Restating my Assumptions

In the movie “Pi” by Darren Aronofsky, the protagonist is working on discovering patterns in pi. Every now and then, he will hit some roadblock or discovery and say out loud the day and the phrase “restate my assumptions.”

Every field of mathematics is built on a fundamental set of assumptions that taken for granted without proof. These assumptions are called axioms, and it is important, when delving into any mathematical realm, to state clearly what one’s assumptions are, and add or subtract to that set of assumptions as necessary.

I am been “restating my assumptions” and changing my personal and professional goals either out loud or in my head over and over again for months now, as I have discovered things about myself and my path, and have encountered roadblocks that I need to circumvent.

So, September 12, 2024, I restate my assumptions:

My personal goal is to become an expert in creating and thinking about how to create lessons that are:

• Interdisciplinary: not only incorporate principles of stem, but can be applied to other disciplines:: writing, (bi)literacy, art, etc. 

• Vertically adaptable to engage different ages of learner

• Adaptable for students with special needs or “honors” level

• Historically and culturally significant.

  
  

One axiom: it is impossible to make sure every lesson addresses every need, and this is one of the problems with teacher education. Whenever I am at some conference or some professional development, the person delivering the message usually says that it does. It’s just impossible to do this for every lesson, but one should try their best to incorporate as many strategies as possible to engage as many learners as possible. If we as educators can do this throughout a UNIT, then it is highly likely that we will have MAXIMIZED our potential impact on our students by year’s end.

I want my student to all be able to do math, and it is my belief that anyone can learn math given the right conditions and motivations. I believe that anyone can learn ANYTHING with the right conditions and motivations. But the truth is, that no one really wants to say out loud as it makes it seem like we are “giving up” on our students or that we don’t “believe in them,” there are so many factors out of any educator’s control that makes reaching our goals as educators not possible for 100% of our students.

We are all working with so many constraints out of our control.

We can’t always make sure our students can DO the math we are teaching in the amount of time and resources given, but we CAN make sure our students understand the significance of being able to perform the mathematics. We can show them how mathematics has made possible literally everything that exists in their lives today, from the apartment they live in, the roads they walk on, the app they are using. Maybe they themselves didn’t make that calculator in their hand, but someone did. And that person needed to be proficient in mathematics.

We can at least show them why what they are learning was or is important.

So when I am writing a lesson based on something that inspires me, I think about things on my checklist. I don’t need for the lesson to hit every bullet point, but I want to incorporate as many as possible, understanding that the lesson(s) prior to or following the lesson addresses the other bullet points I have missed. 

When a teacher is getting observed, often the focus is on what is missing instead of what the teacher did well. Again, it is IMPOSSIBLE to reach every learner every day; instead we should be focusing on reaching as many learners as possible throughout the course of a unit.

My checklists (a non-exhaustive list) 

Is the lesson :

• Inquiry based 

• Connected to other STEM disciplines

• Connected to non-STEM disciplines

• Culturally relevant or sensitive

• Sensitive to minimizing inherent bias, either culturally or socio-economically

  
  

Does the lesson:

• Move between multiple modalities of individual/group participation

• Draw from students’ personal experiences

• Incorporate elements of (bi)literacy

• meet the students “where they’re at”

• provides opportunity for extension for motivated students

  
  

My goal in writing these lessons is not necessarily in delivering these lessons itself, but to create for the sake of creating, to give freely to those who are interested, to create when the inspiration hits, so that I can become an expert in how to see the world around us as an opportunity for STEM engagement.

I am a lifetime world traveler, a lover of language, and have a hunger for learning about cultures outside my own and this has already put me in a unique position to do this; I have been doing it informally since I began teaching almost 30 years ago. I often write as process, and my writing often incorporates mathematical language in a way that people tell me is unique.

I am a logician first, but I am a creative second, and most people see themselves as one or the other.

So if I can become expert in seeing how the world around us contains most aspects of the humanities and mathematics cohesively, then I can help others think this way as well, in order to make mathematics instruction more meaningful for students in a world where AI will be able to do most things for us in an instant.

Not only does the AI currently exist to solve even pretty complicated mathematical problems, its power is increasing exponentially.  I do believe that we still need to teach most students the foundations of mathematics up to calculus, but the reality is and has been for a good generation that the reason students don’t “succeed” at STEM in America is that they don’t see the point in it anymore. 

And they’re not too far off from the truth.

Why do we still focus on rationalizing denominators? Simplifying complex fractions? 

History classes no longer focus on just the ancient Greeks or World War II, students of literature read afro-centric novels instead of just Shakespeare. These disciplines have broadened and modernized their curricula to incorporate current events and the history of people outside of Europe. This is culturally and historically relevant teaching.

In general, mathematics education has not been culturally or historically relevant since… I don’t know when.

We have to change. We have to modernize. And this is how we do it.