Table of Contents
Our School
Our school combines academics and the natural world. We seek to connect ourselves, our students, and our community to the environment in which we live. HMI is not simply an environmental, experiential, or traditional school. We borrow liberally from all three traditions, but also leave ourselves open to the world at large. This allows us to present students with new experiences that they can understand and apply to their lives as a whole.
Mission Statement
The High Mountain Institute engages students with the natural world. Our school boldly unites rigorous intellectual inquiry, experiential learning, wilderness expeditions, and shared responsibility in a strong community. Our students realize their potential—as leaders, independent thinkers, and thoughtful citizens.
Organizational Structure
The High Mountain Institute is a 501(c)(3) educational organization providing opportunities for leadership growth, intellectual maturation, and self-reliance within a traditional academic and wilderness curriculum.
Core Values
The High Mountain Institute promotes excellence in all levels of school life. Classroom, wilderness, and residential life are fully integrated components of the student experience, and faculty members participate as mentors and guides in all aspects of the semester. This interaction promotes close relationships in the community and leads to greater performance and achievement. Students typically leave the High Mountain Institute invigorated academically, intellectually, and socially and are prepared to lead active, achieving, and curious lives.
Mentorship in and out of the classroom
Transference of what students learn beyond the High Mountain Institute
Place-based and community-based education
Processed-based learning that teaches students how to think, not what to think, and conveys a passion for learning
Integration of the natural world, academics, and residential life
Calendar
Each semester is approximately 110 days long. Students spend five weeks in the backcountry of Colorado and Utah, and over twelve weeks on the Leadville campus. In both settings, students participate in a rigorous curriculum. Formally structured contact hours for all courses meet or exceed those of sending schools (60 hours/semester).
Curriculum Overview
The curriculum at the High Mountain Institute includes traditional academic courses in history, literature, mathematics, Spanish language, and science. Students also enroll in a leadership and natural ethics elective. All classes are taught at the honors or AP-level. Course titles are as follows:
Required Elective: Practices and Principles: Ethics of the Natural World
English: Literature of the Natural World
Science: Natural Science
History
Fall
- U.S. History – Foundations in American Thought and Culture
- Advanced Placement® United States History
Spring
- U.S. History – Western Perspectives
- Advanced Placement® United States History
Foreign Language
- Intermediate Spanish
- Advanced-Intermediate Spanish
- Advanced Spanish
Mathematics
Fall
- Algebra II: Algebra and Functions
- Precalculus: A, B or C
- Advanced Placement® Calculus: AB or BC
Spring
- Algebra II: Functions and Trigonometry
- Precalculus: A, B, or D
- Advanced Placement® Calculus: AB or BC
Students attend classes six days a week, taking a minimum of five courses. Independent Studies do not count towards the five class minimum. Each class meets for 90 minute sessions four times weekly. Math courses, Spanish, and U.S. History keep students abreast of progress in classes at their sending school. Remaining classes are placed-based and teach grade-appropriate skills.
Assessment
Through the semester, faculty expose students to as many innovative means of evaluation as possible while honoring traditional and widely utilized assessment methods. Practical exams, field studies, and class participation complement quizzes, tests, and research papers in a holistic evaluation of students. HMI uses a standards- based assessment model, which is a system of instruction, assessment, and academic reporting that is based on specific standards that are directly related to the learning outcomes of each course. Instead of receiving grades on specific assignments and assessments, students are assessed and receive feedback on specific standards. It is our belief that a focus on standards rather than grades places the emphasis on learning and not on a normative comparison of one student to another. Ultimately, standards- based assessment underscores that learning is a process—one that each student has the ability to direct according to their individual efforts.
Students are assessed and receive feedback on the specific Skills of Learning. This may take the form of narrative feedback or a score on a 1-4 rubric. While there is discipline-specific language for each level of the rubric, all classes share the following basic rubric scale:
- 1 = Beginning (55%)
- 2 = Developing (70%)
- 3 = Accomplished (85%)
- 4 = Exemplary (100%)
Each level of the rubric has a descriptive label and is associated with a percentage that may become one part of the final grade calculation.
