Teaching Statistics in an Accelerated Summer Course

Over the past two weeks in my MAT 1272 Statistics course, we have covered a wide range of foundational statistical ideas while balancing computation, interpretation, and technology. Because this is an accelerated summer course, I have been focusing on helping students build intuition through examples, visualizations, board work, and hands-on calculator practice.

We began with the fundamentals of statistics, including populations and samples, qualitative and quantitative variables, and the distinction between descriptive and inferential statistics. Students then learned how to organize and visualize data using frequency tables, bar graphs, histograms, stem-and-leaf displays, and box-and-whisker plots. Along the way, we discussed measures of center and spread, including the mean, median, mode, range, variance, standard deviation, quartiles, percentiles, and outliers.

More recently, we shifted our attention to relationships between two quantitative variables. Students learned how to construct and interpret scatterplots, determine whether a linear trend is present, and identify whether the trend is increasing or decreasing. We discussed how a regression line can be used to model data and make predictions, as well as how the slope and y-intercept describe the behavior of the model. Using the TI-84 Plus calculator, students learned how to compute the regression equation and the correlation coefficient r, which measures the strength of a linear relationship between variables.

Our next unit focused on probability. We studied basic probability concepts, conditional probability, independent and dependent events, the multiplication and addition rules, and counting techniques such as permutations and combinations. Throughout the unit, students used their TI-84 Plus calculators to perform calculations while developing a deeper understanding of how probability can be used to model uncertainty and real-world decision making.

The next chapter introduces one of the most important ideas in statistics: probability distributions. Students will learn about discrete random variables, probability distributions, expected value, and standard deviation for random variables. We will then study binomial and hypergeometric probability distributions and use technology to compute probabilities in realistic scenarios.

One aspect of this chapter that I am especially excited about is helping students visualize probability distributions. By constructing histograms of binomial distributions, students can begin to see how these distributions become increasingly bell-shaped as the number of trials grows. This observation provides a natural bridge to one of the central topics in statistics: the normal distribution.

Throughout the course, my goal has been to connect formulas, graphical representations, technology, and real-world applications so that students can see statistics as more than a collection of calculations. Whether analyzing data, modeling uncertainty, or making predictions, statistics provides a powerful framework for understanding the world around us.

Two Days into a Four-Week Statistics Course

June in New York City, on the way into an intensive summer teaching rhythm.

This summer I am teaching MAT 1272, an introductory statistics course compressed into just four weeks. Sixteen class meetings. One entire semester packed into sixteen mornings.

At the same time, I am trying to keep research projects moving forward before July conference deadlines arrive. Balancing teaching and research is always part of academic life, but summer courses have a unique intensity. There is very little time to waste, and every class meeting matters.

What is remarkable is that we are only two days into the course.

Just two class meetings.

Yet it already feels as though we have covered a tremendous amount of ground. In those first two days, we have discussed descriptive statistics, statistical inference, variables, populations and samples, parameters and statistics, qualitative and quantitative variables, and discrete versus continuous variables. We have also started organizing and visualizing data through bar charts and histograms. These may seem like simple topics, but they form the foundation for everything that follows in statistics.

Before students can analyze data, they must learn how to describe it, organize it, visualize it, and communicate what it means.

A quiet moment between teaching, research, and the pace of summer in the city.

One of the highlights of the course has been the group work. Students come from a wide variety of backgrounds and experiences, and it has been exciting to watch them engage with one another's ideas. Discussions often take unexpected and interesting turns. This week, for example, students have already begun grappling with the distinction between a sample statistic and a population parameter. They are starting to understand that while we may know the average of a sample, the true population mean often remains unknown.

Those are important moments because they signal the beginning of statistical thinking.

The first day of class also brought an encouraging surprise. A student who had previously taken the course approached me at the end of class to introduce herself and tell me that she appreciated my teaching methodology. As instructors, we never really know what students will remember from previous experiences, so moments like that are especially meaningful.

This summer I have relied heavily on the blackboard. There is something timeless about developing ideas step by step in real time, allowing students to see the reasoning process unfold. Eventually I will project visualizations and technology-based demonstrations, but for now the old-school approach seems to be working well. Chalk, dust, and all. The students seem to appreciate it, and the classroom conversations have been lively and engaging.

Chalk, dust, and statistics: the old-school classroom is still alive and well.

