Teaching Geometry Through Metacognitive Journal Writing - An Action Research

Teaching Geometry Through Met a Cognitive Journal Writing

Research

Wow, I have not updated this blog for a longtime. I think I am obliged this time to update considering that I required my BSEd-Math students to have a blog.It would be embarrassing if they found out this blog was updated eons ago.

How time flies; I am done with my academic requirements. My high school dream of becoming a doctor is almost coming true.With hard work and perseverance, I think I can.

I have done my action research, passed the compre, struggled with title defense, and finished my proposal defense.Now here comes the difficult part - the research proper.Oh, God bless me!

I'll be posting my action research abstract and other research related articles.;)

Evaluation Research

Dr. David Garson of North Carolina State University provides an informative website at ncsu.edu. One of the topics he included in Multivariate Analysis is the Evaluation Research. He started with an overview stating that, “Evaluation research seeks to provide objective assessments of past, present, or proposed programs of action”. Here is a summary of Dr. Garson’s article.

There are three basic types of question asked in evaluation research – descriptive, normative, and impact. Descriptive studies are used to describe the goals, objectives, start-up procedures, implementation processes, and anticipated outcomes of a program. Normative studies evaluate programs by multiple values while impact studies evaluate in terms of outcomes.

The four major types of evaluation designs are survey research, case study, field experiment, and secondary analysis of archival data. Both survey and case studies are primarily used in descriptive and normative questions. Field experiments, which are used primarily around impact questions, have three main types – true, nonequivalent comparison, and before-and-after studies. Secondary data analysis is useful for all three types of research questions.

Some research examples cited are pilot studies, cost-benefit analysis, performance reference model, program assessment rating tool, needs assessment, and feasibility studies. Pilot studies are “reality check” trial runs of a full blown research. Cost-benefit analysis deals with measuring costs or benefits. It may sound straight-forward and simple, but a lot of questions arise from this analysis. Benefits may be tangible or intangible. The return of investment is traditionally used for the cost-benefit analysis of tangible benefits. On the other hand, intangible benefits cannot be adequately measured. There is also performance reference model, which is a framework for evaluation developed by the Office of Management. It uses four types of evaluation measure – mission and business results, customer results, processes and activities, and technology.

Another approach to evaluation developed by the Office of Management is Program Assessment Rating Tool, which is designed to assess and improve program performance through a formal review process which was meant to identify a program's strengths and weaknesses.

Needs assessment serves to identify organizational problems (both internal and arising from the organization's environment), to investigate opportunities for change, and to document and defend projects which are proposed to address problems. Needs assessments assure that projects are directed to real problems faced by the organization rather than wasting scarce resources. Needs assessment process is implemented in four stages – collecting information, identifying and prioritizing problems researching alternative possible solutions, and seeking consensus on a proposed solution.

Lastly, there is feasibility study. It is normally undertaken only after the organization has identified and defined a proposed project, and has a written requirements analysis and a general design statement for it. It has three dimensions – operational, economic, and technical.


In general, the article provides substantial information on evaluation research especially for the business sector. It provides specific examples such as questions regarding measurement of benefits and questions regarding measurement of costs. Furthermore, it also compares and contrasts one type of evaluation research from the other. For example, aside from describing feasibility studies, it makes a distinction between feasibility studies from needs assessments.

There are technical business terms used such as cost-benefit, potential value, and present value that might hinder a non-business oriented person from understanding the text. Nevertheless, educators can relate to some of the evaluation research designs such as pilot studies, survey research, and field experiment. An educator, however, will find the article more helpful if the examples given are centered on education research.

Furthermore some organizations cited are not found locally; thus, their standards may not be applicable in our field. It would be beneficial if there is an academic site featuring evaluation research standards in the Philippines.

On the bright side, the article opens a new window for us to expand our knowledge on research. Dr. Garson has done a commendable website, which is informative not only in North Carolina State University but in the research communities worldwide.

Reference:
Garson, G. David (n.d.). "Evaluation Research", from Statnotes: Topics in
Multivariate Analysis. Retrieved 12/28/2008 from
http://www2.chass.ncsu.edu/garson/pa765/statnote.htm.

Making Numbers Make Sense

My research beliefs completely changed when I took up qualitative research under a professor who is quite passionate and well-versed with the subject. I was fascinated with how qualitative researchers collect and interpret data. The “in-depth” analysis of data somewhat made quantitative research less credible. Example, a quantitative researcher might say the result is not significant if there is only one rape case per 10,000; however, the qualitative researcher will consider that lone case and declare the results to be “significant”. This example cited by my teacher keeps reverberating in my mind. After the end of the semester, I developed my utmost respect to qualitative researchers and I stopped cultivating my passion for quantitative research. I even started to think that qualitative research is better.

