Learning Exponential-Logarithmic Equations through Values-Driven Interventions

Learning Exponential – Logarithmic Equations

LEARNING EXPONENTIAL-LOGARITHMIC EQUATIONS THROUGH

VALUES-DRIVEN INTERVENTIONS

by:

Avelino S. Caraan, Jr., DEM

GS Faculty

ABSTRACT

Mathematics is, undeniably, a fundamental skill that a learner should acquire and

master. Its purposes since the era when man learned to write his annals cannot be

overemphasized. The learners should explore independently the intricacies of the subject;

hence, constructivist approach. As developed by Jerome Bruner, it is where the learners

construct new ideas based upon their current or past undertakings.

This study covered the performances of selected 34 College students in learning

exponential-logarithmic equations. Revealed here were: pretest and post-test performances

have averaged differently; the null hypothesis of no significant difference between the two

performances is rejected. The null hypothesis stating that the interventions used have equal

influence to post-test results is accepted; the most predominant behavioral changes are

determination, organization of thoughts, self-confidence, and humility; all interventions used are

assessed effective.

As concluded, a significant difference exists between the two performances and that the

interventions have equal influence over the post-test performances.

Key words: exponential-logarithmic equations, values-driven interventions, constructivism


INTRODUCTION

Mathematics is, undeniably, a fundamental skill that a learner should acquire and

master. Its purposes since the era when man learned to write his annals cannot be

overemphasized. Its rudiments have been perfected generation by generation until such time

when mathematics is difficult to understand. It is when the learners must be provided again, in

the cycle of human existence, the basics of mathematics. The learners should explore

independently the intricacies of the subject. They must create their own constructs or

frameworks of understanding based on the established mathematical principles; hence,

constructivist approach.

By constructivism we mean learning by doing. A learning theory that is developed by

Jerome Bruner, its major theme is that learning is an active process in which the learners

identify, select and transform data into meaningful information to guide them in their formulation

of hypothesis and decision making. In it is this context that learners should be given ample

opportunities to explore by themselves the learning environment they have. Facilitators of

learning should motivate their students to discover and refine information with the very least

intervention they normally do.

It is in this light that the researcher had attempted to explain how the learners, in this

case my research participants, acquire understanding and mastery of exponential-logarithmic

equations when given ample time to work freely on their own through the employment of values-

driven interventions.

Conceptual Framework

The central theory adopted for this study is the importance of independent cognition, or

independent learning. Aptly stated, and I quote, “Jerome Bruner's constructivist theory is a

general framework for instruction based upon the study of cognition.” Originally, Bruner


focused on the mathematical and scientific studies which served as foundation of higher

learning for young children.

At the confines of a constructivist, his concentration is the learner; very minimal

to him or herself. Contradictory to common notion towards constructivism, the

importance of teachers is not neglected. Their roles are just modified. Focus is shifted to

the learners, “away” from the usual instruction and supervision of the teachers. The

constructivist teacher provides tools such as problem-solving and inquiry-based learning

activities with which students formulate and test their ideas, draw conclusions and

inferences, and pool and convey their knowledge in a collaborative learning

environment.

Whitehead (1929) as cited by Slaterry (2013) pronounced that “students are

alive, and the purpose of education is to stimulate and guide their self-development.”

This leads to the universal recognition of the vitality of addressing the nature of the

learners. Kersey & Masterson (2013) added that there is a need for positive guidance

with our young children today. They had elaborated too the essence of having a

creative teachers available for help, coaching, and facilitating.

In the constructivist model, learners are encouraged to work for their own

learning, conceptualizing, and processing. In harmony with what the JRU Faculty

Manual declares, a teacher is expected to guide students in a wholesome environment and in

the adoption of habits that would improve their character and personality, which is the very core

of constructivism.

In the present study, the complementary and supplementary roles of

mathematics teaching and mathematics learning will be both the responsibility of the

learners themselves. In its entirety, the researcher had made used of different values-


driven interventions whereat the participants had engaged themselves actively. These

included socialized blended recital, student-led discussion, board work / demonstration,

and math video / film showing. Adoption of these approaches had subscribed to the

ideas of Zulueta (2006), who emphasized that learning must be interactive. He believes

that it is only when the individual reacts to the stimulus in the environment that learning

is likely to occur.