At some point, the TI-84 Plus calculators will make their appearance in the classroom. For now, however, the focus is on concepts, language, and interpretation. I want students to understand what a histogram represents before asking a calculator to create one, and to understand the difference between a sample statistic and a population parameter before pressing a button to compute a numerical value. Technology is an important tool, but it is most effective when it supports understanding rather than replacing it.

I've also been fighting a cold and have spent much of the week feeling under the weather. Teaching an intensive four-week course leaves little room for slowing down, however, and the positive energy in the classroom has made it easier to push through.

Perhaps my favorite part so far has been getting to know the students. I am still learning names, and they have been amused by some of the memory tricks and mnemonics I use to remember them. There is a good atmosphere in the classroom. Students seem appreciative, engaged, and willing to participate.

What makes me happiest is hearing them begin to use statistical terminology naturally. Words such as population, sample, parameter, statistic, qualitative variable, quantitative variable, histogram, and distribution are already finding their way into classroom conversations. These may seem like small victories, but they represent the beginning of statistical literacy. Students are asking thoughtful questions, debating ideas during group activities, and becoming more confident in their reasoning.

Tomorrow is already our first quiz.

That fact alone captures the pace of a four-week summer course. We have only met twice, yet students have already learned a substantial amount of new material and are preparing to demonstrate their understanding.

Time moves quickly for all of us. One student will be graduating next week, while another will be starting a master's program at the Graduate Center this fall. Other students are balancing work, family responsibilities, and their own academic goals. It is a reminder that every classroom brings together people at different stages of their journeys, each moving toward something new.

Before long, these sixteen class meetings will be behind us as well.

For now, I am grateful for a classroom full of curious students, thoughtful discussions, and the opportunity to spend June exploring statistics together. Only two days have passed, yet the classroom already feels alive with questions, new ideas, and aspirations for the future. It has been an exciting start to the summer.

A Classroom Built on Growth - MAT 1190 (Spring 2026)

As the semester comes to an end and tomorrow’s final exam approaches, I have been reflecting on Math 1190 CO. Independently of the grades my students will receive, this semester has been another reminder that I am not only a mathematician who teaches at the college level, but also a mathematician who continues learning through teaching each semester.

This class became a space where I witnessed growth in many forms. I saw a group of students who showed up regularly, participated actively, and genuinely engaged with the class activities. I watched communities form inside the classroom. I saw students helping one another, discussing ideas together, and becoming increasingly comfortable sharing their thinking openly.

Throughout the semester, we explored many topics: voting theory, probability, statistics, correlation, the normal distribution, z-scores, counting techniques, growth models, compound interest, and linear models. Beyond computations, we focused on interpretation, discussion, and applying mathematics to real situations. Some of the conversations that emerged from these topics were thoughtful, honest, and surprisingly rich.

Yesterday, during our final review session, there were still several review problems left to discuss. Instead of simply presenting solutions myself, I asked students to come to the board and present problems to the class so they could take a more active role in preparing for the final exam. What followed was one of those moments teachers remember.

One student went to the board for the first time all semester. I could see the satisfaction and confidence that came with simply trying. Two students worked together at the board as a team, discussing the exercises openly with the class while I stepped aside and observed. There was collaboration, openness, laughter, and genuine engagement. I saw students explaining ideas to one another instead of waiting passively for answers.

What stayed with me most this semester was not perfection, but growth. I saw integrity and accountability when students admitted they had not studied enough or had made mistakes. That level of honesty reflects maturity and a sincere desire to learn and improve.

One student told me she was actually enjoying studying mathematics. I told her that was a win for both of us.

I will miss this group.

To my students from this semester: thank you for showing up, for trying, for participating, and for contributing to the atmosphere we built together in the classroom. If you ever want to stop by my office just to say hello, please do. I would truly love to be present one day at your graduation. It was a privilege to teach you.

Now I will be shifting gears for the summer — returning more intensely to research, conferences, and catching up with that side of my profession, while also teaching an intensive summer course.

For the students who kept showing up even when things felt difficult: that matters. There is real power in continuing to show up, especially when something does not come easily.