How about marrying the two types of research? I bow my head to the one who first thought of this idea. This would definitely settle the issue regarding the differences of quantitative research and qualitative research. With the “marriage” of the two researches becoming a success, researchers should be keen enough to polish their skills in analysis of narrative and numerical data.

For those who are still groping in the dark on how to interpret numerical data the PowerPoint presentation Making Sense of Numbers by Dr. Jim Adams-Berger would definitely help. Those who have learned the ropes in data analysis could use the presentation to recall the basic considerations on interpreting “numbers”.
The presentation encompasses using data to identify community problems, to explore problem relationships and to choose responsive programming. As a whole, Making Sense of Numbers is anchored on the framework of research (perhaps a research program particularly designed for OMNI Research and Training, Inc.). Berger points out that values serve as a filter of the other major analytic elements, which are beliefs, data and research. There is also a detailed explanation on modeling problem relationships. The use of graphic models makes the presentation more substantial and interesting especially for those who have just started doing research.

A wide range of examples could have been presented in surfacing and identifying problems; however, the presentation focused on the differences of numbers and rates in a particular case. In a certain example, the numbers of aggravated assaults for 4 consecutive years are not enough for us to conclude what year has the worst record. Calculating the rate is more meaningful. The recommended procedure in calculating the rate is number of cases divided by the population and multiplied by a large number (“per” number). That would be acceptable if the number to be multiplied is smaller than the population. What if it is larger than the population? One murder case in a population of 500 may be interpreted as 20 murder cases per 10,000. Is it not misleading? I think it would be better to stick to the usual per 100 in solving rates.

It is also best to consider different viewpoints before making conclusions from a set of data. There are instances when rates are favored than numbers, but there are cases when rates give misleading information.
In the example in calculating rates, the data in year 1997 shows population of 10,000 and number of aggravated assaults of 70. However, the rate per 10,000 is 7. Let us take a moment to ponder if it is correct. Perhaps, a calculator could help.
Aside from faulty calculations, another pitfall of “numbers” is the method of gathering data. There are a lot to consider – from the structure of questions to the respondents’ willingness to answer. That is, we have to ensure validity and reliability.

I consider myself a neophyte in the research arena. I realize there are still a lot to learn. Starting with Making Numbers Make Sense I hope to fill my brain with the skills in numerical data analysis that are useful in research.

Thursdays with Philosophy - the Final Paper

Wherever I go, there is an attractive silvery object floating in midair. It illuminates my path and my eyes are transfixed to it. I tried with all enthusiasm and interest to capture it but it slipped. I had a chance of holding it briefly three times. I felt overwhelmed for the illumination it brought but it burnt my hands if I hold on to it for so long. Now, I just appreciate the light it gives for me to see my way clearly. Though, it is tempting to catch it again, I just let it float by my side wherever I go. I think I am not yet capable of holding it for I might be blinded by its intense glow. I think it would be better left illuminating my path for someday I will be worthy to place it my heart.

That attractive silvery object is philosophy. I had three brief encounters with it. First, it happened in college where Dr. Andora assisted me nearly to the threshold. Next, in master’s degree Dr. Bautista helped me out in nearly achieving enlightenment. Just recently with Dr. Templora, I have another encounter with the blinding light of philosophy.

My Philosophy in Teaching
On my previous paper, I have indicated some of my philosophical beliefs in teaching and learning. Let me substantiate my philosophy in teaching after I have encountered Rizzi's Science Before Science. There are ideas presented by Rizzi, which I am not convinced to accept. Nevertheless, it is overshadowed by some of the good philosophical principles that I would like to adapt.

Learning Through our Senses
Our senses give us our primary knowledge and it is important to start with the physica in teaching (especially with subjects that involve abstraction). Thus, in teaching mathematics we should let students “experience” the essence of mathematics by giving them first the opportunity to do math in a “sensible” way, that is abstracting math in the immediate environment.

As teachers, we should not limit ourselves with the interpretation of math textbooks. Rather, we must first recognize that the classroom, the school and the community as a whole are rich sources of knowledge. It is, therefore, necessary for us to maximize the potential of the students to use their senses in obtaining truth.
Example, in teaching parallel lines, start with sensible examples that students could immediately relate to. Let us not present them with non-intersecting train tracks if they have not seen them. It would be better to cite the railings of stairs found right outside the classroom. After which,we could proceed to the geometric principles that 'define” parallel lines.

