Steven Clontz

Doenet Workshop Test Post

Tue, 02 Jun 2026 03:01:00 +0000

This is my test post!

Dominican University OER Workshop

Wed, 13 May 2026 08:21:00 +0000

Link to notes: https://pretext.plus/projects/7484bb97-484c-4c20-b995-180f579fefe7/share

Topology, Set Theory, and the pi-Base

Thu, 12 Mar 2026 22:53:00 +0000

Talk slides: available at stevenclontz.github.io

Fun in my Math in Society Class

Thu, 16 Oct 2025 16:28:00 +0000

Today was a lot of fun in my MA111 “Math in Society” course, which is taught from Math in Our World: A Corequisite Approach (Sobecki & Mercer) (not an endorsement; y’all know I’d prefer an OER, but I haven’t had a chance to source or write one aligned with our learning outcomes).

In Lesson 2-7 Follow the Bouncing Golf Ball, the authors suggest an activity where students drop a golf ball from 250cm, record its average bounce height after three trials, then repeat this process by dropping the next three from that average, and so on. What’s nice about this is that it models an exponential decay function, but I thought it was lacking in motivation for the students.

So I ran things a little differently. This morning at 7am, I went to their classroom and dropped ten golf balls from the ceiling (101 inches high), and measured their bounce heights. I computed the average on my phone calculator, took a screenshot, and successfully forgot what it was by the time I taught at 2pm.

When class begin, I gave the students the same golf balls, and told them they had 30 minutes to work together to collect data. The only catch was that they were not allowed to release the golf balls any higher than the classroom whiteboards, about 84 inches off the ground.

They ended up collecting this data: golf-ball-data.csv. And I’m really excited to report that they were able to use a linear model, using the line of best fit, to make a prediction of 74 inches for the ball to bounce if released from the ceiling. Given that the actual average was 75.3, that’s not too bad! (Actually, I’m wondering if my records might have overestimated, given that I was looking down at the tape measure at a bit of an angle…)

Overall it went really well; definitely the best day of class so far. Thoughts for next time:

I should have just waited and did my bounces at the end of class with their help. That might have been an even better reveal than just telling them what I did that morning.
I think I know what I’ll do for the make-up: I can set up a tape measure and record a ball bouncing ten times in front of it without interference. But I’ll only share the video of the first eight bounces with the class - they could use an exponential decay model to predict the hight of the last bounce.

Tooling for the Creation and Integration of OER Documents and Technologies

Thu, 11 Sep 2025 13:09:00 +0000

In order for Open Educational Resources to live up to their promise as a viable alternative to paid offerings, authors must have access to high-quality software to produce not only static texts, but also interactive and accessible electronic resources. The presenter will demonstrate how the PreTeXt authoring ecosystem puts powerful tools for creating such resources in the hands of authors, without requiring a significant technical background. This talk is based on work funded by the National Science Foundation’s Pathways to Enable Open Source Ecosystems grant program.

Separation Axioms Among US

Wed, 03 Sep 2025 05:21:00 +0000

Link to slides.

The pi-Base model

Tue, 08 Jul 2025 09:41:00 +0000

Link to slides.

Illustrating versitile selection game techniques

Thu, 06 Mar 2025 14:15:00 +0000

Today Davide gave a very interesting talk in the 2025 Spring Topology and Dynamics Conference on [Aurichi, Bonanzinga, and Giacopello 2024]. Since it reminds me of some pretty versitile techniques I’ve developed for analyzing selection principles/games in [C 2019] and [C 2020], and I’m able to answer a question the paper asks, I thought I’d write up how to apply these general techniques for this specific topic.

This note is much more technical than my typical blog posts. In particular, the reader is expected to be familiar with the basic theory of selection games and principles.

First, we recall the following.

Definition

For a set \(X\), let \(\mathbf C(X)=\{f\in(\bigcup X)^X:x\in X\Rightarrow f(x)\in x\}\) be the collection of all choice functions on \(X\).

Definition

The set \(\mathcal R\) is said to be a reflection of the set \(\mathcal A\) if

\[\mathcal A'=\{\operatorname{range} f:f\in\mathbf C(\mathcal R)\}\]

is coinitial in \(\mathcal A\) with respect to \(\subseteq\); that is, \(\mathcal A'\subseteq \mathcal A\), and for all \(A\in \mathcal A\), there exists \(A'\in \mathcal A'\) such that \(A'\subseteq A\).

