Contributed by:
Throughout the United States, the Bill & Melinda Gates Foundation is supporting teachers and administrators engaged in large-scale high school reform. The ultimate goals of this reform are to increase the college preparedness, college enrollment rates, and academic success of all students, especially those from poor and minority backgrounds. The reform effort includes commitments by individual schools to maintain high expectations of students; create personalized learning environments; facilitate collaboration among teachers, schools, and the surrounding community; and encourage effective teaching by means of active inquiry and in-depth learning. These reform efforts often are summarized in terms of greater rigor, more relevance, and stronger relationships.
This article examines the challenges that foundation-supported schools face in math education during the early years of their reform efforts. Strategies that many of the schools use to address these challenges are presented, along with some promising practices from other sources. Last, this article points educators to additional resources, ideas, practices, and sources of support that may assist them in enhancing their students’ mathematical skills and sophistication.
1.
Improving Math Performance
While students’ weak Introduction • Students entering high school with substantially
math skills are an obsta- deficient math skills;
cle for math teachers at Throughout the United States, the Bill & Melinda Gates
Foundation is supporting teachers and administrators • Teachers having difficulty using nontraditional peda-
most public schools, they
engaged in large-scale high school reform. The ulti- gogies and curricula; and
are particularly prob-
mate goals of this reform are to increase the college
lematic for schools that • Schools struggling to provide adequate professional
preparedness, college enrollment rates and academic
enroll high percentages of development and support for teachers of mathematics.
success of all students, especially those from poor
minority, low-income and and minority backgrounds. The reform effort includes The weak math skills of students entering high school
English language learner commitments by individual schools to maintain high present a problem nationwide. In the past four cycles
students. expectations of students; create personalized learning of the National Assessment of Educational Progress
environments; facilitate collaboration among teachers, (NAEP), for example, the total percentage of eighth
schools and the surrounding community; and encour- graders who achieved proficient or better status in
age effective teaching by means of active inquiry and mathematics did not reach 30 percent (see Figure 1).
in-depth learning. These reform efforts often are sum-
marized in terms of greater rigor, more relevance and
stronger relationships. Figure 1. Cumulative Percentages of
Students Scoring Proficient or Advanced
Studies of student achievement data from foundation- on the National Assessment of Educational
Progress (NAEP) Mathematics Assessment1
supported schools show noteworthy improvements in
English language arts. However, math performance has 50.0%
Advanced
not shown a similar improvement. Additionally, site 45.0% Proficient
visits across a large sample of foundation-supported 40.0%
schools suggest that high schools face several tough 28.8%
29.8%
35.0%
obstacles to improving math performance as they 25.7%
30.0%
undergo foundation-supported reform. 23.3%
25.0%
This article examines the challenges that foundation- 20.0%
supported schools face in math education during the 15.0%
early years of their reform efforts. Strategies that 10.0%
many of the schools use to address these challenges
5.0%
are presented, along with some promising practices
0.0%
from other sources. Last, this article points educators 1996 2000 2003 2005
N=7,100 N=15,900 N=153,200 N=161,600
to additional resources, ideas, practices and sources
of support that may assist them in enhancing their
students’ mathematical skills and sophistication.
While students’ weak math skills are an obstacle
Challenges Faced by Foundation- for math teachers at most public schools, they are
Supported Schools particularly problematic for schools that enroll high
percentages of minority, low-income and English
Over the past four years, the foundation’s evaluation language learner students — groups for which the
partners have conducted classroom observations and proficiency rates entering ninth grade are on average
staff interviews at more than 100 high schools engaged even lower.2 Foundation-supported schools generally
This research brief is based in foundation-sponsored reform. The data collected show fit this latter profile.
on information from the three major challenges to math education in the schools:
American Institutes of
Research database, 2006.
1
National Center for Education Statistics, National Assessment of Educational Progress (2005). NAEP Data Explorer. Retrieved Feb. 7,
2006, from http://nces.ed.gov/nationsreportcard/nde/viewresults.asp?pid=4-2-8-MAT-National---10-TOTAL-20053,20033,20003,19963,
19962,19922,19902--MC-BB,AB,AP,AD-5-0-0--1-0--2-3--0--1.
2
National Center for Education Statistics, National Assessment of Educational Progress (2005). The Nation’s Report Card: Mathematics
2005 (NCES 2006-453). Washington, DC: U.S. Department of Education, Institute of Education Sciences.
2.