The Development of Critical Thinking
We do have a provision in the Philippine Constitution that educational institutions should promote critical thinking. This kind of thinking among students could be developed by developing the students' skill in abstraction. Rizzi presents important key points in abstraction. That is, we should remember that images could hinder us from abstracting ideas. Above, I have pointed out the importance of the physical environment and the senses;however, for us to fully abstract ideas we should transcend beyond physical. That is, for the student to truly understand the essence of parallel lines, they have to “free” their mind from the images of parallel lines in real life.

The Recognition of the Students’ Potentiality
To make teaching effective, let us recognize the potentiality of the students to bring out their best in every situation and let us not forget our role as the mover of such change.

Teaching Science to Prove God's Existence
Our teachings in school should not be in conflict with the moral teachings. That is, we should teach mathematics and science for “glory of God”. Though, we adhere to the mathematical teachings of known idealists, we should be careful to use their teachings so as not to undermine the existence of God. In comparison, we should eliminate bad tomatoes and eat the good ones for one rotten tomato does not spoil the whole bunch.

Importance of Ontological
As a math teacher, sometimes, we make mistake by assuming that the essence of a certain being is on its mathematical aspect. This could be a big hindrance for students if we apply this in the classroom. It is important to note the empiriological (empirioschematic or empiriometric) approach is essential in learning, but we should not fully focus on this. Let us also take into consideration the importance of the ontological method in acquiring knowledge. That is, let us not jut mumble useless mathematical equations and formulas. We should be able to relate its meaning.

Stumbling Blocks
I have encountered some stumbling blocks in studying Science Before Science.

Some Errors
I believe Rizzi should have have written “The apple changed from green to red” instead of “... from red to green”. (page 43). Furthermore, on page 143 he spelled “discrete” as “descrete” and “rhetoric” as “rehtoric”. With these few errors that I have seen, it is but natural for me to doubt the correctness of other sentence structures I find confusing. If Rizzi made mistakes in spelling, what else are his other errors? Is it possible that he wrote some erroneous sentences that are critical in the development of his philosophy? There are also some usage of pronouns, in which the antecedents are not clearly presented.

For the First Time
Even if I have encountered philosophy before, I consider myself as a freshman in this realm. I believe Rizzi's book is not recommended for those who have just met philosophy for the first time. Rizzi usually cites some existing philosophies and it is necessary for the reader to verify that these philosophies are cited properly. He might be giving us sweeping generalizations just to emphasize his point about other philosophies, especially idealism.

Praises
Nevertheless, let me overshadow my previous reactions with my praises for Rizzi. His contemporary view gives timely examples that the mathematical and scientific world can relate to. Furthermore, his phenomenal book serves as a mediator of modern and classical philosophies. It is also a brave attempt to bring forth the issue of religion and God to the scientific world. Knowing that the traditional scientific community seems to have an aversion to anything that pertains to God, Rizzi has indeed done something remarkable for having united the seemingly contrasting ideas of God and science.

Realizations
After “grueling” Thursdays with Philosophy, I have here some of tidbits of realizations.

Nothing beats reading in acquiring knowledge.
Rizzi emphasized that our senses are important in acquiring primary knowledge. However, I believe my environment is limited and I could not depend solely on my sense perception to acquire knowledge. In our philosophy class, I have learned an important lesson about reading. Indeed, a page a day keeps ignorance away.

Philosophy is a strong foundation especially for an educational institution.
When I started teaching at University of San Agustin, Father President Marchan acquainted us about the school. He pointed out that the Augustinian philosophy is the foundation of the school’s mission and vision and eventually the basis of the school activities and classroom instruction. It is heartwarming to embrace the knowledge he has shared. I feel like my restless soul has found refuge in the realms of the university. As a teacher, I sometimes ask, “Why am I doing this”? Philosophy, as Father Marchan has shown, brings forth to light our reason and our purpose. Indeed, teaching in an institution with clearly stated values and goals makes us, the new teachers, more goal-oriented and less confused. Thus, it is vital for school administrators to anchor the school’s mission and vision on a certain philosophy.


Enormous Ocean of Knowledge
It’s an enormous ocean of knowledge out there that I could only swim at the beach to experience some of the sea water's saltiness lest I will drown.


Importance of Christian Teachings
When I was young, parents restricted us, their children, from reading The Bible. But they do believe in the existence of God. My father believed in prayer and my mom devoted a part of her day praying the novena. However, they just didn't want us to be distracted fro our studies ad they don't want us to be mentally deranged.

