Recently President (of NCTM) Trena Wilkerson wrote: Consider these three “Rs” of mathematics: students should engage in rigorous and challenging mathematics that is relevant to their lives and is responsive to their background experiences, cultures, interests, and knowledge.”
Math educators seem to love the term rigor, but for 9th and 10th-grade students it scares the bejesus out of them. The dictionary defines rigor this way: scrupulous or inflexible accuracy or adherence to the logical rigor of mathematics [e.g. rigor-mortis].
Trena continues: But what do rigor, relevance, and responsiveness mean in teaching and learning mathematics? Rigor is not memorizing a myriad of procedures but being able to flexibly analyze and apply mathematics to different situations with a focus on concepts and relationships.
That’s true. But how do we get that across to students? Maybe what we need is a different way to express rigor (or just plain not use it all). For example, we could use the term deep learning which results from a passion for learning mathematics. But what motivates a student to be a passionate math learner? Certainly not calling it rigor, but rather doing activities that motivate a desire to learn.
In the book In Search for Deeper Learning, Jal Mehta and Sarah Fine found that student involvement in extracurricular activities such as putting on a play, being part of yearbook production, or participation in team sports helped to develop deeper, passionate learning.
In math, that would mean doing extended projects such as the Noon Day exploration which has students learn about how Eratosthenes measured the circumference of the earth over 2200 years ago using only shadows, sticks, and brains. See my article: In the Spirit of Eratosthenes: Measuring the Circumference of the Earth
These projects need to be the “meat and potatoes” of math education instead of the Common Core Standards item checking-off approach. One high school curriculum project that did this was the Interactive Mathematics Program (IMP). Here’s what Jo Boaler thought about it.
“I would say that IMP is the best high-school curriculum that I know of that really takes the problem-solving approach. . . In all the IMP classes we worked in, watched, and researched, we found great engagement in mathematical thinking and work. I am a big fan!”
Critics of the program stated that “The new programs (e.g. IMP) are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.” – link
Again, rigor is assumed to be a quality achieved through hard work without the necessary passion.
If doing extended problem-solving mini-projects is overwhelming, start with doing lessons that engage students from the get-go, then follow that with an activity that the students pursue deeply because they are engaged and they complete the activity totally satisfied. It’s at the end of the activity after the teacher asks “What did we learn today?” that the students realize what the “objective” of the lesson was. And what’s most satisfying for the teacher is that the students are still talking about this activity as they leave the classroom.
The rigor focus today assumes that all students are eager to pursue learning at a deep level. This cannot be assumed. The teacher needs to inspire this passion through the activities they present so that their students persevere when challenged by more difficult problems. See the “lessons” that I use in my work with middle school kids. Each lesson includes a student “set the stage” page, teacher notes, and suggested extensions. (It’s a work in progress.)
Closing thought: “In the 21st century, rigor should mean the degree to which a student is in equal parts intellectually challenged, engaged, enriched, and empowered by an instructional program or course of study.” – link