Accreditation
The High Mountain Institute holds dual accreditations. HMI is fully accredited by the Association of Colorado Independent Schools (ACIS), a member of the National Association of Independent Schools (NAIS) Commission on Accreditation. HMI is also accredited by the Association of Experiential Education (AEE).
Course Descriptions
Practices & Principles
Practices and Principles: Ethics of the Natural World (P&P) is a unique and unifying course for HMI students. P&P includes the curriculum taught on the wilderness expeditions and an on-campus, discussion-based class that focuses primarily on environmental ethics. There are two principal goals of the P&P class: first, through the expeditions, we strive to give students a set of tools to camp and travel comfortably in the backcountry for extended periods of time and in adverse conditions. The second goal of P&P is to challenge students to think critically about the way in which they (as individuals, members of society, and members of the HMI community) interact with, use, and think of the natural world. This semester we are exploring the works of a wide variety of authors and media to broaden student perspectives about the human relationship to the natural world. This includes comparing ecological value systems, engaging with personal narratives, and using case studies to elucidate the many relationships with the environment. Students are assessed on their ability to engage with and compare multiple perspectives, critically analyze source materials, and synthesize ideas to arrive at new understandings. They will culminate the semester with a presentation of their own ethic of the natural world.
Enduring Understandings:
Environmental Ethics
- Every individual has a unique perspective that informs how they understand and interpret the world.
- The natural world can be valued in many ways.
- Humans and nature exist in a constant state of interaction, affecting each other in intentional and unintentional ways.
Leadership & Community Studies
- Leadership can take many forms, and effective leadership requires an ability to adapt to context and desired outcomes.
- Leadership and community skills can be taught, practiced, and learned.
Technical Skills
- Backcountry exploration is a means of developing a personal relationship with the natural world
- The simplicity and challenge of traveling safely and living comfortably in the backcountry provides opportunity for reflection and community building.
- The self-reliance necessary for backcountry travel is transferable to “regular” life.
English: Literature of the Natural World
Students in Literature of the Natural World explore the role that language and literature play in shaping human identity and informing our relationship to the land. The course begins with a study of poetic language and concludes with a close reading of Ceremony, a novel by Leslie Marmon Silko. Students refine their analytical thinking and writing skills in short, daily exercises that require them to reflect on the major themes of the course. They write poetry and explore the reciprocal relationship between people and place. Daily discussions encourage students to take ownership over their learning and to manage productive discourse while rooting their contributions in strong textual support. Class assignments and activities offer students the opportunity to refine their authorial voice, synthesize and make sense of diverse literary and critical sources, gain confidence speaking and answering questions in front of an audience, and appreciate the importance of language and literature in contemporary life. Final grades will be derived from student mastery of eight discrete skills of learning under the following headings: “Accountability and Collaboration,” “Critical Analysis,” and “Effective Communication.”
Enduring Understandings:
- Humans’ diverse relationship with the natural world tend to value: spirituality, consolation, solitude, renewed identity, and unbridled identities offered by the natural world.
- Improving our writing is a continual, relational process in which we review and revise our work. The first draft is not the final draft.
- Student-centered learning encourages the development and clarification of ideas supported with evidence.
Science: Natural Science
Natural Science is a field-based class designed for students to practice science outside and develop a stronger sense of place around HMI. On their first expedition in the canyons of Utah, students read about the unique desert ecosystem and present skits demonstrating relationships between local desert flora and fauna. On campus, students study snow and how the snowpack affects local ecology, making entries in their field notebooks and completing reflections during each class meeting. Students practice communicating scientific ideas to hypothetical audiences that vary from scientists to comic-readers. On their second expedition, students contribute to community science observations on snowpack in the Sawatch. Then, students explore the fundamental phenomena that underlie observed effects of climate change. Labs center on researching the plethora of causes and effects of climate change in various ecosystems and investigating areas of ecological disturbance in Leadville such as forest fires. The climate change unit culminates in a TED Talk on how climate change affects our students’ home communities, and each student creates an action plan to effect change. On their third expedition, students pose a question about the desert environment and then design and execute an experimental study to answer it. Finally, our apprentice designs a unit that merges their scientific passions with student interest in our natural laboratory. During each class meeting, two students present to the class about a plant or animal in the Leadville ecosystem, such as aspen trees or elk, or a historical figure in STEM from underrepresented identities. This ongoing practice gives us all a better picture of Leadville’s ecology and of science as a human practice. Through field notebooks, presentations, projects and expedition assignments, students are assessed on their mastery of accountability and collaboration, critical analysis, curiosity and inquiry, and effective communication.
