Genuinely Relevant Math

“When am I ever going to use this?”

For years, students in high school math classes have asked this question. For years, they’ve been given unsatisfying answers - or just ignored. We decided to change that.

Started by teachers, Skew The Script provides free Genuinely Relevant Math lessons. Specifically, our lessons meet the three criteria for genuine relevance:

Topic Relevance: The context is compelling

The lessons explore contexts that are authentically meaningful, compelling, and important to students’ lives.

  • To engage all students, we can’t make the promise that math will, at some point in the vague future, be relevant. Especially for students who work jobs outside of school, support their families, and manage complex problems on a regular basis, this vague promise can feel like an empty one. The math needs to be helpful, useful, and relevant now. Relevant contexts make these connections current and clear.

Content Relevance: The math is essential

The math isn’t a side-show or veneer. Rather, the math is central, and it provides genuine insight into the context.

  • Students should walk away feeling that the math skills they learned were essential for understanding key aspects of the lesson context. Otherwise, while the context may have been relevant, the math used in the lesson will continue to feel like an irrelevant add-on.

Instructional Relevance: The material is instructionally useful

The lessons fit into teachers’ calendars, are aligned to math standards, and prepare students for the assessments they need to take.

  • Math teachers have a short amount of time to cover all the standards for their courses. In addition, for many courses, they have to prepare students for standardized tests. To be useful under these conditions, lessons must be created in well-chunked formats. They must be aligned to course standards. Finally, they must genuinely prepare students for the exams they need to take.

Problems that lack topic relevance -> Boring

Boring Problem: A factory claims that its batteries can recharge in 60 minutes, on average. To test this claim, a statistician gets a random sample of 30 batteries and finds that they take an average of 67 minutes to recharge. Is there convincing statistical evidence that true average recharge time is longer than claimed?

Analysis: This problem sets up a one-sample t-test for a mean, which is a mathematical process that gives students genuine insight into whether the factory’s claim is true. However, the overall context (battery lifetimes) isn’t compelling. The problem is missing topic relevance. It’s boring.

  • ❌ Topic Relevance
  • ✅ Content Relevance
  • ✅ Instructional Relevance

Problems that lack content relevance -> Contrived

Contrived Problem: On any given day, there is a 10% chance that a citizen of Wakanda will require the help of the Black Panther. In a full year, how many days would we expect T’Challa to suit up and save someone?

Analysis: Some students love the Black Panther. However, solving this proportions/expected value problem (with made-up numbers) does not give students genuine insight into the storylines, character, and contexts that they love about the Black Panther. Because the math content doesn’t provide real insight into the context, it feels contrived. The Black Panther becomes a disingenuous “veneer of relevance” on top of a standard math problem.

  • ✅ Topic Relevance
  • ❌ Content Relevance
  • ✅ Instructional Relevance

Problems that lack instructional relevance -> Misaligned

Misaligned Problem: Many assume that electric cars are better for the planet. However, the precious metals in batteries make electric cars quite emissions-heavy to produce. When you consider the full life of a car, does going electric actually reduce emissions? According to MIT's Trancik Lab dataset, re-charging a Telsa typically requires 1,368 kg CO2eq (emissions equivalent to 1,368 kg of CO2) from electric grids per year of driving. By contrast, a Toyota Camry emits far more: 4,525 kg CO2eq per year of driving. However, it takes far more emissions to produce a Tesla (11,074 kg CO2eq for a Tesla vs 7,402 for a Camry). How long do you have to drive the Tesla for it to 'pay off?' Construct a system and solve using elimination.

Analysis: With proper framing, the question of whether electric cars are actually better for the environment is compelling for students. The problem requires students to set up equations like these:

Where 𝑦 = total emissions and 𝑥 = years driven
Tesla: 𝑦 = 1368𝑥 + 11074
Camry: 𝑦 = 4525𝑥 + 7402

Solving this system using elimination would give students genuine insight into the context, as the solution reveals that it only takes 1.16 years of driving for the Tesla to have lower overall emissions. So, barring a car-totalling accident in the first year of driving, going electric (in this case) tends to pay off! However, standardized tests usually assess whether students can use elimination to solve a system of standard form equations. These equations are in y-intercept form. Solving these equations with elimination won't prepare students for the level of algebraic manipulation needed to solve standard form equations. So, this problem is not instructionally useful.

  • ✅ Topic Relevance
  • ✅ Content Relevance
  • ❌ Instructional Relevance

How do we meet all 3 relevance criteria? Using the Students First, Standards Last Method

In the typical curriculum creation process, lesson designers start with the math standards they need to cover. Then, they fit their lesson contexts and tasks to those standards. The result: lessons that are well-aligned to standards (Instructional Relevance) but with either boring contexts that lack Topic Relevance or contrived connections that lack Content Relevance.

Skew The Script takes an inverted approach. We consider the math standards last. That’s not to say that the math standards aren’t important - far from it! We believe that designing lessons aligned to math standards - and to the way those standards are tested - is essential. Otherwise, the lessons would lack Instructional Relevance and would be useless for most classrooms.

While not last in importance, math standards are saved for the last step of our creation process. We start at a very different place: asking students what they care about (Topic Relevance). Then, we see what math naturally surfaces when we start exploring those student-chosen contexts (Content Relevance). This ordering ensures that our lessons investigate compelling contexts, using math that genuinely fits those contexts. Finally, when choosing which ideas to build into full lessons, we only select those that utilized common math concepts from high school courses (Instructional Relevance). In this way, we ensure that all 3 relevance criteria are satisfied.