180
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
The Development and Diagnostic Assessment of
Detailed Framework for Diagnostic Assessment of Science
mass may be used in Grades 1–2 in diagnostic assessments. A simultane-ous analysis of two or more properties may be required in Grades 3–4 (Tasks R1 and R2).
Task R1
We pour the milk from the glass into the bowl. Which statement is true?
The event
changes both the volume and the shape of the milk.
changes only the volume but not the shape of the milk.
changes only the shape but not the volume of the milk.
does not change either the shape or the volume of the milk.
Task R2
We move the marble from a smaller glass into a bigger one. Which statement is true?
The event
changes both the volume and the shape of the marble.
changes only the volume but not the shape of the marble.
changes only the shape but not the volume of the marble.
does not change either the shape or the volume of the marble.
The realisation that certain properties change under certain conditions while others do not (Task R3), and that there are reversible processes – where the original material can be recovered – and there are irreversible ones (Task R4) represents a higher level in the understanding of the changes of materials.
Task R3
Kate wondered what the temperature was outside, so she took the thermometer from the room to the balcony. The picture shows the change that occurred after a few min-utes. Which property of the thermometer fluid changed?
mass volume shape density
Task R4
Are the following changes reversible? Justify your answer.
We burn the firewood. We dissolve the sugar in the tea.
We grate the cheese. We warm up the water.
182
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
Systematising Skills
The operations related to sets and relations constitute the mathematical basis of systematising skills. The subject matter of environmental and nature studies is descriptive, and therefore there are several opportunities to characterise the various living organisms, objects and events accord-ing to given criteria. The criteria of characterisation may at the same time be the criteria of comparison as well.
The development of systematising skills is rooted in COMPARISON, the identifi cation of the similarities and differences between objects based initially on one and then on more criteria, e.g., comparing a horse with a cow in terms of build and feeding habits. We may ask for comparison without specifying the criteria, letting students choose their own (Task R5). In higher school grades, students are able to relate the various cri-teria to one another.
Task R5
What do the phenomena illustrated in the pictures have in common and what are the differences?
CLASSIFICATION involves the comparison of an object to a cluster of properties rather than a comparison between two objects. A cluster of properties defi nes a set. The simplest case of classifi cation is when we have to decide whether a specifi c object belongs to a given set. For instance: Is the cabbage butterfl y an insect? Why? The reverse task is to identify the common properties of objects and label their class, which is a more diffi cult task (Task R6). Classifi cation is even more complicated when a collection of objects must be classifi ed into two or more groups. At fi rst it is advisable to specify the categories avoid-ing intersectavoid-ing sets, and at a later stage students can be asked to label the sets themselves, which may be made easier by pre-specifying an element of one of the sets (Task R7).
Detailed Framework for Diagnostic Assessment of Science
Task R6
Look at the pictures below. Give the four pictures a common title that expresses their similarity. Write a few sentences explaining your choice of title.
Task R7
Sort the birds in the pictures into groups based on the example given. Label the groups.
A) B) C) D) E)
great tit rook white stork swallow house sparrow
SERIATION involves the arrangement of objects based on the relation-ship between them, which requires the identifi cation of the ordering cri-terion. It may be related to chronology, spatial location, quantity or di-mension. Seriation is dependent on knowledge of the words expressing relations, e.g., before, after, in front of, behind, below, above, more, less, smaller, larger. Serialisation skills may be developed using several types of content, e.g., putting objects of equal volume in order according to their weight with the help of a density table; setting up feeding relation-ships, food chains; creating temporal and spatial sequences; ordering the various steps of processes or activities. In Grades 1–2, students may rely on their experiential knowledge when arranging objects by size (Task R8).
E
184
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
In Grades 3–4, we may assess students’ knowledge of simple everyday technological sequences and of the chronological order of events (Task R9), while in Grades 5–6 students’ understanding of part-whole relation-ships may be tested (Task R10).
Task R8
Put the animals in order according to their top speed.
hedgehog cheetah horse bear
Task R9
How does the pepper get from the garden to the market? Put the events in order.
Task R10
What is part of what? Put the parts of a plant in the appropriate places in the diagram.
carpel plant ovule flower
Systematising operations may be combined with other activities related to the subject matter, as demonstrated by the use of maps in Task R11.
Detailed Framework for Diagnostic Assessment of Science
Task R11
Put the four mountains in order according to their height above sea level. The lowest mountain should be the first. Use your book of maps.
.... Kibo .... Elbrus ... Aconcagua ... Etna
Classifi cation and seriation may also be combined. These skills may be assessed even in Grades 1–2 provided that the arrangement of ele-ments can be assisted visually (Task R12).
Task R12
There are four seasons in a year. Every season lasts for three months. Group the months according to the season and put them in chronological order.
December June August February
September April November July
March October May January
Autumn:
Winter:
Spring:
Summer:
GENERALISATION or SETFORMATION involves the identifi cation of shared properties through the comparison of objects (Task R13) and the creation of a set based on these properties. This operation also underlies classifi -cation skills.
186
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
Task R13
The properties of some rodents are described below. Find the properties common to these rodents.
ALPINEMARMOT
It is an almost 70 cm long, chunky animal with an approximately 15 cm long tail. It spends 6-7 months in hibernation. The marmot eats mainly the tender shoots of herbaceous plants, leaves, flowers and fruits.
There is one pair of incisors in the upper and lower jaws that grow through its entire lifetime. Its female gives birth to up to seven hairless offspring.
MUSKRAT
Its body is 20-27 cm long; its tail is fl attened and covered with scales. Its hind feet are webbed. It stays active throughout the winter. It feeds mainly on aquatic vegetation, or occasionally on shells, frogs, fi shes and animal carcasses. There is one pair of incisors in the upper and lower jaws that grow through its entire lifetime. It usually gives birth to 5-6 but sometimes to up to 11 offspring.
CAPYBARA
Adult capybaras may grow to 130 cm long, their tail is vestigial. Their feet are slightly webbed. They feed mainly on aquatic vegetation, leaves, bark, seeds and grass. There is one pair of incisors in the upper and lower jaws that grow through their entire lifetime.
They produce a litter of 2-8 offspring, who follow their mother right after their births.
CATEGORISATION involves the formation of a coherent system of sub-sets. This operation presupposes the identifi cation of order and seriation.
Categorisation may be performed according to one (Task R14) or more criteria, and the criteria may be related to each other, but the application of the latter two types of operation should not be required until Grade 7.
Detailed Framework for Diagnostic Assessment of Science
Task R14
Arrange the resources of energy into two groups. State the basis of the arrangement.
the Sun water wind mineral oil coal
The development of the operation of categorisation may be assisted by visualising the system emerging from the categorisation through tree diagrams, Venn diagrams and charts. These visualisation methods may be used for assessment in the form of completion tasks. Multilevel sys-tems may be created as a result of hierarchical categorisation (Task R15).
Hierarchical categorisation is a core operation in science.
Task R15
Organise the arthropods. Complete the chart in agreement with the text.
Arthropods are the most populous group in the animal world. They include crustaceans, insects and spiders. Insects with chitinous forewings are called beetles. Butterflies with their spiral tongues are also insects.
DEFINING is the development and verbal description of the rule forming the basis of classifi cation. In Grades 1–2 and 3–4, the development of concept formation skills does not necessarily require scientifi c defi ni-tions; teachers usually provide examples and encourage generalisation by fi nding common properties, e.g., observation and testing of the proper-ties of gases. Giving defi nitions may be required in Grades 5–6 provided
188
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
that the classifi cation criteria and the category of the concept to be de-fi ned are pre-specifi ed (Task R16).
Task R16
What kind of animal is the tapir? Complete the sentence based on the information provided by the diagram and on the properties given.
PROPERTIES
They live in tropical forests, they are active at night, they are herbivorous, they have a sensitive and mobile snout.
The tapir is a ... that ...
