This ‘humanities-based math’ course is no average STEM class
Emily Baratta Goodell ’99 is talking about “parallel dot plots” with her AP Statistics class, and she wants her students to compare two different graphs. Audrey Leung ’22 points out a similar “shape” in the two. Avalon Dela Rosa ’22 notes the “spread,” without many “outliers” in either. There is some discussion about the limited “variability” in the graphs as well. The terms and approach are all textbook, the actual assignment a little less so. Because this activity is all about Beyoncé.
Mrs. Goodell introduces this project with some back-information about the band Destiny’s Child. “I may be dating myself here,” she says, laughing. She explains that Beyoncé wrote the entire Destiny’s Child’s song catalogue, and Ms. Goodell is asking the class to use statistics to determine if Beyoncé was also the author of her international mega-hit “Crazy in Love.” Although the mere suggestion would be near-blasphemy for the most devoted Beyoncé fans (cue the buzzing Beyhive), it makes a stimulating classroom activity, with very enjoyable music breaks.
The concept of “bias” comes up early in this activity. Mrs. Goodell shares the lyrics of “Crazy in Love” and asks the class to select five words from the song, count the number of letters in the words, and calculate the average word length. The students collaborate on a graph in Jamboard, and the girls start adding their dots for the mean word length using the numbers 1-8. The class ends up with the average (“true mean”) word length of 4.3 letters. However, Mrs. Goodell reminds them that their preferences show bias, so the girls move their attention to the second graph on the Jamboard.
Graph two is still plotting the word length in “Crazy in Love,” but this one employs a random number generator. This randomness reduces bias, safeguarding that every subject in the study population (aka words in this song) has an equal chance of being chosen. And lo and behold, there is a notable difference! The average word length for this song is settled at 3.53 letters.
The true mean of all of Destiny’s Child songs is 3.64 letters. Based on the samples supplied, did the class find good evidence that Beyoncé did not write the lyrics for “Crazy in Love”?
Karissa Ho ’21 is careful in answering the question. She doesn’t say that all future inquiries into the question are null and void. But with such a small variance between those two true means? “We don’t have enough evidence to say that Beyoncé didn’t write the lyrics to ‘Crazy in Love,’ ” Karissa says. There seems to be a collective sigh of relief from the class, as the crown of Queen Bey remains relatively untarnished.
It is easy to see how this subject, and this class specifically, appeals to those who are deeply interested in STEM classes, but also with those with a more liberal arts bent.
“I remember Mrs. Goodell describing AP Statistics as a ‘humanities’ math class,” says Avalon Dela Rosa ’22. “More than anything when deciding to take AP Statistics was the uniqueness of the class...a combination of math and argument-based learning.”
There are, in fact, a few prerequisites before students can enroll in this “humanities-based math.” They need to meet a minimum grade requirement in their math classes, and also in their history and English courses. Meeting the baseline in all three disciplines helps promote student success in this dynamic course load.
This is the fifth year Mayfield is offering AP Statistics, but it’s Mrs. Goodell’s first year teaching it. Although she had already taken “statistics for math majors” at Villanova University, Mrs. Goodell admits that statistics wasn’t her strongest subject in school. And as a self-professed “perfectionist,” she had an initial reluctance when asked to take on the mantle. Then she got to work. First, she took a statistics course at PCC two summers ago. Then she audited John Romano’s AP Statistics class at Mayfield, completing all the homework and taking all the tests. And finally, she took a college-board approved AP prep course. In this way, she changed her mindset about teaching the subject.
Deeply inspired by the writings of Carol Dweck, Mrs. Goodell looks at all challenges as growth opportunities, very intentional even about the words she uses. “I stopped using the word ‘weakness’ about five years ago,” she says. And Mrs. Goodell relishes exposing her students to this shift in perspective as well, “When students say, ‘I can't,’ ” she corrects them, saying, “maybe you can't right now.” And her approach has a more holistic view of the longevity of the learning process as well. “Every person comes to the table at a different stage in their understanding,” she says. “There might be a unit where it clicks for someone, it makes it real, it's relatable, and then they soar.”
Elise DeGroot ’21 describes her own mindset shift while she was taking this course, “Once I switched from approaching this class like a math class to approaching it as an English class, I became a lot more confident in my reasoning and analysis of problems,” she says. “It also helps that Mrs. Goodell is a great teacher!”
Perhaps one of the reasons Mrs. Goodell is so good at relating to her Mayfield students is that she was one herself. And she has only praise for that journey, saying, “I am who I am and I do what I do because of Mayfield.”
Living through a pandemic is putting statistics front and center in students’ lives. “AP Stats has definitely gotten me to critically think about what’s going on in the news about the coronavirus and its vaccines,” wrote Avalon Dela Rosa ’22. “This was not only relevant in today’s world but very interesting to learn about overall.”
Whether this is the last statistics class her students take or the first of many, Mrs. Goodell just wants her students to be critical about the way information is shared with them. She wants them to be able to pull the story away from the spin.
“It is comforting to know that when I read about opinion polls now,” says Taylor Thorell ’21. “I can identify if they are substantial and trustworthy in measuring the opinion of the population. Also, when I research scientific studies, I will be able to better identify how they are run and work.”
