Connectivism and Math Anxiety…

For the past few days, I’ve been thinking about a new philosophy that might aptly describe the generation of today. Millenials and Generation Z’ers are the digital natives we see in our schools and in our streets today, holding their cellphones, always updated on their friends’ activities, taking selfies and posting them, and the list goes on and on. Then, I happen to see an article by George Siemens written in 2005 entitled Connectivisim: A Learning Theory for the Digital Age. Trying to understand the article, I was directed to this paper by Klinger, titled ‘Connectivism’ – A new paradigm for the mathematics anxiety challenge?, addressing a paradigm shift to reduce mathematics anxiety through this theory.

“Connectivism is the integration of principles explored by chaos, network, and complexity and self-organization theories.” Since new information is continually being acquired, it is driven by the understanding that decisions are based on rapidly altering foundation. In connection to learning, some of its principles are that learning and knowledge rests in diversity of opinions, learning is a process of connecting specialized information sources, capacity to know more is more critical that what is currently known, and that ability to see connections between fields, ideas, and concepts is a core skill. Having an accurate but up-to-date knowledge is the intent of all connectivist learning activities.


Now, how will this theory address mathematics anxiety? The author focused on one of its aspects stated thus as “the act of learning is largely one of forming a diverse network of connections and recognizing patterns”. Recognizing mathematics as a language, students may establish a link that would allow a one-to-one correspondence between mathematical concepts and their numerous abilities and understandings of the world. The learners already knows a lot of things around them and utilizing this idea, an approach or pedagogy could be reframed if they are mathematically anxious. Building on the principle that every new mathematics learning activity should be approached from a language perspective, teachers should identify a common base of understanding with which students can connect so that concepts can be discussed more easily before going formal over definitions and symbols. Emphasize that any mathematics that are written and read makes sense; that is, there is connection in either direction, translating mathematics language to the natural language and vice versa.

“Connectivism is the integration of principles explored by chaos, network, and complexity and self-organization theories.”

In addition, new mathematical ideas can be introduced by referring to what the prior of the students are and capitalizing on the non-mathematical everyday domains in identifying parallel or analogous ideas. By creating familiarity to existing knowledge network, the learners will be able to achieve a cognitive phase transition that transforms information into knowledge and eventually, understanding.

Indeed, this addition to the new set of “-isms” invoked that property of network connectivity in understanding complex system, such as a human’s brain. As a teacher, it is my continuing desire to connect new mathematical information to the existing knowledge-base of my students. Nevertheless, more research must be done to explore further this learning theory.



Kolb’s LEARNING STYLE Inventory: The Result

This week is all about determining and understanding what our learning styles are. A self-assessment instrument known as Kolb’s LSI developed by Robert Vroman was answered and voila, you will have a better idea what kind of a learner you are. This questionnaire was designed to describe the way you learn and how you deal with ideas and day-to-day situations.

To the uninitiated, learners according to David A. Kolb can be classified as Divergers (no relation to the Divergent series by Veronica Roth), Convergers, Accomodators and Assimilators. Divergers take experiences and think deeply about them while convergers think about things and then try out their ideas to see if they work in practice. On the other hand, accomodators have the most hands-on approach with a strong preference for doing rather than thinking but assimilators have the most cognitive approach, preferring to think than act.

Personally, I would say that I belong to the assimilators group of learners. In that I thought that I learn best with lectures that start from high-level concepts and work down to the detail. I imagined myself to prefer organized and structured understanding. But after taking the inventory, I realized that I was wrong. Results revealed that I am more of a diverger type – a reflective observer. Look at my learning style grid below.

Learning Style Grid.JPG

Divergers or reflective observers learn best from activities where:

  • there are opportunities to observe and consider;
  • there is time to think before having to act or contribute;
  • there is opportunity for research and problems can be probed in some depth;
  • they can review what was happening;
  • they are asked to produce reports that carefully analyze a situation or issue;
  • there is interaction with other without any risks of strong feelings coming to the fore; and
  • they can finalize a view without being put under pressure.

Examining the results made me realize a lot of things. First, that to learn best, assess yourself honestly to reveal who you are. This will be very helpful in understanding one’s strengths and weaknesses. Second, it is possible that learning styles may change as we age. How we study when we were in our adolescent years may be different now that we are adults. Third, while it is true that we have a dominant learning style, remember that we also learn if we become assimilators or convergers sometimes. There are situations where have to adapt to our professors or leaders to our best advantage. And lastly, as a teacher myself, the pedagogical strategies that I use inside the classroom have to cater to all types of learners. It would be a good idea to determine the preference of my students before the start of a term to adjust to their needs.

Now, what are you still waiting for? Try to take the inventory yourself by clicking this link: KOLB’S LSI, open the pdf, and share the results in the comments section below. Have fun!


