Active Learning Methods in Math field

After coming from Finland I need to read something about the Active Learning Methods in math field.

So I read:

  • Brame, C. (2016) Active Learning,
  • Active Learning in Post-Secondary Mathematics Education, Conference Board of the Mathematical Sciences,
  • Kerrigan, J. (2018) Active Learning Strategies for the Mathematics Classroom, College Teaching, VOL. 66, NO. 1, 35–36,
  • Freeman, S., Eddy, S.L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H. and Wenderoth, M.P. (2014) Active learning increases student performance in science, engineering, and mathematics, PNAS, Vol. 111, no. 23 pp. 8410–8415.

And I conclude that:

Active learning methods are implemented in many situations with very good results.

I am convinced that opting by active learning methods in the classroom, the students fill more inclusive in the classroom and promote the engagement of all student to learn the subject.

In particularly I like a lot the work Brame, C. (2016) since have a good set of strategies that I can run in my classroom: The Pause Procedure; Retrieval Practice; Demonstrations; Think-pair-share; Peer Instruction; Minute Papers; Strip Sequence; Concept Map; Mini-Maps; Categorizing Grids; Student-Generated Test Questions; Content, Form, and Function outlines; Decision-Making Activities; Case-Based Learning; among others. This paper was very useful to produce new ideas for my classroom.

Some of these strategies I do in my classroom last semester, and some of them work very well.

To terminate, I fill that there is not a right way to teach… the solution for the success is to increase the range of strategies in the classroom.


Ethics in Engineering Programmes

On my recent readings, I have found myself keen on the impact that Artificial Intelligence (AI) might have on society, and how important is the introduction of ethics courses in engineering programmes.

Some innovative systems like the Amazon’s surveillance technology, Project Maven, etc, raised important ethical questions about the development and use of AI/technology and rose some discussions with colleagues on the subject. We went back to the question “what is artificial intelligence?”. In fact, we here trying to define the borderline between computational systems that behave intelligently and the ones that behave rationally. We did not find an answer, but it took me back to Alan Turing, the Turing Test and the spheres of activity of AI. The biography of Turing “The Enigma” by Andrew Hodges was the following step and I took the book with me on my holidays. I did not finish it yet (try to guess: the book is boring or the holidays were too short). With this, I am trying to explain why I have not read (yet) the recommended books during the training course, but the choice of the book for my holidays had an important question behind!

Getting back to the relevant question, ie, the need to incorporate ethical and societal implications of technology in engineering programmes, I would like to share some videos from, on Ethics Education.

“A Conversation About Ethics Education: IEEE TechEthics Interview”

“A Conversation About Autonomous Transportation Systems: IEEE TechEthics Interview”

In order to prevent this post to be the most boring of the blog, let me introduce a beautiful version of the great Alan Turing, played by Benedict Cumberbatch.

“The Imitation Game” Trailer


Food for thought and ignorance

As food for inspiration, I place here a couple of videos:

From the first video I retain mostly a few thoughts:

There is inherent importance to wilful acknowledged ignorance – not just accepting that you don’t know something, but accepting that a present lack of knowledge is a required step to attain further knowledge;

As Stuart Firestein says, in today age of Google and Wikipedia, our students don’t require us as teachers just for the data (mobile phones, and soon IoT devices, will provide them with all the facts in the world – some of them will even be true) but they will still need to have the curiosity to search, and find, where their own ignorance boundaries are – and that task is partially ours;

The evaluation may be useful as a learning device if it provides feedback, and incentive to improve, but if we focus on weeding out, weeding out is what we will get.

I consider this second video matches well with the first, for “not being THE expert” means also to discover (and accept) our personal ignorance, and to act on it also by learning from our students.

The Inspiration: How to Move from a Teacher-Centred to a Student-Centred Engineering Education

Since the Bologna Process vocabulary was brought to the daily basis of the Higher Education Institutions in Portugal, around 2005, the shift of Paradigm, from a Teacher-Centred Education to a Student-Centred Education, was considered deemed necessary. The problem was: what is a Student-Centred Education? Teachers started to find their own definitions giving more study-work at home, more assignments, more group work, among other methodologies, but suddenly realized that the claimed shift of Paradigm apparently didn’t happen… what was then a Student-Centred Education?