Definition

Two games are said to be dual if a winning strategy for Player 1 (resp. 2) in either game using a certain amount of information can be used to define a winning strategy for Player 2 (resp. 1) in the other game using corresponding information.

Note. I’ll point the reader to definitions 16-19 of [C 2020] to more carefully explain what “certain amount” and “corresponding information” mean here.

Theorem 1 (Corollary 26 of [C 2020])

If \(\mathcal R\) is a reflection of \(\mathcal A\), then \(G_1(\mathcal A,\mathcal B)\) and \(G_1(\mathcal R,\neg\mathcal B)\) are dual.

(Here, \(\neg\mathcal B\) is the complement of \(\mathcal B\), that is, Player 1 rather than Player 2 wins if the game produces an element of \(\mathcal B\).)

This provides us the machinery necessary for the following.

Definition

Let \(\mathscr N\) denote the collection of networks of a topological space.

Definition

Let

\[\mathcal P_x(U)=\{S\subseteq U:x\in S\}\]

and

\[\mathcal R_N=\{\mathcal P_x(U):x\in X,U\text{ is an open neighborhood of } x\}.\]

Theorem 2

\(G_1(\mathscr N,\mathcal B)\) and \(G_1(\mathcal R_N,\neg\mathcal B)\) are dual.

Proof

By Theorem 1, we need only show \(\mathcal R_N\) is a reflection of \(\mathscr N\). Let

\[\mathscr N'=\{\operatorname{range} f:f\in\mathbf C(\mathcal R_N)\}\]

We must first confirm \(\mathscr N'\subseteq\mathscr N\), that is, each \(\operatorname{range} f\) is a network. To see this, let \(U\) be an open neighborhood of \(x\), and consider \(f(\mathcal P_x(U))\in\mathcal P_x(U);\) it follows \(x\in f(\mathcal P_x(U))\subseteq U.\) Since \(f(\mathcal P_x(U))\in\operatorname{range} f\), we’re done.

We now confirm that \(\mathscr N'\) is coinitial in \(\mathscr N\). So let \(\mathcal N\in\mathscr N\) be a network. Then for each \(x\in X\) and open neighborhood \(U\) of \(x\), we may choose \(f(\mathcal P_x(U))\in\mathcal N\) such that \(x\in f(\mathcal P_x(U))\subseteq U.\) Then \(f\in\mathbf C(\mathcal R_N)\) and thus \(\operatorname{range} f\in\mathscr N'.\) Finally, note \(\operatorname{range} f\subseteq\mathcal N.\)

Corollary

In the terminology of [ABG 2024], Bob \(\uparrow\) PO-Set implies Alice \(\uparrow\) a modification of R-mw-selective, where Alice is allowed to play arbitrary networks (not just countable networks).

Proof

As defined in [ABG 2024], the PO-set game is exactly \(G_1(\mathcal R_N,\neg\mathscr N):\) Player 1 chooses a point and open neighborhood, then Player 2 chooses some subset of that neighborhood containing the point; Player 1 wins provided the choices of Player 2 form a network. Since only countable collections are constructed in this game, the PO-set game is also exactly \(G_1(\mathcal R_N,\neg\mathscr N_\omega),\) where \(\mathscr N_\omega\) collects the countable networks of the space.

So by the above duality result, the PO-set game is dual to \(G_1(\mathscr N,\mathscr N_\omega),\) which is exactly the R-mw-selective game of [ABG 2024], modified to allow Alice to play arbitrary networks.

Example

[ABG 2024] notes that the R-mw-selective game with countable networks is almost dual to the PO-set game. However, it’s consistent with ZFC that Bob \(\uparrow\) PO-set while Alice \(\not\uparrow\) R-mw-selective: take a subspace of \(\mathbb R\) of cardinality \(\omega_1\) in a model where \(\omega_1<cov(\mathscr M).\) By [Ex 2.7, ABG 2024] we have Alice \(\not\uparrow\) R-mw-selective. However, Bob \(\uparrow\) PO-set (in fact, Bob \(\uparrow_{\mathrm{tact}}\) PO-set): the winning tactic given a point \(x\) and neighborhood \(U\) played by Alice each round is to simply play \(\{x\}\); it’s clear that Bob has successfully avoided constructing a network, and thus wins.

This shows Question 2.5 of [ABG 2024] cannot be answered in the affirmative in ZFC.

