My Epistemological Beliefs

I tried to answer Schommer’s Epistemological Quiz (Schommer, 1998), and my answers has not really changed after my readings. Below are my epistemological beliefs and their effects in facilitating my learning. In rare cases, they have been the reasons of my inhibitions.

1. Control of Learning

For the control of learning, I have the following distribution:

inherited: 80%
acquired: 20%

Implication: This means that I know my limits (inhibition). I believe that there are people who are born genius. Recently, I realized that I cannot be a mathematician because I am not good enough. But this does not prevent me from doing the best that I can in mathematics.

2. Speed of Learning

I believe that there are things that are easy to learn, but more likely, there are more things that require gradual learning. I have the following percentages:

Quick learning: 10%
Moderately quick learning: 20%
Gradual learning: 70%

Implication: I learn things slowly. I tend to go back and forth to what I’m learning in order to have deeper understanding. I also study multiple resources for further learning.

3. Organization of Learning

I believe that a few knowledges are isolated, but most of it are networks with many links.

isolated compartments: 1%
compartments with a few links: 9%
networks with many links: 90%

Implication: I try to reflect on the connections between and among the concepts I’ve learned.

4. Stability of Knowledge

I strongly believe that knowledge is always evolving and there is still vast knowledge that we do not now.

Discovered and unchanging: 1%
Yet to be discovered: 99%
Always evolving: 90% of the discovered

Implication: I always update myself with the new knowledge and discoveries. I read voraciously because I know that there are things that I do not know. I know that there is vast knowledge out there that is waiting to be learned.

Reaction about the Final Exam

I was actually relieved that the examination is open-ended. Given the numerous requirements this trimester, I was happy that I do not have to re-read the entire module. I just have to pick a topic that really captured my attention and then explain it. This is advantageous because I can say a lot of things about the topics that I really enjoyed learning and what I deemed to be the most important.

Further, I personally think this type of examination maximizes students’ creativity. By allowing us to choose the type of presentation that we will use, we can use an unlimited number of methods to show the extent of our understanding of the topics that we have chosen. I’m sure that the teacher will be surprised of the variety of outputs that will be submitted.

Furthermore, I also like this type of examination over the traditional one. I think I will remember what I wrote here compared to the traditional examination where I memorize and try to understand a lot of information.

Looking from a different point of view, one suggestion though, an open-ended
exam is good for mature and experienced students, but I am not sure with younger students. Young students (e.g. those who just graduated high school and taking BES) had been answering specific questions in school all their lives, so this might be a surprise for them. I am sure that they have been answering open-ended questions but not as open as this final exam. Putting guide questions in the final exam will likely help them decide what to pursue and how to do it.

To summarize, personally, this type of examination reinforced and strengthened my knowledge about the course by letting me synthesize my learning.

Thank you!

Relating Bloom’s Taxonomy and the TIMSS Cognitive Domains from a Mathematical Perspective

Bloom’s Taxonomy and the Trends in International Mathematics and Science Study (TIMSS) cognitive domains are two of the most successful hierarchical models in classifying cognitive demands of educational objectives, assessments, and activities. The Bloom’s Taxonomy was named after Benjamin Bloom, the chair of the committee of educators who invented the taxonomy. The TIMSS cognitive domains, on the other hand, was the offshoot of a series of international assessments joined by more than 40 countries for the past 20 years.

Although Bloom’s taxonomy includes three domains namely cognitive, affective, and psychomotor, this discussion will only focus on the cognitive domain. The goal of this post is to relate Bloom’s Taxonomy’s cognitive domains to the TIMSS cognitive domains.

Blooms Taxonomy’s Cognitive Domains

Bloom’s levels of cognitive domains are as follows (Wikipedia).

1. Knowledge-remembering facts, terms, basic concepts, or answers without necessarily understanding what they mean

2. Comprehension – demonstrating understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating the main ideas.

3. Application – solving problems in new situations by applying acquired knowledge, facts, techniques and rules

4. Analysis- breaking information into component parts, determining how the parts relate to one another, identifying motives or causes, and making inferences and find evidence to support generalizations. Its characteristics include:

5. Synthesis – building a structure or pattern from diverse elements; it also refers to the act of putting parts together to form a whole

6. Evaluation – presenting and defending opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.

Image Credit: http://www.nwlink.com/~donclark/hrd/bloom.html

A slight revision about the taxonomy was done in 2001. The nouns used to name the levels were changed to verbs, Evaluation and Synthesis were swapped, and Synthesis was renamed to Creating as shown in the figure below.

