Learnings from EDS111: Principles of Teaching

The learning from this course enhanced my knowledge about the teaching profession. I am probably one of the students in this course who have appreciated the theories very much. My background is pure mathematics and during the early years of my career, I did not really believe that I needed courses in education to be able to teach effectively. The discussions during a 1.5-year training program abroad made me realize that I needed a background in education to be an effective teacher, that is why I enrolled in PTC. In a recent conversation with a former colleague, he told me that I was good in teaching. I just replied that I was not really teaching during that time. I was only talking in front of my students.

One of the realizations that I have is that teaching is complex. There are numerous variables to consider when you teach. You have to consider the students cognitive levels, the students’ background, the curriculum, the theories of learning, the content, the pedagogy, etc.

The Most Important Concepts Learned

Out of the numerous topics that we have discussed in this course, the ones that particularly struck me are technological, pedagogical, content knowledge (TPACK), reflective teaching, and deBono’s thinking hats.

TPACK is important because it is the only thing that the teachers have control of. Teachers cannot control the learning environment, the school policy, or the number of students, among many others. But teachers with strong TPACK will be able to use them to his/her advantage. Among TPACK, I still maintain that a strong content knowledge is the most important. No amount of technology and pedagogy can cure a teacher with a weak content knowledge.

Reflective teaching is also one of the things that I appreciate in this course. I think this calls for attention because a lot of teachers are so overloaded that they do not even have time to reflect on their teaching. Personally, I have also neglected this in the past. I have been too engrossed with the content that I have forgotten think about the other aspects of teaching.

Lastly, I really like de Bono’s 6 thinking hats. I think it is a good framework for analyzing teaching practices. If we combine this with the four reflective lenses discussed in Module 1, then teachers will have a strong framework for looking at their teaching practices from multiple perspectives.

What now?

I will particularly use the knowledge in TPACK as my field as one of my interests is the integration of technology in teaching mathematics. The TPACK will give me a framework in making activities in my lectures on the use of different software in teaching mathematics. I will also use the deBono’s thinking hats in reflecting on the professional development projects that our institute is currently doing.

The learning that I gained in this course gave me a stronger pedagogical knowledge that I lack during the early stage of my career. I still plan to continue my studies in education after my this course (PTC) in preparation for a PhD degree in mathematics education.

Thank you Teacher Roja for your efforts in teaching us.

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Is it Really Creativity?

I personally believe that we are a creative people. Our numerous wins in World Championship of Performing Arts and many other competitions in the arts, particularly in music and dance, show how much of an artist we are as a nation. Being an artist and being good at it is a sign of creativity.

Creativity should be encouraged as early as possible. From the time that the children begin to speak, they should be encouraged to be creative. Creativity should also be taught in the classroom where students will spend much of their adolescent life.

Creativity however is usually associated with the arts and sometimes overemphasized in the classroom. I distinctly remember my teacher when I was in elementary school who scoffed because of the plain label of the folder that I submitted. When she received the folder, she said “Wala man lang kadesign design to.” She took her colored pen and traced the border of the letters to make it more colorful. From then on, I spent a considerable time designing folder labels every time I submit a projects and portfolios in a folder.

That was a long time ago, but things have not changed, really. In around 90% of the mathematics classes that I have observed, at least one group of students will have a cartolina designed where their solutions are written. Out of curiosity, I once asked a student what was the design for. He answered that designs are given credits. I even observed a math class where a student in the entire duration of the group work (around 20 minutes) spent her time cutting art papers for the border design and not participating in the discussion about the problem. She was entirely in her own world of cutting and did not show any sign that she was listening to the discussion. But is designing such as in the examples above can be considered creativity? What is creativity really?

Sternberg (2006) argues that creativity involves thinking that is aimed at producing ideas or products that are relatively novel and that are, in some respect, compelling. As we can see from Sternberg’s definition, the idea or product must be relatively new. In the case of students, it should be new to them even though it might not be new to the teacher and older people. In an earlier publication, creative work requires three abilities according to Sternberg(1985). These are

1.) Synthetic ability – the ability to generate novel and interesting ideas
2.) Analytic ability – the ability to critically analyze and evaluate ideas
3.) Practical ability – ability to translate theory into practice and abstract ideas into practical applications

As we can see, cutting the cartolina and making designs is not really a creative work. What is more dismal is that it has no purpose at all and it is not related to the lesson. Creativity in the mathematics classroom could be seen in the novelty of the students’ solutions to problems. If teachers give extra credit to designs, then students would be distracted and would spend their time designing cartolinas rather than learning mathematics. Creating these designs require time – time that they should be spending in learning mathematics or other subjects for that matter.
Designing maybe a sign that a student is interested in the arts, but the subjects being learned should not be sacrificed.

Art has its own place in the curriculum, we should spend time learning it, but we should not learn it in other subjects and call it “creativity.”