Correspondence with Dr. E

TERM B-R-E-A-K means no blogs, right? Partly yes. But then after some hiatus here in wordpress, I have to say I miss flexing my fingers just to share some thoughts related to technology. So after reading two emails from Dr. Peter E of the fame, I’ve decided to share my correspondence with HIM to my “followers” out there. Again, my intentions would be to promote his site plus I am partly bored now… Hehehe… So, here they are.

Aug 18
Good day Dr. Peter,

I am Clem, one of the attendees of your lecture last August 4 at De La Salle. Anyway, I would just like to REQUEST for pdf copies of your researches related to the Flipped Learning Model. My research interests are in technology integration. Kudos to Dr. Bing and madam Minie for the encouragements.
Further, thank you by the way for instilling to us that being a math teacher and using the model requires lots of PASSION. Here is also my blog, although late, about your lecture: I took the freedom to promote your site, too. Hope you won’t mind.
Thank you for granting my request.
Animo La Salle!
Yours truly,
Clem Aguinaldo

Aug 18
Hello sir!

Btw, I just saw the article you wrote on our seminar last August 4.  Thank you so much for the kind gesture and for helping me share my website and youtube channel.  I am sincerely honored and humbled on the things you wrote in your blog.
I am looking forward for more collaboration with you and other educators in the Philippines who would want to have me as a guest speaker to share with them not only my flipped classroom but also my experience as an educator that might be able to encourage other teachers to always push the envelope and go beyond the 4 walls of the classroom.
Here are some of the journals I have published on flipped classroom: [Note: Files were attached instead here…]
If you have an iPad, you can download my iBook from iTunes here. Just to give you an Idea on how I implement FC in my math class:
and a video on YouTube of me showing how I create my own video for my  flipped classroom:
I hope these helps.
All the best!
 Apple Distinguished Educator
math teacher | math instructor
Barstow High School | Chapman University

Aug 19
Dear Doc Peter,

Thanks a lot! May you have a thousand more videos and a million followers to come… When I met my Diff. Equations 4th year students last Friday, I promoted your site and encouraged them even more to spread the word and use them during their internship next semester…
Unfortunately, I was not given any subject next sem at PNU due to our scholarship grant. That means, I won’t be using YET your Filipino version of CALCULUS which I intended to use with our teacher education students in the campus as a possible research study. I will keep on promoting your YouTube channel and numberbender site though…
Again, thank you and more videos to come. God bless you sir.
In St. La Salle,
Aug 26
Dear sir Clem,

Maraming salamat po sa pagsupport nyo sa flipped classroom model and pag gamit sa mga math videos ko online.  I am really grateful na through you eh naiibahagi ko sa mas maraming teachers at students sa atin yung mga ginagawa kong videos.
If makauwi po ako ulit sa Pilipinas, kontakin ko kayo para magkaroon naman ako ng chance na makabisita sa PNU.  Matagal ko na pong gustong mabisita ang PNU, kaso wala naman akong kakilala.  I would love to share my work as a teacher na alam kong pwedeng magamit ng mga future teachers natin sa Pilipinas.
Again, maraming salamat po ulit.  Sana po eh makatulong yung mga research papers namin sa mga gagawin nyo in the future as an educator.
 Apple Distinguished Educator
math teacher | math instructor
Barstow High School | Chapman University

These are all folks. On a side note, the internet really gave us all the chance to communicate with each other even if they are halfway on the globe. Gone now are the glorious days of sending a courier mail using an actual paper and envelope and waiting for months to reach your intended addressee. I miss the actual cards, though. Hehe…
OKAY, back to vacation mode again…

FLIPPED Classroom Model with Dr. Peter Esperanza

[BLOG 12. This is a late blog post, you may call it, but I’m still posting it anyway. :D]

Last August 4, 2017, yours truly together with madam Evelyn were able to attend a lecture/seminar sponsored by the Mathematics Department of the College of Science at DLSU. The title alone would really spark your interest: How to Flip Math Classrooms and Publish Math Lessons Online. Who would NOT be interested to join this free activity?!? WELL, with the busyness of our colleagues, only TWO of us managed to attend. It was a good thing that the activity fit into our “hectic” schedules.

Dr. Peter Joseph Esperanza, an alumnus of the university and currently teaching at Barstow High School and Chapman University in California, delivered an excellent intellectual lecture on flipped learning. Just for the uninitiated, he defined the term FLIPPED CLASSROOM as a model “in which students watch and complete online lectures on the subject matter at home, and use their classroom time to work on problem sets with the help of their teacher and classmates”. HOW COOL IS THAT? Imagine giving beforehand the needed fundamental concepts or ideas about the new lessons through videos. Then, instead of discussing them again inside the classroom, the focus will be more on follow-up activities or some clarifications, if there are. He shared how he started making online videos, uploading them in YouTube, and requiring his students to watch them and take notes prior to conducting his classes the following days. Challenges were shared on preparing the lessons, recording the educational videos and sharing them, as well as some problems encountered during those early days of doing the tasks. But after a while, Dr. E got the hang of it.