It was with these doubts and mind confusion that I arrived Proakatemia in February 2018. During 15 days I was subjected to an amazing Kafkian Process, Mind Deconstruction, Emotional Breakdown and gradually started to Trust the Process and to understand the Power of Active Learning and Team Work Learning… a blink finally appeared in my mind showing the light towards the path to understand what is truly a Student-Centred Education. Ok, I was inserted in a learning environment for Team Entrepreneurship and Leadership… but can the models and tools I’ve learned be applied in Engineering Education?

It was this question the basis for my agile experiment during the spring when returning to IPB, which resulted on The Plan shown in Tabula, reflecting the desire to shift the teaching/learning process from a Teacher-Centred approach to a Student-Centred Learning environment. To support this shift some reading was necessary. One of the recommended readings is that from Catalano and Catalano [Catalano G.D., Catalano K.C., Transformation: From Teacher-Centred to Student-Centred Engineering Education, Journal of Engineering Education 88, 1999, 69-64]. From the publication year it was clear that the subject was not new, but it was to me, so I started my journey…

I found that the key challenge is to promote the full engagement of the students in active learning methodologies, which are robustly documented to be more effective in the learning process than passive classical methods. Calvano and Calvano compared both approaches and suggested specific activities for teachers who wish to explore the shift in their classrooms. While in passive-teaching methods the students only need to perform timely quality-control inspections (evaluation moments), in active-learning methods, the creativity and full potential of the students for learning are maximized. Among several methods, team work and team building were incorporated in My Plan.

To enable the shift from a Teacher-Centred approach to a Student-Centred Learning environment, teachers have to gain new roles and to develop coaching skills, namely model thinking/processing skills to facilitate student exploration/growth, defining the cognitive level of the students, implementing inquired-based and mind-mapping strategies to consolidate information and to develop new insights, implementing group-learning and peer-learning settings for higher students involvement and responsibility, having the capacity to use analogies and metaphors to allow learning hard engineering concepts and to create the capacity to tolerate failure (and to learn with it).

Another important challenge in a Student-Centred Engineering Learning approach is the required assessment. Although diversified assessment tools can be used, by comparing the performance of students under the two different educational approaches to perform classical exams, it is concluded that the Student-Centred Education approach leads to better results than the Teacher-Centred Education (or at least doesn’t penalize them on standardized exams).

As final remarks it should be taken into consideration that a shift from a Teacher-Centred to a Student-Centred Engineering Education will face the resistance of some students that prefer passive learning (more comfortable) than active learning (responsiblization of their learning process), the resistance of some colleagues that judge a student-centred model as having lack of rigor and will face the resistance of ourselves, since we are afraid to lose the control of the class to be apparently only an observer of the learning process…

I am convinced this is the way Education should move and the time to shift has come… are you also convinced?

Inspiration : Book “Drive – The Surprising Truth About What Motivates Us”

Daniel H. Pink

Daniel Pink suggests that the world currently does not acknowledge one of the human drives that motivates us in the twenty-first century. Pink argues that there is a third drive that motivates people, one that is actually hampered by rewards and punishments.

Pink summarizes Harry F. Harlow’s 1949 experiment on primates, which found that the ability of monkeys to solve puzzles was inhibited by rewards and punishments. Harlow posited that the performance of the task offered an intrinsic reward. His research into motivation was largely ignored, and motivation systems based on rewards and punishments continued to thrive.

Carrots and sticks, or Motivation 2.0, fail to motivate people in the twenty-first century.

Employers and supervisors will get better results by adopting strategies that take into account the third drive. “[T]he ingredients of genuine motivation,” he suggests, are “autonomy, mastery, and purpose.” Allow workers to strive towards mastery, and they will do better work. The tendency to focus on short-term goals and to take shortcuts will be reduced. After all, “goals that people set for themselves and that are devoted to attaining mastery are usually healthy.” In contrast, goals imposed by others—such as sales targets, quarterly returns, and standardized test scores—”can sometimes have dangerous side effects.” Pink suggests that both Enron’s collapse and the American recession can be attributed to the short-term thinking that comes from Motivation 2.0.

