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Teaching Math |
Advisories |
Research & Evaluation |
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& Notes | Voices from the Field
Integral Learning
The Why and the How of Higher Level Math Courses
Mathematics has emerged as a leading indicator of college-readiness and longitudinal success. These “gateway” courses – more specifically Algebra 2 and higher level classes – are an important predictor of longer term achievement in school and work and are a key component in a college-prep curriculum.
Among the high school class of 1992, 83 percent of students who took Calculus in high school had at least a bachelor’s degree eight years later, compared to just 10 percent of those who only completed Algebra 1. According to education researcher
Clifford Adelman, “Finishing a course beyond the level of Algebra 2…more than doubles the odds that a student who enters post-secondary education will complete a bachelor's degree."
And even for those who choose alternate pathways after high school, the
American Diploma Project, released by Achieve, Inc. in February 2004, established that the essential skills needed to be college-ready are the same required to be work-ready in the 21st century – a key rationale for adopting a rigorous default curriculum for all students.
Uri Treisman, professor of mathematics at The University of Texas at Austin and executive director of The Charles A. Dana Center for improving education, also placed the demand for higher level courses, specifically math courses, in the context of the workplace.
“The jobs that are associated with high income and with upward mobility either require mathematics or they’re in a field in which math is used as a screen… It’s not that doctors really use calculus, but you’re not going to be a doctor unless you distinguish yourself in that course,” said Treisman. “Should we allow 14- and 15-year-olds to make a decision that will determine their ultimate career paths?”
Despite a growing understanding of the importance of math, student performance continues to lag. Only 17 percent of 17-year-olds scored at or above the Proficient level on the 2000 National Assessment of Educational Progress (NAEP), while a third scored below the Basic level. U.S. high school students score below average internationally, and employers say that two out of five high school graduates are inadequately prepared in math.
But raising requirements alone will not boost math achievement. Teachers need materials and guidance to elevate all students through advanced math; fortunately, a number of schools and organizations provide this kind of technical assistance.
At Mastery Charter High School in Philadelphia, where incoming ninth graders are typically 2 years behind in English and 3 years behind in math, both general and remedial support are at the core of the academic program.
Like the name of the school suggests, the goal here is mastery as measured by course skills, prescribed assignments, and Pennsylvania standards. At the end of the first marking period 3� years ago, the school-wide mastery rate for math, science, and humanities was 35 percent. Students graded out at an 80 percent mastery rate at the latest marking period. At present, 7 of this year’s 51 seniors are enrolled in Calculus, and the bulk of the remaining seniors are in pre-Calculus.
To facilitate this improvement, teachers maintain office hours until 4 pm two days a week, and bi-weekly progress reports track individual student performance. Regularly scheduled tutoring is available and additional extra help can be arranged by pulling students from elective classes as needed.
Intense professional development including frequent classroom observations, especially for math teachers, allows the school to maintain high levels of quality control. Instructional differentiation helps teachers to reach students with special needs while also offering a running assessment of understanding across the entire class.
Key Steps Toward Improving Math Instruction and Student Outcomes:
- High expectations for all students – graduation requirements that include Algebra 2
- Intense professional development opportunities, partnered with classroom observations
- Heterogeneous, inclusive teaching practices
- Targeted remediation for students beginning in the 9th grade
- Easy student access to extra help
Researchers at Johns Hopkins University outlined similar supports in their Talent Development High School, a comprehensive reform model to help troubled large schools solve problems of low achievement and high dropout rates. It focuses on building a positive school climate, preparing all students for advanced courses, encouraging college awareness, and supporting reform through teacher professional development. The design provides ninth graders with a “double dose” of instruction designed around the NCTM standards as a transition to advanced mathematics. Teachers are equipped with instructional best practices; they attend monthly workshops and receive weekly support from a peer teacher; they have access to a Hopkins instructional facilitator; and they are part of a support network via the Internet, video-conferencing, or other means.
In Washington state, the
Transition Mathematics Project is helping define college-readiness standards in math that identify the skills and knowledge graduates need to succeed in college without remediation. The Project is developing curricula and materials around these standards, and has begun to identify and highlight teachers’ activities. It is also creating a clearinghouse of best practices from around the state.
The advanced study of mathematics at Mastery – where about 95 percent of the students are African American or Latino and 70 percent of the students qualify for free and reduced lunches – and at schools like it can have a profound impact toward improving life options for all students. And for those who have been disempowered by the lower expectations of the past, there is another effect the subject matter has had, according to Professor Treisman.