Question

Is there a model of ZFC where if Alice \(\uparrow\) R-mw-selective with arbitrary networks, then Alice \(\uparrow\) R-mw-selective with countable networks?

TBIL Library Notes

Mon, 06 Jan 2025 00:00:00 +0000

The TBIL Resource Library

A key outcome of the Team-Based Inquiry Learning NSF project is our TBIL Resource Library hosted at TBIL.org.

Includes resources for Calculus and Linear Algebra.
Through initial volunteer efforts, and later supplemental suppport from NSF, Precalculus is in the works!

Backwards Design

Ideally, TBIL Resource Library courses are developed using backwards design.

Backwards design is a course development philsophy based upon first identifying desired results, determining how to gather evidence of learning, and finally designing activites to prepare students to demonstrate that evidence.

Activity!

Order the following steps in order to implement backwards design for a Team-Based Inquiry Learning module.

Create fluency builder 4-S activities to prepare students for success on assessments.
Design scaffolded exploration and flexible extension 4-S activities to build up understanding and connect outcomes together.
Determine how to assess each learning outcome, by designing appropriate exercises.
Identify the learning outcomes for a course (or module for a course).
Identify pre-readings and videos to help students prepare for the module.
Identify learning incomes that students must be comfortable with to engage in class activities.
Write a readiness check quiz to be completed at the beginning of the module.

TBIL Resource Library Backwards Design

Identify the learning outcomes for a course (or module for a course).
Determine how to assess each learning outcome, by designing appropriate exercises.
Create fluency builder 4-S activities to prepare students for success on assessments.
Design scaffolded exploration and flexible extension 4-S activities to build up understanding and connect outcomes together.
Identify learning incomes that students must be comfortable with to engage in class activities.
Write a readiness check quiz to be completed at the beginning of the module.
Identify pre-readings and videos to help students prepare for the module.

Activity!

Which of these is not prescribed by TB(I)L pedagogy?

A. Learning outcomes and assessments.

B. Scaffolded exploration, Fluency builders, and flexible extension.

C. The 4-Ss for in-class activities.

D. The readiness assurance process

Activity!

What considerations should be made when selecting learning outcomes and developing appropriate assessments?

Each group should list 2 or 3 ideas.

One helpful framework: Bloom’s Taxonomy

Each outcome is generally a predicate finishing “At the end of the semester, each student should be able to…”. The verbs in this taxonomy can help inspire these predicates (and help encourage a breadth of skills beyond the lower levels).

Another helpful framework: S.M.A.R.T.

I consider each letter when designing both outcomes and assessments.

Specific: Minimize ambiguity and tell students what you’re looking for!
Measurable: Ensure your questions illicit responses that can be used to measure the outcome at hand.
Attainable: Outcomes and assessments should be of appropriate depth/difficulty for students in the course.
Relevant: Outcomes should be relevant to the course, and exercises should be related to the outcome.
Timely: Outcomes should be scaffolded in an appropriate order so as to lead to one another.

Activity!

Following are a list of technologies that we’ve chosen to incorporate into the TBIL Resource Library. Discuss them in your team and identify a benefit and a shortcoming for each.

PreTeXt XML vocabulary for our activity books
CheckIt randomized exercise generator for assessments
SageMath programming language for randomized exercises and image generation
GitHub for asynchronous discussion forums / issues, and collaborating on digital content
Slack for synchronous community chats and communications.

Sociotechnical Infrastructure

The interconnections between these various technologies and our community members form our sociotechnical infrastructure.

Communities can build more through appropriate leveraging of technologies.
Technologies are useless without the people to wield them for good.

Our infrastructure is largely open-source, which means (very roughly) that we use free tools to create free content for the benefit of society at large.

Transitioning to an Open-Source Ecosystem

Modeling and Verifying Mathematics by Computer

Thu, 03 Oct 2024 00:00:00 +0000

Recording: https://www.youtube.com/watch?v=skdxWKyxETI

Notes for today’s South Alabama colloquium talk:

Slides: https://docs.google.com/presentation/d/15VpaFgdW2UXuId-6y1WiCv9_M2mXvGU1DVq6aZuz_5c/edit?usp=sharing
Lean Game Server: https://adam.math.hhu.de/
mathlib project: https://leanprover-community.github.io/mathlib-overview.html
code4math.org community: https://code4math.org