# Examining Inquiry Based Learning in the Math Department

Written By: Eli Baum

Photo Credit: Eli Baum

While math class at most other schools consists of a teacher standing at the front of the room and talking to silent students, Packer math classes involve small groups puzzling over problems themselves, excited students yelling as they reach an understanding, and frustrated students trying to crack the same problem for the fifth time.

For the past decade or so, the math department has applied a philosophy of learning by inquiry to their courses, in which students discover mathematical concepts for themselves rather than having their teachers simply giving them formulas to apply. This style of teaching accounts for the packets, group work, and independence that have become characteristic of Packer math classes. As Ms. Amy Hand, Head of the Math Department, described it, “The skills exist in service of the problems… [rather than] the problems [being] invented so the students can practice the skills.”

In other words, students use their own skills to solve problems that add to their mathematical knowledge rather than having a teacher explaining math concepts to students and then asking them to solve problems. This method of teaching has been validated by numerous studies that have consistently shown inquiry based learning to cause better performance for the majority of students participating.

For many Packer students, this method of teaching works. “I can figure things out by myself and then come back to the classroom the next day and talk about it with my teachers and the rest of the class,” explained Henry Petrini (‘21).

Other Packer students feel that the freedom they gain when they are forced to figure out a mathematical concept by themselves is daunting and leads them adrift.

“I like it when people guide me in learning and thinking,” said one anonymous junior. “It makes a lot of people feel lost and not knowing what to do [when teachers are] just giving [us] packets and expecting [us] to solve things.”

“You can’t learn math the way you learn English. You can’t just sit around and discuss mathematical concepts; you have to have some structure,” added another anonymous junior.

While Packer math classes do have some structure, to this student and many others it does not feel like enough.

But the decision to teach an inquiry based curriculum despite the fact that students sometimes end up feeling lost was a conscious one on the part of the math department. According to Mr. Tom James, an Upper School Math Teacher, “Math knowledge is looked at as something possessed by the expert and imbued upon the students. It can be scary to be taught that you are empowered to discover and personalize the math on your own.”

In order to prevent the feeling of math being “imbued upon students,” and gain the positive experience of independent discovery, students sometimes have to go through negative experiences as they struggle. Sam Levine (‘21) illustrated this sentiment: “There’s no better feeling than [figuring something out for yourself], but there’s no worse feeling than not understanding something.”

Other students do not feel the ownership the math department is trying to give them over their work. “The packets are organized in such a way that you’re sort of led through it.You’re doing an inquiry—you’re learning for yourself, but you still do it in a way that’s stilted and not as natural,” said one anonymous student.

However, Upper School Math Teacher Mr. Ian Rumsey has a slightly different reason for supporting an inquiry based curriculum. “If we believe that grit [is a desirable characteristic for] students, then the model that best addresses [it] is an inquiry model over a traditional model,” he explained.

In this way, learning by inquiry is working. When asked about whether the way in which they were being challenged was beneficial, one of the same students who claimed that math class was not working for them said that “[it challenges people] in a good way, if your willing to be challenged.”

Another main criticism that some students share is that they are not learning enough of the actual math concepts. “It takes us a week to get to an equation that they could have explained in five minutes,” said one anonymous student.

However, Ms. Hand argues that math is more than just getting to know as many equations as possible. “Math can be reduced to recipe following, where you memorize a series of steps, but that’s not interesting thinking,” she said.

In other words, while students do not learn as many concepts as they otherwise would, the inquiry based curriculum maximises the amount of critical thinking they have to do.

Is this increase in critical thinking worth the decrease in the number of concrete math concepts we are taught?

Sam thinks that the trade-off is worth it, saying, “When I’m out of college, I don’t think I’m gonna need to be finding the inverse of functions in my daily life, but the problem solving skills—being taught how to approach a problem and look for its solutions—is what you should be taking out of math and applying to life. Pretty profound.”