# SA NC Doing Investigations/Chapter 9
## Scientific and mathematical literacy

Science and mathematics education, projects and investigations have one, common goal: to develop a scientifically and mathematically literate society. In Chapter 10 of this resource book, you are given a number of internet addresses of "websites" that you can visit if you are connected to the internet. (The government is committed to providing all schools with computers in due course.) Useful websites are being created all the time and even though many more may be available by the time your school is connected, those in Chapter 10 are a good entry point.
The definitions given below of the characteristics of science have been adapted from "Explanations of the Factors in ... Scientific Literacy" which can be found at [www.sasked.gov.sk.ca/docs/chemistry/ns_a.html/]
The website contains material from "Student Evaluation: An Educator Handbook" by Saskatchewan Education (1991). The authors have broken scientific literacy down into its components to help educators to assess learners' progress in science. The examples given apply as much to us in South Africa as they do to Canadian students. As you examine them see which component skills etc. can be developed using an investigative approach to science education.
To be scientifically literate is to understand what science is, its "nature" [A] and its relationship to technology and society [D]; what science is about, the key concepts we study in science [B] and how we study them [C & D]; skills that we need to develop [E] and the values and attitudes that good scientists and scientifically literate people will hold [F & G]. The lists actually tell us about the content of science education. Reflect on them and how investigations can help us to achieve our science education aims. Lists A, B and C are described in detail because they are closely related to investigations.

### A. Nature of Science

Scientifically literate people understand the nature of science and scientific knowledge. Science experiences should expose learners to ... scientific inquiry and discovery as ...
public and private: Science is based on evidence developed privately by individuals or groups that is shared publicly with others.
holistic: All branches of science are interrelated. E.g. The principles of chemistry govern how an animal digests food.
replicable: Science is based on evidence that could be obtained by other people working in a different place and at a different time under similar conditions.
empirical: Scientific knowledge is based on experimentation or observation. E.g. Scientists perform experiments and gather data from the things they observe.
probabilistic: Science does not make absolute predictions or explanations. E.g. A weather forecaster predicts a 20% chance of rain tomorrow.
unique: The nature of scientific knowledge and the procedures for generating new scientific knowledge are different from those in other fields of knowledge such as philosophy.
tentative: Scientific knowledge is subject to change. It does not claim to be truth in an absolute and final sense. E.g. As new data become available, theories are modified to encompass the new and the old data. Our views since 1900 of atomic structure have changed considerably for this reason.
related to human culture: Scientific knowledge is a product of humankind. It involves creative imagination and is the product of a culture and its technologies. E.g. The use of biotechnology has resulted in the production of synthetic insulin for the treatment of diabetics.