Autonomy is distinguished from independence and the “rely-on-nobody individualism of the American cowboy” because autonomy emphasizes choice. It is not necessarily opposed to interdependence. Pink argues that autonomy is a part of human nature. Pink argues that autonomy is the opposite of control.

Pink turns his attention to another element of the third drive: purpose. Pink argues that the pursuit of purpose is a part of the third drive, and that it is no surprise it is manifesting itself in the twenty-first century. Under Motivation 2.0, there was no need for a purpose beyond the profit.

Pink offers advice to people that want to align their lives with the third drive. He suggests a number of strategies to help people examine the way they live their lives and identify ways to achieve “flow.” For example, he suggests that people try to summarize their life in a sentence. He also advises people to adopt strategies that will allow them to bring mastery into their life.


‘Explore to Inspire to Transform’

A Journey to the 21st Century Education

This video sparked my curiosity about reading the book ‘A Journey to the 21st Century Education – This is how the world´s most innovative schools work’.


A book that has allowed me to discover new educational opportunities (methodological enrichment, culture of thinking, authentic evaluation, potential learning spaces…) and new methodologies (personalised learning, design thinking, cooperative learning, project-based learning, learning communities…) through examples from the world’s most innovative schools that can help transform education.


A school21 is a personalised learning community that acts, changes, and grows, one that is attentive to the present, to research and to both global and local realities. It teaches each student to live, to carve his/her own identity, and to discover and transform the world of the 21st century (Hernando Calvo, 2015, 22).


Hernando Calvo, Alfredo. (2015). A Journey to the 21st Century Education - This is how the world´s most innovative schools work. Madrid: Fundación Telefónica. Retrieved from 

Fundación Telefónica (01/02/2017) 'Viaje a la Escuela del Siglo XXI’, de Alfredo Hernando (English). Available in

Hernando Calvo, Alfredo. (2013) Escuela21. Available in


“Inspiration exists, but it has to find us working.”

Pablo Picasso

             I would like to begin this task reflecting on that quote of Pablo Picasso. Many people think “inspiration” as being mystical and somehow supernatural thing. For me, inspiration is the alignment among desire, will and action. A mind walking in search of solution will find ways to get there.

            I decided to study more about The Dialogue because I understand the Dialogue is the most effective educational tool ever invented by mankind. Sure It’s not something new. However, the Dialogue has been forgotten in recent times.  It’s must bring this practice back in education.

For talking about the Dialogue is must remember Socrates and his Maeutics. (By the way, I had a honor to watch a very good class of profa. Maria Augusta Romão da Veiga Branco about Socratic Maieutics in the beginnig of this semester. I learning a lot, thanks, Augusta!)

            Therefore, my inspiration starts with the Socratic Dialogue concept as a cooperative work based on asking and answering questions to stimulate the critical thinking  and to draw out ideas and find  the truth.

Now we live in the world of complex systems, it is not possible to solve problems alone. It is must to think together and the Dialogue is a suitable method for thinking together. For that, Willian Isaacs gave the title “The Art of Thinking Together”  to  his book about the Dialogue.

            For Willian Issacs, the definition of the Dialogue is precisely “to think together”. Therefore, I decided to read the book “The Art of Thinking Together” with the objective of extracting ideas to introduce the Dialogue as a educational tool in my classes and also to get insights on how to develop this important skill:  to think together to solve complex problems.

            I’m convinced that thinking together is a Professional key competence, but it is not properly encouraged and learned during education time.

            Already at the beginning of the book, Willian Isaacs presents a very strong and poetic image associating the ancestral talking around the fire with to thinking together.

The second thing I learned from Willian Issacs: Debate is diferent to Dialogue .





