Research Interest

• I am a lifelong learner and I aim to study, research, and deliver the knowledge and the experiences
  based on teaching methodologies and new findings that have proved to be successful. As you can see from my
  scholarly work provided in my curriculum vitae, I actively participate in various activities that promote
  my continuous professional growth. Considering the teaching process as a learning and researching
  experience, I could say that my contribution and the input in scholarly work have been quite rewarding.
  I have contributed to creating OER-s, activities, and materials that have enriched my teaching, and
  constantly shared with other colleagues in various professional developments, conferences, etc.
  Developing interactive STEM applications activities, and real-life group projects for my students have
  pushed not only my students but also myself to learn more about connections between applied
  mathematics and real life.
• As a researcher, I am interested in finding new methods and pedagogical approaches that help
  understand and deliver mathematical concepts. I see the intersecting between pedagogy and
  mathematics in the topic of proofs and logic in mathematics. While teaching mathematical concepts I
  approach by using the discovery method starting with small observations and operations, then asking
  students to look for patterns, and algorithms procedures and generalize by writing theorems, formulas,
  and conclusions. My intuitive thinking, the need for solving real-life problems, and curiosity often push
  me to research and study more about things that matter. Always researchers are driven to study and
  observe things that matter, whether those problems are immediate or long-term issues. These days,
  because of COVID 19 doctors, researchers, and other health care organizations, are interested and are
  working on collecting data, analyzing, and modeling the spread of the virus to track epidemics and make
  predictions about the progression.
• To prove mathematical statements, and theorems, we use approaches that are motivated by
  philosophical questions and recursively look for consistency in reasoning until all is proven.                                                                                                                                                                                                                                                                              Rapid changes and the technology used for computing have evolved the perspective of learning and applying
  mathematical concepts. It would be helpful to approach the search for new axioms in a scalable way.
  That means that we’re seeking first axioms that resolve certain low-level questions and then proceeding
  to questions of greater complexity. Starting the justification of new theorems by using axioms demands
  more axioms. We know that in reasoning about a given domain of mathematics question of justification
  is successively pushed back until ultimately one reaches principles with no more fundamental
  justification. The statements at this terminal stage are elected as axioms and the subject is then
  organized in terms of derivability from that base.
• The reason why I am interested to explore more logic, and logical reasoning is because it helps in
  connecting and interacting more with new era learners. So, I would like to look more into propositional
  logic, logical operations, propositional forms, purse trees and operator hierarchy, truth tables,
  tautologies, and contradictions, propositional equivalences, propositional identities, and logic in circuits
  and predicate logic, quantifiers, etc. Most importantly, I am interested to explore more mathematical
  proofs and logical reasoning methods applied in most of the mathematics fields: -Direct proofs:
  theorems, mathematical inductions, -Indirect proofs: -Contrapositive proofs, -Proofs by contradiction, –
  Proofs by cases, Equivalence proofs, -Counterexamples which are used to prove the importance of the
  conditions in a true statement.
  Please refer to my CV, CUNYFirst, and my sites to learn more about my scholarly work.
  https://openlab.citytech.cuny.edu/members/luciemingla/,
  https://openlab.citytech.cuny.edu/lmingla-portfolio