The second challenge facing foundation-supported used at foundation-supported schools, while others
schools arises from the schools’ commitment to imple- are examples of promising practices in use elsewhere.
ment nontraditional math instruction methods and
Strategies for Addressing Challenges
curriculum. This commitment requires the use of more
to Math Performance
concept-oriented, project-based pedagogies that are
relevant to students’ lives and futures. Moving from Supporting Students
a theoretical commitment to actual implementation,
however, has proven to be difficult for many schools. When a student arrives in high school substantially
deficient in math skills, it can be quite difficult to
Research indicates that implementing effective bring that student up to grade level. Foundation-
problem-based instruction requires in-depth training supported schools have relied on a variety of strate-
for teachers and continued support, preferably from gies to address this challenge, such as additional
While there is a shortage
within the school.3 While math teachers at foundation- instructional time and courses, tutoring and other
of certified math teachers supported schools expend great amounts of labor and focused supplemental instruction, and curriculum
nationwide, that issue is time to improve their materials and instruction, they restructuring and software.
compounded for low- often operate without a great deal of knowledgeable
income, high-minority support, quality curricula or professional experience in Additional instructional time. To provide additional
schools, such as those the the methods they wish to use. Many teachers inter- instructional time, one period in the student’s sched-
foundation supports. viewed during site visits indicate, for instance, that ule may be reserved for an extra class in the subject
they have had difficulty creating or finding interdisci- of need. According to teachers at some schools,
plinary projects that use grade-level math. Also, many these classes — called “shadow classes” or “chal-
math teachers report difficulty in finding conceptual- lenge classes” — work best when aligned closely with
based curricula or teaching methods that address the the curriculum and methods of the core classes that
needs of students whose skills are below the levels they are supplementing; they should not be time to
tested in state-administered mathematics assessments. do homework or to learn unrelated concepts. After-
school programs also provide students the benefit of
The third challenge that foundation-supported schools extra instruction. Like shadow classes, after-school
face is setting up adequate support for their math- programs reportedly provide the greatest benefit when
ematics teachers. While data point to many successes the instruction is coupled closely with the goals of the
resulting from foundation-supported reforms, one main class, either through the main teacher’s direct
trade-off of the creation of smaller high schools is that involvement or through communication between that
the schools’ faculties now are generally smaller. For a teacher and after-school program staff.
subject such as math that can be difficult to weave
into interdisciplinary work, this decrease means that Tutoring and other focused supplemental instruction.
sources of support and networking within a school Within the classroom, math teachers at foundation-
for math teachers may be diminished. Furthermore, supported high schools sometimes employ peer
smaller faculties at reformed schools often also mean tutoring and differentiated instruction as supports
that teachers face a narrowed circle of co-workers with to students’ mathematical learning. Speaking of his
whom to share curriculum ideas and a regular flow of instruction methods since teaching at a new school,
information that is specific to math instruction. In one math teacher reported, “I have a lot more peer
fact, some foundation-supported schools have as few tutoring going on, and that’s when [the students]
as one or two math teachers. Sometimes this shortfall really get it.” Similarly, some teachers are attempting
means that a teacher is asked to teach beyond his or to use differentiated instruction techniques as they
her experience or credential to cover all mathematics confront classrooms of students with wide ranges of
courses. While there is a shortage of certified math mathematical skills. Speaking of his switch to forming
teachers nationwide, that issue is compounded for student work groups based on ability and tailoring
low-income, high-minority schools, such as those the instruction for different groups in the classroom,
foundation supports.4 one math teacher at a foundation-supported school
reported that “that’s when things got much better
The following section presents strategies for address- in terms of teaching the math, and the kids’ scores
ing these challenges. Many of the strategies are being improved a lot.”
3
Teacher Education Materials Project: A Database for K–12 Mathematics and Science Professional Development Providers (2005).
Building on Current Knowledge About Professional Development. Retrieved Nov. 7, 2005, from www.te-mat.org/building.
U.S. Department of Education, National Center for Education Statistics (2004). The Condition of Education 2004 (NCES 2004–077).
4
Washington, DC: U.S. Government Printing Office.
3.
