Math in the Upper School: “Delivering rigorous and thorough content at all levels”

Math in the Upper School: “Delivering rigorous and thorough content at all levels”

Math in the Upper School: “Delivering rigorous and thorough content at all levels”

Covering an array of disciplines, faculty offer multiple pathways to higher-level math and preparation for college while ensuring students feel supported and successful.

As one of the core academic disciplines — and with an ever-growing list of real-world applications — mathematics is at the heart of students’ experiences at Ravenscroft. Whether it’s being able to understand the concept of one-to-one correspondence when counting or the complex functions of multivariable calculus, students digging into math rise to the challenge and find satisfaction in success.

In the Upper School, teachers approach their work in an array of mathematical disciplines with a keen understanding of the importance of providing students at all levels of interest and acumen with a challenging and worthwhile experience. The department’s comprehensive approach creates multiple pathways to higher-level math and preparation for college while ensuring students feel engaged, supported and successful.

Geometry students get help from teacher Renee Cholkar as they work to discover the formula for a circle using the center and radius of the circle.

“The full spectrum”

Students arrive in the Upper School with a full four years of discovery and challenge ahead. The division’s rigorous and well-rounded college-preparatory curriculum includes a four-year math requirement and many opportunities to apply math in other subjects — such as physics, chemistry, computer science and engineering — as they begin to eye college applications, graduation and everything that comes next.

In the Upper School Math Department, the starting point for many students is Algebra I, which covers topics including polynomial operations, factoring, graphing in the coordinate plane and solving quadratic equations. In geometry classes, students explore reasoning and proofs, line and angle relationships, triangles, circles, quadrilateral properties and similarity. Algebra II extends students’ knowledge of the real number system, introduces the imaginary number system and explores polynomial, rational, radical, exponential and logarithmic functions. As students move into precalculus, they revisit all of these function types and move to a full investigation of trigonometry.

Amber Whitney explains to her Statistics class how they will use quantitative variables such as hand measurements to identify a candy thief.

Statistics students Kyle Hawkins ’23, Andrew Nickolas ’23 and Yogin Patel ’23 put their collected data into a shared spreadsheet.

And that’s just the typical four-course progression. Some Ravens’ mathematical journeys take them to statistics and calculus — including Multivariable Calculus, a challenging course similar to what’s taught to second-year university students.

The department also offers multiple degrees of rigor in each discipline, a practice built on years of data and feedback suggesting that a more tailored approach to course content — factors such as pace, breadth of study and degree of scaffolding — is the best way to meet all students’ needs. They use both teacher-designed and Advanced Placement courses to offer students a rich progression of topics at the standard (“college-prep,” or CP), honors and AP levels.

“We have the full spectrum. Many of our students take Algebra I in ninth grade, many take Geometry and some are in more advanced classes,” department chair Michael Erikson said. “We want them to feel appropriately challenged, and that doesn’t look the same for each kid.”

Work samples from students learning algebra and geometry (left) and AP Calculus AB (right) show the range of mathematical experiences students have in the Upper School.

That thoughtfulness is seen across the department’s series of offerings and includes a rigorous approach to determining course placement for the coming year that considers the student’s level of commitment to the subject, current math grades and grade trends over time, and long-term goals. Students also work with their advisors to consider these math recommendations in the context of other coursework and extracurricular activities.

“There can be a lot of individual considerations, and ultimately we’re committed to doing what’s in the student’s best interest,” Erikson said.

“We take making a student’s math placement very seriously,” Jessica Cummings, who teaches Geometry and Honors Geometry, added. “I want my students to feel confident about their abilities — because they can all do it!”

“Truly transformational work”

In accordance with that belief, the department has continued over time to review and refine its courses and the levels offered for each. The goal is to provide each student with an appropriate pathway to meet both their needs and their goals for college and beyond.

The Math Department’s course flowchart for 2022-23 shows the range of disciplines and levels within each one, designed to support the needs and goals of all Upper School students.

In recent years, a new option for Algebra II — Algebra II/Trigonometry — was added between the CP and honors levels.

“We have split our course sequence this way to better help our population of students. Differentiating the courses into Algebra II, Algebra II/Trig and Honors Algebra II/Trig has allowed teachers to better meet their needs,” Renee Cholkar, who teaches Algebra II/Trigonometry, said. “Students get diverse lesson plans based upon the course they are enrolled in, as well as content.”

“Having multiple levels of courses allows us to meet students where they are in their math journey,” Nicole Lane, who teaches Algebra II, added. “We can then work on building their confidence and improving skills to help them continue moving forward.”

Another change was replacing the yearlong CP Calculus survey course with two semester-long classes that provide students with introductions to both calculus and statistics, giving them what Erikson described as “a natural launch point to go into Calc I or Stats I in college.”

Students who want to stretch into college-level math (such as AP Calculus or AP Statistics) before graduation have a pathway to achieving that goal as well — even if they take Algebra I as ninth-graders.