Enduring Understandings:
- Everything, biotic and abiotic, interacts in dynamic relationships.
- Scientific findings are more powerful when they can be communicated to varied audiences.
- Scientific observation is an active way to cultivate curiosity of place.
- Engaging with science improves our ability to think critically.
United States History
Enduring Understandings:
- History is a foundational narrative; it provides insight into the origins of our nation and our world and helps us better understand ourselves.
- The ideals that shaped the founding of the United States continue to exert a profound influence over the social, cultural, and economic life of the nation.
- Historical analysis is an inherently biased and subjective enterprise. Challenging traditional or predominant narratives and seeking out alternative perspectives is crucial to thinking critically about the past as well as the present.
- The way in which we interpret the past informs how we understand the present and often defines our possibilities for the future.
Advanced Placement® United States History
In Advanced Placement© United States History, students use the tools of the historical discipline to examine some of the defining questions of the American past. Students focus on ideological continuity and discontinuity, authorial biases, historical causality, and cultural mythmaking in the years between the early colonial period and Reconstruction (fall) and the Gilded Age through the end of the twentieth century (spring). The course engages foundational primary documents and secondary texts by scholars and critics such as Edmund S. Morgan, Pauline Maier, Ta-Nehisi Coates, Eric Foner, Drew Gilpin Faust, Herbert Marcuse, Howard Zinn, and Francis Fukuyama, among others. Students grapple with enduring ideas and themes from the American past, such as the relationship between narrative and history, the evolution of gender roles and American understandings of race, the shifting meanings of freedom and equality in political discourse, debates over democracy and conscience, populism, liberalism, modernity, and competing notions of “progress.”
In the Fall Semester, students consider and challenge prevailing historical interpretations while also creating their own narratives that explain the relationships among historical events and make meaning from the broader trajectory of American history. Chronologically, this course moves from the pre-colonial period through the end of the Civil War and Reconstruction and prepares students to reenter the second half of an American history survey or AP® United States History course. Primary source documents—letters, works of art, political cartoons, court proceedings, speeches, photographs, advertisements, and poems—provide the foundation for historical inquiry in this class. A variety of secondary source readings by scholars such as Gordon Wood, Mary Beth Norton, Ronald Takaki, Annette Gordon-Reed, Susan-Mary Grant, and others complement these documents and bring students into the ongoing historiographical debates that give life to the discipline. Students examine, in particular, the relationship between history and narrative, the connection between liberty and slavery in the antebellum period, the construction and reification of early-American gender roles, the contested role of equality in the colonial and Revolutionary periods, the tension between individualism and communitarianism, and the evolving meaning of freedom in American political discourse. Students have the opportunity to refine their authorial voice in analytical essays, gain confidence in front of an audience through class presentations, and link the past to the present through student-led discussions.
In the Spring Semester, students focus on ideological continuity and discontinuity, authorial biases, historical causality, and cultural mythmaking in the years between Reconstruction and the end of the twentieth century. Using foundational primary and secondary texts by Frederick Jackson Turner, Ronald Takaki, Richard White, Emma Goldman, James Loewen, Jane Addams, James Baldwin, and others, students engage with concepts such as race, modernity, populism, ideology, liberalism, and historical objectivity. Analytical essays, class presentations, student-led discussions, and group work form the basis for evaluation and provide students with the opportunity to refine their authorial voice, synthesize and make sense of diverse historical evidence, gain confidence in front of an audience, and explore the significance of historical narratives. At the end of the semester, students will leave the classroom with the skills and content necessary to succeed in advanced history seminars.