“[Math] gave them the power that nobody – no matter who – could tell them they were wrong,” said Treisman “This is the power of the discipline.” ^ back to the top
MAKING THE THIRD “R” A PRIORITY
HOW TO FACILITATE VALUABLE RELATIONSHIPS THROUGH ADVISORIES
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Additional Resources on
Advisories:
Small Schools Project
http://www.smallschoolsproject.org
The Simple
Complexity of Advisories
By Jill Davidson. Horace Vol. 20 No. 4, Fall 2004
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In many American high schools, counselors with caseloads of 400-500 students are forced to make difficult choices, splitting their time between crisis counseling, social service communications, and administrative duties. Little time remains for the academic, career, college, and personal guidance students desperately need to succeed.
In these situations, doubling or tripling the number of counselors still couldn’t provide sufficient resources; such measures still couldn’t provide parents with a single point of contact or increase students’ sense of attachment. The solution many schools and systems have chosen is to create advisories, distributed counseling networks that connect groups of 15-20 students to a single teacher/adult.
Currently, however, these programs are meeting with mixed degrees of success. Teachers often can feel ill equipped to facilitate advisories and remain unconvinced of their relative value – it is time they think would be better spent on instruction. Many students view advisories simply as a break from the rest of the class day, an unstructured time to hang out and talk.
In these cases, the understanding of advisories is limited, the practices are poor, and the potential for strong supportive relationships remains unrealized. It is a series of conditions that must be changed if student outcomes are to dramatically improve.
“One of the biggest challenges I’ve seen in schools is confusion around the purpose of advisories,” said Loren Fields, director of Chicago International Charter School’s Northtown Academy. “Particularly because students don’t receive a traditional letter grade for their work, there can be initial confusion and lack of motivation if the advisory’s purpose is not well-communicated.”
While advisories can take many forms, the overarching goal should be to ensure that all students have an adult advocate who knows them well and is committed to their academic success. Critical functions, distilled from the most successful advisory programs, include:
- Monitoring academic progress and communicating with parents
- Coordinating post-secondary academic or work plans
- Connecting students and parents with appropriate school/community services
Variations beyond these core functions depend on the individual school culture and the needs of individual students.
At Big Picture schools, advisory groups of no more than 15 students meet regularly, and students work with the same advisor throughout their four years. Activities range from team building and time management exercises to discussions on social issues and critiques of student work. As they explore new ideas and topics together, advisors get to know the “whole student.”
Based on the successful experience of Northtown Academy, the Big Picture Company and others, establishing clear goals and expectations among teachers, students, and parents around the purpose and goals of an advisory is an important place to start. Teachers and administrators must work together to assess the needs of the school community and culture, consider school resources including staff and time, and look to other schools with successful advisories in place. This process of self-examination and change often is more difficult at existing schools than at new ones.
“Every advisory will be different because every student within each advisory is different,” said Fields. “Strong advisories will provide enough guidance that advisors feel supported, and enough flexibility that it will be adaptable to students’ needs and each advisor’s unique strengths.”
As a guide, the Power of Advisories workshop, developed by The Education Alliance at Brown University, identifies five general key dimensions of successful advisory programs:
- A stated purpose that all members of the school community (including teachers, students, and parents) understand and support
- Thoughtful organization of people and size, time and space, professional development and support, and student ownership
- Relevant content that reflects the program’s purpose and provides a basic structure for advisors and students
- Ongoing assessment to determine if the purposes of the program are being met
- Strong leadership to provide support, create buy-in and ensure that advisors have the training and resources they need
*Adapted from “Changing Systems to Personalize Learning: The Power of Advisories,” The Education Alliance at Brown University, 2003.
As with any other program, professional development and program assessment are vital to ensure the success and sustainability of advisories. At Northtown Academy, advisors are trained throughout the year on the logistical and academic aspects of advisories, and they often talk through potential activities as a team. As the primary contact between the school and parents, advisors also receive guidance on how to talk with parents.
Other key considerations on advisory design, development, and implementation include: Will advisories be grade-specific or mixed-grade? Will every faculty member act as an advisor? Will the focus be primarily academic, or will community-building and specialized curricula be incorporated? How often will advisory groups meet and where? And how will we know if the advisory program is successful?
And though relationships may be the least quantifiable of the three R’s, it is by no means the least important. Both Fields and Battaglia emphasize the benefits of continuity for the students and their families, and the role that the advisor-student relationship plays in supporting a rigorous and relevant curriculum.