Figure 1 The Conceptual Framework

Figure 1 shows the conceptual framework of the study. As the learners are

exposed to their own learning environment, they could explore the lessons on hand,

determine what is essential from peripheral, and crystallize what are the precise

preconceptions. These will lead to their improved academic performance and behavioral

changes. While these are for students to experience, it is also expected that the

curriculum would be further enriched through modelling learning exercises.


Significance of the Study

Bearing in mind the relevance of student-centered approach of teaching nowadays, this

present research would be beneficial to the following:

School administrators. They will be able to formulate classroom policy in institutionalizing

administrative support to independent learning environment.

Teacher-facilitators. They will be able to effectively gauge their students and provide

academic support in order to make the learners understand mathematical concepts and acquire

necessary competencies through learner-centered approach.

Learners. They will be provided with optimum collaboration for individualized instruction

and independent exploration giving them opportunity to unlock their own learning difficulties and

misconceptions.

Scope and Limitations

This evaluative study covered the performances of the participants in acquiring

understanding and skills involving exponential-logarithmic equations, an Advanced Algebra

lesson. I did not attempt to compare and contrast performances of the participants according to

their strategies/approaches employed rather focused on the overall pretest and post test results

only. This limitation I have positioned outset could prevent the direct comparison of the

interventions used by the participants. Instead, I reduced to the comparative analysis of their

overall improvement marks.

While it is true that I also gave consideration to the participants’ perceptions, these had

been corroborated by their post-test performances. Likewise, I had made simple linear

regression analysis to further explain the findings revealed.


Definition of Terms

The following terms were operationally defined by the present researcher.

Behavioral Changes. This term refers to the manifested behavioral change of the

participants from pre-intervention to post-intervention when learning the logarithmic-exponential

equations.

Constructivism. As a learning theory, this refers to the process / approach employed in

the present undertaking whereby the participants were allowed to explore their own potentials in

acquiring pre-determined mathematical competencies of understanding and applying

logarithmic-exponential equations.

Values-driven interventions. These interventions were determined by the researcher in

which the participants could employ independent learning. These were specifically limited to

blended recital, student-led discussion, board work/demonstration, and math video / film

viewing.

Hypothesis

The following are the null hypotheses that I had tested at 0.05 alpha level of confidence:

Null Hypothesis 1 There is no significant difference between the performances of

the participants during the pretest and post-test administration.

Null Hypothesis 2 The independent variable INTERVENTIONS USED has equal

influence upon the dependent variable (Y) POST-TEST

RESULTS

(Statistically stated: b1 – b2 = 0 ... bn - bn+1 = 0)

Research objectives

Based on the problems that I wished to address, the following objectives have directed

my study:


1. To assess how the participants performed during the pretest and post-test covering

Exponential-Logarithmic Forms;

2. To check if there were behavioral changes in learning mathematics when different

teaching-learning interventions were employed;

3. To determine how effective learning mathematics subject content is when values-

driven interventions were employed; and

4. To create model on writing / developing learning exercises that promote values

Statement of the Problem

Stemmed logically from the premises set earlier pertaining to independent learning and

research objectives, I sought the answers for the following problems:

1. What were the performances of the participants during pretest and post-test?

2. Is there a significant difference on the performances of the participants during the

takes of pretest and post-test?

3. What values were predominant among the participants in learning mathematics

through programmed interventions?

4. How effective integrating values were in learning math subject content after the

intervention period?


Chapter 2

METHODOLOGY

Research Design Used

I employed mixed experimental-descriptive design of research. As such, I ascertained

that there were planned interferences in the natural order of learning events among my

participants. This prompted me since I wished to obtain information concerning the current

status of the phenomena (mathematics teaching) and to describe "what exists," which in this

research pertains mathematics learning with respect to variables or conditions in a situation

(referring to the interventions employed during the data-gathering phase). Essentially, the

overall research design is that of an action research. Navarro & Santos (2013) explained that

action research is an inquiry process conducted by any stakeholder in the teaching-learning

environment to address a felt need or address daily problems.