“Many students will be ready for calculus by their senior year. We only have them for four years, so we created an opportunity for them to take geometry in summer school after their freshman year so they can go into Algebra II as a sophomore,” Erikson said. “Or they can take the two courses concurrently in their sophomore year, because they’re fairly independent of one another. We don’t have a lot of students who do that, but it’s an option.”

Chris Speranza ’25 and Lexi Davis ’25 work on a problem in Jessica Cummings’ Geometry class last spring.

Karen Carroll, who teaches AP Statistics as well as Honors Precalculus BC and Honors Algebra II/Trigonometry, is proud of this approach.

“I think our department does a wonderful job of delivering rigorous and thorough content at all levels, while giving students the support they need,” she said. “Tutorial is invaluable in our department, and all of our teachers provide a lot of support outside of class time.”

That range of courses is notable for a secondary-school department of its size.

“As Head of Upper School, I’m regularly impressed by the math department’s agility, dedication and teamwork in delivering such a robust and varied curriculum,” Aaron Sundstrom said. “As a former member of the department, I’m proud of the truly transformational work they’re doing with our students of all levels of interest and ability in math.”

“Finding success in their best placement”

As with the school’s other two divisions, the Upper School math department has moved away from the teacher-centered, rote-learning model many parents and guardians will remember from their high school years. Students synthesize, apply and extend classroom learning in small groups, considering and reconsidering possible approaches to problem solving, developing as they do a deeper conceptual understanding of their course material.

“We push our students to justify or explain their answers,” Erikson said. “For example, in a precalc class, I might give an equation of a function and provide a graph. The question would say, ‘This graph does not match this equation. Give three reasons why.’ It’s a very different question type, an interesting application of what we’ve been working on in class.”

AP Statistics teacher Karen Carroll goes over a problem from a prior AP exam before having students break into groups to solve it.

Lilla Megyeri ’25 and classmates work on the sample problem at the whiteboard, talking through their approach to the solution.

“I particularly like to send students to the whiteboards to work on practice problems,” Carroll said. “It gets them talking to each other, working together and helping each other, and it allows me to see their work and make suggestions or corrections.”

The department’s approach — student-centered learning in courses designed to meet students where they are — has most definitely been successful.

“One of the things that I’m particularly proud of is that over half of our students graduate with an AP math credit and do so successfully. Looking at our data going back to 2010, our average AP exam score is 4.3 [out of 5]. And that includes the years of the pandemic!” Erikson said. “So it’s not that we’re getting kids into those levels and they’re floundering; we put a lot of time and effort into that placement process each year so that when they get there, they’re successful.”

And that’s not just true of AP courses. The department has had great success with Advanced Functions and Modeling, a precalculus course primarily for seniors who have taken CP courses through Algebra II. The course, pioneered by longtime math teacher Kat Belk, provides a clear benefit with its slower pace and more focused course of study to get students ready for college-level math.

“Many schools will focus on their accelerated math courses, such as AP and post-AP offerings. I’ve always appreciated Ravenscroft’s focus on every student and ensuring our curriculum is robust across all courses,” Sundstrom said. “AFM is a model of that approach, where students firm up foundational concepts, stretch themselves with new content and, most importantly, gain confidence in their ability to be successful in a college math course.”

“It’s a course that really restores their confidence, and not because we’re making it easy,” Erikson added. “Many of these kids report from college that they’re tutoring their freshmen roommates in math. They have found their footing in a subject that challenged them for years.”

Students find many ways to apply their ever-growing understanding of mathematics (such as quantitative analysis), including in disciplines such as physics and in IDE opportunities such as engineering and robotics. At left, Chris Lorenz ’23 tests a race car he designed and built in Lorre Giffords’ Physics class; at right, the robot designed by Automated Admiralty, one of Ravenscroft’s three varsity robotics teams.

College counselors Lia Prugh and Bill Pruden said they see ample evidence that Ravenscroft’s well-rounded slate of offerings benefits students as they prepare to move on to the opportunities ahead in college.

“Our students are well-prepared for college math, which makes them competitive applicants for the many different schools they apply to and attend,” Prugh said.

“I have had four children come through Ravenscroft and each took a different math sequence, a fact that in its own way reflects how the Upper School math program provides a strong foundation for students while meeting each where they are and allowing them to build upon that in an appropriate manner,” Pruden added.

“We have all of the bases covered in our department,” Erikson concluded. “It’s exciting to see how many kids reach the top of the mountain — but, even more importantly, to see all of our students find success in their best placement.”

Want to learn more? Read about math instruction in the Lower School and in the Middle School.

Grace Petrov ’24 works with partners to solve a sample AP exam question in Karen Carroll’s AP Statistics course.

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Students in courses such as chemistry enjoy opportunities to apply and extend their math skills.


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