Kaufman, J. C., & Sternberg, R. J. (Eds.). (2006). The international handbook of creativity. Cambridge University Press.

Sternberg, R. J. (1986). A triarchic theory of human intelligence. In Human assessment: Cognition and motivation (pp. 43-44). Springer Netherlands.

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On the Continuous Learning of Teachers

by Guillermo Bautista Jr.

You probably hear phrases like “continuous learning” and “lifelong learning” in teacher discussions, conferences, or trainings, but it does not actually happen in reality (at least in mathematics). In almost every teacher training in mathematics that I have attended or conducted, teachers would always say that they do not know a particular topic because they are not teaching it. Although this admittance is a form of humility, in my opinion, this is only acceptable if you are teaching higher mathematics in college or university, but I personally think that teachers in high school should have a good grasp in every subject whether it is Algebra, Geometry, Probability, or Basic Calculus. Costa(2008) argues that

To ensure high quality of instruction in the academic disciplines, we must continually deepen our knowledge of the structure and organizing principles, modes of inquiry, and habits of mind that distinguishes that discipline.

A deep knowledge in mathematics, or other subjects for that matter, will let us have a wider perspective on how to teach the subject. For instance, in the case of mathematics teaching, one of its strengths is to be able to show students the connection among the different subjects even from different grade levels. For example, if you are teaching about triangle similarity in Grade 9, you should at least be able to connect the topic to proportion which is discussed in the elementary school level as well as the trigonometric functions discussed in Grade 10 and Grade 11. Teachers must be able to relate the similarities and differences between triangle similarity and triangle congruence and relate these concepts to transformation and dilation. Not knowing these connections will only show the students that mathematics is a fragmented subject.

The point of the discussion is that we teachers must continue learning in order to strengthen our content as well as their pedagogy. This can be done by reading books, watching video lectures (there are thousands of them in Youtube), attending trainings and seminars, or joining a professional learning communities.


Costa, A. (2008). Teachers as Continuous Learners. Retrieved June 15, 2017, from https://www.nesacenter.org/uploaded/conferences/FLC/2011/handouts/Watts/Teachers_as_Continuous_Learners.pdf

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Activity 4 Part 2

by Guillermo Bautista Jr

Hi everyone. Here’s my answer for Activity 4 Part 2. I hope you enjoy.

a. How would you describe your teaching perspectives prior to your reading of the module resources? How would you compare your prior conceptions about learning and teaching to the ideas discussed in the resources of this module? What factors influenced your conceptions about teaching and learning?

Before reading Module 4, I was a person who would probably ignore the social and emotional aspects of teaching and learning. I was mostly concerned about the cognitive part of teaching and learning and my interest was finding the best way to teach a particular topic so that students can maximize their learning. I think this perspective originated from my background in pure mathematics where rigorous cognitive training was given the utmost importance.

Resource 2 which is about Social-Emotional Learning widened my perspective about teaching and learning and its affective side. Now, I know that teaching is not just about the knowledge that students learn but also about the environment as well as the social and emotional aspects of students which include as self awareness, social awareness, relationship management, and many others.

b. Have your perspectives’ changed after studying the module resources? How or how not?

Yes, my perspectives have certainly changed. First, reading about the contemporary theories of learning made me realize that teaching is the most complicated job. Second, Resource 2 which is about social and emotional learning is new to me. I learned that teachers have to consider both the emotional and social aspects of students’ learning in order to maximize learning in the classroom. I will particularly re-read and refer back to the 10 teaching practices that promote students’ learning in my future teaching endeavors.

c. How willing or open are you in challenging your prior conceptions about teaching and learning, and applying contemporary teaching perspectives and approaches that would better serve the need of the students for more holistic and active learning?

I am very willing to learn new conceptions that will improve my teaching. Maybe, if I have read this module 10 years ago, I would probably shrug them off and say no. But having 15 years of teaching experience prior to reading the modules made me appreciate the theories because I can relate many of them to my teaching experience. I am certain that I will read more and will reflect on how these new learning can be integrated to my work as a teacher.

d. Which among the contemporary teaching perspectives and approaches discussed in this module resonates with you? Why?

Cognitive constructivism is one of the teaching perspectives that I am interested. I agree that students construct their own meaning of the knowledge we teach in the classroom (Wilson & Peterson, 2006). That means that if we have 30 students, the worst case scenario is 30 interpretations.

The cognitive constructivist perspective is important because it shows that teachers need to create an environment where they can clarify students’ thinking. This means that teachers need to make students think and communicate their thinking to the class so that the whole class can agree or disagree if the thinking is correct. It is the teachers job to mediate these discussions.

e. Knowing your inclination for specific teaching perspectives, how can you ensure that you will not fall into the trap of a one-size-fits-all teaching and that you will observe the teaching principles as intellectual and varied work – “adopting appropriate teaching roles to support learning goals” (Eberly Center, 2015)?

