Category: Engagement

Using Rubik’s Cubes to Teach Math

I enjoyed this opinion piece about creative ways to use a Rubik’s cube to engage reluctant students in a mathematics class.

As an added bonus, the article provides a link to You Can Do The Cube, which includes complex mosaics that can be built by arranging one side of multiple Rubik’s cubes, suggesting this as a strategy for getting children hooked on Rubik’s cubes (instead of frustrating novices with the complex task of solving the cube completely).

Veteran teacher shows how achievement gaps in STEM classes can be eliminated

This press release from UC Santa Cruz definitely gave me food for thought about new things to try in my own classes. A few short snippets:

[Professor Tracy Larrabee] uses a three-pronged approach to support underrepresented students in her class.

“The first is that we have had a very diverse teaching staff,” she said. “We have one professor, four TAs and four MSI tutors, and during this time it just happened that of those people, half were female, we always had at least one African American, one Latinx, and one non-gender conforming tutor so that everyone could feel a connection to someone on the teaching staff.”

“Another technique I use is to emphasize failure as the appropriate path to learning,” she said. “Engineering is hard; it’s good to fail the first time you attempt a problem. People who fail at a problem the first time tend to retain things better than those who luck into the right answer.”

Her final tactic is to explicitly discuss stereotype threat. This is the risk that someone (i.e., from an underrepresented minority) might take routine negative experiences as confirmation that they are fundamentally unsuited for something like higher education.

“One of my African American MSI tutors—who are extremely high achieving students selected to provide supplemental tutoring to others—told me it was like having a light bulb go off for him,” Larrabee said. ”Until I discussed the issue in class, he felt like he didn’t belong in this major, but after we talked about stereotypes, he realized it wasn’t that he was unsuited for the material. It was hard for everyone!”

Predicate Logic and Popular Culture (Part 206): Jack Johnson

Let H be the set of all things, let T be the set of all times, let G(x) be the proposition “x is good,” and let R(x,t) be the proposition “x remains at time t.” Translate the logical statement

\forall x \in H(G(x) \Longrightarrow \forall t \in T(R(x,t))).

This matches a line from “Mudfootball” by Jack Johnson.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 205): Bob Marley

Let T be the set of all things, let L(x) be the proposition “x is a little thing,” and let A(x) be the proposition “x is going to be all right.” Translate the logical statement

\forall x \in T(L(x) \Longrightarrow A(x)).

This matches a line from “Three Little Birds” by Bob Marley.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 204): Billy Joel

Let T be the set of all times, and let W(t) be the proposition “She is a woman to me at time t.” Translate the logical statement

\forall t \in T( W(t)).

This matches a line from “She’s Always a Woman” by Billy Joel.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 203): Bill Withers

Let P be the set of all people, let T be the set of all times, let P(x,t) be the proposition “x has pain at time t,” and let S(x,t) be the proposition “x has sorrow at time t.” Translate the logical statement

\forall x \in P( \exists t_1 \in T(P(x,t)) \land \exists t_2 \in T(S(x,t)).

This matches a line from “Lean on Me.” Note: while I think the translation above matches the intent of the song, a case could be made that, literally rendered, the “there exists” symbols should come first — that there’s a single time that everyone has pain at that one time.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 202): The LEGO Movie

Let T be the set of all things, let p be the proposition “You’re part of a team,” let A(x) be the proposition “x is awesome,” and let C(x) be the proposition “x is cool.” Translate the logical statement

p \Longrightarrow \forall x \in T(A(x) \land C(x)).

This matches the opening line of “Everything is Awesome!!!” from The LEGO Movie.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 201): Hamilton

Let T be the set of all times, let time 0 be now, and let L(t) be the proposition “I like the quiet at time t.” Translate the logical statement

\forall t \in T(t < 0 \longrightarrow \lnot L(t)).

This matches a line from “It’s Quiet Uptown” from the hit musical Hamilton.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 200): Spider-Man

Let T be the set of all times, and let R(t) be the proposition “I will rest at time t,” and let M(t) be the proposition “You are unmasked and eliminated at time t.” Translate the logical statement

\forall t \in T(\lnot M(t) \Longrightarrow \lnot R(t)).

This matches a line by J. Jonas Jameson in the 1990s Spider-Man cartoons.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 199): Justin Bieber

Let T be the set of all times, let K(t) be the proposition “You knock me down at time t,” and let G(t) be the proposition “I am on the ground at time t.” Translate the logical statement

\forall t \in T(K(t) \longrightarrow \lnot (\forall s \ge t (G(s)))).

This matches part of the chorus of “Never Say Never” by Justin Bieber.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.