The following skill categories serve as the basis for evaluation: Accountability and Collaboration, Critical Analysis, Curiosity and Inquiry, and Effective Communication.
United States History: Foundations in American Thought and Culture (Fall Semester)
History is a dynamic and ever-evolving enterprise; this course, therefore, focuses on the contested nature and unresolved questions of the American past. Students consider and challenge prevailing historical interpretations while also creating their own narratives that explain the relationships among historical events and make meaning from the broader trajectory of American history. Chronologically, this course moves from the pre- colonial period through the end of the Civil War and Reconstruction and prepares students to reenter the second half of an American history survey or A.P. United States history. Primary source documents—letters, works of art, political cartoons, pamphlets, speeches, photographs, advertisements, and poems—provide the foundation for historical inquiry in this class. A variety of secondary source readings by scholars such as Gordon Wood, Edmund S. Morgan, Mary Beth Norton, Ta-Nehisi Coates, Pauline Maier, and others complement these documents and bring students into the ongoing historiographical debates that give life to the discipline. Students examine, in particular, the relationship between history and narrative, the connection between liberty and slavery in the antebellum period, the construction and reification of early-American gender roles, the contested role of equality in the colonial and Revolutionary periods, the tension between individualism and communitarianism, and the evolving meaning of freedom in American political discourse. Students have the opportunity to refine their authorial voice in analytical essays, gain confidence in front of an audience through class presentations, and link the past to the present through student-led discussions.
The following skill categories serve as the basis for evaluation: Accountability and Collaboration, Critical Analysis, Curiosity and Inquiry, and Effective Communication.
United States History: Western Perspectives (Spring Semester)
The United States History: Western Perspectives course is designed to provide students with the analytical tools and enduring understandings necessary to deal critically with the major themes and questions in western American history. Using nineteenth and twentieth-century primary source documents in addition to the work of leading scholars, writers, and critics of the American West–from Frederick Jackson Turner, William Cronon, and Patricia Nelson Limerick to Quintard Taylor, Marc Reisner, and Terry Tempest Williams –students approach the West from a variety of perspectives and through multiple conceptual lenses. History is a dynamic and ever-evolving enterprise; this course, therefore, focuses on the contested nature and unresolved questions of the western past. Students consider and challenge paradigmatic historical binaries such as frontier versus border, place versus process, individualism versus community, and “New” West versus “Old” West, while also considering the role of environment, ideology, race, technology, economics, and politics in shaping the course of western development. To elucidate the links between past and present, this course also examines crucial contemporary issues such as water, land use, and how social change occurs from an historical perspective. Regular readings, class presentations, discussions, and group work provide students with the opportunity to refine their authorial voice, gain confidence in front of an audience, and critically interrogate the significance of western narratives and values in contemporary society. The following skill categories serve as the basis for evaluation: “Accountability and Collaboration,” “Effective Communication,” “Critical Analysis,” and “Curiosity and Inquiry.”
Spanish
Spanish at HMI focuses on the exploration of grammar topics, vocabulary, and incorporation of the four major linguistic skills—reading, writing, speaking, and listening—in order to advance language proficiency. Spanish is offered at three different levels and students are placed in the level that will best prepare them for success upon return to their sending school. While the specific content that students learn varies considerably, the Spanish department strives to develop in students habits of mind that they can apply across and beyond the Spanish curriculum. During the semester, students will both review familiar verb tenses and grammar topics and explore new vocabulary and tenses. The grammar “nuts and bolts” will support our study of Latino immigration to the United States. This knowledge will be the basis for building skills of thinking and questioning critically, providing feedback, taking responsible risks, finding humor, leading, and communicating with clarity paired with dispositions of persistence, empathy, and social responsibility. Specific tasks such as daily informal conversations, skits, reading discussions, presentations, letter writing, formal discussions and debates and creative writing are assigned to assess the development of students’ skills in each of the four major linguistic skills. By the end of the course, students will have honed their skills to further study and explore the Spanish language as well as cultural topics and immigration issues across the globe.