### B. Key Science Concepts

Scientifically literate people understand and accurately apply appropriate science concepts, principles, laws and theories as they interact with society and the environment.
Among the most important concepts of science are: change: Change is the process of becoming different. It may involve several stages. E.g. Seasons change throughout the year. Rocks are eroded.
interaction: This happens when two or more things influence or affect each other. E.g. Some animals living in the same place have to compete for available food and space.
orderliness: This is a regular sequence that either exists in nature or is imposed through classification. E.g. The Earth moves about the Sun in a regular manner.
organism: An organism is a living thing or something that was once alive. E.g. Plants and animals are organisms.
symmetry: This is a repetition of a pattern within some larger structure. E.g. Most animals appear to have matching halves. Most wallpaper patterns exhibit symmetry.
force: It is a push or a pull. E.g. A magnet can pick up a paper clip. Pedaling a bicycle causes it to move.
quantification: Numbers can be used to convey important information. E.g. There are 60 seconds in one minute. There are 206 bones in the human body.
reproducibility of results: Repetition of a procedure should produce the same results if all other conditions are identical.
cause-effect: It is how one thing affects another. E.g. Walking outside in the winter may cause your face to get cold.
predictability: Patterns can be identified in nature. From those patterns we make predictions. E.g. When a seed receives enough moisture in a warm place it will germinate. From this, one might predict that to keep seeds from germinating they should be kept cool and dry.
conservation: An understanding of the finite nature of the world's resources, and an understanding of the necessity to treat those resources with prudence and economy, are underlying principles of conservation. In physics, the term `conservation' also has a unique meaning, as in the conservation of energy. E.g. Insulating a home will save energy. Smaller, more efficient cars can be designed to use less fuel.
energy-matter: It is the interchangeable and dependent relationship between energy and matter. E.g. When a candle burns, some of the energy stored in the wax is released as heat and light.
cycle: Certain events or conditions are repeated. E.g. The seasons change during the year. Some birds migrate in the spring and autumn. A pendulum on a clock swings back and forth in a regular manner.
model: It is a representation of a real structure, event, or class of events intended to facilitate a better understanding of abstract concepts or to allow scaling to a manageable size. E.g. A globe is a model of the Earth. Marbles and styrofoam balls can be used to make models that represent atoms.
system: A set of interrelated parts forms a system. E.g. The Earth is a planet in the solar system. A stereo sound system consists of speakers, an amplifier, input devices such as a CD player, and other parts that are all connected together. field: A field is a region of space that is influenced by some agent. E.g. Two similar magnetic poles repel one another. If a ball is thrown into the air, it returns to earth because of the pull of gravity.
population: A population is a group of organisms that share common characteristics.
probability: Probability is the relative degree of certainty that can be assigned to certain events happening in a specified time interval or within a sequence of events. E.g. The probability of getting some types of cancer increases with prolonged exposure to large doses of radiation.
theory: A theory is a connected and internally consistent group of statements, equations, models, or a combination of these that serves to explain a relatively large and diverse group of things and events. E.g. One theory suggests that there are periodic mass extinctions of species.
accuracy: Accuracy involves the recognition that there is uncertainty in measurement. It also involves the correct use of significant figures. E.g. A watch with a minute hand is more accurate for measuring time than an hourglass.
fundamental entities: They are units of structure or function that are useful in explaining certain phenomena. E.g. The cell is the basic unit of life. The atom is the basic unit of matter.
scale: Scale involves a change in dimensions. This may affect other characteristics of a system. E.g. A paper airplane made from a sheet of notebook paper may fly differently than a plane of identical design made from a poster-size sheet of the same paper. time-space: It is a mathematical framework in that it is convenient to describe objects and events. E.g. An average human being has an extension in one direction of approximately 1,75 metres and in another direction of about 70 years.
evolution: Evolution is a series of changes that can be used to explain how something got to be the way it is or what it might become in the future. It is generally regarded as going from simple to complex. E.g. Organic evolution is thought to progress in small, incremental changes. Similarly, scientific theories undergo change to accommodate new data as they become available.

### C. Processes of Science

Scientifically literate people use appropriate processes of science to solve problems, make decisions and further their understanding of society and the environment.
Integrated processes include the more basic skills. Skills are acquired and practised throughout life and information processing and problem solving abilities eventually go beyond any curriculum. The basic processes of science are:
classifying: Classifying is a systematic procedure used to impose order on collections of objects or events. E.g. Objects can be grouped in a variety of ways, such as by size, shape or colour.
communicating: Communicating is any one of several procedures for transmitting information from one person to another. E.g. Writing reports, or participating in discussions in class are examples of communicating.
observing and describing: This is the most basic process of science. The senses are used to obtain information about the environment. E.g. During an investigation a student writes a paragraph recording the progress of a chemical reaction between hot copper metal and sulphur vapour.
working co-operatively: This involves an individual working productively as a member of a team for the benefit of the team's goals. E.g. While one member of a group is stirring a mixture of reactants in a beaker, another is reading the temperature whiles another member of the group is writing down the temperatures.
measuring: An instrument is used to obtain a quantitative value associated with some characteristic of an object or an event. E.g. The length of a metal bar can be determined to the nearest millimetre with an appropriate measuring device.
questioning: It is the ability to raise problems or points for investigation or discussion. E.g. A student should be able to create directed questions about observed events. When migratory birds are observed, questions such as, "Why do birds flock to migrate?", "Do some birds migrate singly?", and "How do birds know where to go?" should direct further inquiry.
using numbers: This involves counting or measuring to express ideas, observations, or relationships, often as a complement to the use of words. E.g. One orange had seven seeds in it, while another orange had no seeds.
hypothesizing: Hypothesizing is stating a tentative generalization that may be used to explain a relatively large number of events. It is subject to immediate or eventual testing by experiments. E.g. Ask students to explain what they think might happen to a plant if it is placed in a dark place for several days. Then ask them to explain how to design and conduct experiments to test their explanations.
inferring: It is explaining an observation in terms of previous experience. E.g. Because clay is a less permeable material, puddles of water do not soak away as quickly on clay soil as they do on sandy soil.
predicting: This involves determining future outcomes on the basis of previous information. E.g. Anticipate whether or not it is likely to rain later in the day based on current cloud conditions.
controlling variables: Controlling variables is based on identifying and managing the conditions that may influence a situation or event. E.g. In order to test the effect of fertilizer on plant growth, all other factors that may be important in plant growth must be identified and kept similar so that the effect of the fertilizer can be seen.
interpreting data: This important process is based on finding a pattern in a collection of data. It leads to a generalization. E.g. The grass under a carpet that is thrown on a lawn turns yellow. Removing it eventually allows the grass to turn green again. One might infer from the observations that a lack of light, or an increase in pressure on the plants, caused them to turn yellow. In a different experiment, leaves turn yellow when a plant is kept in the dark. The leaves on a similar plant kept in the light remain green. From this, one might suppose that there is a link between the amount of light a plant receives and the colour of its leaves. A piece of glass can then be placed on the lawn to see if pressure alone will cause plants to turn yellow.
formulating models: Models are used to represent an object, event, or process. E.g. The globe is a model of the Earth.
problem solving: Scientific knowledge is generated by, and used for, asking questions concerning the natural world. Quantitative methods are frequently employed. E.g. A student sees a bat one evening and cannot remember ever seeing one during the day. A question arises: "Why is it that I have never seen a bat before dark?" This leads to a series of investigations and research in an attempt to find an answer to the question.
analyzing: It is examining scientific ideas and concepts to determine their essence or meaning. E.g. Groups of students observe satellite weather images. Each group tries to develop a forecast based on the satellite images and their knowledge of weather patterns, the characteristics of weather systems, the motion of weather systems, and so on.
designing experiments: Designing experiments involves planning a series of data-gathering operations that will provide a basis for testing a hypothesis or answering a question. E.g. Car manufacturers test seat belt performance in crash tests. using mathematics: When using mathematics, numeric or spatial relationships are expressed in abstract terms. E.g. The area of a rectangular surface can be found by multiplying the length by the width.
using time-space relationships: These are the two criteria used to describe the location of things or events. E.g. The position of a star on any given date can be determined from astronomical reference tables.
consensus making: Consensus making is reaching an agreement when a diversity of opinions exist. E.g. Discussion of disposal of toxic waste, based on student research, gives students a chance to evaluate information.