Although both use critical thinking as a tool, the purposes are different. The Dialogue as  it said before, aims to find the truth, build knowledge, share thought, while the debate aims to establish the best argument, then at the end of a debate there will always be winners and losers.

            In my opinion this is the trap of current education. We have prepared our students to be “fencer” of ideas, but not a collective thinkers.

            I recommend the article of Liz Karagianis based on Isaacs book that emphasizes the Dialogue “is essential to solve the large problems of a multicultural, global society”. Can you see it in:


            In the RoadtoPeace Blog,  dedicated to researching the origins of terror toward eventually enabling dialogue among people, I found  a simple, and meanfull concepts about levels  of communication:

            The levels of communication are: 

  • Edict (one way, master and slave, only recourse is violence),
  • Argument (emotions prevail, a winner and a loser or two losers, violence possible),
  • Debate (most logical case wins, in eyes of third parties),
  • Dialectic (seeks compromise, both sides give and agree), and
  • Dialogue (earnest, mutual search for “truth” in harmony as well as it can be known; partnership in mutual interest results.)

            If you want more, you can visit:

                        How does the Dialogue process work? William Isaacs states four elements  are needed. These elements are “mental states” wich dynamically produce dialogue. They are:

LISTENING — We must listen not only to others but to ourselves, dropping our assumptions, resistance, and reactions.

RESPECTING — We must allow rather than try to change people with a different viewpoint.

SUSPENDING —We must suspend our opinions, step back, change direction, and see with new eyes.

VOICING —We must speak our own voice. Find our own authority, giving up the need to dominate.

In order to create a efective process of the Dialogue is required exercise, practice, training and … perseverance!

            The following figure summarized the route of the Dialogue in the Willian Isaacs view:

Source: Isaacs, William. Dialogue and the Art of Thinking Together: A Pioneering Approach to Communicating in Business and in Life. New York: Currency, 1999.

            Finally, what is the first requirement to establish the dialogue process in the classroom? Many people can disagree with me, but I think it’s must bringing people together in a circle. So how about we change the layout of our classrooms as a firts step?


Essay – Designing Powerful Professional Development for Teachers and Principals


Title:Designing Powerful Professional Development for Teachers and Principals

Author:Dennis Sparks

Editor: National Staff Development Council

Retrieved from:

The book presents an important reflection about professional development and changing schools, and describes some strategies and the key steps to improve the quality of professional learning in schools.

The intention of the author is to deepening the reflection about how to make effective changes in workplaces. He thinks that many research studies, reports, articles and books have been published, but, unfortunately, seldom surpasses marginal improvements in the quality of professional development in schools. About that, the author highlights that “tinkering around the edges of improvements in staff development is insufficient” (Sparks, 2002, p. i.i).

The text intends to promote, among educational leaders, a more detailed and fine-grained vision of professional development, deeper understanding of standards-based professional learning, clarity regarding next steps, and a sense of accountability for implementing improvement plans. It also aims to stimulates discussion and dialogue over a period of weeks and months by leader groups in the workplace. It is assumed that changing the practices is an ongoing process that needs time, reflection, ripping on suspension, and action to be successful. It is not only a mere application of strategies. It needs professional awareness and conscientization (Freire, 1999). Another assumption is that principals, school leaders and teacher leaders are key people to change the organizations.

The book is intentionally designed as a guide for readers, not for a simple reading but to enable them to deepen the engagement, discussion and intensity of motivation, provided by a study group.

The book is divided into five parts, with each part containing several chapters. In the end of each chapter, the author proposes some assumptions and reflection-questions. The parts are

(1) Set the Stage for Powerful Professional Learning;

(2) Provide a Supportive Context;

(3) Develop School Leaders;

(4) Develop Teachers; and

(5) Get to the Heart of the Matter.

Part I:Set the Stage for Powerful Professional Learningprovides a rationale for sustained professional learning, discusses the advantages of stretch goals and deep change, and offers a detailed description of what new forms of professional development might look like in schools.