Enduring Understandings:
- The building blocks of language—grammar, vocabulary, correct language structures and patterns, phrasing, and pronunciation—are vital to conveying meaning. Mastering these building blocks takes imagination, persistence, and commitment to practice.
- Every individual has a unique perspective that informs their understanding and interpretation of the world around them. Studying a language allows one to better empathize with others perspectives and cultures, explore new disciplines and knowledge from a broader variety of sources, and thoroughly examine one’s own culture with a more informed lens.
- Immigration is a complex issue and has a significant effect on the cultural identity of the United States. Seeking out diverse perspectives is crucial to thinking critically about this issue as the immigration experience can be different for all.
Intermediate Spanish
The Intermediate Spanish course, conducted primarily in Spanish, focuses on the exploration of grammar topics, vocabulary, and incorporation of the four major linguistic skills—reading, writing, speaking, and listening—in order to advance language proficiency. During the semester, students usually operate between the ACTFL Novice High to Intermediate Medium levels. Students in this class focus on expanding their vocabulary and ability to express themselves more quickly and fully. This course is conducted in 70% Spanish immersion. The course is divided into three thematic units: (1) Identity and History; (2) Storytelling; and (3) Modes of Communication. Over the course of the semester, students study the present, preterit, imperfect, future, as well as conditional and perfect tenses. Students complete a horror story script and presentation, a 6-minute investigative report and presentation on an indigenous group of Latin America, a poetry project, a reflective one-page essay, and various other smaller projects, particularly informal skits and speaking exercises, to practice speaking, listening, and learning grammar and vocabulary in context.
Intermediate-Advanced Spanish
The Intermediate-Advanced Spanish course, conducted almost entirely in Spanish, focuses on the exploration of grammar topics, vocabulary, and incorporation of the four major linguistic skills—reading, writing, speaking, and listening— in order to advance language proficiency. During the semester, we will move quickly through a review of familiar verb tenses and grammar topics in order to explore new vocabulary and tenses. Intermediate-Advanced Spanish students usually operate between the ACTFL Intermediate Medium to Advanced Low proficiency levels. Students in this class will focus on speaking proficiency and expression, as well as starting to delve into essay writing and formal presentations. Over the course of the semester, students review and study the preterit, imperfect, future, conditional, and perfect tenses as well as the present and past tense subjunctive mood. This course is conducted in 90% Spanish immersion. The course is divided into three thematic units: (1) Identity and History; (2) Latin American Revolutions; and (3) Contemporary Latin America. Students complete two poetry projects, a 10-minute investigative report and presentation on an indigenous group of Latin America, a 600 word persuasive essay, and various smaller projects to practice speaking, listening, and learning grammar and vocabulary in context.
Advanced Spanish
The Advanced Spanish course, conducted entirely in Spanish, focuses on the exploration of grammar topics, vocabulary, and incorporation of the four major linguistic skills—reading, writing, speaking, and listening—in order to advance language proficiency. Advanced Spanish students include AP and native speakers and usually can operate at an ACTFL Advanced Medium to High level. Students in this class focus on formal writing, discussions, and presentations. This course is conducted in 100% Spanish immersion. The course is divided into three thematic units: (1) Identity and Indigenous History; (2) Latin American Revolutions; and (3) Contemporary Latin America. Over the course of the semester, students review the preterit, imperfect, future, conditional, and perfect tenses as well as the present and past tense subjunctive mood. Students complete two poetry projects, a 15-minute investigative report and presentation on an indigenous group of Latin America, a 1000 word persuasive essay, and various smaller projects to practice speaking, listening, and learning grammar and vocabulary in context.