Population, Sample and Sampling Scheme

For this School Year 2014-2015, I handle eight (8) mathematics classes. Four (4) of

these are Advanced College Algebra and the remaining four (4) classes are all Elementary

Statistics. Considering that Elementary Statistics are already conducted through Course

Redesign Program (CRP), these classes were no longer included in the selection of the sample;

thus, only the Advanced College Algebra classes remained. I resorted to fishbowl lottery

sampling which gave me the 102G class as research samples.

Data Gathering Procedure

The data gathering protocol that I had observed entails the following – initialization,

evaluation, and post-evaluation.


During the initialization, I had informed the class (102G) that they were randomly

selected as research participants. During the first week of January when classes were resumed,

I had emphasized to the participants that their involvement in my research is voluntary, non-

discriminatory, and non-bearing either to their periodic or overall mathematics g.p.a.; thus,

consent forms were distributed and retrieved before the evaluation phase (Please see Appendix

A). When properly filled up consent forms were received, I proceeded in administering the

pretest to the 48 participants. Their corresponding scores were recorded afterwards. I grouped

the participants into four comprising 12 members each. Each group was assigned with a values-

driven intervention – one to employ blended recital; a separate group to do student-led

discussion; another group to do board work / demonstration; and a different group to view math

videos / films.

The four groups had utilized the assigned intervention strategies in acquiring knowledge

and understanding of exponential-logarithmic equations. This is my evaluation phase. In here,

they were given one and a half (1 ½) weeks, January 19-27, in teaching-learning the said

mathematical concepts. I sometimes allowed the participants to argue among themselves as to

the accuracy of their own processes, solutions, and answers. After the intervention period, I

administered the post-test and again recorded their corresponding stores. It must be noted here

that during post-test administration, only 34 participants were available. Some of them did not

come for the post-test while one (1) was no longer allowed by her guardian to participate. This

prompted me to remove from the records their respective scores previously tallied during pre-

test. Then, I applied necessary statistical treatments to reveal findings and eventually guide me

to appropriate rejection-acceptance of null hypotheses.

On my post-evaluation, I endeavored to solicit qualitative feedbacks from the participants

using a separate research instrument. This, when returned and assessed, amplifies the

available statistics derived from tests analysis.


The Research Instruments

There were two research instruments that I had used namely Pretest-Post-Test on

Exponential-Logarithmic Equations developed and copyrighted by Dr. Abdelkader Dendane, a

UAE Professor, and a Post-Test Evaluation Sheet I purposively created to gather substantial

feedbacks from the participants.

I had communicated with and requested from Dr. Dendane for the use of his Pretest-

Post-Test on Exponential-Logarithmic Equations (Please see Appendix B). Dr. Dendane

instantly and gladly granted permission to use his material provided that it (the pretest-post-test

material) will only serve educational research purpose as guaranteed.

To bolster my data gathering, I developed a Post-Test Evaluation Sheet (Please see

Appendix C) where the participants provided more specific details vis-à-vis to the interventions

they employed and their perceptions on its effectivity on promoting values.

Statistical Treatment of Data

I had used both the descriptive and inferential statistics to complement and supplement

all the findings in this study. Descriptive statistics that I had employed were frequency counts,

percentage, means, weighted means, and standard deviations. As regards to the inferential

statistics, separate-variances t-Test for the difference, ANOVA (F-Test), and simple linear

regression were utilized in order to propose later on further studies to ascertain generalizability

of the present research.


Chapter 3

RESULTS AND DISCUSSIONS

To answer Research Problem 1 which asks for the performances of the participants

during pretest and post-test, Tables 1 and 2 exhibit the findings enhanced with essential

analyses and interpretations.