The TIMSS Cognitive Domains

Over the past two decades, the TIMSS cognitive domains have evolved and have been simplified into three levels: Knowing, Apply, and Reasoning. The definitions are as follows:

1. Knowing – knowing facts and procedures, recalling and understanding concepts

2. Applying – applying concepts to solve problems; applying mathematics in a range of context

3. Reasoning – solving novel problems, systematic thinking, inductive reasoning

These domains have sublevels (See (Grønmo, Arora & Mullis, 2015) for details).

Relating Bloom’s Taxonomy and TIMSS Cognitive Domains

Bloom’s Remembering and Comprehension/Understanding levels of objectives clearly fall under the Knowing domain of TIMSS domains. This involves knowing facts and procedures like remembering a formula and understanding a certain procedure such as getting the root of a quadratic equation using the method of completing the square. The TIMSS Knowing domain involves familiarity with mathematical concepts (understanding) as well as procedural fluency.

I have placed Bloom’s Applying and Evaluating fall under the Applying cognitive domain. This is a bit tricky because Evaluating is one of the highest levels of the Bloom’s but note that the taxonomy was originally created for college students. Evaluating in college is a different level in elementary and high school. Evaluation in elementary and high school can range from thinking if a particular reasoning is correct or not or at the highest level evaluating someone’s solutions. In higher mathematics, of course, evaluating will be more complicated than analyzing since Evaluation will require analysis.

I have placed Creating and Analyzing are under the Reasoning domain. According to both taxonomies, Analyzing is breaking information into parts. This is one of the skills that students should learn in order to solve problems.

Creating (originally Synthesis) is the highest form of reasoning since it includes creating something new or ideas that are new at least in the perspective of the students. This includes new ideas that cannot be reached by many students or at least some novel solutions to problems.

Bloom’s Taxonomy and the TIMSS Cognitive domains are hierarchical models that can be used to guide us in creating educational objectives, tasks, and assessment items. Let’s use them to improve our teaching and produce better learners.

References

Bloom’s taxonomy. (2017, June 8). In Wikipedia, The Free Encyclopedia. Retrieved
June 25, 2017 from https://en.wikipedia.org/w/index.php?title=Bloom%27s_taxonomy&oldid=784477848

Clark, D. (n.d.). Bloom’s Taxonomy of Learning Domains. Retrieved June 25, 2017, from http://www.nwlink.com/~donclark/hrd/bloom.html

Grønmo, L. S., Lindquist, M., Arora, A., & Mullis, I. V. (2015). TIMSS 2015 mathematics framework. TIMSS, 11-28.

On Cognitive and Social Constructivism

by Guillermo Bautista Jr.

There are two types of constructivism. The first one is cognitive constructivism proposed by Jean Piaget. According to Piaget, learners construct their own knowledge based on the information given to them. Learners use this information to create schemas about the world.

The second one is social constructivism proposed by Lev Vygotsky. According to Vygotsky, learners learn from social interaction. Vygotsky argues that the child’s cultural development starts from the social level, and then later on the cognitive level.

In my personal opinion, these two types of constructivism are true and are used at different points in life of a learner. I believe that you cannot totally separate them. You use a combination of cognitive and social aspects of your life to learn; however, only using one of them more at different points in your life.

I think that at an early stage of childhood, learning is developed mainly using social constructivism. Children learn language through interaction with adults such as parents, classmates, and teachers. As the learners mature, after having developed enough schemas to learn on their own, learning begins to shift to cognitive constructivism. They begin to process new information based on their set of schema and learn to assimilate and accommodate new concepts. During the adult life, cognitive constructivism is used more than social constructivism.

On Cognitive Load Theory and Dual Coding Theory

by Guillermo Bautista Jr.

Among the readings in Module 5, there are two things that I have learned that I am really interested: Cognitive Load Theory and Dual Coding Theory. In this post, I am going to explain some possible applications of these theories in the classroom as well as education in general based on my experience as a teacher.

Cognitive Load Theory states that the brain has a limited number of stimuli that can be processed at a time. Psychologists now agree that the there are only 3-7 stimuli that can be processed at a time depending on maturity and experience. This means that the teacher has to be mindful of how to design instructions and to make sure that the tasks do not require too much cognitive demand that may hinder learning. Teachers should also take note of the cognitive abilities of students and the environment. Further, from a broader perspective, it is also imperative to examine the curriculum. In my study during a teacher training in Japan, I have personally compared the curricula of Japan and the Philippines and found out that our curriculum has too many topics compared to that of Japan’s.