Starting the Spring Semester (S26) with Conversation

Starting the Spring Semester with Conversation

The spring semester for MAT 1190 CO at New York City College of Technology (City Tech) began in an unusual way. Our first day of classes was held on Zoom due to a snowstorm. Rather than letting the format create distance, I made a conscious effort to turn that first meeting into an interactive space—one where students could talk, reflect, and begin to see each other as part of a learning community.

That first day already revealed how different this group is from last semester’s. As students introduced themselves, I learned that some love basketball, others work with children with special needs, some are majoring in hospitality or human services, and others are pursuing nursing. It is a uniquely diverse group, shaped by very different paths and motivations, all coming together in the same course.

A colleague later mentioned that this course can be challenging because many students do not arrive with the math background I am accustomed to seeing. That comment made me pause—not in disagreement, but in reflection. The course uses Math in Society, and one of the first topics we explore is voting theory. Almost immediately, I could tell the students were engaged. They were not just learning procedures; they were thinking about fairness, decision-making, and how systems affect people’s lives. There is a lot of group work, discussion, and interaction, and I make it clear from the beginning that they need to get to know one another and work as a team. I often tell them: never turn your back on your teammate.

On our second day of classes, our first meeting in person, something unexpected happened. As soon as class ended, six students followed me to my office. They wanted to keep working. We stood at the board, solved problems together, and worked through the new material until it started to make sense. There was no requirement for them to be there—just curiosity and a desire to understand. I started calling them the class “ambassadors.” Not because they are the strongest mathematically, but because of their attitude. Their engagement and openness toward learning has already begun to influence their peers and shape the culture of the classroom.

Later that same day, another moment quietly stayed with me. A student stopped by my office before class—not to work through problems, but to look for a new friend she had met in the course, and also to see me. As she was leaving, she told me she was genuinely looking forward to coming to campus—to seeing her friend and coming to class, and to seeing me as well. She shared this simply, almost in passing.

That comment touched me deeply. Sometimes we create spaces where connection happens without even realizing it. A classroom becomes more than a place to learn material—it becomes a reason for someone to show up, to feel connected, to feel seen. And when that happens, it reinforces what I believe deeply: teaching, especially in a course like this, is not just about math. It is about conversation, community, and the small moments that can quietly light someone’s path.

A proud MAT 1630 moment: when a former student became the “guest panelist” we didn’t plan

This week, something happened in MAT 1630 that reminded me exactly why my colleagues and I do this work.

During class, while my students were working on an activity, I stepped out briefly—and I ran into a familiar face in the hallway: a former student from our department.

She graduated with honors this past summer. She was a mathematics student, worked with me on a machine learning research project, and now she’s starting a master’s program in mathematics at NYU Courant, one of the most respected places in the world to study math.

I made a quick, spontaneous decision.

I asked her if she could stop by the classroom for a few minutes and talk to my current students. She said yes.

What happened next turned into something I didn’t plan, but honestly couldn’t have designed any better.

---

The Best Panels Are Sometimes Improvised

The last part of class became a mini “panel experience.”

My students jumped in with real questions, the kind students actually want answers to:

• How did you get from City Tech to a top graduate program?
• What is the workload really like?
• How many hours do you study each week?
• How do you stay focused and consistent?
• What do you do when things get difficult?

She answered with honesty and confidence.

She didn’t make it sound easy. She talked about discipline, learning how to manage time, and staying committed even when motivation isn’t there.

---

A Moment I Won’t Forget

One of the things that moved me the most was when she said something very personal:

She told me she once wanted to follow my path—“to be like me”—and that in a way, she’s now doing exactly what she said she would do back when I first interviewed her for a seminar and workshop I co-organized with colleagues from Utah.

That hit me.

Not because it was about me, but because it showed how powerful it is when students can see a future and then work their way toward it step by step.

She’s not just dreaming about the next level. She’s doing the work to reach it.

And she’s already talking about her next goal: a Ph.D. in Mathematics!

---

“Don’t Listen to People Who Underestimate You”

She also shared advice that my students needed to hear:

Don’t listen to people who underestimate you.

Some people will assume you can’t do it. Some people will try to limit you based on what they think is realistic.

But you are the one who decides what is possible.

Then you prove it through your actions.

She also spoke about being an immigrant and an ESL student and how she never stopped believing in herself.

---

Why This Matters at City Tech

My colleagues and I do what we do because we want to see students graduate, succeed, and go further than they thought they could.