Table No. 1

Pretest and Post-Test Performances of the Participants Clustered According to

Intervention Used

INTERVENTION USED NO. OF

EXAMINEES PRETEST POST-TEST VARIANCE RANK

Blended recital 8 2.30 7.38 5.13 2

Student-led discussion 10 2.30 6.30 4.00 2

Board work/ Demonstration

8 2.00 7.13 5.13 4

Math video / film viewing 8 2.50 7.63 5.13 2

AVERAGE 2.28 7.11 4.85

It can be gleaned from the table above that there were notable changes on the

performances of the participants when they took the post-test. Initially in the pretest, the

participants had attained only an average of 2.28 points. When they took the post-test, their

performances had leaped to and hit a very high average of 7.11 points. Evaluating from within,

among the four interventions used, student-led discussion posted the lowest positive variance of

4.00 points, while the blended recital, board work/demonstration, and math video/film viewing

posted bit higher positive variances of 5.13 points each.

Gleaning further, the average positive variance of 4.85 suggests that the four values-

driven interventions, when properly and timely executed, could improve low mathematics

performances. I observed, while the students were constructing their own concepts on

exponential-logarithmic equations, students were initially adamant to participate. This is perhaps


apparent due to their low performance during the pre-test administration. Gradually, participants

were able to engage themselves on the process.

Figure 2

Average Test Performances during Pre-Intervention and Post-Intervention

Figure 2 shows the comparison of two test averages attained during the pre-intervention

and post-intervention. Glaringly noticeable is the big gap or difference between the two tests

administered purposively.

Table No. 2

Frequency Distribution of Participants’ Improvement Marks according to the

Interventions Used

INTERVENTIONS USED INC (f)

% DEC (f)

% UNCH

(f) %

Blended recital 7 87.50 0 0.00 1 12.50

Student-led discussion 9 90.00 1 10.00 0 0.00

Board work/ Demonstration 7 87.50 1 12.50 0 0.00

Math video / film viewing 7 87.50 1 12.50 0 0.00

TOTAL / AVERAGE 30 88.13 3 8.75 1 3.13

UNCH – Unchanged

As reflected in the table above, there were 30 participants or 88.13% whose

performances have increased while there were 3 participants or 8.75% whose performances

0

1

2

3

4

5

6

7

8

Pre-Intervention Post-Intervention

2.28

7.11


have decreased. Only one (1) participant or 3.13% has an unchanged performance.

Interestingly, that sole participant came from blended recital group only. Analyzing it further, the

results posited that student-led discussion, board work/demonstration, and math video/film

viewing as learning interventions had slightly decreased the performances of those who had

employed them. Caution, however, must be recognized too. Such decreases do not

substantially affect the accomplishment level of those who had improved a lot.

To answer Research Problem 2 which asks if there is a significant difference on the

performances of the participants during their pretest and post-test, Tables 3-5 reveal the

findings followed by supplemental analyses and interpretations.

Table No. 3

Separate-Variances t Test for the Difference between Pretest and Post-Test

Results Means t-computed Critical value Decision Remarks

Pretest 2.28 -45.9438 ±2.0195 Reject Ho Significant

Post-Test 7.11

Two-tailed test; α = 0.05

Table 3 shows the test of significant difference between the pretest and post-test

performances of the participants. It can be seen from the table that the mean performance

during pretest is 2.28 while during post-test is 7.11. Based on the computations made, the t-

statistic absolute value of –45.9438 which is lower than the absolute t-critical value of –

2.0195.Thus, the null hypothesis which states that there is no significant difference between the

pretest and post-test performances of the participants is rejected. Therefore, a significant

difference exists between the two performances of the participants.

While there is a significant difference that exists between the participants’ pretest and

post-test performances, the ANOVA (F-Test) results for interventions used and the post-test

performances provide another interesting result as explained in the succeeding texts.


