classes) according to the discovered value of the examined feature and count the frequency of specimen within individual groups (classes). Statistical surveys can be organized as an exercise of individuals (if the teacher can provide each pupil with specimen of the given product of nature), or as a group exercise, where each pupil will contribute to the final outcome by examining only a portion of the total number of specimen of one kind (they will measure the length of 10 seeds, examine 10 flowers or spikelet, count the rays in 10 poppy head crowns, etc.) The teacher asks the pupils to summarize the results on the blackboard (interactive whiteboard or flip chart). For greater clarity, it is possible to ask the pupils to pour the particular bean seeds divided by size into 7 classes into the corresponding 7 glass cylinders, which would visually show the explored rule. Advanced pupils can be assisted in processing the found results for individual examined types of products of nature via computer by producing bar charts (place classes on the x-axis and frequencies on the y-axis). The teacher coordinates and motivates the pupils to draw conclusions: What do you observe in the frequencies of groups (classes) for each individual product of nature? Try to formulate the statistical rule, you have discovered. Think of what other effects you might expect the same rule to work. Ask the pupils to evaluate their own contribution to the discovery of the rule according to the Worksheet for pupils The pupils communicate spontaneously and compare the obtained results with each other after the survey has been done. They look for evidence to confirm or reject their hypotheses.

3 3. Evaluation The main finding is to identify a statistical rule based on the number of specimens with different values of the examined feature or effect, and to understand that the sought statistical rule could become evident only after examining a large number of specimen of a given type: The carriers of mean values of the examined feature or effect are of the largest frequency. This statistical rule was discovered 200 years ago by the mathematician Gauss, who described it as a curve, which was named after him (Gaussian curve). It has somewhat of a bell shape. It can be of different height, different flatness, and different steepness and can be tilted to one side (asymmetric). Therefore for the vast majority of the phenomena and processes, the frequency of extreme values, whether low or high, is minimal and the highest frequencies accumulate around the middle. Based upon teaching science as inquiry (Carin et al., 2005) ; Inquiry-based science instruction What is it and does it matter? (Minner et al., 2009) ; the psychology of teaching Scientific Thinking: implications for science teaching and learning. (Li, Klahr, 2006)

4 Teachers Guide: Assignment Didactic Tools Products of nature (the number of products of nature or parts thereof presented bellow represent the amount needed for individual pupil activity). In the case of a group exercise the material is distributed so that the minimum number of the product of nature specimen is 10 pieces to one pupil, while the total number of specimen for one group should be at least 100 pieces of each type of product of nature): Notes And Tips Before the first exercise with natural material (bean seeds, poppy heads, brome spikelets), check whether it is possible to sort the obtained material according to the template in the Worksheet for students, or whether the sorting needs amendments. As mentioned above, dried parts of plants can be stored, recollected from the pupils after the lesson and used again in years to come. If fresh material is used, this should for the same reason also be subject to checking before the first exercise. Statistical surveys can be organized as an exercise of individuals (if the teacher can provide each pupil with specimen of the given product of nature), or as a group exercise, where each pupil will contribute to the final outcome by examining only a portion of the total number of specimen of one kind (they will measure the length of 10 seeds, examine 10 flowers or spikelet, count the rays in 10 poppy head crowns, etc.), and the results are summarized prior to the formulation of the rule. 1) Large bean seeds Best to use are the seeds of the scarlet runner bean (Phaseolus coccineus) The Scarlet runner bean bean (Phaseolus coccineus) The seeds of the runner bean Phaseolus coccineus are commonly sold as ornamental flowering plants. They differ from common beans Physeolus vulgaris since germination the sprouting plant of the common bean lifts the cotyledons (i.e. the two green halves of the bean) above the ground, whereas the scarlet runner bean cotyledons remain underground. You can buy them in shops that sell seeds. The seeds are not recommended for consumption. Note: A large bean flat caps are large-variety beans in appearance and size similar to scarlet bean seeds, but suitable for consumption. Fruits are 3 to 4 times larger in size than regular beans. Seeds are up to 3 cm long - white, brown, black or variously speckled, mostly lavender with black spots. Time allocation: Observation and formulation of hypothesis: 20 minutes Statistical survey in groups: 30 minutes Comparing the results of the experiment among pupils, summarizing the results: 30 minutes The inference of the Gaussian curve through glass cylinders filled with bean seeds sorted according to length: 20 minutes Creating bar charts of the frequency of all three examined products of nature on the computer: 30 minutes Final conclusion and discussion, which other features and effects could show the discovered rule. Notes for teachers Other materials: Statistics exercise Detailed instruction on the collection and identification of the products of nature needed to complete the exercise

