1. Inductive and Deductive Inquiry
What
“The kind of inquiry that calls for students to investigate rules, principles and generalizations is called inductive; it requires that students examine an array of models, finally concluding what law is operating within them. The learners state the law in their own words and then create examples. In addition, they identify further examples provided by the teacher or other students” (Grambs and Carr, 1991, p. 125).
Inductive inquiry may be approached at least in two ways:
(i) Guided inductive inquiry
(ii) Unguided inductive inquiry
If the teacher wishes to provide basic elements of a lesson- i.e. the specifics but wants the students to make the generalizations, then the teacher is conducting a guided inductive lesson.
If the teacher decides to allow the students to provide the cases and to make the generalizations, the process may be unguided inductive strategy. Such a distinction between guided and unguided inductive inquiry is very essential. In most cases, the teacher will begin to build the processes of induction through a set of guided experiences. In this manner, a teacher knows that there are fixed number of generalizations or conclusions that can be reasonably inferred. The teacher can then go about helping various students to make the observations that lead to these conclusions.
Inductive inquiry is appropriate at all levels of instructions, from pre-university to university graduates schools. Obviously the kinds and quality of induction will vary considerably. An important aspect of inductive inquiry is that the processes of observation, inference, classification, formulating hypothesis, and predicting are all sharpened (or reinforced) by the experiences.
Why
· Allows the students to draw generalization or concept from a particular unit of study.
· Allows the students to be a discoverer in the learning process.
· It allows the students to apply generalization or concept to a new circumstance
· Students gain investigative skills.
· It is student-centered.
How
Phases in Inductive inquiry: General
Phase I: The Open-ended Phase
i) Show the students examples of a concept or generalization.
ii) Students observe and describe the example.
iii) Give another example.
iv) Again have students observe and describe.
v) Give some more examples followed by observation and description.
vi) Students compare the examples and find the similarities and differences.
Phase II: The Convergent Phase
Prompt students to identify (find) patterns in the examples.
Phase III: Closure
Arrive at definition by explicitly stating the patterns in the examples.
Phase IV: The Application Phase
Application of definition with additional examples.
Sample
The following piece of information is adapted from Grambs & Carr (1991. p. 125 -126).
The math teacher, Miss Sonam wanted her students to discover the principle of determining the square of numbers ending in 5. She presented students with statements showing the squares of 15, 25, 35, 45, and 55 (152 = 15 X 15 = 225...). Next Miss Sonam asked them to tell her the square of 95 without figuring on paper. When students admitted they were stymied, Miss Sonam led them through a series of questions about the given arithmetic statements which showed that the first digit(s) of the answer turn out to be the first digit(s) of the initial number multiplied by one more then the number represented by the first digit(s). Once the principle was uncovered, students quickly gave the square of 95.
In seventh-grade home economics class, Mr Tenzin presented students with numerous pieces of different fabrics, asking them to suggest ways in which the materials were similar and dissimilar. Through examination of the fabrics and a series of observations and questions such as "In what ways are they alike?" "In what ways are they different?" "Describe the way they feel." "What causes the difference in appearance and touch?" the students concluded that fabric differences occur because of fiber content, weave, and finishing procedures.
In physical education class, Mr. Sharmaji had his students stand, lean forward and backward, and return to position, considering as they did so, what was happening to their bodies in the process. Ideas such as "weight shift" and "balanced state" were clarified in a discussion centering around "how one maintains balance". Students ultimately generalised that in order for balance to be maintained the weight mass (or center of gravity) must fall over the base of support. Following student-given examples of bases of support other than feet, the principle was applied to the squat balance tumbling skill as the first of a series of tumbling activities.
English students were confronted by Mr. Dorji with a series of sentences, all of which contained appositive words or phrases. Through analysis of the sentences, and generalisation reached about them, his students not only determined a definition of appositives but also made conclusions about case, number, and punctuation. Mr. Dorji then asked the students to write a series of paragraphs (on topics he suggested) in which appositives were freely employed.
What
Deductive inquiry is defined as a method of instruction in which principles or generalizations are presented initially and then are followed by the application or testing of these principles or generalizations (Orlich, Harder, Callahan, Kravas, Kauchat, Pendergrass & Keogh, 1985, p. 297).
Why
· Students tend to retain information better through deductive mode of learning.
· It includes most forms of inquiry which results in better transfer of learning.
· Deductive mode of inquiry is effective when the students have a limited background of the subject.
· The deductive mode of inquiry is less time-consuming because of its focus on content.
· The teacher can use a broad spectrum of materials and means of presentation in the class.
How
Phases in deductive inquiry: General
Phase I: Presentation of the Abstraction
The teacher defines the concept or states the generalisation.
Phase II: Teacher illustrates abstraction with examples.
Phase III: Students give examples of concepts/students apply generalization to a new situation.
Phase IV: Students restate what they have learned concept/generalization.
Sample
A typical example in mathematics is: Students read and classify the rule, “Two triangles are congruent if all three sides are equal.” Students then solve a series of problems in which they employ the rule.
A typical example in English is: Students read the rule, “Use commas to separate parenthetical words, phrases, or clauses from the rest of the sentence.” Students then place commas in a series of sentences provided by the teacher.
2. Problem Solving
What
Stephen and Gallagher (1983) define problem solving as “a curriculum development and delivery system that recognizes the need to develop problem solving skills as well as the necessity of helping students to acquire necessary knowledge and skills”. Simply put, it is a teaching strategy that focuses or emphasizes on the development of problem solving skills in the children.