Dual Coding Theory, on the other hand, states that the brain represents and processes information verbally and visually. These representations are processed separately, but connections are made in order to store and retrieve information. One of the implications of this theory for teaching is the emphasis on visual aids as early as possible as well as making connections between visual aids and verbal explanations whenever possible. For instance, in mathematics, it is recommended to use multiple representations in almost every concept. For example, relationships between two variables, particularly functions can be represented numerically, algebraically, and geometrically.

Numerical representations involve tables or ordered pairs, algebraic representations involve equations, and geometric representations involve graphs. The task above is an example that highlights these connections: it asks students to match the graphs, equations, tables, and rules.

The two theories above are very important for teachers and educators to know. Teachers should reflect on how to use these theories to improve teaching.

References

Kirschner, P. A. (2002). Cognitive load theory: Implications of cognitive load theory on the design of learning.

Paivio, A. (2006, September). Dual coding theory and education. In Draft paper for the conference on “Pathways to Literacy Achievement for High Poverty Children,” The University of Michigan School of Education.

Important Behaviors that Should Be Acquired Distance Learning

by Guillermo Bautista Jr.

Distance learning can be very demanding in terms of time. This course is even more demanding because it’s a trimestral course. Students have to read and accomplish things in almost half the time of the semestral courses.

I think that the most important behavior that learners should acquire in a distance learning environment is self-motivation. In face-to-face classes, students are forced to accomplish things because of their physical presence in the classroom. A student who is assigned to present a report and who could not do it would really look “bad” in front other students and the teacher. A scenario such as this does not usually happen in a distance learning environment. Most of the time, it is up to the student if he will accomplish the tasks and if he will accomplish them on time. Hence, self-motivation is very important in distance learning.

Self-motivation is an example of self-efficacy. According to Albert Bandura cited in Cherry(2017), self-efficacy is “the belief in one’s capabilities to organize and execute the courses of action required to manage prospective situations.” Here, prospective situations mean the goals or objectives that a person is trying to reach. For example, in distance learning courses, one of the goals of a student with high self-efficacy is to finish the course on time, with maximum understanding as well as high grades. Goals such as these will motivate that student to be more organized in his or hear learning and he or she will make every effort to submit the requirements on time to the best of quality.

New students in distance learning have to make adjustments too. I remember observing how my classmates answer questions. Later in this module, I realized that I was using mediational processes proposed by Bandura which is cited in McLeod (2011). According to Bandura, there are four meditational processes in observational learning: attention, retention, reproduction, and motivation. Attention is observing behavior, retention is remembering the observed behavior, reproduction is performing the observed behavior, and motivation is the will to perform the observed behavior.

In my case, during my first trimester, I observed how my classmates answer questions. Some would just post their opinions to questions, while others will have references (attention). Of course, I picked up the latter. This is which is observing behaviors. According to Bandura, many of the daily behaviors are not noteworthy, so it is very important for us to be attentive in observing. In my case, I picked up the noteworthy one which is having references every time you write your answer.

I also have remembered what I have learned (retention) and I applied it by including references every time I post my answer in a discussion forum (reproduction). Lately, I already became motivated to do it (motivation).

These changes in behavior did not just happen to me. I have observed these changes happen to other students too. Some students who post without references later post references after seeing other students do it.

These changes also relate to self-motivation. You observe to learn from others because you are motivated to learn.

References

Cherry, K. (2016). Self Efficacy: Why Believing in Yourself Matters. Retrieved May 28, 2017, from https://www.verywell.com/what-is-self-efficacy-2795954

McLeod, S. (2011). Saul McLeod. Retrieved May 28, 2017, from https://www.simplypsychology.org/bandura.html

On Behaviors and Corporal Punishments

by Guillermo Bautista Jr.

Most of my life, I was the only child in the family, so as you can imagine, I would receive mostly reinforcements and very few punishments. One of the reinforcements I remember was that my mother would buy me some clothes or ice cream when I got high grades or when I won in singing contests. As far as punishment is concerned, I cannot remember a major one.

I had my first taste of corporal punishment when we lived with my uncle and his family for almost a year. His wife was a disciplinarian and there were numerous times where she hit her children using sticks, brooms, or twigs for the simplest of mistakes. The strikes were intended to hurt because you could hear the sound and you could see the children panicking and trying to hide in every corner possible. Minutes after such events I could hear the sobs of my cousins in their sleep. Even though I was five years old at that time, I could still remember how sorry I was for them.