“I was an advisor for four years,” said Joe Battaglia of the Big Picture Company. “Knowing students well meant that I knew what could motivate and inspire them and could tailor their learning plans accordingly. I couldn’t have made good decisions for those students if I hadn’t known them as well as I did through advisory.”
Additional technical assistance:
- First Things First’s
A Guide to the Family Advocate System helps teaching staff to develop their capacity as student and parent advocates.
- College Board’s CollegeEd is a middle school program – soon to include a 6-12 advisory curriculum – designed to inspire and guide families in their preparation for college.
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RESEARCH AND EVALUATION
Learning to Change: School Coaching for Systemic Reform
Learning to Change: School Coaching for Systemic Reform
By Carol J. Brown, Heather R. Stroh, Jeffrey T. Fouts, and Duane B. Baker.
February 2005. Fouts & Associates, L.L.C.
http://www.gatesfoundation.org/NR/downloads/ed/researchevaluation/SchoolCoachingStudy05.pdf
Many schools and districts across the country enlist “coaches” to work with school and district leaders to build internal capacity for system redesign. Learning to Change: School Coaching for Systemic Reform examines the role of coaching in system reinvention and provides direction to organizations that want to provide coaching support. The report highlights four coaching organizations representing a cross-section of approaches and activities.
- The Change Leadership Group (CLG) at Harvard University: Coaches are directed by a clear set of guiding principles about why and how institutions should change
- The Small Schools Coaches Collaborative (SSCC) at the University of Washington: There is no specific coaching program or template per se; coaches tailor their work to individual schools
- The Southern Maine Partnership (SMP) at the University of Southern Maine: Its program aligns their technical assistance work with state standards and the state’s vision for secondary school reform
- Bellingham School District in Washington State: The program operates on the belief that the key to increased student achievement and systemic change is adult learning – including coaches, teachers and principals
Based on their experiences, observations, and assessment, the authors recommend that coaching organizations develop clear theoretical models to guide practice; clearly define roles and activities for coaches; ensure that coaches are strongly qualified; provide extensive and on-going training to coaches; and match coaches’ skills and qualifications to the needs of schools or districts.
Included in the report are one-page profiles of over 30 other coaching organizations and programs. The profiles provide contact information, a description of coaching activities, grades served, funding sources, cost, examples of work, and frequency of coaching visits. These brief descriptions are not intended to provide a comprehensive portrait; instead, readers are encouraged to contact each organization directly to obtain more detailed information.
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News & NOTES
High School Dropouts More Likely to be Unemployed; Earnings Linked to Education
Recent data on earnings and high school dropout rates illustrate the importance of staying in school and continuing on to college. According to the U.S. Bureau of Labor Statistics, the unemployment rate for recent high school dropouts was 40 percent, compared to 20 percent for high school graduates who did not go to college.
Nationally, 2.8 million students graduated from high school in 2003-04, and 1.8 million (66.7 percent) of them were enrolled in college by October 2004. Data from the U.S. Census Bureau reinforces a direct connection between educational achievement and earnings. Workers without a high school diploma averaged $18,734 in wages, high school graduates earned an average of $27,915, college graduates averaged $51,206, and those with advanced degrees averaged $74,602.
States Raising Graduation Requirements
Recognizing that students will rise to the challenge of higher standards, several states are increasing course requirements and mandating a college-preparatory curriculum for all students. The governors of Wisconsin and Oklahoma have proposed increasing math requirements by a year. Indiana, which raised the percentage of graduates in its college-preparatory Core-40 program from 49 percent in 1999 to 65 percent in 2004, will automatically enroll all students in Core-40 starting with the class of 2011 (although students can opt out). Texas has a similar college-preparatory default curriculum, and Arkansas will require its current seventh graders to take math through Algebra II. Some fear the higher requirements will cost more money and lead to more students dropping out. Currently, only five states require four years of mathematics, while 13 require just two years. Eight states let local districts set their own graduation requirements.
High School Students Earning College Credit
Two Department of Education studies found that it is fairly common for high school students to take college courses through dual enrollment programs such as those offered in early college high schools. More than half (57 percent) of colleges had some high school students taking courses for credit, and 1 in 20 high school students took a college course in 2002-03. In addition, more than 1 million students took Advanced Placement courses. President Bush has proposed spending $125 million on community colleges, mainly for dual credit programs.