5 2) Poppy heads Opium poppy (Papaver somniferum L.) There are two types of this poppy according to use properties: - Opium poppy, which has in the walls of the head heavily branched network of finials rich in alkaloids. Opium is obtained from driedup latex which spurts from cut-up heads. Their collection and then cutting the dried latex obtained by opium. The most important region where this poppy is grown are the countries of so called Golden Triangle (Burma, Thailand, Laos), but also the Golden Crescent countries (Iran, Afghanistan, Pakistan). - Oil poppy is grown in many other European countries. The main use of the oil seeds is for household food and oil industry. However only a small part of production is processed in the oil industry, a somewhat larger part is used in in bakery and confectionery production. The seeds contain 40-55% fat. Cooking oil is obtained by cold pressing and it solidifies in the margarine with a stiffness point of 18 C. It is widely used in some areas of France and Germany. By hot pressing or by extraction semi-drying oil is obtained that is used to produce paint, varnish, and soap. Threshed poppy heads with stem up to 15 cm long are called poppy straw and are used in the pharmaceutical industry for alkaloid production. The amount of extracted alkaloids depends on the poppy variety and the method and place of cultivation. Gradually, about sixty of them were isolated, with the most frequent being morphine, codeine, thebaine, noscapine, known also as narcotine, and papaverine. These alkaloids do not appear independently, but mostly as salts of various acids. Morphine is a strong analgesic and inhibits the respiratory centre. It causes euphoria and is addictive. Codeine has similar effects as morphine, but it does not affect the respiratory centre and its euphoric effects are smaller. It suppresses cough by affecting the cough centre in the medulla. Noscapine (narcotine) has the same effects on cough as codeine. Papaverine has no narcotic effect and it does not affect the respiratory centre. It causes relaxation of the smooth muscle tissue and is therefore used as a spasmolytic, for example in cases of colic and intestinal cramps associated with diarrhea - Corn poppy (Papaver rhoeas L.) is an annual, cm tall herb with a simple or only slightly branched bristly stem, which bears bristly, sessile pinnatified leaves. Linen and wool are dyed red when stained by the juice of the latex cells in the plant. The individual blossoms in the ends of the stems are bent before developing. The four big deep red petals are wide and overlap each other and often have a red spot in their base. The stamens are black-and-purple, filamentous and not widened under the anthers. The shape of the fruit is also characteristic a capsule (poppy head), which is glabrous and broadly ovoid.. It probably originates in the warmer areas of Europe, but it spread all over the world in the temperate climates as a general field weed in cereal and root crop cultures. Its petals contain many alkaloids, as well as sugars and mucus. Since ancient times they were used to treat lung diseases and as a sleep-inducing agent. In the Mediterranean they were used for production of syrup. The leaves (and the whole plant except of the seeds) are poisonous and if consumed, they can cause digestive problems to farm animals. Fig: Opium Poppy, oil poppy, and corn poppy v

6 3) Spikelets of panicles of the poverty brome (Bromus sterilit L.) It is also possible to use spikes of another brome variety (e.g. Dropping Brome, Bromus tectorum) or of fescues, which have large multiflorous spikelets. Barren Brome / Poverty Brome (Bromus sterilis L.) Family: Poaceae. Light green annual grass, usually cm high, slightly tufty. The stems are glabrous, usually with bulging nodes. The leaf sheaths are enclosed with only the top open and have soft hairs. The leaf blades are 2-6 mm wide, rough on the edges and have soft hairs. The ligulae is approximately 4 mm long and cut-leaf. The panicle is large, noticeably thin, over 20 cm long, up to 12 cm wide and spreading to all sides. The panicle branches are very rough (hairs aimed forward), thin, sticking almost perpendicularly to the main stem, often overhanging to all sides at the end. Each branch of the panicle usually bears only 1 spikelet, widened at the top. The spikelet is approximately mm long, flattened, green and later brownish purple, wide open. There are 4 and more blossoms in the spikelet. The chaffs are mm long, narrowly lanceolate, unequally long (the lower ones one-veined, the upper ones threeveined). The lemmas are narrowly lanceolate, distinctly veined, rough, with the awn being mm long (1.5-2x longer than the lemma). The number of log awns is the best way to determine how many blossoms the spikelet consists of. It blooms from May to July, it withers in August. It is considered to be a weed. It grows in soil rich in nitrogen and is not able to tolerate wet, acidic and poor soils, preferring sandy, loose, and nutritious soils. It has low competitive ability and does not grow in integrated covers. It inhabits rubble fields, road edges, grows along railroad tracks and can be found on THE edges of forests. 4) Oxeye daisy (Chrysanthemum leucanthemum) This plant from the Asteraceae family is so well-known that it might not be necessary to introduce it. It is a perennial, cm long herb. The stem is straight, the leaves are petiolate in the base of the stem, and sessile, from spoon-leaved to lanceolate, or serrulate in the middle and upper part. The blooms are in individual end anthodia (anthodia is a type of inflorescence), the tubulose flowers in the centre of anthodium are yellow, the ligulae flowers on the edges of the anthodia are white. It blooms from May to October and it is very common in the meadows across Europe.

7 5) Anemone hepatica (Hepatica nobilis Schreber) Family: Ranunculaceae It is a perennial, 5-15 cm high spring grove herb with a short darkbrown rhizome, from which a great number of ground leaves grows. The leaves are three-lobed, long, petiolate, leather-like, with entire margin, green above and slightly purple underneath, persisting till the next spring. It blooms from March to May, usually before the sprouting of new leaves. The blossom grows at the end of a 5-15 cm long, thin stem, next to last year s leaves and it is supported by three ovate bracts, similar to calyx. There are 5-10 petals, the bloom is azure, rarely also pink or white. The fruit is achene. The seeds have fleshy appendages, so called flesh, which serves as food for ants, therefore contributing to the expansion of the species (myrmecophyte plant). Anemone hepatica grows almost everywhere in broadleaf forests, from lowlands to mountains, sometimes rising fairly high (up to 2200 m in the Alps). It is common in almost all of Europe in the temperate climate (with the exception of the British Isles and Iceland, certain countries like Holland, France, some parts of the Iberian Peninsula, northern Scandinavia, Ukraine and southern and northern parts of the European Russia).