Table 4

ANOVA Matrix for Intervention Use and Post-Test Results

df SS MS F-value Significance F

Regression 1 0.0016 0.0016 0.0148 0.9039

Residual 32 3.5278 0.1102 Total 33 3.5294

As shown in Table 4, the computed F-value is 0.0148 is lower than the critical F-Value of

0.9039; thus, the null hypothesis which says that the INTERVENTION USED (Blended recital,

student-led discussion, board work/demonstration, and math video/film viewing), as a set, have

equal influence to Post-test results is accepted. This means that the four (4) intervention

methods have the same influence over the performance of the participants during their post-

test.

However, as revealed in Table 5 below, the coefficient’s p-value of 0.904 is greater than

the 0.05 alpha level of significance. This implies that all the values-driven interventions

employed are statistically insignificant at that level.

Table 5

Regression Coefficient Matrix for Interventions Used and Post-test Results

Coefficients Standard Error t Stat P-value Remarks

Intercept 0.8889 0.0783 11.358 0.000

Interventions Used -0.0139 0.1141 -0.122 0.904 Not Significant


Figure No. 3

Scatter plot and the Regression Equation

Figure no. 3 shows the scatter plot for Interventions Used and Post-test Results data. It

shows the regression equation y = –0.0139x + 0.8889. Meaning, for any Pre-test (x) score, say

8, the post-test (y) score of the student would be 0.7777 higher.

To answer Research Problem 3 which inquires what values were predominant among

the participants in learning mathematics through programmed interventions, Tables 6-9 show

the findings where analyses and interpretations follow.

Table No. 6

Predominant Behavioral Changes as Ranked by the Participants

in Blended Recital

Predominant Behavioral Changes Participants’ Ranking

Raw Translated

Attentiveness. I became alert during random calls. 2.50 2

Determination. I became eager to participate, answer, and share.

2.00 1

Patience. I became patient to wait for my turn to be called. 3.63 4.5

Readiness. I became readily available for help when nobody wants to answer.

3.63 4.5

Responsiveness. I became focus on the learning content. 3.25 3

y = -0.0139x + 0.8889 R² = 0.0005

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Y

X

Scatter Plot


Table No. 6 exhibits the rankings made by the participants who have the blended recital

discussion as learning intervention on the predominant behavioral changes they experienced.

Based on the table, Determination ranks first with a raw rank of 2.00 which was followed by

Attentiveness with a raw rank of 2.50. Responsiveness is ranked third with a raw rank of 3.25.

Tailing at the end are Patience and Readiness with the same raw ranks of 3.63. Accordingly, a

constructivist teacher provides tools such as problem-solving and inquiry-based learning

activities with which students formulate and test their ideas, draw conclusions and

inferences, and pool and convey their knowledge in a collaborative learning

environment. This is observed too during the blended recital.

Table No. 7


in Student-led Discussion


Raw Translated

Attending to details. I became sensitive and particular to words, symbols, and sounds during discussion.

2.30 2

Clearness / organization of thoughts. I became organized when discussing with my group mates.

2.20 1

Enthusiasm to share. I became animated and passionate during my discussion time.

3.10 3

Keenness. I became perceptive on others’ shortcomings in learning mathematics.

3.70 4.5

Precision. I became meticulous on the procedures involved when doing mathematical tasks.

3.70 4.5

Table No. 7 exhibits the rankings made by the participants who have the student-led

discussion as learning intervention on the predominant behavioral changes they experienced.

Based on the table, Clearness/organization of thoughts ranks first with a raw rank of 2.20 which

was followed by Attending to details with a raw rank of 2.30. Enthusiasm to share is ranked third

with a raw rank of 3.10. Tailing at the end are Keenness and Precision with the same raw ranks

of 3.70. As expected among the learners, they have become organized when discussing with


their own group members. This is evident especially when the leader responsibly managed their

work. In a constructivist environment, though there is minimal supervision of the teacher, a

leader among the learners could surface during the process. Their emergence must be

supported. It is when a leader is born among the learners, an optimization of the potential of an

individual.

Table No. 8


in Board work / Demonstration


Raw Translated

Articulacy. I became expressive during board work / demonstration of the mathematics content.

3.38 3.5

Compliance. I became conforming to the requirements of the task.

