Math – Always Something New or Different

If you hadn’t heard, a group of Georgia Tech Mathematicians have proved the Kelmans-Seymour Conjecture, a 40-year old problem. Here is a an article that describes the conjecture and its proof in more detail for those of you interested: Georgia Tech Mathematicians Solve 40-year old Math Mystery” Now, I personally had no idea what this conjecture was till after reading the article – Graph Theory was not something I spent a lot of time on in college or in my teaching career.  What struck me was that this conjecture has been out there for 40 years with people trying to prove it, and it took a collaboration of over 39 years between six mathematicians to prove it:

“One made the conjecture. One tried for years to prove it and failed but passed on his insights. One advanced the mathematical basis for 10 more years. One helped that person solve part of the proof. And two more finally helped him complete the rest of the proof.”

Elapsed time: 39 years.” (Ben Brumfield | May 25, 2016)

Here’s what I love about this – it shows that math is a collaborative endeavor, that takes time and different approaches and insights and that something new can always be discovered or proved. Which is what we should be focusing on in K-12 math education, instead of the idea that there is one answer to a problem.  The standards for mathematical practice (part of the Common Core and based on NCTM Principles to Actions) are all about this collaboration, problem-solving, communication. It’s slow to take hold, and politics is working against it, but look at what can be accomplished when mathematicians, i.e. students, work together to problem-solve?

Math is not a single-solution, one-way only, or  learn-in-isolation. Let’s support the practices, let’s support teachers, let’s support students and create mathematical learning experiences that promote collaboration, real, relevant problem-solving.  It requires teachers being willing to accept multiple approaches and multiple methods of explanation (verbal, written, visual). It requires noise – collaboration is not sitting quietly at your desk.  It requires “mess” – using whatever tools or resources help students think about problems. It requires time.  But think about the new and different math that students will create and explore – and think about how much better prepared they will be for the mess that is the world.  That’s ‘college and career ready’ in my opinion.


Mathematics and History – Cross-curricular Learning

Obviously with it being February and Black-history month and Presidents Day, a lot of teachers are trying to find ways to bring some of that history into their classrooms, no matter the subject. The sad thing here is that we should be doing these types of cross-curricular learning regularly, not just when there is a designated day, or week, or month. In math and science in particular, there are so many historical events and people that have impacted the study of these subjects, therefore bringing in history, writing, and art really shouldn’t be that much of a stretch. And, vice versa – if you are a history teacher or an English teacher or an art teacher, there are mathematical and science connections that you can be using regularly.  Heck – the Common Core ELA standards actually have a huge focus on students reading in social studies, science and technical subject areas. Cross-curricular learning helps students make connections to not only where these subjects they are learning came from and who helped develop them, but how they work together and apply to life and future skills.

During my middle-school teaching years, it was easy to focus on cross-curricular learning because I was part of a cross-curricular team where we made a concerted effort to focus the learning on themes.  So maybe if we were learning about astronomy in science, then in math we were talking about planetary distances and gravitational forces, and in history they may have been learning the history of space travel and writing about it in English.  As I moved into high school and teaching, where there was more isolation of subjects, I still created opportunities for my students to connect history, science, art, and writing to mathematics. Some of my favorite resources were the AIMS Historical Connections in Mathematics books, which had summaries of various historical mathematicians, some sample problems related to their discoveries or work, and provided connections and timelines.  These were great starting points, often with hands-on activities, that helped support student projects or investigations.

What is probably of most importance, is to try to find historical figures or artistic applications of the math/science your students will be learning so that they see relevance to either a) what they are learning and where it came from; or b) why they are learning it and what they can use it for in the future. Learning is so much more interesting if there is a reason why or and understanding of how the math/science contributed to some point in time, some event, etc.

So – in light of the fact that it is February and Black-history month, I thought I would share a few influential mathematicians/scientists, with some links to what they did to maybe get you or your students thinking and connecting. Let’s write.  Let’s research.  Let’s connect math/science to other subjects so that learning is not an isolated topic but an interconnected experience.

  1. Benjamin Banneker (1731-1806) – mathematician, astronomer, writer of Almanacs
  2. David Harold Blackwell (1919-2010) – mathematician, first African-American inducted into the National Academy of Sciences
  3. Kelly Miller (1863-1939) – mathematician, first African-american to attend Johns Hopkins University
  4. J. Ernest Wilkins, Jr. (1923-2011) – nuclear scientist, chemical engineer, mathematician; contributed to The Manhattan Project; the youngest ever student to enter The University of Chicago (at age 13)
  5. Elbert Frank Cox (1895-1969) – first African-American to earn a Ph.D. in Mathematics
  6. Marjorie Lee Browne (1914-1979) – noted mathematics educator
  7. Charles L. Reason (1818-1893) – mathematician, linguist, educator; first African-American professor to teach at a predominantly white U.S. college
  8. Katherine Johnson (1918 – ) – physicist, space scientist, mathematician; early application of digital electronics as part of NASA space program

This is just my first posting trying to connect mathematics/science to other subject areas. Each month I will share some historical mathematics/scientists to help provide some resources for those of you who wish to incorporate cross-curricular learning.