BUA Math Curricular Evolution
We are excited to share news about an upcoming revision to BUA’s math curriculum – a change our math department has been planning for several years and is eager to now make a reality. BUA’s math teachers are designing a curriculum from the ground up, specifically tailored for our exceptional students. While the changes will impact no current BUA students and a subset of incoming students next year, we think it is important for the broader community to understand the direction and why we believe so strongly in it.
Our Math Program
BUA’s math program is an area of strength and a key differentiator in the market. Students appreciate that they can begin their math journey at whatever level is right for them, depending on the results of their placement test and evidence of their preparedness through their transcript and application to BUA. Currently, BUA offers four year-long math courses – Advanced Algebra, Geometry, Precalculus, Calculus – and two semester-long courses: Calculus 2 and Multivariate Calculus. All courses are honors-level, with no tracking. Roughly half of our new 9th graders begin in Advanced Algebra or Geometry, with the other half mainly in Precalculus and Calculus. Calculus is a graduation requirement.
Students and families also appreciate the upper-level course math offerings at BU – offerings no high school in the country can match. A significant number of BUA upperclassmen take two or more semesters of BU math courses after having completed BUA’s multivariate course.
These two key features – placing into courses based on experience (rather than grade level) and the availability of upper-level math offerings at BU – will not change.
Curricular Reform
Our plan is to build on strength. For several years, the department has been discussing an evolution in the first two levels of BUA math offerings (Advanced Algebra and Geometry) – moving those courses in an integrated and problem-based direction. We are now in a position to do just that.
– Integrated: Rather than distinct Advanced Algebra and Geometry as the first two levels of BUA math, we will move to an approach where each of the first two courses in the sequence integrates algebraic and geometric concepts, while also introducing students to other topics like combinatorics, number theory, statistics, and data analysis. While blended, this first-level course will focus more on algebra, and level 2 more on geometry. The primary advantages of this approach are (1) avoiding a year-long “geometry gap” between algebra and precalculus; (2) inviting students to see connections between topics that are artificially separated by traditional approaches; and (3) deepening understanding of concepts as they spiral through the multi-year curriculum.
– Problem-Based : For many years, Precalculus at BUA has been taught through a problem-based approach, and we will adopt this approach for the preceding courses as well. Students in Precalculus do not work from a textbook, but instead spend the year working through a problem set consisting of hundreds of problems. Whereas in a traditional curriculum, problems of the same type are presented and practiced together in a block, topics in this approach are interleaved – spaced and mixed so that students encounter a topic multiple times over a period of weeks and learn to recognize the problem type, not just solve it as a mechanical exercise. The problem sets are carefully constructed sequences of problems where all needed information is embedded in the questions themselves. In class, students work together to present and discuss the solutions to those problems with one another, under the careful guidance of their teacher. The primary advantages are (1) building students’ confidence as problem solvers; (2) avoiding the learning limitations of traditional approaches, where students sometimes struggle to determine what tool to apply to a problem if it is not presented in the context of other similar problems; (3) boosting long-term retention; and (4) strengthening math communication skills.
While the curricular changes mainly impact the first two levels of BUA math, there will also be a revision of the current level 3 course (Precalculus) in light of the changes in levels 1 and 2. No changes are envisioned for Calculus and beyond.
The rollout plan is:
– Fall 2025: Algebraic Thinking & Coordinate Geometry: Integrated Math 1 launched for 9th-grade students placing into the first level of BUA math.
– Fall 2026: Euclidean Geometry, Functions, & Graphs: Integrated Math 2 launched for rising 10th graders who took Algebraic Thinking & Coordinate Geometry in the previous year and any new students who place into the second level of BUA math.
– Fall 2027: A revised course – Precalculus: Integrated Math 3 – launched to align with the previous two courses for any returning students who took Euclidean Geometry, Functions, & Graphs in the previous year and any new students who place into the third level of BUA math.
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In making these changes, BUA teachers are building on years of their own experience with these approaches. They are tailoring the curriculum to the needs and talents of our students. As a school, we are joining some of the most rigorous high schools in the country that have adopted similar approaches. Our conversations with those schools, review of the academic literature, and conversations with some of the leading math education researchers in the country all indicate that our students will be even better served as we embark on this path. We are excited to get started.
Frequently Asked Questions
What is the planned BUA math course sequence?
– Algebraic Thinking & Coordinate Geometry: Integrated Math 1 (fall 2025)(year-long)
– Euclidean Geometry, Functions, & Graphs: Integrated Math 2 (fall 2026)(year-long)
– Precalculus: Integrated Math 3 (fall 2027)(year-long)
– Calculus (year-long)
– Calculus II (one semester)
– Multivariate Calculus (one semester)
Are BUA teachers writing this curriculum?
Yes. Our faculty is excited about this direction and is engaged in a process of writing a curriculum tailored to the talents and needs of BUA students. Phillips Exeter was one of the first schools to adopt a problem-based and integrated math curriculum. Since then, several other schools have adopted the Exeter materials. While our faculty has consulted those materials, they have decided that a more BUA-tailored approach makes sense.