3.38 3.5

Cooperation. I became supportive with my colleagues while demonstrating the process of solving mathematics problems.

2.50 2

Neatness of work. I became aware of the necessity to work with efficiency especially with numbers.

4.00 5

Self-confidence. I became confident / buoyant while it was my time to demonstrate on the board.

1.75 1

Table No. 8 exhibits the rankings made by the participants who have the board work /

demonstration as learning intervention on the predominant behavioral changes they

experienced. Based on the table, Self-confidence ranks first with a raw rank of 1.75 which was

followed by Cooperation with a raw rank of 2.50. Articulacy and Compliance are ranked third

with the same raw ranks of 3.38. Tailing at the end is Neatness of work with a raw rank of 4.00.

Perhaps the primary reason of such low ranking of neatness is the practice the participants

have been accustomed to. Erasures and trials are allowed in mathematics as we attempt to

answer or prove mathematical equations.

In here, Whitehead (1929) gets affirmation. Students are truly alive and must be

encouraged to work for their own learning, conceptualizing, and processing. In the

board work or demonstration, participants have acknowledged the significance of the


concept of self-worth apropos learning by doing. This may be the underlying reason why the

participants have ranked self-confidence the highest.

Table No. 9


in Math video/film viewing


Raw Translated

Creativity. I became creative in approaching mathematical problems, thus helping me to solve correctly.

3.38 4

Exactitude. I became careful when complex mathematical problems are at hand.

2.75 2

Humility. I became unpretentious knowing that there are people who deal mathematics with difficulty.

2.00 1

Promptness. I put emphasis on the essentiality of learning mathematics.

3.63 5

Vigilance. I became fully aware that when mathematics is overused, it gives adverse results.

3.25 3

Table No. 9 exhibits the rankings made by the participants who have the math video /

film viewing as learning intervention on the predominant behavioral changes they experienced.

Based on the table, Humility ranks first with a raw rank of 2.00 which was followed by Exactitude

with a raw rank of 2.75. Vigilance is ranked third with a raw rank of 3.25, followed by Creativity

with a raw rank of 3.38 and tailing at the end is Promptness with a raw rank of 3.63.

Bruner is right when he said that in the constructivist milieu, learners should be given

ample opportunities to explore by themselves the learning environment they have. Upon doing,

they are moved, changed, transformed. These are the primary impacts of viewing Math –

related films. Most of the videos that the participants have watched have promoted special

consideration to people of different learning backgrounds. Most of the participants have watched

ABAKADA INA (Philippines), A BEAUTIFUL MIND (U.S.A.), and CITY HUNTER (S. Korea) that

shows struggles of, and compassion to people who are either mathematically gifted or

challenged.


Across all interventions employed, the most predominant behavioral changes are

determination, clearness / organization of thoughts, self-confidence, and humility substantiated

by their high raw ranks made by the participants.

And finally, to answer Research Problem 4 which probes if integrating values was

effective in learning math subject content after the intervention period, Table 10 shows the

findings where analyses and interpretations follow.

Table No. 10

Distribution of Participants’ Perception on the Effectivity

of the Interventions Used

PERCEPTUAL RESPONSE FREQUENCY

(f) PERCENTAGE (%)

Effective 34 100.0

Not Effective 0 0.00

TOTAL 34 100.0

Table No. 10 exhibits the frequency and percentage distributions of the participants on their

perceptions on the effectivity of the interventions used. All of the 34 participants claimed that the

interventions the specifically used during the acquisition of exponential-logarithmic equations

are effective. Interspersing these perceptions on their post-test performances, their aggregate

belief is evidently true. Their perceptions are supported and validated by very high improvement

marks of 4.85 points from a low average of 2.28 points to 7.11 points. This positive leap is

enormous considering that the participants were just given a rationed time allotment of two

classroom meetings. At this point, Kersey & Masterson (2013) had emphasized the impact

of positive guidance with the learners no matter how short the contact is. Creative

teachers do give meaningful experience to the children and influence how the learners

perform. Concerning this assessment of the participants, they acknowledge the


operative influence of the values-driven interventions where they had engaged

themselves worthily and actively.


