Specific principle for selecting learning experiences

Chapter 3: Conceptual Framework

3.2. Selection of the learning experiences

3.2.2. Specific principle for selecting learning experiences

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Page | 30 Figure 3.2: Some of the thinking sequence to follow when solving problems.

Figure 3.3: Two joined right-angle triangles that require steps of thinking to find the unknown angle.

Page | 31 Example 3.1

Figure 3.3 shows two joined right-angle triangles, where the first one is ABC and the other one is ACD. By using the given information, calculate the angle 𝐵𝐴̂𝐷.

Solution:

Step 1: Sensing the dificult problem

This step is about identifying the avaliabity of all the necessary tools to solve the problem, in order to decide whether the problem can be solved at present.

In our case, we have all the required theoritical (knowledge) and physical (writing equipments) tool that we need to solve the problem. Therefore we decide to solve the problem at present.

Step 2: Proper analysis of the problem

This step is about identifying all the required small missing information that can help to solve the bigger problem.

In our case we need to find:

(i) the magnitude of the angle α, (ii) the length of AC,

(iii) the magnitude of the angle β and (iv) the length of CD.

Step 3: Collecting the relevent facts

As the caption of this step says, here we collect all the relavent facts applicable to our problem.

By relating trigonometry and triangle facts in our problem, we get that:

(i)

𝛼 = 𝐶𝑜𝑠⁻¹(𝐵𝐶

𝐴𝐵), (3.1)

Page | 32 (ii)

𝐴𝐶 = 𝐴𝐵 × 𝑆𝑖𝑛 𝛼, (3.2) (iii)

𝛽 = 𝑆𝑖𝑛⁻¹(𝐴𝐶

𝐴𝐷), (3.3) (iv)

𝐵𝐴̂𝐶 = 180⁰− 90⁰− 𝛼 (3.4) (Applied triangle rule: Sum of the interior angles is equal to 180⁰),

(v)

𝐶𝐴̂𝐷 = 180⁰− 90⁰− 𝛽, (3.5) (Applied triangle rule: Sum of the interio angles is equal to 180⁰),

(vii)𝐵𝐴̂𝐷 = 𝐵𝐴̂𝐶 + 𝐶𝐴̂𝐷 (3.6) and

(viii)

𝐵𝐴̂𝐷 = 180⁰− 𝛽 − 𝛼 (3.7) (Applied triangle rule: Sum of the interior angles is equal to 180⁰).

Step 4: Drafting of possible solutions

This step is based on organising the facts found in step 3 and decide upon a better and easy or possible solution.

In our case, from step 3 we found 2 possible ways to get to the solution.

Option 1

From step 3 apply: (i), (ii), (iii) and (viii) Option 2

From step 3 apply: (i), (ii), (iii), (iv), (v) and (vii)

Therefore according to our analysis, option 1 is the best option for us due to it having minimal steps.

Page | 33 Step 5: Testing of the hypothesis

This step is application of step 2 and 3 to the problem.

In our case we chose option 1 in step 3, by applying all the necessary values displayed in Figure 3.3 we get that:

(i)

𝛼 = 38,942⁰ (3.8) (ii)

𝐴𝐶 = 56,566⁰ (3.9) (iii)

𝛽 = 70,521 𝑐𝑚 (3.10) (viii)

𝐵𝐴̂𝐷 = 70,537⁰ (3.11)

Step 6: Drawing conclusions

This last stage it about justification of the final unswer.

In our case, even when we use option 2 we get the same answer. Therefore our final answer is:

𝐵𝐴̂𝐷 = 70,537⁰ (3.12)

➢ Objective(s) focusing on acquiring information: This class of objectives involves developing understanding of things, expanding knowledge about various things, and the likes. Normally the type of information to be acquired includes laws, principles, facts, ideas, theories, terms and many more. During acquiring information, there are commonly identified challenges such as: i) students normally memorize instead of acquiring the real understanding, ii) students turn to forget the acquired information and have a huge number of inaccuracies in what they can remember and iii) students lack adequate organization, they are unable to relate the information in any organized or systematic fashion. Therefore, the suitable learning experiences for acquiring information would be the ones that can counteract the mentioned challenges and the likes. The first suggested learning experience is to acquire information in a form of

Page | 34 problem solving. This kind of the learning experience is said to be less likely to produce a rote memorization but rather produce understanding in students. Secondly is the one with only important selected information worthy to be remembered. Instead of having numerous technical terms which some of them are more important to the next level or class, rather the number of terms chosen should be minimal and frequently used for students to acquire information with accuracy. Also, the kind of suitable experience is where intensity and variety of expressions is the priority. This combination is said to increase the likelihood of remembering in students. Thirdly, it is a learning experience that will present different schemes of information organization. This experience enables a student to organize the same material in two or more ways effectively for use.

Example 3.2 below is one of those that could assist in attaining the objective(s) focusing on acquiring information, taken from the curriculum. It pushes someone to remember several branches of acquired information such as: logarithmic laws, exponential laws, knowledge of quadratic equations and factorization [Tyler, 1949].

Example 3.2

Solve for 𝑥 in the following equation:

𝑙𝑜𝑔₂(𝑥² − 2𝑥) = 3. (3.13)

Solution

By applying the logarithmic law (3.13) becomes,

𝑥²− 2𝑥 = 2³. (3.14)

Changing the exponential number and rearrange (3.14) we get,

𝑥² − 2𝑥 − 8 = 0. (3.15)

Factorizing (3.15) we get,

(𝑥 + 2)(𝑥 − 4) = 0 (3.15) and

𝑥 = −2 𝑜𝑟 𝑥 = 4 (3.16) Substituting (3.16) into (3.14), it is found that both solutions satisfy (3.14).

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➢ Objective(s) focusing on developing interests: This is a class of objective(s) that enables students to derive interest from areas of experiences in which the interest is to be developed. Therefore, the suggested learning experience is the one which allows students to be exposed to areas in which interests are to be developed and have satisfaction from their explorations. If possible, the learning experience should also provide students with a chance to obtain fundamental satisfactions from the explorations, where some of the fundamental satisfactions are presented in Figure 3.4.

In this case we wouldn’t know a precise example, given a separate data is needed to know the students’ interests. Also, students’ interest will differ according to colleges and locations [Tyler, 1949].