### D. Science-Technology-Society-Environment Interrelationships

Scientifically literate people understand and appreciate the joint enterprises of science and technology, their interrelationships and their impacts on society and the environment including issues such as:
* scientists and technologists are human and fallible;
* the public understanding gap;
* resources required for science and technology;
* taking variable positions on important debates;
* the limitations of science and technology; and
* social influences on science and technology.

### E. Scientific and Technical Skills

Scientifically literate people have developed numerous manipulative skills associated with science and technology. Scientific and technical skills include:
* using magnifying instruments;
* using natural environments;
* using equipment safely;
* using computers;
* making measurements;
* manipulative ability;
* measuring time as accurately as the instruments allow;
* measuring volume, temperature and mass;
* using electronic instruments; and
* using quantitative relationships.

### F. Values That Underlie Science

Scientifically literate people interact with society and the environment in ways that are consistent with the values that underlie science. Values include ...
* longing to know and understand;
* questioning;
* searching for data and their meaning;
* valuing natural environments;
* respect for logic;
* consideration of consequences; and the
* demand for verification.

### G. Science-Related Interests and Attitudes

Scientifically literate people have developed a unique view of science, technology, society and the environment as a result of science education and continue to extend this education throughout life. Observable attitudes include their ...
* interest and interests;
* confidence;
* commitment to continuous learning;
* choices of vocation;
* preferred methods of explanation; and
* attitudes to the contributions of others.