Chapter 4

SUMMARY OF FINDINGS, CONCLUSIONS, AND RECOMMENDATIONS

Findings

As revealed, I took notice of the following:

1. In the pretest, the participants had attained only an average of 2.28 points. When

they took the post-test, their performances had leaped to and hit a very high average

of 7.11 points. Evaluating from within, among the four interventions used, student-led

discussion posted the lowest positive variance of 4.00 points, while the blended

recital, board work/demonstration, and math video/film viewing posted bit higher

positive variances of 5.13 points each.

2. The t-statistic absolute value of –45.9438 is lower than the absolute t-critical value of

–2.0195, which had prompted the researcher to reject the null hypothesis which

states that there is no significant difference between the pretest and post-test

performances of the participants.

3. The most predominant behavioral changes are determination, organization of

thoughts, self-confidence, and humility

4. All values-driven interventions employed are assessed effective by the participants.

CONCLUSIONS

Based on the foregoing findings that were revealed in this study, I formulate the following

inferences:

1. The participants have yielded higher test performances during the post-intervention

phase.


2. A significant difference exists between the pre-intervention and post-intervention

performances and that the interventions (blended recital, student-led discussion,

demonstration, and have equal influence over the post-test performances.

3. In each values-driven intervention, a predominant behavioral change surfaces.

4. The participants claimed that the post-intervention measures explored and employed

by them were effective in learning exponential-logarithmic equations.

Recommendations

Congruent to the findings revealed and conclusions formulated, I hereby recommend the

following:

1. Extend the values-driven interventions to other classes. This is to support or negate

the positive results that the interventions have caused to the performances of the

participants.

2. Expose the students to different teaching strategies/approaches and learning styles.

3. Explore student pre-conceptions from where to build firmer foundation of new

mathematical learning.


BIBLIOGRAPHY

A. Books

Caraan, Jr. A. S. (2011). Introduction to Statistics and Probability: A Modular Approach. Jose

Rizal University Printing Press. Mandaluyong City, Philippines.

Kersey, K., & Masterson, M. (2013). 101 Principles for Positive Guidance with Young Children:

Creating Responsive Teachers (3rd ed.). Routledge, New York.

Navarro, R., & Santos, R. (2011). Research-Based Teaching and Learning. Lorimar Publishing,

Inc. Quezon City, Philippines.

Slaterry, P. (n.d.). Curriculum Development in the Postmodern Era Teaching and Learning in an

Age of Accountability (3rd ed.). Routledge 711 Avenue, New York.

Zulueta, F. (2006). Principles and Methods of Teaching. National Bookstore. Mandaluyong City,

Philippines

B. Internet Searches

http://www.analyzemath.com/LogEqTest/LogEqTest.html

C. Other References

JRU Faculty Manual (College Division)

http://www.analyzemath.com/LogEqTest/LogEqTest.html


APPENDIX A

CONSENT FORM USED

BACKGROUND

The Graduate School, as a component and partner of Jose Rizal University in promoting

research culture, has chosen you as a respondent of this survey. Ethical considerations regarding research on human subjects require that you or, if you are not of age, your parents or guardian sign the following consent form.

The primary purpose of the research is the determination of the behavioral impacts as

students acquire a predetermined mathematical competency.

CONSENT

I understand that my (my son's/daughter's) participation as a respondent in this survey of

college freshmen is not compulsory and that I can withdraw my consent at any time without penalty and have the results of my (my son's/daughter's) participation, to the extent that it can be identified as mine (his/hers), removed from the records.

I agree (I am allowing my son/daughter) to participate as a respondent in the survey of college freshmen. I also agree (I am also allowing my son/daughter) to participate in follow-up surveys that may be undertaken in the future as well as in possible follow-up interviews that may be undertaken.

