Blogs | ShalmaliB

Learning, Teaching, and Quiet Work

Some of the most meaningful work we do as educators is quiet.

It happens when a student feels safe enough to ask a question.
When a classroom becomes a place of trust rather than fear.
When learning feels possible again, even during difficult weeks.

Over time, I’ve learned that teaching is not only about delivering content. It is about pacing. About listening. About creating conditions where thinking can happen. Mathematical understanding often arrives not through speed, but through clarity, patience, and space.

I am continually reminded that education is relational. Students bring their full selves into the classroom, and so do we. When we lead with respect, consistency, and care, students respond with effort and integrity.

I remain deeply grateful for the mentors, colleagues, and students who continue to shape how I think about learning and teaching. Each semester offers new lessons — not only in mathematics, but in humanity.

Quiet work matters. And its impact lasts.

Learning First Confidence Last

Students often believe that confidence comes first.

They think they need to feel ready before attempting a problem, asking a question, or engaging fully with new material. But in practice, learning rarely works that way. Confidence is not a prerequisite for understanding. It is usually the result of it.

Most learning begins in uncertainty. It begins with not knowing, with hesitation, with ideas that feel incomplete. When students are allowed to sit in that space without judgment, something important happens. Understanding starts to take shape, and confidence follows naturally.

As educators, this asks us to rethink what support looks like. Encouragement does not always mean reassurance. Sometimes it means giving students permission to struggle, to think out loud, and to try without the guarantee of being correct. It means creating environments where uncertainty is treated as a normal and necessary part of learning.

In mathematics, this is especially true. Insight often emerges only after repeated attempts, false starts, and quiet reflection. When classrooms prioritize speed or performance, students may appear confident while understanding remains fragile. When classrooms prioritize thinking, confidence grows more slowly, but it lasts.

Learning before confidence requires patience. It asks instructors to resist filling every silence and students to trust the process even when answers are not immediate. Over time, that trust becomes internal. Students begin to recognize that they can engage with difficult ideas and persist through discomfort.

Confidence, then, is not something we give students directly. It is something they earn through experience. Our role is to design learning spaces where that experience is possible.

When learning comes first, confidence follows. And it tends to stay.

An Academic Advent Calendar

24 days to internalize one research paper

Advent calendars are usually associated with small daily surprises and a way of slowing down December by opening one door at a time. This year, instead of chocolate or luxury items, I made an academic advent calendar.

The idea is simple. Choose one research paper you genuinely want to understand and spend a short, non negotiable amount of time with it each day. There is no rushing and no pressure to produce results. The goal is steady, intentional reading and thinking.

24 Day Plan

Day 1: Read the abstract and introduction. Identify why this paper exists.
Day 2: Read only the theorem statements. Distinguish main results from secondary ones.
Day 3: Skim the paper structure and section flow. Locate where the main difficulty lives.
Day 4: Read all assumptions and hypotheses carefully. Decide which are structural.
Day 5: Identify the spaces, operators, and solution concepts used in the paper.
Day 6: Locate where regularity, compactness, or comparison principles are used.
Day 7: Identify the single lemma or proposition on which the paper depends most.
Day 8: Read that key result carefully. Understand why the argument works.
Day 9: Ask how the argument could fail. Identify which step is most fragile.
Day 10: Reconstruct the logical flow of the paper from memory.
Day 11: Choose one proof to study in depth.
Day 12: Read that proof line by line. Identify where ideas are hidden.
Day 13: Rewrite the proof outline in your own words.
Day 14: Decide which parts of the argument are reusable and which are problem specific.
Day 15: Modify one assumption mentally. Note what breaks first.
Day 16: Change the operator, domain, or boundary condition. Observe new difficulties.
Day 17: Read one closely related paper. Compare tools and ideas.
Day 18: Write down what you still do not understand.
Day 19: Summarize the paper in one paragraph.
Day 20: Reduce the summary to three sentences.
Day 21: Reduce it to a single sentence.
Day 22: Identify what the paper does not address.
Day 23: Think about possible extensions or directions.
Day 24: Write brief personal notes on what you gained by slowing down.

One paper. One small step per day. Something new learned every day.