Combinatorial Reasoning
Combinatorial abilities give rise to new knowledge by considering various possibilities based on existing information. Their functions are to consider and enumerate all the possibilities; to bring unusual connections to sur-face, e.g., combining different organisational and classifi cation criteria, to differentiate between the actual, the possible and the thinkable; and to construct complete systems. Combinatorial operations include the construction of a Cartesian product, the creation of combinations with or without repetition, the creation of permutations with or without repeti-tion, the creation of all possible permutations and the creation of all pos-sible subsets. The emergence of the operations of combinatorial skills presupposes an ability to generalise the operations of ordering and clas-sifi cation.
Children in Grades 1-6 typically try to solve problems by random guessing. Since they have not yet acquired algorithms allowing a system-atic search through possible solutions, whether all solutions are found is a matter of chance. The studies on the development of combinatorial skills suggest that when solving tasks with similar structure presented
Odd-toed ungulata horse rhinoceros tapir
Detailed Framework for Diagnostic Assessment of Science
with either visual or formal content, better performance is to be expected in the case of visual tasks indicating that visualising the situation pre-sented in the task facilitates the fi nding of the solution. The recognition and consistent application of algorithms appear only later, around the age of 13, with the emergence of formal reasoning.
The fostering and assessment of combinatorial abilities can be started in the fi rst years of schooling. The tasks relate to simple concrete situa-tions; they are illustrated by pictures and contain only a small number of elements, which can all be stored easily in short-term memory. The pos-sible solutions may be presented in a manipulative or picture format, as in Task R17, which may be used to assess the operation of permutation without repetition, where ordered subsets of a given size are selected from a given set.
Task R17
Children brought different kinds of fruit to their environmental study class:
chestnuts, walnuts and acorns. They can examine only two kinds of fruit during a lesson. Draw all the possible orders in which they can examine the collected fruits.
chestnut walnut acorn
190
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
Task R18 is relevant to the development of environment-conscious behaviour and assesses the operation of permutation where all elements of a given set must be ordered.
Task R18
The students organised waste collection in the village. The students in Grade 2 had to clean three areas: the river bank, the area around the waste yard and the playground. In what order could they do the work?
List all the possibilities. Use the letters below.
the river bank (R) the area around the waste yard (W) playground (P)
R W P
Task R19 is related to the topic of healthy diet and requires the listing of combinations without repetition.
Task R19
Peter and his family follow a healthy diet, they always have fruit at home.
They’ve bought bananas, oranges, apples and pears this week. Peter packs two different kinds of fruit for his mid-morning snack at school. Which two can he take with him to school? List all the possibilities. Use the letters below.
banana (B) orange (O) apple (A) pear (P)
In addition to the development of reasoning skills, knowledge of the subject matter can also be assessed with tasks where the question ele-ment testing one of the components of combinatorial abilities, e.g., com-bination in Task R20 is supplemented with a question about the subject matter.
Detailed Framework for Diagnostic Assessment of Science
Task R20
Tom, Anne, Ben and Carol went to the playground to play on the seesaw.
Each child sat on the seesaw with each of the other children. List all the possible pairs. Use the letters below.
Tom (T) Anne (A) Ben (B) Carol (C)
T A T B
The children have different weights. Which pair could seesaw the most easily?
The weight of the children:
Tom: 56 kg Anne: 42 kg Ben: 63 kg Carol: 57 kg
Combinatorial reasoning is required for designing experiments where the values of the different variables are combined in order to defi ne the experimental conditions. An example is shown in Task R21.
Task R21
We investigate the effect of light and water on the development of plants. Our hypothesis is that plants require light and water to stay alive. We have four pots of wheat. In what kind of environment should we keep the plants to find evidence for the hypothesis? Put a circle around the name of the appropriate environmental conditions below the individual plants.
light − water light − water light − water light − water
192
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
Deductive Reasoning
The deductive and inductive modes of reasoning are often interpreted relative to each other. Using the deductive method, we can only state in a different way the information that is already included in the starting claims (the premises) and therefore we cannot acquire fundamentally new knowledge, while inductive reasoning can lead us to new knowledge.
Practice exercises using elements of deductive reasoning, e.g., the op-erations of classic bivalent logic, deductions and quantifi ers) assist the acquisition of the subject matter and scientifi c terminology, successful everyday communication and the mastery of verifi cation and falsifi cation skills. The results of empirical studies indicate that the development of logical ability in a large part takes place before puberty, therefore foster-ing these skills is especially important in the fi rst few years of schooling.
