I totally agree with such approach. I am firmly convinced that student thinking is a fundamental part of the learning process.
Additionally, I do observe the pedagogical principles stated in George Pólya's 1945 book How to Solve It. In general terms, Pólya suggests the following steps when solving a mathematical problem:If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem?"
Another scientist that has much influenced my way of teaching is Richard W. Hamming. (By the way, Hamming is one of the scientists I admire the most.) In his book Numerical Methods for Scientists and Engineers, Chapter "N+1: The Art of Computing for Scientists and Engineers" opened my eyes even more. Hamming suggests the following thread of questions when thinking about a problem:
Often students pose questions. I believe that giving plain answers is wrong. As an educator, I try to establish a dialogue, returning to the students a sequence of easier questions, which they are hopefully able to answer. I try to guide them through their own answers. By the end, the original question is answered by themselves. Reading Plato's Dialogues and similar literature directly influenced my views on this matter.
I am an outspoken admirer of Professor Richard Feymann. It is impossible to deny the significant amount of influence his books, lectures, audio/video recordings, etc have cast on me. For sure, I deeply admire his teaching style (if there is such a thing), his way of looking at nature, and his free spirit. To some extent, I try to convey these feelings to my students.
I am also indebted to Dr Ricardo M Campello de Souza's way of teaching. As a student I attended to at least four courses taught by Dr Campello de Souza. During these courses, I have learned much about answering a question with another question.
Dr Fernando M Campello de Souza's lectures also influenced me. In particular, his way of conducting a lecture, and making the blackboard uncopyable. The rationale is: students should consult good textbooks and appropriate references, not digests or blackboard notes.
Dr Martin P Mintchev has also his share of influence. My constant demand for professionalism and quality of presentation was learned from him.
And last but not least, a great deal of my way of viewing science and research is due to Dr De Oliveira advices and guidance through years of collaboration as one of his graduate students. Dr De Oliveira enthusiasm and motivation is inspiring. His magnetic lectures certainly had influenced me.
List of former students from regular courses.
Letters from former students. / Cartas de ex-alunos.
Collected texts about the prospective career as a statistician. Intended audience: Undergraduate students in Statistics.
Course Politics and Classroom Etiquette [Política do Curso e Etiqueta em Sala de Aula]. Intended audience: Undergraduate students.
The Fist Bank of Flatland was founded in Dec 1, 2010 and is in good standing.
20??.? - Processamento de Sinais (Signal Processing) (Undergrad course)
20??.? - Processamento de Imagens (Image Processing) (Undergrad course)
20??.? - Teoria da Informação (Information Theory) (Graduate/Undergrad course)
20??.? - Estimação Espectral (Spectral Estimation) (Graduate/Undergrad course)
20??.? - Sinais e Sistemas Probabilísticos (Random Signals & Systems) (Undergrad course)
2017.2 - EE960 - Topicos em Comunicacoes 1 (Topics in Communications) (Graduate course)
2018.1-2018.2 - Sabbatical leave at University of Calgary
2017.1 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2016.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2016.1 - EE925 - Processamento Digital de Sinais (Digital Signal Processing) (Graduate course); equivalent to "PGE971 - Processamento de Sinais (Signal Processing)"
2014.2-2015 - Sabbatical leave at INSA, Lyon, France
2014.1 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2014.1 - PGE952 - Seminários de Pós-graduação (Seminars) (Graduate course)
2013.2 - PGE960 - Séries Temporais (Time Series) (Graduate course)
2013.2 - EE925 - Processamento Digital de Sinais (Digital Signal Processing) (Graduate course); equivalent to "PGE971 - Processamento de Sinais (Signal Processing)"
2013.1 - IF311 - Métodos Numéricos (Numerical Methods) (Undergraduate course)
2013.1 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2012.2 - PGE971 - Processamento de Sinais (Signal Processing) (Graduate course)
2012.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2012.1 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2011.2 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2011.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2011.1 - PGE960 - Séries Temporais (Time Series) (Graduate course)
2011.1 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2010.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2010.2 - ET589 - Introducção à Optimização (Introduction to Optimization) (Undergrad course)
2010.1 - PGE971 - Processamento de Sinais (Signal Processing) (Graduate course)
2010.1 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2009.1-2 - Sabbatical leave at University of Calgary, Canada
2008.2 - PGE971 - Processamento de Sinais (Signal Processing) (Graduate course)
2008.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2008.1 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2008.1 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2007.2 - ET589 - Introducção à Optimização (Introduction to Optimization) (Undergrad course)
2007.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2007.1 - PGE971 - Processamento de Sinais (Signal Processing) (Graduate course)
2007.1 - ET592 - Processos Estocásticos (Stochastic Processes) (Undergrad course)
2006.2 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2006.2 - ET610 - Programação Linear (Linear Programming) (Undergrad course)
2006.1 - ET583 - Probabilidade III (Probability III) (Undergrad course)
2006.1 - MES905 - Probabilidade (Probability) (Graduate course)
2005.2 - ET301 - Elementos de Estatística (Elements of Statistics) (Undergrad course)
2004.2-2005.2 - [At Boa Viagem College] Operations Research: Deterministic Models (Undergrad course for Industrial Engineering)
2004.2-2005.1 - [At Boa Viagem College] Numerical Analysis (Undergrad course for Industrial Engineering)
2003.1 - [At University of Pernambuco] Microprocessors (Undergrad course for Electrical Engineering)
2003.1 - [At University of Pernambuco] Electrical Instrumentation (Undergrad course for Electrical Engineering)
2002.2 - [At University of Pernambuco] Control Systems (Undergrad course for Electrical Engineering)
2001.2-2005.2 - [At Boa Viagem College] Operations Research: Probabilistic Models (Undergrad course for Industrial Engineering)