Dual Enrollment of High School Students at Postsecondary Institutions: 2002-03
http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2005008
Dual Credit and Exam-Based Courses in U.S. Public High Schools: 2002-03
http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2005009
More Students Going to College
In the past 25 years, the percentage of young people participating in postsecondary education increased for all groups except Hispanic males. Postsecondary Participation Rates by Sex and Race/Ethnicity: 1974 –2003, an issue brief from the National Center for Education Statistics, examined the percentage of Americans ages 18 to 24 who were either enrolled in college or had completed at least an associate’s degree or its equivalent. Differentiating by gender, the percentage of women participating in college rose from 32.9 percent to 50.9 percent while male participation increased from 28.4 percent to 41.4 percent. According to racial breakdowns, the percentage of whites increased from 38 percent to 53.1 percent, blacks from 25.7 percent to 38 percent, and Hispanics from 22 percent to 27.6 percent. Black and Hispanic females saw the greatest percentage gains, while the percentage of Hispanic males participating in college was the only one to drop – by 1.4 percentage points.
Postsecondary Participation Rates by Sex and Race/Ethnicity: 1974-2003
http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2005028
Seeking Out Best Practices: Successful Special Needs and English Language Learning Programs The feature article in the May newsletter will offer technical support for addressing special needs and ELL in a small school. If you have a best practice you think could benefit others, please contact Eli Yim at
eliy@gatesfoundation.org.
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VOICES FROM THE FIELD
Yvette Crespo spoke of her daughter’s education, opportunity, and achievement at a grant announcement ceremony in New York City February 15.
My name is Yvette Crespo and I am the mother of two students attending public schools in the Bronx. My son, Dakotah, is a sixth-grader at CIS 166, and my daughter, Yesenia, is a graduating senior at the Bronx School for Law, Government & Justice (LGJ). I’m speaking today to share the experience my daughter and I have had at LGJ and the impact it has had on both our lives.
When Yesenia was first accepted to LGJ, I was nervous and apprehensive, and I’m sure she was too. When we walked into school orientation, we didn’t know anyone and all I could think was that Yesenia was 14 years old, barely 4� feet tall, and shy. I was scared of her going to high school, someplace new where she had no friends. How would she survive?
But that first day, all my doubts were cast aside. The school’s principal, David Banks, spoke clearly about the school’s tone and culture and the high expectations that were held for both students and their parents. I believed him when he assured us that LGJ would provide a safe and structured environment for our children.
But more importantly, what will always remain on my mind and in my heart was when Meisha Ross, a staff member I didn’t even know, walked up to Yesenia, hugged her and said, “I’m adopting this little one.” In that moment, I immediately felt a sense of relief and a connection to the school. Someone was going to look after my baby.
And they have.
Over the past four years, LGJ has supported Yesenia emotionally and academically. When she arrived in ninth grade she was quiet and not very confident; she faired all right academically but wasn’t thriving. Her time at LGJ has changed all that. Yesenia has grown as a young lady and also as a student. Through a buddy system she got involved with debate and student government her freshman and sophomore years, which helped her to focus and become competitive. In her junior year she had a wonderful experience when she lived on campus at Georgetown University for 8 weeks and studied AP Government.
Yesenia is now a senior and president of her school. She is ranked first in her senior class, and I say with much joy and pride she has earned a $100,000 college scholarship through the Posse Foundation to attend Brandeis University in Massachusetts. Who would have thought that the shy little girl who walked into that orientation would have grown into such a strong, vocal young lady?
As she now gets ready to go away to college, I am not as apprehensive as I was four years ago. Although this is a new challenge, I am confident that LGJ has equipped Yesenia with the skills she will need to succeed in this new venture. Yesenia has begun her journey to becoming a great leader and to realizing her dreams.
I believe that it was not only Yesenia’s hard work that got her here, but also attending a small high school where she wasn’t just a number, where the school staff knew her as a person. Inspired by the teachers, lawyers, and judges that have mentored her over the past four years, she has decided that she wants to some day become a leader and make changes through politics or the court system. I am very proud of the young woman Yesenia has become.
Not only will she be the first in our family to go to college, but she has even inspired me to go back to school and further my education, helping me realize that it is never too late to make a difference no matter what obstacles come your way. Next September, we will both begin on our paths to gaining our bachelor degrees.
Just the other day Yesenia said to me, “Mami, one day I’m going to become the chancellor.”
I smiled at her and said, “Baby, the world is yours.”
She laughed and said, “Look out, Brandeis, here I come!”
Yvette Crespo was born and raised in New York City. The Bronx School for Law, Government and Justice was the first school opened by the Urban Assembly, an intermediary that currently operates nine small schools throughout New York City. LGJ integrates the study of law and government into a standards-based core curriculum, and through internship and mentoring programs, provides students with exposure to the real-life world of law where they can then put that knowledge to use.
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