What followed next are research projects verifying and exploring the effects of the model on the attitude, perceptions and performance of students who were taught with this model. These completed researches were even presented in France, Germany and UK. Wow!

Now, just out curiosity, you might want to watch two of his videos before I continue…

The first video was done in 2014 while the second one is in 2017! WE really CAN see the improvements, eh! You would also be surprised that there are a lot of tutorials in math he did in Filipino! Now, for me, that was the BEST and moving gesture he did. Giving back to our kababayan students across the globe by dedicating lots of his time explaining topics from the most complex but useful subject, M-A-T-H.

“.. the focus will be more on follow-up activities or some clarifications, if there are.”

With his passion for teaching, he was awarded in 2015 as Apple Distinguished Educator, Barstow Teacher of the Year, and first Filipino-American Community Hero. He shared that even up to this day, with over 600+ clips over there, he continues to make MORE, he never quits and he never plans to stop. Now, that’s the mark of a TRUE educator!

True to his calling, Dr. E even made a website thru a friend from the university so that everyone can access his tons of work, FOR FREE!. Please hold your mouse and click now this link: Feel honored to visit, browse through the videos and more importantly, SHARE SHARE SHARE to every learner out there, young, old and retired, who just wants to learn and appreciate the beauty of numbers once more…

Thanks sir Peter for the inspiration. May there be more teachers like you out there. NOW, where are my lecture notes, Camtasia software, microphone and camera… 🙂

HERE is a snapshot of the site



Technology Integration Seminar: A PHOTOBLOG

[BLOG 11] Just barely three hours ago, my classmates and I with the guidance of our professor, Dr. Maricar Prudente, conducted the TITLE (Technology Integration in a Teaching and Learning Environment) seminar at the Br. Andrew Gonzales FSC College of Education. Majority of our basic education teacher-participants came from Cavite (Thanks to Madam Lea!).

Since the pictures are still fresh from my Samsung Galaxy J7 Prime cellphone, I’ve just decided to post these photographs. At first I thought that “photoblog” or “photolog” as a term does not exist. But using the friendly GOOGLE at my disposal, the term DO exist (!?!). Wikipedia defined it as “a form of photo sharing and publishing in the format of a blog. It differs from a blog through the predominant use of and focus on photographs rather than text. Photoblogging (the action of posting photos to a photoblog) gained momentum in the early 2000s with the advent of the moblog and cameraphones.” And another site named invites web users to share their photos and tell the stories they’re a part of.

Without much further ado, here are the photos I have in my first ever PHOTO-blog.


LUNCH TIME: [Happy happy birthday Madam!]



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So here they are! ‘Till next seminar my friends…

Become a RESPONSIBLE social media user!

Forgive me for the use of an exclamation point (!) in the title. Nope, I am not angry. Rather, there is a tinge of disappointment by how lots of people, including those in the academe, use social media irresponsibly nowadays. First, allow me to jog your memory as to what SOCIAL MEDIA really means and proceed by giving some thoughts, call it preaching or nudging, on how to be on the right track towards becoming the most responsible social media user on the web.

Here is how the net defines the term.


Originally, social media is for sharing one’s thoughts, notes, pictures or videos to update our friends and loved ones about what’s been happening in our lives lately. The intention is not to broadcast to the whole world, except perhaps if you are a celebrity or a public figure, what you do in detail for each moment of your life. Neither is it used as a vehicle to bully someone you don’t like nor as an excuse to engage in an online WORD war against your enemies. On the contrary, it was designed to deepen our friendship with others, to rekindle old memories with acquaintances whom we seldom meet, or to gain even more friends.

Clearly, the SOCIAL part of the term comes first before MEDIA, or the internet, to give emphasis that the jargon was introduced as a way to INTERACT with other persons either by SHARING a wide variety of information with them and RECEIVING information from them as well. As expected, there are many types of social media platforms anyone can use. Social networking, being the most popular type, is one of them along with blogging, podcasting, photo sharing and gaming. Here is the social WEB as a reference.

NOW, back to my goal for this blog: BECOMING A RESPONSIBLE SOCIAL MEDIA USER. Let me be very straightforward by using the first letters of the word R-E-S-P-O-N-D to drive at my point. (Actually, I was just inspired by the acrostics that my son participated in during their nutrition month program…:)

R is for RESPECT. Due respect should be given to other persons’ posts. Refrain from giving snide remarks when we don’t like what we see or read. The old adage still holds in this digital age, that is, RESPECT begets respect.