I understand that the results of my (my son's/daughter's) participation in this survey as well as in other follow-up surveys or follow-up interviews will be held in the strictest confidence and will not be released to any school administrator, faculty member, staff, or person other than the research team in any individually identifiable form without my prior consent. Signed:

______________________________ _____________________________ Parent/Guardian/Date University/College

_______________________________ Student Participant


APPENDIX B

SOLVE EXPONENTIAL AND LOGARITHMIC EQUATIONS

Questions on solving exponential and logarithmic equations and, indirectly, on all

properties of exponential and logarithmic functions are presented. These questions may be used as a self-test. Select the right answer by writing the letter before the question statements.

© Dr. Abdelkader Dendane

Question 1: Find all real solutions to the logarithmic equation. ln (x) = 2

a: 2 b: 2

e

c: 1 , 0 d: no real solutions e: e

2

Question 2: Find all real solutions to the exponential equation. e

x = 6

a: 6 b: 6 / e c: ln (6) d: e

6

e: no real solutions Question 3: Find all real solutions to the logarithmic equation. ln (x) + ln (2) = 3

a: no real solutions b: e

3 / 2

c: e 3 / ln (2)

d: 3 e / 2

e: 3 / ln (2) Question 4: Find all real solutions to the exponential equation. e

3x = -1

a: no real solutions b: ln (-1) / 3 c: -1 / ln (3) d: 0 e: e

-1 , 3

Question 5: Find all real solutions to the exponential equation. e

2x - 3e

x + 2 = 0

a: 1 , 2 b: e , e

2

c: no real solutions d: 0 , ln (2) e: e

2

Question 6: Find all real solutions to the logarithmic equation. ln (x + 1) + ln (x) = ln (2)

a: 1 , -2 b: 0 , ln (-2) c: e , e

2

d: -2 e: 1 Question 7: Find all real solutions to the logarithmic equation. ln (x + 1) - ln (x) = 2

a: 1 b: e

2

c: 1 / (e 2 - 1)

d: 1 / (ln (2) - 1) e: no real solutions Question 8: Find all real solutions to the logarithmic equation. ln (x

2 - 1) - ln (x - 1) = ln (4)

a: [ 1 + sqrt(17) ] / 2 , [ 1 - sqrt(17) ] / 2 b: -2 , 3 c: no real solutions d: ln (3) e: 3 Question 9: Find all real solutions to the exponential equation. e

2x e

3x - 3 = 2

a: ln (5) / 5 b: no real solutions c: 1 d: -1 , 1 e: ln (5) Question 10: Find all real solutions to the logarithmic equation ln (x

4) + ln (x

2)-ln (x

3)-2 = 7

a: 9 1/3

b: e

3

c: 1 d: no real solutions e: 0


APPENDIX C

POST-TEST EVALUATION SURVEY

1. Rank from 1 to 5 the following changes of behavior you have experienced when you are

expected to acquire mathematical competencies. RANK ONLY THE ITEMS WHERE YOU HAD YOUR INTERVENTION.

a. BLENDED RECITAL (RECITATION)?

_____ Attentiveness _____ Determination _____ Patience _____ Readiness _____ Responsiveness

b. Student-led DISCUSSION? _____ Attending to details _____ Clearness / organization of thoughts _____ Enthusiasm to share _____ Keenness _____ Precision

c. BOARD WORK / DEMONSTRATION? _____ Articulacy _____ Compliance _____ Cooperation _____ Neatness of work _____ Self-confidence

d. MATH-ORIENTED FILM VIEWING? _____ Creativity _____ Exactitude _____ Humility _____ Promptness _____ Vigilance

2. Did your score improve? _____ Yes _____ No

3. Were the examples during the teaching-learning of the math lesson enough to promote

values? _____ Yes _____ No


APPENDIX D

PHOTO DOCUMENTATION

In the student-led discussion, one leader

emerged to explain to his colleagues the

topics on hand.

The group of students who watched Math

films are sharing their thoughts about the

movie contents.

Students from the blended-recital group

attempt to solve exponential-logarithmic

problems before raising their hands for an

answer.

Students actively participate and listens to

their colleague who demonstrates how to

solve the math problems given to them.

Learning Exponential-Logarithmic Equations through Values-Driven Interventions

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