Mathematics
Math courses at HMI reflect a carefully curated range of curriculum options which meet the majority of student needs. Students are placed in courses that will both set them up for success upon return to their sending schools and create a coherent course of study for the class as a whole. The math department works to develop in students habits of mind that they can apply across and beyond the math curriculum, including: reasoning abstractly, finding patterns and making generalizations, constructing logical arguments, probing for deeper structure, using technology strategically, attending to precision, and modeling with mathematics. These heuristics are embedded through all of our courses; while the course descriptions below outline specific content that students will work to understand over the course of the semester, these broader habits of mind support each of our courses and guide our daily pedagogy.
Enduring Understandings:
- Math is for everyone; everyone can do math.
- Effective collaboration and sustained inquiry grounds our understanding of math and helps us develop robust and dynamic problem solving strategies.
- The building blocks of math–noticing patterns and making generalizations, constructing viable and logical arguments, and reasoning abstractly–are useful both in learning content and in contexts outside of a math classroom.
- Mastering the building blocks of math takes care, persistence, curiosity, and ownership.
Algebra II: Algebra & Functions (Fall Only)
This course is for students who have studied a full year of Algebra I and are beginning their study of Algebra II. The focus is on manipulating algebraic expressions and working with a variety of common functions. This course begins by studying expressions and equations of a variety of types, including linear, exponential, radical, and absolute value equations and inequalities, with a focus on common misconceptions. This is followed by a study of functions, including properties of functions, function transformations, quadratics, and complex numbers.
Algebra II: Functions & Trigonometry (Spring Only)
This course is for students who have completed their first semester of Algebra II. Students in this course will be prepared for a Precalculus or Algebra III course following their time at HMI . Algebra II: Functions and Trigonometry focuses on building fluency with a variety of common functions, making connections between various function representations and transformations. Topics include function transformations, polynomials, rational functions, exponential and logarithmic functions, with supplementary topics in algebra as necessary. Then, students move into a brief study of trigonometry, including an introduction to the unit circle and graphing basic trig functions.
Precalculus A (Fall & Spring)
In Precalculus A, students study a range of topics that both prepare them with the skills necessary to take a calculus course in the future and link mathematical ideas to culminate their study of algebra and functions. Specific course topics include polynomials, rational functions, exponential and logarithmic functions, graphing and modeling with trigonometric functions, connecting trig functions and the unit circle, inverse and reciprocal trigonometric functions, solving trigonometric equations, proving trigonometric identities, and the Law of Sines and Cosines. While engaging with these topics, students practice looking for patterns and making generalizations based on them, constructing viable arguments, and reasoning abstractly. Students are assessed based on their command of skills in the course, their ability to communicate mathematical ideas while solving novel problems, and their engagement with peers in active problem-solving. Standards under “Critical Analysis” represent assessments that students take at the conclusion of each week. Students are able to retake these assessments to demonstrate their content knowledge if they would like. Standards under “Accountability & Collaboration” represent daily homework, graded at the culmination of each academic block. Standards under “Effective Communication” represent bigger projects that are worked on throughout the academic block. Assessment reflects the two complementary goals of this course: that students develop deep knowledge of topics in algebra and that these topics act as a platform to improve students’ mathematical reasoning.
Precalculus B (Fall & Spring)
In Precalculus B, students study a range of topics that both prepare them with the skills necessary to take a calculus course in the future and link mathematical ideas to culminate their study of algebra and functions. Specific course topics include graphing & modeling with trig functions, the unit circle, reciprocal & inverse trig functions, trig equations and identities, the Law of Sines & Cosines, polar coordinates & graphs, and sequences & series. The common thread in these topics is that students practice looking for patterns and making generalizations based on them, constructing viable arguments, and reasoning abstractly. Students are assessed based on their command of skills in the course, their ability to communicate mathematical ideas while solving novel problems, and their engagement with peers in active problem-solving. Standards under “Accountability & Collaboration” represent homework and regular assessments of course content. Students can retake these assessments twice in order to demonstrate their content knowledge. Standards under “Critical Analysis” represent synthesis assessments: larger tasks, begun in class and completed independently, that ask students to bring together multiple concepts and patterns to solve problems and articulate mathematical arguments. Standards under “Effective Communication” and “Curiosity and Inquiry” reflect skills that were vital to student success in this class and are evaluated through synthesis assessments and expedition assignments. Assessment reflects the two complementary goals of this course: that students develop deep knowledge of topics in precalculus and that these topics act as a platform to improve students’ mathematical reasoning.
