Negative b, negative b, plus or minus square root, plus or minus square root, b squared minus 4ac, b squared minus 4ac, over 2 a, over 2 a.
I was a sophomore in high school when my Algebra II teacher stood in front of a room full of hormonal teenagers and bravely sang this quadratic formula song to the tune of “Are You Sleeping?” He finished with a beet-red face, and only the ring of the bell broke the awkward silence that followed. Why are teachers soooo lame? we all recounted in the hall, but I secretly sang the song in my head the rest of the day, and after the teacher announced that the class average on the follow-up test was the highest of the semester, I could only assume that others sang the song as well.
One might conclude that this was an authentic learning moment, the proof being my performance on the test as well as my still being able to recall the song today, but I would challenge you to consider: what did I truly learn from the quadratic formula song?
I was successful on the algebra test because it was closed book, and I knew the formula. Suppose I had forgotten the formula. What difference would it have made, aside from a lower-performing score?
We have learned to like grades because grades measure learning, and when we ask students what they have learned, we are impressed that they can rattle off the quadratic formula. And yet, we never stop and ask, why is this important? We confuse learning with performing, and I would argue that these are not the same.
Randolph’s 3rd grade teachers recently had a similar conversation as we began planning for the new school year. Traditionally, 3rd grade covered many different units, ranging from landforms to maps, owls, and rainforests. Although students learned a variety of skills through these units, we worried that the disjointed structure of progression focused more on performance-based understanding rather than authentic learning. These concerns led us to develop an entirely new structure for the upcoming school year.
This year, our 3rd graders will spend the first quarter studying ancient civilizations. This unit will focus on the development of critical thinking skills. The students will analyze and evaluate many different cultures and eras and discover what contributed to the rise and fall of each. Next, they will study inventions and famous inventors, where their focus will shift to divergent thinking skills. During this study, our students will create, generate, and explore many possible solutions to a single problem.
In the third quarter, they will explore ecology and sustainability as they move on to convergent thinking; students will learn to gather facts and data and apply logic and knowledge to make informed decisions. By the fourth quarter, our students will enter the independent thinking phase, where each of them will identify an area of interest and apply all three types of thinking to research a problem and develop a solution.
As with my experience in Algebra II, many of us are comfortable with the idea that rigor means hard work, which means knowing cold hard facts, and while I agree that knowing facts has a unique and significant place in schools, I am challenging you to question your understanding of rigor. This is exactly what Middle School history teacher Betsy Allen did in her redesign of the 8th grade curriculum.
I am challenging you to question your understanding of rigor.
As a student, Betsy remembers feeling frustrated with teachers who expected her to fill her brain with dates, documents, and other superfluous information. She vowed not to be that teacher, and she has never put a large emphasis on knowing dates. However, sometimes convention dictates our actions, even when a part of us rebels.
When Betsy began teaching, rigor in history class meant cramming your brain with facts. We are now in a transitional phase in education, where the rapid progression of technology has forced many educators to question these preconceived notions.
During our discussion of a rigorous curriculum, Betsy stated, “Learning the reasons behind an event is far more important than focusing on the specific dates, because so much of history is all tied together through these reasons. This is what I want the students who leave my class to know.”
One way she is doing this is through a cross-curricular study on the American Revolution. Students will choose one personality from this era to research. They will be required to complete the project entirely from the person’s point of view.
Through the research and presentation of specific people, Betsy hopes her students will gain many different perspectives of the American Revolution and question their initial understanding of the era. The research and outline will happen in History class, while students will spend English class writing a document from the person’s perspective and creating a visual. By creating these authentic learning experiences, we are teaching our students how to think rather than what to think.
By creating these authentic learning experiences, we are teaching our students how to think rather than what to think.
The project becomes a tool for learning rather than the end result. Establishing this mindset in the Lower School and maintaining it throughout their time at Randolph is an essential progression. It is our hope that through these experiences, you will question your understanding of a rigorous curriculum and that the distinction between learning and performing will become clear.