Educating Mathematical Thinkers – Our Mathematics Program

Educating Mathematical Thinkers – Our Mathematics Program

Park’s Mathematicians at a Glance

Park’s curriculum produces independent, resourceful, and rigorous thinkers who succeed in mathematics. 

  • 99% have current seniors have elected to take four years of math.
  • 28% of current seniors are enrolled in a post-calculus elective. 
  • 58% of freshmen, sophomores, and juniors who took the AP Calculus AB exam over the last ten years scored 5, the highest possible score.
  • 64% of Park’s current senior class is currently studying or has studied calculus. 
  • Out of approximately 40 schools statewide (plus D.C.), Park placed fifth overall in the 2018 Maryland Mathematics League competition. Over the last five years, Park has placed first twice and finished second three times among schools in the Baltimore region.
     

The Approach

At Park, conceptual understanding and mastery of basic skills are linked, not separated. Students’ learning of standard mathematical procedures is grounded in an understanding of why and how these procedures work. From pre-kindergarten on, students learn strategies to solve problems rather than memorize formulas. The youngest children begin to look for patterns among numbers or in geometric forms. They visualize problems by making drawings, charts, or graphs. They work with manipulatives to understand essential number concepts. They learn to estimate to check on the reasonableness of their solutions. As students move into higher levels of mathematics, these strategies continue, but others are added: for example, taking ideas apart (breaking a large or complex problem into smaller parts or cases) or using inverse thinking (working backwards). In total, we term these strategies habits of mind. They are essential to mathematical thinking.

Students learn and practice habits of mind in a variety of ways, including direct instruction. However, most typically, students learn them through investigations (problems and projects), which they work on in small groups. This active approach to learning involves students in sharing ideas, trying out strategies, and working through problems to find accurate solutions.

student and teacher at white board

The Content 

Park covers the content common to traditional programs—and content beyond what those programs offer—but in a different sequence. Park’s program integrates different strands of mathematics rather than separating them (e.g., into the traditional Algebra and Geometry high school sequence). The aim is to create flexible thinkers who can draw on different aspects of mathematics in solving real world problems. 

lower school 

Students work on computational understanding and skills, ranging from whole numbers through Fractions and Decimals. They also have extensive exposure to geometric concepts, algebra, measurement, data analysis, and problem solving.

middle school 

The program begins with an intensive focus on applications of fractions, decimals, and percents, and moves into concepts and interrelationships among arithmetic, geometry, algebra, probability, statistics, programming, trigonometry, and spreadsheets. 

upper school 

Traditional content of algebra, geometry, trigonometry, and pre-calculus is covered. Students then choose from an array of electives such as Calculus, Advanced Calculus, Complex Analysis, Abstract Algebra, Linear Algebra, and Topology and Knot Theory. Other offerings include Statistics, Functions and Calculus, and Discrete Mathematics. 

park student doing math

Opportunities for Advanced Work 

lower school 

The emphasis on small group work provides flexibility to accommodate different paces and support higher levels of mastery. The Lower School math coordinator and faculty members provide specific targeted enrichment that leads to higher order problem solving and collaborative thinking. In addition, after-school clubs, such as Puzzles and Problem Solving, Destination Imagination, and First Lego League enable students to explore math concepts that further augment their classroom experiences.

middle school 

Extensions provide opportunities for a faster pace or greater depth in exploring topics. Students are clustered by ability in sixth grade and grouped in seventh and eighth grades according to their facility with abstract concepts and demonstrated work habits. Extension work challenges students and varies the curriculum as needed to accommodate advanced students.

upper school 

The program has the scope to take students as far as they can go. There is great flexibility in both the range of courses taught and students’ pace in moving through the program. Students are grouped by demonstrated interest and ability; those with particular talent and interest in mathematics cover the standard algebra/geometry/pre-calculus curriculum by the end of tenth grade. This sequence allows students to spend two years studying college-level calculus (Calculus and Advanced Calculus) before leaving high school. Students can carry their mathematics study further by taking advanced college-level courses such as Abstract Algebra, Linear Algebra, and Topology and Knot Theory.

The Outcomes of Park’s Program

The proof is in the numbers. Park students continue their study of mathematics to advanced levels and perform competitively on a variety of national and state assessments.

AP Calculus AB Test Results (college level course)

  • 58% of freshmen, sophomores and juniors from the last ten years who took the AP Calculus AB exam scored 5, the highest possible score. 
  • 97% scored 3 or higher (the College Board standard for college credit or advanced placement in college courses).