This was one of my proud moments of the year, because my current students got to meet someone who walked the path they’re on right now and is already opening the next door.

Sometimes students need more than encouragement. They need examples. They need proof that it can happen.

This was proof.

---

To My Students Reading This

Dream big.

But don’t stop there.

Work for it.

Stay consistent.

Ask questions.

Seek mentors.

And when someone tells you it’s not possible—remember: you are the one who decides what’s possible.

Teaching with Google Colab + Private GitHub Repos

This semester in MAT 1630 I tried a small change that made a big difference: I created a private GitHub repository for each student and added them as the sole collaborator, then had them work in Google Colab and submit via a pull request. Everything happens in the browser, every step is a click, and yet students are quietly learning real professional habits—commits, branches, pull requests, merges—without touching a command line.

The day-to-day is simple. Students open my Colab notebook, work through the exercises, and when they’re ready, choose File → Save a copy to GitHub. On GitHub they press the big green button to open a pull request, and then merge. On my side, each pull request becomes a clean, time-stamped submission with a place to leave feedback. Because I own the repositories, nothing gets lost, I can always see the work, and the record is there if we need to revisit grading or progress later on.

Why Google Colab clicks with students

• No setup, no stress: opens in a browser—no installs, no configuration, works on Chromebooks and shared lab machines.
• Autosave peace of mind: work is saved to Google Drive, so nothing vanishes with a laptop hiccup.
• Clear, beautiful results: run cells, see output immediately, add explanations in Markdown or LaTeX.
• Easy help: sharing a notebook link makes quick coaching in class painless.

Why private repos owned by the instructor help everyone

• Reliable access: I keep ownership, so submissions don’t disappear if a student changes settings or accounts.
• One tidy place: consistent naming and structure make reviewing and grading faster.
• Natural feedback loop: pull requests are built-in checkpoints for comments and review.
• Privacy by default: student work stays private, and GitHub masks personal emails with a no-reply address.

The submission flow students actually follow

1. Open the assignment in Google Colab.
2. Work through the notebook and verify outputs.
3. Choose File → Save a copy to GitHub and select their private repo.
4. On GitHub, click Compare & pull request, then Create pull request, then Merge.

What I appreciate most is how this nudges students to see programming as collaboration. They start to understand version control as a normal part of the process: small commits, clear messages, respectful reviews. It also happens to be free—private GitHub repos and Colab are both zero-cost—and it keeps everyone’s personal email private. For instructors, the setup is sustainable because once the repositories are created, everything else runs smoothly: students submit with a few clicks, feedback happens directly on GitHub, and there’s no need to chase files or manage endless attachments. The workflow stays organized, low-maintenance, and easy to reuse each semester, which lets us focus our energy on teaching, not on handling logistics in classes with a coding component.

Welcome Back, Fall 2025

What I’m Teaching (and why I’m excited)

Intro to Computer Science (Python)

I started teaching Intro to CS this semester and I’m keeping the momentum going. We’ll learn to solve problems by thinking first and coding second. Expect small, meaningful projects that build real skills, live coding in class with my inevitable typos and quick fixes, and lots of practice turning a messy idea into a clean plan before we touch the keyboard. If we do it right, you’ll feel your problem-solving muscles getting stronger each week.

Discrete Structures

In Discrete, we’re in the middle of propositional logic: truth tables, connectives, and the whole toolkit for precise thinking. Students already completed their first group activity, and it was great watching people learn each other’s names while debating whether one statement is truly equivalent to another. I’m sticking with the Socratic method, asking more questions, keeping explanations short, and giving space to wrestle with ideas out loud.

Why This Work Feels Big

I’ve been thinking about our mission at City Tech. We’re here to support and uplift a new generation of students so they can flourish in school, at work, and in life. I’m lucky to be around colleagues who are strong researchers and who also believe in giving back and paying it forward. That kind of community keeps me grounded and pushes me to show up better for my students.

What You’ll See on This Blog

Expect class updates and project highlights, little teaching wins along with the flops we learn from, Python tips and discrete math nuggets, and thoughts about learning, belonging, and building confidence.

If you’re in my classes, welcome. Bring your questions and your curiosity. If you’re reading from afar, I’m glad you’re here too. Here’s to a semester of clear thinking, kind collaboration, and code that finally runs after that one missing parenthesis.