The parts II, III IV and Velaborate on the types of professional development for teachers and principals that produce high levels of learning and performance for all students and staff members. The chapters they contain describe ways to:

  • Surround teachers and principals with a culture and support them with structures that encourage professional learning, innovation, experimentation, and the collegial sharing of new ideas and practices;
  • Engage teachers and principals in professional learning that is standards-focused, intellectually rigorous, part of their daily work, and continuous;
  • Deepen teachers’ knowledge of the content they teach;
  • Expand teachers’ repertoire of research-based instructional skills to teach that content;
  • Provide ongoing classroom assistance in implementing new skills;
  • Create small teams of teachers who meet several times a week to plan lessons, critique student work, and assist in problem solving, among other tasks;
  • Provide teachers with the classroom assessment skills that allow them to regularly monitor gains in student learning resulting from improved classroom practices;
  • Connect teachers to teachers within and beyond their schools and to outside sources of knowledge and skill; and
  • Overcome the underlying problems that serve as significant barriers to the widespread use of the practices described in the book

As learning tools, the book highlights the role of dialogue as a strategy that can strengthening the understanding of a subject. The author, based on the book by Daniel Yankelovich, The Magic of Dialogue: Transforming Conflict into Cooperation (1999), mention that dialogue induces a rigorous discipline on the participants, includes equality among them, an absence of coercive influences, listening with empathy, and bringing assumptions into the open while suspending judgement

Another important assumption that I retrieved from the book was that the role of the leader is not to tell teachers what the best practices are, but to create opportunities for educators to discover them for themselves.

Coachingis about building capacity, motivation, and commitment to engage in improvements. It is important to understand that it is not so much the processes that worked elsewhere that needs to be replicated, but the conditions under which they worked (Fullan, 2001 p. 191). A deep understanding of local context and culture are critical to successful change efforts.


Cristina Mesquita Gomes


The Circle of Safety

My name is Hermanni and I’ll be joining you at the end of this month in Braganza as an Assistant Coach to Hanna. And, as you might be able to see from the title, there might be a trend in books written by Simon Sinek around this team learning method.

A few weeks ago, as I was finishing my Team Master-training in a beautiful setting of an old farmhouse in Central Finland, we sat in a circle with a group of people (teachers, principals, entrepreneurs) I had not known 2 days before. We sat in that circle and we cried, because we were coming to an end of something meaningful and important. We cried, because we didn’t want it to end. But, at the same time we cried from the joy of having shared that experience.  We cried in front of strangers, because we felt safe enough to do so.

Team Master was 1 year program focused on the coaching and team learning mentality and practicality. On the last session, the topic was the Coaching Character. Who are we as coaches, what is our approach, what is our mentality? In those two days we had explored the deepest parts of our personas, both work and civil and created a new image of ourselves as coaches. In words and thoughts, we were reborn.

All of this was made possible because in those Team Master sessions we share a deep trust towards one another. It is a haven, where no one will be judging you based on your results. You are not graded, branded, classed or divided into groups based on your skill. We face each other with an open mind and listen to what the other wants to say. And because of that safety, we are able to openly explore new ideas, new theories and learn new things.

Being afraid takes a lot of energy. Suppressing ideas takes a lot of energy. A culture that drives you into groupthinking, where no one is brave enough to have a different opinion is the recipe for doom.

All of this came together as I was reflecting on my soon-to-end journey as the CEO of our company and took form as one of the three core principles in my Character as the quote from Tootic from the moomins:

All things are so very uncertain, and that’s exactly what makes me feel reassured.

Thats the kind of trust that I want to cultivate in my teams. A trust that even when everything else changes around you, you still trust the that the team will manage to find its way. And that kind of trust is exactly what Simon Sinek explores in his theory of The Circles of Safety.

Why do you get up in the morning? – and other questions related to my favourite “Start with WHY”

…I always like – and need – to start with a why 🙂

Here are couple of videos that explain the why thing. The other one is in English (5 minutes), the other one has Portugese subtitles but it is longer (17 minutes).

I understand the word ‘buy’ as willingness to participate, motivation to learn, and the word ‘customer’ as a student – and a ‘great leader’ as a great teacher, leader of the learning process. Do you agree?