I got my share of corporal punishment when I was told to buy sardines for breakfast around 8 am and I was not able to come back until 11 am. I was invited by my playmates to look for spiders since fighting spiders was very popular among kids in our place. My aunt went to fetch me with kakawate twigs and she continually hit me on our way home. The back of my legs was swollen and according to my mother, I also sobbed at my sleep. She cried too.

I think my aunt failed to understand that when you are 5 years old, you do not have a clear concept of time. For me, I was just looking for spiders for a while. Of course, she also failed to understand that she is not supposed to hit somebody’s child.

The Changes in My Beliefs About Intelligence

by Guillermo Bautista Jr. 

My strength in terms of intelligence is logical-mathematical under Gardner’s multiple intelligence. When I was young and naïve, I did not really consider non-logical, non-scientific, and non-mathematical fields as a challenge and did not consider people who chose those fields intelligent. Please don’t hate me.

I first encountered Howard Gardner’s multiple intelligence during my undergraduate studies. I was not convinced by it. It was only in my recent readings that I have accepted that there are other forms of intelligence. In addition, my readings about savants who are very good at one thing and totally useless in other things have also persuaded me that there are different types of intelligence. In fact, I have moved a step further. I am now convinced that intelligence is the ability to combine different types of intelligence to adapt to any environment. Intelligent people are those who can easily adapt to new environment and learn new skills in the shortest possible time.

***

Emotional intelligence is also quite interesting. We see people who are very relaxed and cool under extreme pressure. There people who panic in the littlest of problems. And there are people who can manipulate other people by tapping into their emotions.

Nurture Supports Nature

by Guillermo Bautista Jr.

I came from a poor family and was raised by a single parent who values education so much. The first phrase that probably stuck in my mind before even entering grade school was that “education is important.” My mother would repeatedly say that education is the only legacy that she can give me since she has practically nothing at all. So during grade school, I always looked forward to going to school every morning even though I had to walk around two kilometers. At night, I had to study under the canopy of light emanating from a gasera since we had no electricity back then. Now, I realized that from that very moment, my mother was already nurturing me by encouraging me to study hard as a preparation for my future.

After graduating sixth grade, we went to Manila. My mother went abroad to work in order to support my studies. The new environment was not very encouraging. Some friends influenced me to play video games, so I was distracted. Although I was on the top section during my high school, I forgot the “study hard for your future” phrase. I abandoned studying other subjects except for mathematics.

The reason for this long narrative is to give an example that a nurturing environment can shape a person. The talent of a person can be better maximized if the environment is encouraging and if other persons around then push them to their limits.

Srinivasa Ramanujan, a brilliant mathematician from India is a supporting example of the strong influence of nurture. When he was about 13, he read a book on Advanced Mathematics and discovered and proved theorems which were not proved by mathematicians during his time. His mentor in India discovered that Ramanujan was extraordinarily gifted, so he contacted G. H. Hardy, a mathematician from Britain to train him. Ramanujan solved some of the most difficult problems during his time but he had to attend classes in order to improve and formalize his knowledge.

The moral of the story is although we have gifts from nature, we also need and environment and people to nurture those gifts. For example, studies show that by the age of three, children with professional parents heard 45 million words addressed to them as opposed 26 million words of working class kids (Lindsay, 2012). This only shows that some children are already at an advantage very early in their lives.

To conclude, nature is a gift but nurture will make the most of those gifts. We may have extra gifted genes, but we need people to nurture us. That’s why nature and nurture share the responsibility of shaping us to who we are and will continue to shape us to who we will become.

References

Lindsey, B. (2012). The Real Problem With Helicopter Parents: There Aren’t Enough of Them. The Atlantic.

Kanigel, R. (2016). The man who knew infinity: A life of the genius Ramanujan. Simon and Schuster.

Welcome to my blog in EDS103

Hi everyone. I am Guillermo Bautista, a student at the University of the Philippines Open University.

This is my blog in EDS103 – Theories of Learning, a course which I am currently taking at the UP Open University. In this blog, I will post my insights and realizations about my learnings in the course. I hope that my posts will help me reflect on my learning habits and teaching practices and in turn will be an instrument for me to become a better teacher. In addition, I hope that this blog will contribute to the learning of readers as well.

Happy reading!