Lesson 9: Concept Attainment

Write a lesson plan which allows the students to discover a rule inductively. If appropriate, use the same topic as in your HARNESS in Lesson 7. This activity will be part of the learning portfolio which you will compile at the end of this module.

Observe

Hypothesize

Generalize

Summary

Inductive learning is about the students discovering the mathematical concepts by themselves with the teacher as a guide. In this strategy, students observe, hypothesize, collect evidence, and generalize.

Objective

Plan a lesson that applies concept attainment strategy

Intro du ctio n

The inductive learning strategy in the previous lesson is most useful in discovering rules. In mathematics, students do not only study rules, but they also need to remember and understand many definitions of terms. For better retention, it is best for students to discover the meaning of the different mathematical terminologies that they encounter. The concept attainment strategy is useful for this, purpose.

Think

Concept attainment is another instructional strategy anchored to the constructivist learning theory. In this strategy, the concept is not directly taught to students. Instead, the students understand and learn concepts by identifying common attributes through comparison and contrast of examples and non-examples. Since concept attainment is used in understanding meanings, it is often applied in English vocabulary lessons. However, it is also useful in learning mathematical terminologies.

There are five simple steps in the concept attainment strategy: (1) presentation of examples and non-examples, (2) listing of common attributes, (3) adding student-given examples, (4) defining the mathematical term, and (5) checking of understanding.

P resen tatio n of e x a m p le s and n o n -e xa m p le s

Alternately give examples and non-examples. The students should be able to guess some common attributes based on the examples alone so non-examples are given to confirm their guesses.

L is tin g of co m m o n a ttrib u tes

List the common attributes given by the students. This may be done as a whole class or by pairs or traits first. Some listed attributes may be later on crossed out as the listing of examples and non-examples go on.

Ask students to provide their own examples based on the listed attributes. Then confirm whether their suggestion is indeed an example. Based on the students' answers, some of the attributes may be revised to make them clearer for the students.

D e fin in g th e m a th e m a tica l term

Help the students come up with a word or phrase for the concept. The exact term may not come from them, especially when it is too technical (e.g., polyhedron), but the etymology of the word may be derived from them (e.g., many polygonal faces).

C h e c k in g o f u n d e rsta n d in g

To verify that the students have understood the concept, give them a list and ask them whether each item on it is an example or a non-example.

E x p e r i e n c e

Study the lesson plan below which applies the concept attainment strategy. The goal of the lesson is for the students to define a prism. Instead of listing examples on the board, real object examples and non-examples will be provided.

Topic: Square

Grade level: 1

Target learning competency: By the end of the lesson, the learners will be able to define a square, draw examples of a square, and identify whether a given figure is a square or not.

Prerequisite knowledge and skills:

Definitions of:

1. Straight and curvy lines

2. Plane figures

3. Solid figures

Identifying common attributes based on examples and non-examples:

Tell the students that they will be detectives for today. Their goal is to discover the common characteristics of the figures which will be shown to them.

Give the following examples and non-examples by batch.

Below are the expected common attributes that the students will provide, refined through the batches. Ask guide questions if the students do not arrive at these.

Batch

1

2

3

4

5 Common Attributes Made of straight lines; no curvy lines Has four sides

The sides have equal length All the angles are right It is a plane figure

In between batches, ask the students to look around the room and give examples of what they think are squares. Classify the student-given objects as examples or non-examples of prisms.

Defining the mathematical term

Lead the students to agree that a square is a four-sided plane figure whose side lengths and angle measures are equal.

Checking of understanding

Show 10 real objects and let the students identify each as a square or not.

Assess

Doing the following activity will strengthen your understanding of the concept attainment strategy.

1. Use the Venn diagram below to compare and contrast inductive learning and concept attainment strategies.

Challenge

The following activity will challenge you to ponder on things to consider when thinking of the order of examples and non-examples that you present when applying the concept attainment strategy.

1. Interview a Kinder, Grade 1, 2, or 3 mathematics teacher. Ask him/her what mathematical term the students have a hard time remembering, or that which they find confusing. List three mathematical terms and explain why each term is difficult to remember.

Term 1 : ______________________________________________

Term 2:

2. Choose one math term from your answers in #1. List examples and non-examples of the concept and group them by batch according to how you would present them. What were your considerations in grouping them?

Term :______________________________________________

Examples Non-examples

Considerations: