From Math Anxiety to Mastery in 6 Stages: Stage 2: Encoding Conceptual Understanding (From Math Anxiety to Mastery in Six Stages)

“The depressing thing about arithmetic, badly taught, is that it destroys a child’s intellect, and to some extent his integrity. Before they’re taught arithmetic children won’t give their assent to utter nonsense: afterwards, they will. Instead of looking at things and thinking about them, they make wild guesses in the hope of pleasing the teacher or an examiner”. (W.W. Sawyer: “From Abstract to Concrete” (1962). That was written 60 years ago. How much has changed since? A lot, but also not that much. A lot, because school-going students have more career options today that stretch beyond wanting to be a doctor, engineer, lawyer or scientist. They can aspire to be musicians, dancers, performance artists, actors or film-makers, social media advocates for Climate Change, pioneers of alternative Energy, digital journalists, sports-people, techie-nerds toying with new forms of intelligence at work, even internet celebrities with the potential to seriously monetize their following of millions. None of these careers require high-level math. But they do require, increasingly, a mindset that only true, meaningful mathematical learning can promise. It is one that is more needed than ever before. That being said, it is true that the world of math education has not changed much. The STEM paradigm still staples Mathematics to Science,Technology and Engineering at a time when a new generation of learners seek to be liberated from prefabricated models of self-and-career development that are intimately connected. STEM stands distantly silhouetted against their life’s horizon. Indeed it stands tall and true and beckons the future. But the learners’ inner world seeks more immediate, self-immersive pursuits that tease out hidden passions and converge upon more desirable learning experiences. There is a growing need to learn mathematics from very different perspectives, for different reasons and different needs, in addition to the conventional ones reserved for mathematicians and scientists. There is something starkly different about being inspired by career choices that today’s generation is making. What sets their new choices apart are learning experiences that reach deeper into their hearts and minds. Furthermore, they are cognitively and emotionally interfacing with exemplary models of gurus, masters, protagonists, medals-and-award winning celebutantes achieving, in growing numbers, what were once, rare skills levels. The resources and skills they apply to achieve basic mastery levels are available to all who are interested, often at very little cost. Consequently, many more can boast of achieving close-to-mastery levels in their areas of interest. More importantly, their fields are leveling at much higher plateaus of proficiency. The Encoding of Conceptual Understanding (Stage 2) in math takes place inside our Deep Knowledge (Acquisition) Systems. It is where all the big ideas get watermarked. It is where mathematical concepts evolve as core learning. It fosters knowledge that helps learners multiply and divide, increase and decrease, vary, convert and transform and generate insights that feel true and meaningful. All through sheer reasoning. Perhaps mathematics learning can reach into the inner world of the learner and nestle there feeling owned, making the learner feel right, in-sync, in-tune and on-the-beat with something that once felt pretty spooky. Such learning encounters are organic to healthy self-growth in terms of achieving deeper understanding and greater self-confidence. Stage 2, it is hoped, introduces math content and pedagogy in ways that makes trainers, teachers, students and others interested, to “look at things and think about them” without having to make “wild guesses in the hope of pleasing the teacher or an examiner” .