Mathematics Department
The Shady Side Academy Senior School Mathematics Department spent three years considering the third and fourth form mathematics program. Based on research and best practices accepted among our peers, we adapted materials from Phillips Exeter Academy to create a new curriculum and pedagogy for teaching under-form students. This program began in the 2010-2011 school year. Third Form students now take Mathematics I and Fourth Form students take Mathematics II. Together, these two courses will replace the previous Geometry/Algebra II sequence.
Math I and Math II
In 1989, the National Council of Teachers of Mathematics (NCTM) articulated the rationale for precisely this kind of curriculum shift and outlined the following goals for students:
- That they become mathematical problem solvers,
- That they learn to reason mathematically,
- That they learn to communicate mathematically,
- That they learn to value mathematics, and
- That they become confident in their ability to do mathematics. [1]
The teachers at SSA espoused the same goals and attempted to attain them using a traditional, textbook-based, teacher-centered curriculum. Over the past several years, many members of the department began augmenting traditional textbooks with the problem-based curriculum developed at Phillips Exeter Academy. This trend grew into a two-year pilot program from 2008 to 2010 which employed Exeter's materials and their Harkness Table method of teaching mathematics. This student-centered teaching methodology along with Exeter's problem-based materials form the basis for our curriculum change.
Math teachers at Exeter created “books” of word problems through which students achieve the above noted goals. The substance of the experience requires students to thoughtfully consider problems, being led by the teacher to develop problem-solving strategies rather than formulaic answers to the problems posed. The change in our approach is the difference between teaching students to think of math as abstract concepts and formulas that students learn through rote memorization versus teaching students to think of math as a conceptual and practical framework for describing and solving meaningful problems. We recognize that this is a departure from more traditional math curricula and that it requires students and teachers to learn and teach in new ways. In particular, it requires teachers to be highly skilled at knowing how each student is doing and providing the right challenges at the right times. We have met with teachers from Exeter to aid us in the development of the skills necessary to do this most effectively. We have also worked with brain researchers and learning specialists to improve the awareness and communication skills of the teachers, better enabling them to interact with the students and to compare strategies used with various types of learning styles exhibited by the students.
Senior School Course Progressions in Mathematics
For students entering 9th grade having already completed both Algebra I and Geometry: |
Grade 9: Algebra II --> Grade 10: Trig/Precalculus --> Grade 11: Calculus --> Grade 12: Elective |
For students entering 9th grade not having completed both Algebra I and Geometry: |
Grade 9: Mathematics I -->Grade 10: Mathematics II --> Grade 11: Trig/Precalculus -->Grade 12: Calculus |
The holistic goals of Mathematics I and Mathematics II align with the stated goals of the senior school mathematics department as found on our web page:
The Senior School mathematics department encourages creative problem-solving based on logical thinking and computational skills, while striving to promote an appreciation for the beauty and rigor of mathematics. Through a variety of teaching methods and activities designed to enhance understanding, we work to maintain a balance between mathematics as an abstract discipline and as an application for use with other disciplines. In all that we do, we hope to promote a lifelong love of mathematics.
We emphasize the importance of student participation in classroom discussion, and our students develop the ability to communicate effectively in mathematical discourse by using current technology.
The particular goal of these courses is to prepare our students for upper form mathematics, namely Trigonometry, Precalculus and Calculus. In keeping with the NCTM standards, emphasis will be shifted as follows:
Increased emphasis on
- The active involvement of students in constructing and applying mathematical ideas
- Reading, writing and speaking mathematics
- Solving open-ended word problems
- The interrelatedness of mathematical topics
Decreased emphasis on
- Teacher and text as exclusive sources of knowledge
- Instruction by teacher exposition
- Rote memorization of facts and procedures
- Teaching isolated topics in separate chapters
- Less coverage of rational expressions and equations and factoring [2]
These two courses will form the foundation of our students' mathematical studies. Topics from algebra and geometry will be interwoven throughout the two years. Real-life applications are emphasized in the context of word problems and student discourse is emphasized in the implementation. The list of topics that will be introduced and explored through the solving of significant word problems can be found below. Parentheses indicate the former course where this topic would have been covered.
Mathematics I Topics
- Dimension Analysis (Algebra 1)
- The Distributive Property (Algebra 1)
- Order of Operations (Algebra 1)
- Percent and Fractions (Algebra 1)
- Slope (Algebra 1)
- Linear Equations and their Graphs (Algebra 2)
- Perimeter, Area and Volume (Geometry)
- Linear Inequalities and their Graphs (Algebra 2)
- Direct Variation (Algebra 2)
- Uniform Motion (Algebra 2)
- Linear Systems of Equations (Algebra 2)
- Exponents (Algebra 2)
- Radicals (Algebra 2)
- Pythagorean Theorem (Geometry)
- Triangles (Geometry)
- Distance Formula (Algebra 2)
- Proof (Geometry)
Math II Topics
Continuing and deepening topics from Mathematics I plus:
- Absolute Value Equations, Inequalities and their Graphs (Algebra 2)
- Quadratic Equations and their Graphs (Algebra 2)
- Factoring (Algebra 2)
- Vectors (Precalculus)
- Transformations (Precalculus)
- Parametrics (Precalculus)
- Coordinate Geometry (Geometry)
- Solid Geometry (Geometry)
- Exponential and Logarithmic Functions (Algebra 2)
- Circles (Geometry)
- Quadrilaterals (Geometry)
[1] Curriculum and Evaluation Standards for School Mathematics, NCTM. p. 5
[2] Ibid, p. 126
Important Resources
Math Competitions
American Mathematics Competition (AMC)
www.artofproblemsolving.com/Wiki/index.php/AMC_Problems_and_Solutions
1989 | 1990 | 1991 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999
2000AMC10 | 2000AMC12 | 2001AMC10 | 2001AMC12 | 2002AMC10
2002AMC12 | 2003AMC10 | 2003AMC12 | 2004AMC10 | 2004AMC12
2005AMC10b | 2005AMC12 | 2005AMC12b | 2006AMC10b | 2006AMC12b
2007AMC10a | 2007AMC10b | 2007AMC12b | 2008AMC10a | 2008AMC10b
2008AMC12a | 2008AMC12b | 2009AMC10a | 2009AMC12a
2010AMC10a 2010AMC10a key 2010AMC10b 2010AMC10b key
2010AMC12a 2010AMC12a key 2010AMC12b 2010AMC12b key
American Invitational Mathematics Examination (AIME)
www.artofproblemsolving.com/Wiki/index.php/AIME_Problems_and_Solutions
1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001
2002 | 2002alt | 2003 | 2004 | 2004alt | 2005
2006 | 2007 | 2008 | 2008alt | 2009-1&2 2009-1&2 key
2010-1 2010-1 key 2010-2 2010-2 key
Mathematics League (MCWP) Problems
1997-1998 | 1998-1999 | 1999-2000 | 2000-20012001-2002 | 2002-2003 | 2003-2004 | 2004-2005
2005-2006 | 2006-2007 | 2007-2008 | 2008-2009