From among the BINARY OPERATIONS, conjunction (Task R22) and dis-junction (Task R23) assist the acquisition of the logical meaning of the connectives ‘and’ and ‘or’, which is a precondition for instance to the recognition of the logical connection between conceptual features, and to the proper use of the connectives used to link features in defi nitions.
At later stages, the understanding of the equivalence operation plays an important role in the recognition of the logical relationship between the name of the concept and its feature structure, and in the linguistic encoding of the concept.
Task R22
The sentence below appears on the poster calling for waste paper collection:
SORT THE PAPER AND TIE IT UP.
Put a circle around the letter of the statement where the paper was handled as the poster requested. Cross out those where it wasn’t.
A) The paper was sorted but wasn’t tied up.
B) The paper wasn’t sorted or tied up.
C) The paper was sorted and tied up.
D) The paper wasn’t sorted but it was tied up.
Detailed Framework for Diagnostic Assessment of Science
Task R23
Four teams (A, B, C and D) investigated the properties of granulated sugar in the school science study group. It is easy both to melt the granulated sugar in a test tube and to dissolve it in water. They read the instructions below on the task card:
Every team should perform exactly one experiment with the granulated sugar:
EITHER MELT OR DISSOLVE THE SUGAR.
Put a circle around the letter of the team that followed the instructions. Cross out those that didn’t.
A) The team both dissolved and melted the sugar.
B) The team melted the sugar but did not dissolve it.
C) The team didn’t melt the sugar but dissolved it.
D) The team neither melted nor dissolved the sugar.
Among the binary propositional logic operations, the correct interpre-tation of equivalence and implication (reversible and irreversible state-ments) is the most diffi cult. Most students handle these two operations as if they were identical, or they often interpret them as conjunction (as an
‘and’ operation). These operations can be developed in the fi rst few grades through tasks based on simple situations taken from the students’
everyday life, e.g., Task R24.
Task R24
You can hear or read news stories about UV-radiation every day in summer.
We know that we should protect ourselves against the harmful UV-rays. Eve wanted to sunbathe one afternoon. Her mother said to her:
YOU CAN ONLY SUNBATHE IF YOU USE SUN-PROTECTION.
Put a circle around the letter of the statement where Eve followed her mother’s instruction. Cross out those where she didn’t.
A) Eve sunbathed and used sun-protection.
B) Eve sunbathed and didn’t use sun-protection.
C) Eve didn’t sunbathe but she used sun-protection.
D) Eve neither sunbathed nor used sun-protection.
194
Korom, Nagy, B. Németh, Radnóti, Makádi, Adorjánné, Revákné, Tóth, Csíkos and Wagner
DEDUCTION involves the interpretation of complex sentences encoding conditional statements − using the linguistic elements of ‘if... then’ or ‘if and only if’. Both the forward implication elimination (Modus Ponens) and the backward implication elimination (Modus Tollens) (Task R25) use the operation of conditional deduction: the fi rst by affi rming the an-tecedent and the second by denying the consequent.
Task R25
Draw a conclusion from the statement. Complete the sentences.
If the air is polluted, tree leaves dry up partially or completely at the beginning of summer. We didn’t find any dry spots on the leaves of the horse chestnut tree at the beginning of summer, therefore
If the temperature drops below zero, the water freezes. The water is not frozen and therefore
If a vertebrate animal is a bird, then its body is covered with feathers. The body of the squirrel is not covered with feathers and therefore
A sequence of deductions (Task R26) is based on two conditional statements where the consequent of the fi rst statement is the antecedent of the second statement. An important consideration in the choice of the content of deduction tasks is that the tasks should strengthen the connec-tions between different pieces of knowledge and encourage the discovery of new connections.
Task R26
Continue the sentence.
If the vegetation is destroyed on a hill-slope, then rain will wash the soil away. If the rain washes the soil away, then crops can only be grown in the valley. Therefore, if the vegetation is destroyed on a hill-slope, then...
In quantifi ed reasoning tasks the linguistic phrases ‘all’ and ‘some’
and their paraphrases should be used (Task R27).