Knowing that teaching is a varied work reminds me to use different strategies grounded on theories of learning, experience, students’ abilities, and other factors. With the further reinforcement of my constructivist frame of mind, I know that there is no single way to teach effectively.


Wilson, S. M., & Peterson, P. L. (2006).Theories of learning and teaching: What
do they mean for educators?. Washington,DC: National Education Association.

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TPACK Explained in the Context of Quadratic Functions

by Guillermo Bautista Jr. 

In this post, I am going to use quadratic functions as a context to explain TPACK. The purpose of this post is to clarify ideas about the relationships among content knowledge, pedagogical knowledge, technology knowledge and all their possible combinations.

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Content Knowledge (CK) is the knowledge about the subject matter. For example, if the topic in mathematics is quadratic functions, a teacher with deep content knowledge should know about its definition, properties, and applications. The teacher should also know how to represent the quadratic function verbally, numerically, algebraically, and graphically and should know how to solve and identify the roots of quadratic functions using different representations.

Pedagogical Knowledge (PK) is the teacher’s knowledge in the methods and processes of learning. In teaching quadratic functions, teacher should know that students would be able to make deeper connections if mathematical concepts are represented in different ways.

Pedagogical Content Knowledge (PCK) is the combination of the content and pedagogy. A teacher with a deep pedagogical content knowledge should know that quadratic functions should be taught in different representations namely numerically, verbally, graphically, and algebraically.

Technology Knowledge (TK) is the teacher’s knowledge about the tools that can be used to teach quadratic functions. The teacher should be aware that there are graphing software and computer algebra systems that can be used to teach the said topic.

Technological Content Knowledge (TCK) is the teacher’s knowledge about how technology and content influence each other. The teacher should know about the advantages of some software over the others in a particular context. The teacher should be aware that even though graphical representations can explain functions, they do not capture the entirety of the function. For instance, a graph shown in a window, no matter how large, is only a portion of the function.

Technological Pedagogical Knowledge (TPK) is the teacher’s knowledge that learning can change depending on the technology used. During the time when blackboard was the only visual to teach graph, drawing graphs are the highlights of the lesson. Now that graphs can be constructed instantly students should be able to know the effects of parameters among graphs.

The Technological and Pedagogical Content Knowledge (TPACK) is the teachers’ ability to combine the knowledge above to deliver effective teaching.


M. (2012, September 24). TPACK Explained. Retrieved May 30, 2017, from http://matt-koehler.com/tpack2/tpack-explained/

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What is a professional teacher for me?

by Guillermo Bautista Jr.

I took note of my view of teacher professionalism before reading Module 2. Below was what I wrote about my view of professional teachers.

Professional teachers are those who are expert in their field both in content and pedagogy and those who contribute to the existing body of knowledge through research and publications.

The definition above sets some criteria for professionalism, so that means that not all teachers can be considered professional.

My view about teacher professionalism is quite similar to the criteria for professionalism mentioned in the module particularly its measurement by the best and highest standards ((Phelps, 2003) as cited in the module). It was not clear in what I wrote above whether I prefer old professionalism or transformative professionalism, but after reading about them, I realized that my view is geared toward the transformative professionalism. I believe that teachers should be empowered in making decisions about their teaching, curriculum materials development, and they should be involved in policy-making and curricular decisions. One of the most important things that teachers should also do is to be involved in research and professional development projects to be able to contribute to knowledge. The knowledge can be new which could be published in journals or local theories that could be shared with fellow teachers. This criterion was mentioned as knowledge building by Sach (2003) as cited in the module.

After all the readings, I would like to revise my definition above. Here is my new definition of a professional teacher.

Professional teachers are those who are experts in their field both in content and pedagogy and they contribute to the existing body of knowledge through research, publications, and development of local theories. They serve as a role model in the community. They should be collaborative and collegial, responsive to change, policy-active.

This view encompasses the expertise of teachers in terms of content and pedagogy, their involvement in the community, as well as in policy making. I would like to be this kind of teacher. Every step I make is continually preparing me to be this kind of teacher.

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My realizations about reflection

I have realized a lot of things after reading Module 1. When I did Task 1 Part 1 of Activity 1, I noted my definition of reflection before reading the module. My definition was as follows.

Reflection is thinking about an event and analyzing why it happened as well as its future consequences.

My definition has some similarities with the definition in the text. Moon(2005); for example, defined reflection as a form of mental processing that we use to fulfill a purpose or to achieve some anticipated outcome. She also mentioned that reflection is used to gain a better understanding of complicated ideas.

Below are some parallel words and phrases between Moon definition and explanations and mine, respectively.

mental processing – thinking
gain better understanding –analyzing
fulfill a purpose – consequences

One of the most important things I learned from this module about reflection is putting yourself outside a situation and looking at that situation from multiple perspectives gives you a better understanding of the situation at hand.

After all the readings, I decided to adapt Moon’s definition as it is more general and more encompassing.

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