## Mathematical Literacy

Material from the Programme for International Student Assessment (PISA) is equally useful from a mathematical point of view. It does not analyze the components of mathematical literacy in as much detail as the Saskatchewan group analyzes scientific literacy. PISA starts with the assumption that in order to assess learner achievement of certain outcomes, you must have clear definitions. The PISA definitions, developed between 2000 and 2003, provide us with international standards of mathematical literacy, scientific literacy and cross-curricular problem solving, all of which are Critical Outcomes of the new South African curriculum. Compare the PISA view of scientific literacy with that of Saskatchewan Education. The websites containing the PISA 2003 definitions are:
[www.erc.ie/pisa/maths.html/]
[www.erc.ie/pisa/science.html/]
[www.erc.ie/pisa/probsolve.html/]
The PISA definitions are useful yardsticks against which to assess both one's teaching and the learners' progress. According to PISA, mathematical literacy entails "the use of mathematical competencies at several levels, ranging from performance of standard mathematical operations to mathematical thinking and insight. It also requires the knowledge and application of a range of mathematical content that is drawn from areas such as chance, change and growth, space and shape, quantitative reasoning, uncertainty and dependency relationships. These include specific areas of the mathematics curriculum, such as algebra, statistics and geometry."
PISA assesses mathematical literacy in three dimensions: What is the relevance of this compared with the revised national curriculum statements on assessment?
1. First, the content of mathematics, as defined mainly in terms of broad, overarching concepts underlying mathematical thinking, and only secondarily in relation to traditional curricular strands (such as algebra and geometry). ... The four overarching ideas are: Quantity, Space and Shape, Change and Relationships, and Uncertainty.
2. Second, the process of mathematics as defined by general mathematical competencies. These include the use of mathematical language, modeling and problem-solving skills. The idea is not ... to separate out such skills ... rather, questions are organised in terms of three clusters defining the type of thinking skill needed: a) The Reproduction Cluster - is mathematical competencies consisting of simple computations.
b) The Connections Cluster - requires connections to be made to solve straightforward problems.
c) The Reflection Cluster - consists of mathematical thinking, generalisation and insight, and requires students to engage in analysis, to identify the mathematical elements in a situation and to pose questions and reflect on problems.
3. Third, the situations in which mathematics is used, ranging from private contexts to those relating to wider scientific and public issues. An important reason for distinguishing between different mathematical contexts is to embed mathematical problems in real-life contexts that are broader and less abstract than those found in traditional school curricula. According to PISA, scientific literacy involves the use of key scientific concepts to understand and make decisions about the natural world. It also involves being able to recognize scientific questions, use evidence, draw scientific conclusions and communicate these conclusions. (Compare this with the Saskatchewan facets of scientific literacy.) PISA suggests using scientific concepts relevant to the students' world both now and in the near future. These include concepts related to science in life and health, earth and the environment and in technology.
PISA defines scientific literacy as "the capacity to use scientific knowledge, to identify questions and to draw evidence-based conclusions, in order to understand and help make decisions about the natural world and the changes made to it through human activity."
PISA suggests assessing scientific literacy in three dimensions:
1. First, scientific concepts, which are needed to understand certain phenomena of the natural world and the changes made to it through human activity. ... concepts ... are the familiar ones relating to physics, chemistry, biological sciences and earth and space sciences (but) they need to be applied to real-life scientific problems rather than just recalled. The main content of the assessment is selected from within three broad areas of application: science in life and health; science in earth and environment and science in technology.
2. Second, scientific processes, which are centred on the ability to acquire, interpret and act upon evidence. Five such processes ... relate to:
* the recognition of scientific questions
* the identification of evidence
* the drawing of conclusions
* the communication of these conclusions
* the demonstration of understanding of scientific concepts
3. Third, scientific situations, selected mainly from people's everyday lives rather than from the practice of science in a school classroom or laboratory, or the work of professional scientists ... .

### Cross-Curricular Problem-Solving

"Problem-solving is an educational objective that is common across countries and school subjects, particularly science, mathematics and technology. Students' ability to solve problems in everyday situations is ... of particular interest to educators ... . Problem-solving is a competency essential to successful participation in society and an integral part of the learning process."
PISA defines problem-solving as
"an individual's ability to use cognitive processes to confront and resolve real, cross-disciplinary situations where the solution path is not immediately obvious and where the literacy domains or curricular areas that might be applicable are not within a single domain of mathematics, science and reading."
PISA assesses problem-solving in three dimensions: 1. Three broad Problem Types:
a) Decision Making, which requires the student to make a decision under certain constraints, and taking a number of features of the situation presented into consideration.
b) System Analysis and Design is concerned with either the analysis of a complex situation in order to find out what is the cause of the problem to be solved, or the design of a system that works and achieves certain goals
c) Troubleshooting problems require students to diagnose a faulty or underperforming system or mechanism, and to suggest solutions.
2. Problem Solving Processes The assessment of cross-curricular problem-solving focuses on five processes that students may implement when attempting to solve a problem. These include:
a) Understanding the information given
b) Identifying the critical features and their inter-relationships
c) Constructing or applying an external representation
d) Solving the problem
e) Evaluating, justifying and communicating the problem solution
3. Real-life Contexts The contextual nature of problems in PISA 2003 involves the use of life skills. Rather than using contexts presented as part of the school curriculum, an attempt has been made to develop questions which simulate real-life situations.
Make three comparisons. First, compare the three PISA definitions and see how much they are interrelated. Second, compare the PISA definition of scientific literacy with the Saskatchewan lists and see how well they are matched. And third, compare your own teaching and assessment with the PISA and Saskatchewan Education aims. You will gather that the international aims of science and mathematics education are very consistent with our own here in South Africa.
Look again at the emphasis placed on "real-life situations" in all three PISA definitions (mathematical- and scientific literacy and problem solving). Now think of this aim in terms of investigations which involve real-life situations in learners' own lives. We hope that you will agree that investigations in science and mathematics education are both a modern and internationally respected approach to teaching these very important subjects.