Actually only two of my siblings were quite interested in studying religious materials – my brother Ric and my sister Rosevelle ( who, because of her creative mind, was told to seek psychological help by her high school teacher). They were always reprimanded because they used to ask about and quote certain Biblical verses during family discussions. My father would emphasize that some Biblical verses are confusing and inconsistent for they depend on the apostle who wrote them.

My brother was particularly interested in searching for the right religion and he is a bookworm. He reads the Book of Mormons, The Holy Bible, Awake magazine, Time and Reader's Digest. When he was in high school, my parents were particularly concerned with academic achievement. When my father caught my brother reading Archie comics and Reader's Digest Condensed Book (and other materials not required in school) right before exam, he was in rage. He literally split the Reader's Digest Book using his axe. After which, he burned the precious pages. Good thing, some pages were saved from turning to ashes. I could still show you the half-burnt book preserved at home. However, the Archie comics and Time magazine did not survive. They were returned back to ashes. Sigh! What if my brother was caught reading The Bible? Will my father do the same?

Now, I have mixed feelings when I see The Holy Bible. I feel a little bit of fear that it might be misleading the Christian world after all this time. I also feel guilty for not having read it and for holding such doubt regarding its validity.

As a child, I was not also well acquainted with the Catholic teachings for I have not attended Catholic catechism when I was young. The truth is even if my parents would want us to attend, we did not have money for the fare going to the church. So we settled attending mass and other religious classes in Aglipay and Protestant churches for they are nearer.

After taking up Philosophy, I have realized that the Bible after all is important in the formation of sound Christian teachings. I am happy to have known Dr. Templora for she (despite her scientific orientation) talks with eloquence the Biblical truths.

Nevertheless, I still respect my parents. I am also thankful for what they have done. There is always a time for everything, and studying The Holy Bible and the Catholic teachings when I was young might not be right time. Our inquisitive mind be blinded at such a tender young age.

That “silvery thing” is indeed enticing and it is human nature to want it. However, one needs the proper attitude and the readiness to learn and unlearn.

Stand and Deliver

I have experienced how difficult teaching is especially for Math teachers. I have tried with all enthusiasm and genuine concern to teach mathematics to slow learners with no significant results. When almost all my energies have been exhausted, I would just sigh and hope that someday these mathematically-challenged students will eventually improve on their own. But of course, for someone to change (e. g., improve), one needs a mover to “move” potentiality to act.

Such a good example of a “mover” is Jaime Escalante, a math teacher portrayed as the main character in the movie, Stand and Deliver. Escalante is a new math teacher at James A. Garfield High School – an impoverished school in Los Angeles – where teachers are more focused on discipline than academics clearly because of students’ behavior. He is unlike other teachers because he did not simply accept the situation; instead he used innovative ways to improve the situation. He was not at first liked by students for he has received several insults and threats from them. Despite the disrespect he has experienced, he is able to implement effective teaching styles to convey the importance of mathematics in everyday life. His troublesome students are transformed to dedicated math learners. In fact he introduced Calculus to his students despite the skepticism of his co-teachers.

Escalante’s efforts paid off when his students passed the AP Calculus exam, a feat done by few in the state. However, a shocking accusation is made. The Educational Testing Service (ETS) calls into question the validity of their scores when it is discovered that similarities between errors is too high for pure chance. It is a big insult for Escalante for the implication of cheating. Nevertheless, his students took the exam again with flying colors. They have shown not only to ETS but to the whole world that despite their social and racial status, they are worthy of their achievement.

The movie shows that our assumptions and expectations are important in teaching. If Escalante assumed that his students are losers in Mathematics, he would not be as well known as he is now today. His firm belief that his students have the capability to rise from the depressed school environment is such a strong motivation that caused the students to achieve what seems to be impossible at first. As a teacher, I realized that we have the responsibility to unlock the talents and all other potentials of the students. Even if we are faced with gang members or brats in the classroom, we should not think that they would stay like that forever. We should remain hopeful that our students will shine in a certain field. A teacher’s mantra should be, “Bring out the best in others”. That is, be the “mover” of our students’ change from potentiality to act.

Stand and Deliver also presents the challenge to us Math teachers to be result-oriented. It is not enough that we are pursuing a high degree or that we have an almost endless list of seminars attended or that we have known and applied several teaching strategies in the classroom. Most importantly, we must make sure that what we are doing have helped our students develop their love for learning math. It is quite useless to have a Ph. D. with out the skill to make students learn. It is futile to have known truth without the capability to share it.