E is for EXCELLENCE. Not all of us are perfectionists and we do not write using the perfect tenses. However, we should strive for excellence when it comes to the content of our blogs or notes. A helpful suggestion is to READ and RE-READ what we have just typed before deciding to press that BIG ENTER button in the keyboard. But when you are a teacher, you owe it to your students to become a good role model when it comes to giving comments or to just simply posting whatever those brain cells tell you to encode. One advice from our mother’s professor is this: IF IT DOESN’T SOUND RIGHT, THERE MIGHT BE SOMETHING WRONG.

“… let us utilize social media to BUILD BRIDGES and not to CREATE WALLS.”

S is for SELF-REGULATION. Yeah, yeah, yeah, there are no censorship bodies out there to police every post you make. But please, before hitting the OK or Publish button, think again and again about how your peers will react. We don’t have to please everyone I know but we have THE control about how we want others to perceive us.

P is for PURPOSE. Be reflective in using social media. What’s YOUR MAIN AGENDA behind posting the new dress you bought or the sumptuous expensive food you are about to eat? What will you gain from sharing your recent misadventures and problems in public? Again, think before you click.

O is for ORDER. We do not want to create confusion about who we are as a person. To avoid that, be very logical and consistent about what we share regarding ourselves. You present yourself to be a messy person and your friends will perceive you as such. But try to be prim and proper and your “trust” rating will be boosted.

N is for NETIQUETTE. Observe some ethics whenever you post. Ask yourself: “Will anyone’s sensibilities be offended by what I am showing or posting over the net?” We might have that it-is-my-wall-it-is-my-site excuse to justify this behavior but then again, there have to be some boundaries.

D is for DISCIPLINE. C’mmon, your friends have many REAL tasks to do other than just gawk at your memes, problems and selfies every minute. Will ONE or TWO posts be not enough for the day to let others know that you are still alive and doing well? More is less and less is more. Post only what is important and you’ll get more likes and comments. Do it every second and NOBODY will care about YOU anymore. Flooding other’s walls with just your own is SO IRRITATING that some might be tempted to unfollow or unfriend you instead.

SO there you have it. R-E-S-P-O-N-D. Respond to these tips and be the responsible social media user everyone expects to be. And remember this, let us utilize social media to BUILD BRIDGES and not to CREATE WALLS. So go on and POST now responsibly!

Instructional Scaffolding, anyone?

Opening an email from De La Salle had been a habit lately. Waiting for some announcements such as suspension of classes, new schedules of courses and dates of online enrollment, friendly reminders to return overdue books borrowed from The Learning Commons, and of course, LOTS of invitations to attend lectures, workshops and seminars.

Last week is no different. We were invited to attend a seminar-workshop by Dr. Josefina Goodwin, a Science Teacher at the MCS and a Science Instructional Coach at Shelby County Schools, Memphis, Tennessee. The invitation reads:

Do you find that you waive scaffolding a lesson because it seems like a lot of work to do? As teachers, we already have a lot on our plates, so scaffolding may not be at the top of our list. But if you don’t scaffold a lesson, then it’s like teaching a child to ride his bike without the training wheels on. It’s important that we teachers don’t just say “I would like you to study chapters 1 and 2.” We have to give our students the tools to know what to do and how to do it.

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In this session, you will be able to:

  • Describe scaffolding and how it is used in instruction .
  • Look at the different scaffolding strategies and what they look like in science.
  • Visit the Gradual Release of Responsibility Model and define its components.
  • Plan for instruction within the framework of the Gradual Release of Responsibility Model
  • Look at several examples of C-E-R (Claim, Evidence, and Reasoning)  as applied in different areas of science.
  • Utilize new tools and strategies for instruction

This kind of invitation makes you really want to listen to the lecture and learn as much as you can. Dr. Goodwin explained well the two types of scaffolding strategies, GRR and CER, and even gave numerous activities demonstrating how to use the said strategies. Though the discussion focused more on its applications to science, teachers from all subject areas may adopt scaffolding technique to actively engage students to think critically, work independently, and reason out in a very logical manner.

In this age where learners are dependent on the internet (hello Google!) to supply a quick information when it is needed, scaffolding as a strategy would train students to look for evidences and give valid arguments whenever a conclusion or claim will be arrived at. As teachers’ roles are shifting from being mere authorities to facilitators in the classrooms, it would be best to use scaffolding in a wide repertoire of methods where we expect students to take responsibility for their own learning.

How I wish I could share everything that were learned from the seminar but hey, the net offers a lot of articles dealing with this pedagogy. We are free to search activities, materials, sample plans, discussions and forums about instructional scaffolding. Happy surfing!

Here are our pictures during and after the workshop.

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