Who will be impacted by this curricular change?
No current BUA students will be impacted by the curricular change, and a subset of new students will engage with the revised curriculum in the fall of 2025.
In the 2025-26 school year, BUA will offer Algebraic Thinking & Coordinate Geometry: Integrated Math 1. Only new students who place into level 1 of BUA’s math program will engage in the new curriculum. Other new and all returning students will enroll in our traditional math sequence (Geometry, Precalculus, etc.) depending on placement.
In the 2025-26 school year, BUA will add Euclidean Geometry, Functions, & Graphs: Integrated Math 2. New students who place into this course or Algebraic Thinking & Coordinate Geometry will engage with the new curriculum, as will students who took Algebraic Thinking & Coordinate Geometry in the previous year. All other returning students will enroll in our traditional course sequence: Precalculus, Calculus, or beyond.
In the 2026-27 school year, BUA will roll out a revised Precalculus: Integrated Math 3 course, completing the new sequence.
What is special about the planned first three levels of the BUA math curriculum?
The first three years of the BUA math sequence will take an integrated approach. Rather than treating fields of math as distinct, these courses will integrate algebraic and geometric concepts, while also introducing students to other topics like combinatorics, number theory, statistics, and data analysis. Concepts will spiral across the three courses at increasing levels of sophistication.
The courses will also be problem based. Rather than following a textbook, students will spend the year working through a problem set consisting of hundreds of problems. In a traditional curriculum, problems of the same type are presented and practiced together in a block. In our problem-based courses, topics will be interleaved – spaced and mixed so that students encounter a topic multiple times over a period of weeks and learn to recognize the problem type, not just solve it as a mechanical exercise. In class, students will work together to present and discuss the solutions to those problems with one another, under the careful guidance of their teacher.
What are the advantages of an integrated and problem-based curriculum?
We believe strongly that these approaches will help students build an even stronger and deeper mathematical foundation, and hopefully inspire a lifelong love for mathematics.
The primary advantages of an integrated approach are (1) avoiding a year-long “geometry gap” between algebra and pre-calculus; (2) inviting students to see connections between topics that are artificially separated by traditional approaches; and (3) deepening understanding of concepts as they spiral through the multi-year curriculum.
The primary advantages of a problem-based curriculum are (1) building students’ confidence as problem solvers; (2) avoiding the learning limitations of traditional approaches, where students often struggle to determine what tool to apply to a problem if it is not presented in the context of other similar problems; (3) boosting long-term retention; and (4) strengthening math communication skills.
How will math placement be determined?
All new BUA students sit for a required math placement exam. The results of this exam, along with the student’s transcript and previous math experience, are used to determine the best math placement for a student. A student may place into any of the BUA math courses listed above.
Is it possible for a student to accelerate through a course in this sequence?
Yes, but only in limited cases. Each course is designed to build on the one before, and students are well served by following the sequence as devised. The school may approve a request for summer math advancement, which requires, among other things, successful completion of an approved summer course and a BUA-administered mastery test. More information about summer math advancement is available in BUA’s Student and Family Handbook.
What is the math graduation requirement at BUA?
All students are required to complete three years of math, including Calculus. Most students take four years of math, going beyond the three-year requirement. Many will complete Calculus and then go onto BUA’s Calculus II and Multivariate Calculus courses, and higher-level math classes at Boston University.
Will this curricular change affect students’ standardized testing schedule or results (e.g., SAT, ACT)?
Most BUA students take the SAT or ACT for the first time in the spring of their junior year. At that point, all students are in Precalculus, Calculus, or a higher math class and are well prepared for those tests. This curricular change will not change the material covered in advance of these tests.
Do other schools use this integrated and problem-based approach?
Several peer independent schools (as well as public-school systems) have adopted approaches similar to the one we have described. Some examples include Phillips Exeter Academy (Exeter, NH), Milton Academy (Milton, MA), Spence School (New York, NY), and The College Preparatory School (Oakland, CA).
What evidence supports the effectiveness of integrated and problem-based math over traditional approaches?
Below is a sample of academic research exploring and supporting the advantages of problem-based and integrated approaches to math education.
Grouws, D., Tarr, J., Chávez, O., Sears, R., Soria, V., & Taylan, R. Curriculum and Implementation Effects on High School Students’ Mathematics Learning From Curricula Representing Subject-Specific and Integrated Content Organizations. (2013) Journal for Research in Mathematics Education, 44 (2). 416-463.
Hmelo-Silver, C. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3). 235-266.
Strobel, J. & von Barneveld, A. (2009) When is PBL More Effective? A Meta-synthesis of Meta-analyses Comparing PBL to Conventional Classrooms. Interdisciplinary Journal of Problem-based Learning. 3(1).
Reys, R. and Reys, R. (2009) Two High School Mathematics Curricular Paths – Which One to Take? Mathematics Teacher, 102(8).
Tarr, J, Grouws, D., Chávez, O., & Soria, V. (2013) The Effects of Content Organization and Curriculum Implementation on Students’ Mathematics Learning in Second-Year High School Courses. Journal for Research in Mathematics Education, 44 (4). 683-729.