Inquiry or Direct Instruction? A False Narrative

I have made it my life’s work to research and write about how we engage and motivate learners to encourage deep learning. I was fortunate to find my passion for teaching and learning over 30 years ago and my goal is to prepare our young for an exciting, dynamically changing world. Focusing curriculum and instruction on developing deep transferable conceptual understandings will allow our students to develop the ability to critically think, navigate ambiguity and build creative confidence.

Recent media posts that have been shared with me about a focus on emphasising direct or explicit instruction as being more effective for learning over inquiry based learning has compelled me to share my thoughts about this matter (re: https://www.facebook.com/NZQandA/posts/4005633756165102 and https://www.facebook.com/StCatherinesSchool/).

We live in complex, scientifically exciting times! The exponential growth in technology of the last few decades has led to many breakthroughs in innovations such as Global Positioning System (GPS), social networking, advances in robotic medicine, and quantum computing to name a few, however, this has also resulted in the disappearance of many jobs due to automation. Thus, human skills such as creativity, originality, and initiative, which cannot be replaced by artificial intelligence, are now more valued characteristics in the ever-changing job market. Creativity is known to be the driving force for innovation and technological advancements, and mathematicians and scientists play a significant role in this ecosystem. Cutting-end mathematicians have pioneered the way forward using mathematical ideas and insights to develop the info-technology and biotechnology arenas. Ultimately, the need for innovative thinkers for the 21st Century creates a need for education reform to prepare the next generation of students to be successful world citizens of the modern age (Lin, 2016).

We live in a sad state of affairs when it comes to maths education. The false dichotomy that you either teach facts and skills or you teach for conceptual understandings, is a deeply ingrained belief, unfortunately, in many countries around the world. In fact, another false binary belief is that you either employ direct/ explicit instruction techniques or inquiry based learning. The push for only employing pedagogies involving direct or explicit instruction where mathematical understandings are transmitted to students is gaining traction with leading educationalists around the world. An explicit instruction method is a teacher-centred approach that often adopts a cycle of explaining, modelling, scaffolding and practising. I facetiously call this the monkey see monkey do technique. This transmission method of teaching stifles a learner’s ability to think independently, to be curious and creative. Research cited to support direct instruction as the sole effective teaching methodology often relies on the measurement of student achievement based on standardised tests. Undoubtedly, educators agree that standardized test results generally reflect a snapshot of low order thinking and do not reflect an individual’s talents and achievements over sustained periods of time.

In places such as Ontario, Canada, the government has announced a move towards a back to basics approach, which involves teaching students facts and skills, very often, in isolation and without context or conceptual understanding. I am very concerned that this is also gaining traction in the Antipodes This type of approach encourages a focus on “teaching to the test” with the ultimate goal to increase standardized test scores. It is indeed a sad state of affairs for teachers who are robbed of their own creativity when designing learning experiences for their students.

In an authentic deep learning classroom, there is a dance between both explicit/ direct instruction and inquiry based learning. Direct instruction may be used to deliver low order facts and skills, when necessary in the scaffolding process and when learners require the skills and facts in order to make further progress in the unit of inquiry. Inquiry embraces and invites uncertainty (Murdoch, 2015) allowing learners to explore and arrive at deep conceptual understandings in a constructivist environment. Progressive mathematics education reform has focused on helping learners to understand the concepts of mathematics through a constructivist approach. This includes learning theories that are underpinned by Vygotsky’s (1978) social constructivist and social-cultural theories; however, in reality, many mathematics classrooms around the world still rely on didactic, delivery-transmission mode approaches of the 1950s rather than more investigative and inquiry methods that foster creativity. “Mathematics is a process of inquiry and coming to know, not a finished product, for its results remain open to revision” (Ernest, 1989, p. 250). I like to use the analogy of learning music to illustrate my point. Imagine learning music by only focusing on scales and reading notes and never having the opportunity to appreciate and play a piece of music! We do not want to rob our students of the beauty of playing or even composing a musical piece! I have a dear friend who is a self-taught pianist who has never played scales in his life! He could mentally hear pieces of music in his head and in order for him to express these melodies he learned which notes to play.

The late great mathematician George Polya said:

"Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself."

Immersing learners in an inductive learning environment promotes motivation and engagement (McTighe & Silver, 2020). Inductive learning is a student-centred, inquiry-based approach where learners are encouraged to pattern seek, make predictions and form generalisations. In turn, inductive learning supports the development of brain schemas which are cognitive frameworks that help learners to organise and structure knowledge.

Many countries value the importance of mathematics learning, and mathematics achievement is viewed, rightly or wrongly, as one of the measures of educational success and economic potential when preparing citizens for the future job market.

Traditional approaches to learning mathematics reduce the discipline to a set of low-level algorithms and memorized formulae, and, unfortunately, procedural mathematics persists. Thus, it is vital that mathematics education incorporates the development of creativity to continue innovating in a world where many jobs will be replaced by machines. Creative mathematical thinking is a highly valued asset that can be used to address current and future global economic challenges. Cultivating creativity has become a global imperative.

References

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. Mathematics teaching: The state of the art, 249, 254.

Lin, C.-S., & Wu, R. Y.-W. (2016). Effects of web-based creative thinking teaching on students’ creativity and learning outcome. Eurasia Journal of Mathematics, Science and Technology Education, 12(6), 1675–1684. Retrieved from http://www.ejmste.com/Effects-of-Web-Based-Creative-Thinking-Teaching-On-Students-Creativity-and-Learning-Outcome,61457,0,2.html

McTighe, J. & Silver, H. F. (2020). Teaching for deeper learning: tools to engage students in meaning making. ASCD.

Murdoch, K. (2015). The power of inquiry. Seastar Education.

Vygotsky, L. S. (1978). Mind in society: The development of higher mental process. Cambridge, MA: Harvard University Press.

Wathall, J. T. (2016). Concept-based mathematics: Teaching for deep understanding in secondary classrooms. Corwin Press.

Wiggins, G., & McTighe, J. (2006). Understanding by Design, Expanded 2nd Edition. Retrieved from http://www.ascd.org/Publications/Books/Overview/Understanding-by-Design-Expanded-2nd-Edition.aspx