Mathematics at Orchard House School

Revisiting Math and Middle School Girls

Background Information
A driving factor in the creation of Orchard House School in 1998 was designing a middle school for girls that was committed to opportunities and access to math.  Research at the time showed again and again that algebra, primarily, and calculus, secondarily, were gatekeeper classes to a future full of options, whether those options regarded education or employment.   

The research connecting girls’ math proficiency and achievement with later educational and employment opportunities has not changed.  What has changed is the information and research linking how critical the middle school years are to a girl’s sense of mathematical competency, what that sense of mathematical competency implies for the future, the role of mindset, and the information comparing the mathematics curriculum in the United States with higher performing countries across the globe (Singapore, China, Finland).  

So we have math, already a high stakes class, compounded by curriculum and gender.  Specifically, a distillation of the research from the last five years shows this
  • The United States ranks 24 out of 29 countries in global mathematical achievement (Spicer, 2009).  
  • When one examines the differences between the math programs in the United States and those of top-performing countries there are striking curricular differences.  Comparative data on the use of classroom time shows (Mintz, 2008):

Percentage of Classroom Time Spent on Topics


Practicing Procedures

Applying

Concepts

 Investigating New Ways of Thinking

Top-Performing Countries

41%

15%

44%

United States

96%

4%

Less than 1%

  • The math curriculum in the United States is considered a mile-wide and an inch deep (Usiskin, 2009); depth of understanding is often exchanged for quick exposure (Schmidt & Houang, 2007).
  • The United States is inclined to educate for self-esteem or for institutional  or regional success rather than to educate the learner (Davies, 2010).
  • The United States often educates for the quick, the easy, and the apparent, rather than educating for learning and depth of understanding, which often require labor and effort over time.
  • Whereas top-performing countries have mathematical failure rates between 1-4%, in the United States the failure rate is 10%.  There is a different level of commitment to every learner in top-performing countries than there is in the United States (Loveless, 2007).  There is also the cultural valuation of education that is an important factor (Ahtee, M., Lavonen, J. & Pehkonen, E., 2008).
  • High stakes testing in the United States focuses on single, simple answers that are correct rather than demanding multiple paths to solutions that reflect depth of thinking or creative problem solving.  A linear approach to learning is substituted for the complexity of thought that is required in solving complex problems.  This approach, of the single, correct answer, to learning and thinking feeds the perfectionist mindset of high-achieving girls.
  • How a girl perceives her ability is often linked to her sense of competency and achievement as a seventh grade math student (Dweck, 2008).
  • A girl’s mindset of being fixed or growth-oriented directly impacts her achievement (Dweck, 2008).
The United States is currently at odds with itself.  It needs students with mathematical proficiency to fuel its future scientists, engineers, technology experts, and inventors.  Yet, most mathematical learning communities in the United States are not geared towards the type of learning that fosters long-term mathematical success and proficiency.  There are growing voices that claim the current state of mathematical education has become a question of national security.
©Nancy Davies, 2011
 

 

Orchard House School Math Program

Changes in 2010-2011

At Orchard House, we are committed to strengthening our math program continuously. For the last two years, we have examined our own data and researched global math programs, girls, and middle school education. As a result, we are shifting the emphasis in parts of our program. Our fifth and sixth grade programs will offer more opportunities for concept development and multiple paths to solutions. The fifth and sixth grade courses will serve as a foundation to algebraic concepts with a particular emphasis on properties, number sense, identification of patterns, and representative and systems thinking. Increasingly the girls will be asked to study math, to read and write about math, and how to prove what they know. They will work more with data, real life situations, spatial relationships, and geometry. We are working to strengthen their conceptual base so when they get to seventh grade they are competent and confident at the time when research shows that girls associate their overall intellectual competency with their mathematical achievement. Part of the shift in the program will teach the girls directly how their mindset affects their learning and brain development and how exploring multiple paths to solutions is a long-term benefit, even if in the short-term it is uncomfortable. We will emphasize the benefits to the labor of learning so when they are struggling with hard problems they dig deeper to employ strategies for solutions. From these changes, our intent is to cultivate students who are vested in math and in themselves and that the connection between the two is positive and strong.

Fifth Grade Math 2010-11

Orchard House continuously holds its math program up for review. Recognizing that our entering students have significantly different backgrounds and experiences with math, we will pilot a new approach in the upcoming year. 

Beginning in 2010-2011, we will offer two distinctly different math programs for our fifth grade students. Our two programs are the Saxon 76, which we currently offer, and Pre-Transition Math, from the University of Chicago Math Project, which we will add this year. We believe by offering these two distinctly different programs, we will more effectively reach each of our students.

There are significant strengths to each program depending on the past experiences, the style, and the interests of the learner. Essentially, if a girl has had past experiences in math that left her wobbly or uncertain of herself as a successful math student, she would likely benefit from Saxon 76. If a girl has met with success in math, is fairly confident of her math ability, and seems to sail through math, she would likely benefit from the Pre-Transition Math. The Saxon 76 program is spiraling; it builds concepts more predictably and concretely, and it provides continual review. The Pre-Transition program is designed more conceptually, and it often challenges and expands a student’s knowledge base.  

Attitude, effort, and mindset are chief contributors with girls to later math proficiency, understanding, and success. The aim of the school is to set-up all incoming fifth grade students to maximize their ability and their proficiency- both short and long term. From offering these two distinctly different programs we believe we will target each girl’s learning style and preferences more directly, setting her up for success at that critical juncture in seventh grade. As a result of offering these two programs, we believe more of our girls will be math students who are willing to do their best, who have confidence in their ability through hard work, and who have solid foundations, strong conceptual bases, and increased facility with math.

Figuring out how the pilot program complements our current seventh and eighth grade course offerings will be under examination this year. The current plan is to continue both the Saxon and the Chicago math programs through fifth and sixth grades and then to evaluate carefully the needs of each girl and to place her into one of our three math courses currently offered. As part of the pilot aspect of the school’s approach, we will evaluate continuously what best serves each girl.

In very different ways, both programs offer tremendous benefits to our varied learners.  We are excited at this juncture in the school’s development to offer two strong programs to our students. Both programs support the school’s commitment to the development of confidence, long-term understanding, and success in math.

©Nancy Davies, 2011