It is a teacher’s task to bring down the wall that divides. Some students would feel insecure because of the teacher’s implicit message, “I am the best and you are nothing”. Thus, it is but proper for a teacher to reach out to the students and to accept them despite their shortcomings. In the movie, Escalante embraces his students despite their racial and social inferiority.
The movie also inspired me to show genuine concern to the students and not to give up even if the tough gets going.

It is heartwarming to note that there is someone who has shown that it is possible to make students learn despite the hindrance. What we usually believe to be an insurmountable problem in the classroom has been solved by Escalante. But, he did it with struggles, pains and frustrations along the way. So, for a young teacher like me, I should not lose hope. Someday, I could make a dramatic change – like what Escalante did – starting in the classroom. Yes, someday… but I should start now!

Lorenzo's Oil

Even though, Susan Sarandon is the only actress that I can identify in the movie, Lorenzo’s oil, I could consider the movie to be interesting. This time, the movie caught my interest not because of the blaring special effects and not because of the impeccable cast performance. It is the movie’s message that makes Lorenzo’s Oil worthy to be included in my personal watch list.

The story revolves around a seemingly ordinary family – the Odone family – that made an extraordinary contribution in the medical field. Lorenzo, the son, exhibited abnormalities at the age of 7. Strange mental phenomena began to occur. The family was brokenhearted when they learned Lorenzo was suffering from a very rare disease called ALD - adrenoleukodystrophy.

What is ALD? It is a progressive degenerative myelin disorder, meaning that myelin, the "insulation" around nerves, breaks down over time. Without myelin, nerves can't function normally, or at all. Unfortunately, the body can't grow replacement myelin, so the disorder is progressive--it gets worse over time (Kugler, 2006).

In the movie, medical experts are skeptics about the disease. They said that Lorenzo will not survive until the age of 8. However, the Augusto and Michaela Odone did not give up in seeking for their own cure. They spent time in the library finding researchers related to the disease. It was heart wrenching at first that in most studies, ALD patients did not survive. But in the end, they finally came up with a research suggesting some changes in the patient’s diet including introducing a certain kind of oil in the diet. Thus, the title is Lorenzo’s Oil.

The movie clearly highlights the importance of medical research as well as the correct attitude that goes with it. Some students hate research because it’s tedious, time consuming and expensive. This movie, however, clearly presents the occurring benefits of research especially in medicine. It is important to emphasize in research class that results of research are not merely for the sake of passing the course or for gaining a scholarship. It is about adding new knowledge to make our life better or even to save lives. That is why, it is also important to note that researches published in journals must be checked for validity. It is important to verify whether the facts presented in journals conform with reality or else some people will be deceived. How lucky the Odones are that they have encountered a reliable research result that they effectively replicated for the benefit of Lorenzo.

Furthermore, the movie also gives us the reason to value the seemingly small gifts given to us by God. There are times when we use our tongue to slander or our hands to hurt other people. But when we recall what happened to the speech and limbs of Lorenzo, we can’t help but value the power of our words and the abilities of our hands. Thus, we could not think of using our faculties for evil purpose. During those times when we feel depressed and oppressed, we should be thankful that God has been so good to us for giving us the small significant gifts (that we should not take for granted). When we complain about our imperfections, it is important to recall that we are at least not suffering from a dreadful disease.

I am also touched by the unconditional love shown by the Odones to Lorenzo. Despite Lorenzo’s disease, the Odones stood firm with their family values. They continue to hold on for the survival of their son. Even if ALD disrupt their everyday lives, they did not consider this as a hindrance to nurture Lorenzo with their unconditional love.

What is also striking about the story is that it is based on true events. In fact the real life Lorenzo Odone just died on May 30, 2008 at the age of 30! Lorenzo’s oil has also found its way in mainstream medicine in curing ALD. It has profound benefits especially for those who have taken medication before they have shown ALD symptoms (Concar, 2002).

Overall, the movie may not be appealing to some young viewers who are used to like movies at face value only. However, it is a vital teaching tool especially in Biology and in Research. It is also an inspiration for those who seek for truth amid insults and skepticism.




References:
Concar, D. (2002). Lorenzo’s Oil finally proven to work. Retrieved October 2,
2008 from http://www.newscientist.com/article.ns?id=dn2851.

Kugler, M. (2006). ALD and Lorenzo's Oil. Retrieved October 1, 2008 from
http://rarediseases.about.com/cs/ald/a/041301.htm.