Why
The most obvious (but not necessarily the best) reason for teaching problem solving is to help children develop critical and creative thinking skills. Education can be more wholesome and realistic if children are more able to use their school learning in solving problems in their day to day life situations.
The following are some reasons that are frequently suggested as to why this form of learning should be encouraged:
· It bases students’ development on their current knowledge.
· It is an interesting and enjoyable way to learn.
· It is a way to learn new things with greater understanding.
· It produces positive attitudes towards learning.
· It develops a sense of inquiry and research in children.
· It teaches thinking, flexibility and creativity.
· It teaches general problem solving skills.
· It encourages cooperative skills.
· It is a useful way to practice skills learned by other means.
How
IDEAL is a mnemonic device proposed by Bransford and Stein (cited in Crowl, et al. 1997, p. 161) and it is considered to be an effective strategy of problem solving.
· I: Identify the problem.
· D: Define and represent the problem.
· E: Explore possible strategies.
· A: Act on the strategies.
· L: Look back and evaluate the effects of your activities.
Here is another problem-based learning model:
1. Read and analyze the problem scenario
Check your understanding of the scenario by discussing it within your group. A group effort will probably be more effective in deciding what the key factors are in this situation. Because this is a real problem solving situation, your group will need to actively search for the information necessary to solve the problem.
2. List what is known
Start a list in which you write down everything you know about this situation. Begin with the information contained in the scenario. Add knowledge that group members bring. (You may want a column of things people think they know, but are not sure!)
3. Develop a problem statement
A problem statement should come from your analysis of what you know. In one or two sentences you should be able to describe what it is that your group is trying to solve, produce, respond to, or find out. The problem statement may have to be revised as new information is discovered and brought to bear on the situation.
4. List what is needed
Prepare a list of questions you think need to be answered to solve the problem. Record them under a second list titled: "What do we need to know?" Several types of questions may be appropriate. Some may address concepts or principles that need to be learned in order to address the situation. Other questions may be in the form of requests for more information. These questions will guide searches that may take place on-line, in the library, or in other out-of-class searches.
5. List possible actions
List recommendations, solutions, or hypotheses under the heading: "What should we do?" List actions to be taken, e.g., question an expert, get on-line data, visit library, etc.
6. Analyze information
Analyze information you have gathered. You may need to revise the problem statement. You may identify more problem statements. At this point, your group will likely formulate and test hypotheses to explain the problem. Some problems may not require hypotheses; instead a recommended solution or opinion (based on your research data) may be appropriate.
7. Present findings
Prepare a report in which you make recommendations, predictions, inferences, or other appropriate resolution of the problem based on your data and background. Be prepared to support your recommendation.
Sample problem-solving strategy on concept mapping
A particularly good way to organize information about a problem or subject is to construct a "concept map." Construction of concept maps helps us pull together information we already know about a subject and understand new information as we learn.
Concept maps consist of nodes and labeled lines.
Figure 1
Node is the name for important terms or concepts. Nodes are usually depicted with circles drawn around the term or concept, such as the nodes for "Living Things" and "Plants" drawn above (Figure 1). Lines between nodes show which concepts are related. The label on the line tells how or in what way the concepts are related. For example, plants "are" living things.
We can use concept maps when we begin working together on a problem, during the problem solving steps, and at the end of problem solving.
Steps to Constructing a Concept Map (Adapted from White and Gunstone, 1992)
1. Write down the major terms or concepts you know about a selected topic. For example, if we are studying living things, some of the terms might include: animals, dogs, plants, cows, or grass (Figure 2).
2. Write each concept or term on a separate piece of paper or 3 x 5 cards.
3. Sort through the cards, putting terms you DO NOT understand to one side. Also put aside those that ARE NOT related to any other term. The cards left over are the ones we will use to construct the concept map.
4. Arrange the cards so that related terms are close to each other.
5. Stick the cards to a piece of paper as soon as you are satisfied with the arrangement. Leave a little space for the lines we'll draw. Here is what your terms might look like if you used the ones we mentioned above:
Figure 2
6. Draw lines between the terms you think are related.
7. Write on each line the nature of the relationship between the terms. Here is what the terms above might look like after we draw the lines (Figure 3):
Figure 3
8. If you put any card/s aside in step 3, go back and see if some of them will fit into the concept map you have constructed. If they do, be sure to add the lines and relationships of the new items.
9. Summary: The concept map drawn in Figure 3 is very simple. Maps can become very complex and require a great deal of your time and attention, but they are useful in organizing, learning, and demonstrating what we know about a particular topic.
Extension: How would you arrange the following terms to fit into the concept map drawn above: Beagle, rocks, rose, hunting, guard dog, rabbit?
3. Project Learning
What
Project is an activity willingly undertaken by the pupils for the solution of a felt problem. The activity undertaken leads to learning as prescribed in the curriculum. It is a form of concrete activity directed towards the learning of a significant skill or process. It has a wide connotation and can be taken to include any activity like dramatics, pageants, making models, drawing maps and charts, collecting pictures, preparing scrap books, going on historical tours and exhibitions, preparation of wall newspaper, organization of debates, etc. The method transcends the subject-barrier because while undertaking a project in a particular discipline, it is possible to learn other useful knowledge and skills needed in one’s life (Kochhar, 1998. p. 109).
Why
· It extends beyond classroom teaching.
· The method is carried out in natural setting or real life situations.