Precalculus C (Fall Only)
In Precalculus C, students study a range of topics that both prepare them with the skills necessary to take a calculus course in the future and link mathematical ideas to culminate their study of algebra and functions. Specific course topics include quadratic functions and applications, function transformations, polynomials, rational functions, exponential and logarithmic functions, and function operations (composition and inverse functions). While engaging with these topics, students practice looking for patterns and making generalizations based on them, constructing viable arguments, and reasoning abstractly. Students are assessed based on their command of skills in the course, their ability to communicate mathematical ideas while solving novel problems, and their engagement with peers in active problem-solving. Standards under “Critical Analysis” represent skills assessments that students take at the conclusion of each week. Students can retake these assessments if they’d like in order to demonstrate their content knowledge. Standards under “Accountability & Collaboration” represent daily homework, for which they are graded on completion through binders checks that occur at the end of each academic block. Standards under “Effective Communication” represent projects that are worked on throughout the academic block. Standards under “Curiosity and Inquiry” reflect skills that are vital to student success but are not evaluated. Assessment reflects the two complementary goals of this course: that students develop deep knowledge of various topics in precalculus and that these topics act as a platform to improve students’ mathematical reasoning.
Precalculus D (Spring Only)
This course surveys a variety of precalculus topics in the Spring semester, with a specific focus on topics that are necessary to move successfully into a calculus class upon completion. This course begins with a study of polar and parametric functions. From there, students move into topics including combinatorics, sequences and series, limits, and probability. The latter part of the course introduces the principle of mathematical induction, and the Binomial Theorem. While engaging with these topics, students practice looking for patterns and making generalizations based on them, constructing viable arguments, and reasoning abstractly. Students are assessed based on their command of skills in the course, their ability to communicate mathematical ideas while solving novel problems, and their engagement with peers in active problem-solving. Standards under “Critical Analysis” represent assessments that students take at the conclusion of each week. Students are able to retake these assessments to demonstrate their content knowledge if they would like. Standards under “Accountability & Collaboration” represent daily homework, graded at the culmination of each academic block. Standards under “Effective Communication” represent bigger projects that are worked on throughout the academic block. Assessment reflects the two complementary goals of this course: that students develop deep knowledge of topics in algebra and that these topics act as a platform to improve students’ mathematical reasoning.
Advanced Placement® Calculus AB (Fall & Spring)
This course is designed to prepare students for the AP® Calculus AB exam in the spring. The fall semester course is suitable for students who have completed precalculus, while the spring semester course is appropriate for students having studied differential calculus in the fall. The course covers a traditional AP curriculum. In the fall, the course begins with a study of limits and derivatives, and covers all of differential calculus, including applications of the derivative, implicit differentiation, optimization and related rates, and an introduction to antidifferentiation. In the spring, the course begins with a review of antidifferentiation, and moves into an in-depth study of integration and its applications, solving differential equations, with some time set aside for AP exam review.
Advanced Placement® Calculus BC (Conditional on Minimum Enrollment)
This course is designed to prepare students for the AP® Calculus BC exam in the spring. The fall semester course is suitable for students who have completed precalculus, while the spring semester course is appropriate for students who have studied differential calculus and significant integral calculus in the fall. The course is typically small, and covers a traditional AP curriculum. In the fall, this course begins with a brief overview of limits and derivatives, but it is important to note that many students enter the course having already studied limits and some differential calculus the previous spring; in any case, the course is fast paced and rigorous. In the fall, topics are covered through differential calculus and applications of integration. In the spring, the course begins with applications of integration and then finishes a study of advanced integration techniques, examines Taylor polynomials, and the calculus of polar and parametric functions before moving into some AP exam review.
It is important to note that we only offer this course if we have a minimum of 3 students enrolled; if we do not meet minimum enrollment, you will need to arrange an Independent Study.