AP Calculus BC Test Results (upper level college course)

  • 64% of students from the last ten years who took the AP Calculus BC exam scored 5, the highest possible score. 
  • 95% scored 3 or higher.

SAT Scores

  • Over the last five years, the mean Mathematics SAT score has ranged from 634-655. 

SAT Subject Exam Scores

SAT subject area tests measure mastery of content taught in mathematics programs.

  • Over the last five years, the average score for Park students on the Mathematics Level 2 exam (higher level exam) has ranged from 667-713.

Awards and Independent Study

  • In 2017, a Park student qualified for the United States of America Mathematical Olympiad (USAMO), the exam to select students to represent the United States at the International Mathematical Olympiad. Three Park students qualified for the American Invitational Mathematical Exam (AIME), the feeder exam for the USAMO.
  • In 2017, a Park student was an inaugural winner of the Spirit of Ramanujan Math Talent Initiative, a global search for undiscovered mathematical talent.
  • In recent years, interested students have taken on a variety of independent study topics, including Symmetry and Shape, Group Theory, Analytic Number Theory, Real Analysis, and Game Theory.

Maryland Mathematics League Results

The Maryland Mathematics League sponsors statewide contests in which approximately 40 schools participate, including leading public and independent schools. The test evaluates mathematical competency and conceptual understanding at a high level. A number of schools coach students for this competition; Park does not.

  • Out of about 40 schools statewide (plus D.C.), Park placed fifth overall in the 2018 Maryland Mathematics League competition.
  • Among all participating schools in the Baltimore region, Park has placed first or second 8 times in the past 10 years.
  • Students who have come through our Lower and Middle School math programs are consistently Park’s highest performers.

park upper school math faculty

The Faculty

Teaching an ambitious mathematics program requires exceptional teachers. Consider the following: 

  • Average teaching experience of Park’s mathematics faculty is 17 years. 
  • All Park Middle and Upper School math teachers have substantial formal training in mathematics. Two have Ph.D.s, two have dual master’s degrees, and seven others have master’s degrees or have done substantial graduate coursework. 
  • Minimum qualifications for an Upper School mathematics position include the ability to teach courses through Calculus and upper level college courses such as Abstract Algebra and Knot Theory. Only a fraction of candidates seeking mathematics positions meets this requirement; Park recruits nationally—and sometimes internationally—to find highly talented teachers. 
  • Most of Park’s mathematics faculty have department chair experience, including some who chaired two or more departments at other private schools before coming to Park. 
  • Math faculty have come to Park from leading independent schools and universities, including Isidore Newman (LA), Poly Prep (NY), Millbrook (NY), Codman Academy Charter School (MA), and St. Mary’s College of Maryland. Park’s faculty have taught the International Baccalaureate program and other international programs at schools in Brazil, Colombia, and Puerto Rico.
  • Park teachers from all three divisions participate in professional activities. They have offered training workshops for teachers at other schools, been presenters at the National Association of Independent Schools conferences, the National Council of Teachers of Mathematics (NTCM) conferences, and the joint meetings of the American Mathematical Society/Mathematical Association of America; published in professional journals, served as readers for the AP Calculus exam, attended the Park City Mathematics Institute, and served as consultants to the American Association for the Advancement of Science. 

Curricular Work: Developing a K-12 Program 

Developing an outstanding mathematics program requires extensive professional development work by faculty. Park’s distinctive FACA (Faculty and Curricular Advancement) program has supported 17 intensive summer projects in mathematics. In addition, Park has supported training of Lower School teachers through multiple institutes and in-house workshops. Work has included the following: 

  • For Lower School, projects focused on number skills to delineate essential concepts and grade-to-grade progression 
  • For Middle School, creation of textbook supplements to reinforce algebraic concepts and skills, and curriculum for all grades 
  • For Upper School, writing an original series of texts now in use in the 9–11 grades 
  • Implementation of software (such as Desmos, Geogebra, and Mathematica) across the curriculum
  • Development of tools to focus instruction on the habits of mind central to mathematical thinking 

Summary 

Park School has a coordinated Pre-K–12 mathematics curriculum. Opportunities for advanced work are provided in Lower, Middle, and Upper Schools. Inspired by an exceptional faculty, Park students enroll in upper level courses and achieve at high levels on standardized tests and in math competitions. Following graduation from Park, students are prepared and motivated to continue their study of mathematics in college and to pursue a variety of professions which require a strong mathematics background.