In a time of so much uncertainty and doubt, the analytical skills embedded in this statistics course couldn’t be more useful to these students. “I think that's also a testament to Mayfield,” says Mrs. Goodell. “Empowering us to be strong, independent women and thinkers and advocates. You're not going to tell me ‘no.’ If I want to do this, I can achieve it.”
Back
The concept of “bias” comes up early in this activity. Mrs. Goodell shares the lyrics of “Crazy in Love” and asks the class to select five words from the song, count the number of letters in the words, and calculate the average word length. The students collaborate on a graph in Jamboard, and the girls start adding their dots for the mean word length using the numbers 1-8. The class ends up with the average (“true mean”) word length of 4.3 letters. However, Mrs. Goodell reminds them that their preferences show bias, so the girls move their attention to the second graph on the Jamboard.
Graph two is still plotting the word length in “Crazy in Love,” but this one employs a random number generator. This randomness reduces bias, safeguarding that every subject in the study population (aka words in this song) has an equal chance of being chosen. And lo and behold, there is a notable difference! The average word length for this song is settled at 3.53 letters.
The true mean of all of Destiny’s Child songs is 3.64 letters. Based on the samples supplied, did the class find good evidence that Beyoncé did not write the lyrics for “Crazy in Love”?
Karissa Ho ’21 is careful in answering the question. She doesn’t say that all future inquiries into the question are null and void. But with such a small variance between those two true means? “We don’t have enough evidence to say that Beyoncé didn’t write the lyrics to ‘Crazy in Love,’ ” Karissa says. There seems to be a collective sigh of relief from the class, as the crown of Queen Bey remains relatively untarnished.
It is easy to see how this subject, and this class specifically, appeals to those who are deeply interested in STEM classes, but also with those with a more liberal arts bent.
“I remember Mrs. Goodell describing AP Statistics as a ‘humanities’ math class,” says Avalon Dela Rosa ’22. “More than anything when deciding to take AP Statistics was the uniqueness of the class...a combination of math and argument-based learning.”
There are, in fact, a few prerequisites before students can enroll in this “humanities-based math.” They need to meet a minimum grade requirement in their math classes, and also in their history and English courses. Meeting the baseline in all three disciplines helps promote student success in this dynamic course load.
This is the fifth year Mayfield is offering AP Statistics, but it’s Mrs. Goodell’s first year teaching it. Although she had already taken “statistics for math majors” at Villanova University, Mrs. Goodell admits that statistics wasn’t her strongest subject in school. And as a self-professed “perfectionist,” she had an initial reluctance when asked to take on the mantle. Then she got to work. First, she took a statistics course at PCC two summers ago. Then she audited John Romano’s AP Statistics class at Mayfield, completing all the homework and taking all the tests. And finally, she took a college-board approved AP prep course. In this way, she changed her mindset about teaching the subject.
Deeply inspired by the writings of Carol Dweck, Mrs. Goodell looks at all challenges as growth opportunities, very intentional even about the words she uses. “I stopped using the word ‘weakness’ about five years ago,” she says. And Mrs. Goodell relishes exposing her students to this shift in perspective as well, “When students say, ‘I can't,’ ” she corrects them, saying, “maybe you can't right now.” And her approach has a more holistic view of the longevity of the learning process as well. “Every person comes to the table at a different stage in their understanding,” she says. “There might be a unit where it clicks for someone, it makes it real, it's relatable, and then they soar.”
Elise DeGroot ’21 describes her own mindset shift while she was taking this course, “Once I switched from approaching this class like a math class to approaching it as an English class, I became a lot more confident in my reasoning and analysis of problems,” she says. “It also helps that Mrs. Goodell is a great teacher!”
Perhaps one of the reasons Mrs. Goodell is so good at relating to her Mayfield students is that she was one herself. And she has only praise for that journey, saying, “I am who I am and I do what I do because of Mayfield.”
Living through a pandemic is putting statistics front and center in students’ lives. “AP Stats has definitely gotten me to critically think about what’s going on in the news about the coronavirus and its vaccines,” wrote Avalon Dela Rosa ’22. “This was not only relevant in today’s world but very interesting to learn about overall.”
Whether this is the last statistics class her students take or the first of many, Mrs. Goodell just wants her students to be critical about the way information is shared with them. She wants them to be able to pull the story away from the spin.
“It is comforting to know that when I read about opinion polls now,” says Taylor Thorell ’21. “I can identify if they are substantial and trustworthy in measuring the opinion of the population. Also, when I research scientific studies, I will be able to better identify how they are run and work.”
In a time of so much uncertainty and doubt, the analytical skills embedded in this statistics course couldn’t be more useful to these students. “I think that's also a testament to Mayfield,” says Mrs. Goodell. “Empowering us to be strong, independent women and thinkers and advocates. You're not going to tell me ‘no.’ If I want to do this, I can achieve it.”
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Established in 1931, Mayfield Senior School in Pasadena, CA is a Catholic, independent, college preparatory school for young women grades 9-12. Noted for its rigorous academic program, which includes 28 Advanced Placement and Honors courses, Mayfield’s curriculum is underscored by a philosophy of educating the “whole child,” which also encourages commitment to and excellence in the arts, athletics, community service and spiritual growth. The nurturing environment at Mayfield Senior School allows each student to flourish in an atmosphere of personal attention.