Curriculum restructuring. Facing high school programs that include books, workbooks and full-scale
students who need to review middle school math con- curriculum for a year or more. Interactive Mathematics
cepts, some foundation-supported schools have made Program (IMP) and College Preparatory Mathematics
Algebra I a two-year course instead of the traditional (CPM) are two such examples.7 These packages are
one-year sequence. The prolonged time frame is used mapped to standards set by states or by the National
to review older concepts and provide supplemental Council of Teachers of Mathematics (NCTM). Accord-
skill work, often through computer software or Web- ing to one teacher, this kind of curriculum “brings it
based programs. Such additional work in basic math all around for you,” integrating cooperative learning,
and algebra allows many students to successfully con- student presentations, problem-solving strategies and
tinue on through Geometry and, in their senior years, multiple skill levels into the daily lessons. Some teach-
Algebra II. Some students are able to satisfy college ers find these packages helpful in developing the skill
entrance requirements by completing three yearlong levels of low-achieving students because the materials A high-quality curricu-
units of college-preparatory math, though the courses balance basic skills with more advanced analysis and lum can assist teachers
comprising these units are taken over four years. inquiry-based learning. in their efforts to help
Increasing Teacher Access to Quality The materials are not without their detractors, however. students advance their
Nontraditional Curriculum Some teachers note that students with low literacy skills learning. For foundation-
struggle with some of the math programs that are text supported schools, which
A high-quality curriculum can assist teachers in their heavy, further compounding the students’ low achieve- often enroll students with
efforts to help students advance their learning. For ment. Other teachers feel that these programs do not weak mathematics skills,
foundation-supported schools, which often enroll stu- provide enough complex, interesting projects or concept the need for such a cur-
dents with weak mathematics skills, the need for such learning. Indeed, some teachers find it necessary to riculum is even stronger.
a curriculum is even stronger. Steps taken by these supplement the curriculum because their students start
schools to obtain such curricula include the introduc- the program so far behind in basic math skills.
tion of mathematics curricular software, concept-
oriented, packaged mathematics curricula and school- At some schools, teachers use the prepackaged cur-
wide project-based curricula. riculum as a supplement to project work. These teach-
ers often devote a great amount of time and energy
Mathematics curricular software. Many schools are to developing classroom projects. Such projects have
experimenting with computer-based or Web-based included asking students to prove math theories, solve
math programs. Math computer programs used at real-life scenarios or create objects using mathemati-
some foundation-supported schools include Riverdeep, cal principles. Students in one project at a founda-
BoxerMath and Accelerated Math.5 These programs tion-sponsored school used logarithms to determine
often are used to supplement project work with grade- a person’s time of death. Another project required
level skill work. Teachers’ reviews of the efficacy of students to use linear algebra and graphing to make
software-based math remediation programs vary, but predictions and find the best trail in a cross-country
with proper training, there is some evidence that if a trip. These projects ask students to apply their math-
quality computer-based program is used as a course ematical learning to real-life scenarios and complex
supplement, the software can aid students by increas- projects.8
ing the amount of time students spend on level-
appropriate tasks.6 Introduction of schoolwide, entirely project-based
curricula. Some foundation-supported schools have
Concept-oriented packaged mathematics curricula. curricula that are entirely project based. In these
Many schools have adopted concept-oriented, pack- instances, schools pick a theme or unit, and teach-
aged math curricula as a means to raise student math ers work in an interdisciplinary manner to integrate
achievement. These programs may include software skill development into a project designed around the
aides, but they differ from the software programs theme. These projects often are based on real-life
discussed previously because they are comprehensive experiences, and their topics can be student
For additional information on Riverdeep, see www.riverdeep.com; for additional information on BoxerMath, see www.boxermath.com;
and for additional information on Accelerated Math, see www.renlearn.com.
Ysseldyke, J., Spicuzza, R., Kosciolek, S., Boys, C. (2003). “Effects of a Learning Information System on Mathematics Achievement and
Classroom Structure,” Journal of Educational Research, Jan./Feb. 2003, Vol. 96, No. 3, pp. 163–174.
For additional information on IMP, see www.mathimp.org, and for additional information on CPM, see www.cpm.org.
The issue of low student skills again presents a barrier for teachers, who find it hard to introduce classroom projects if their students
lack a strong foundation in basic skills. Teachers have tried to address this obstacle by providing skill-based lessons that complement
classroom projects so that students have support as they try to apply math to classroom projects.
4.
generated. As one student says, “We’re not going to system that continues to emphasize lectures followed
be doing math worksheets on future jobs. Here, we by individual practice. The professional training should
create things; we use math.” For example, one student be designed to improve teachers’ understanding of
at a project-based school was doing an internship in and abilities in nontraditional teaching methods,
a cooking business. She used math to project future particularly problem-based learning. The training also
earnings for the business, based on current sales, so should take into account teachers’ prior experience
that they could plan for future work. and knowledge, operate with a close connection to the
teachers’ school, and give teachers opportunities to
The mathematics focus in interdisciplinary, project- practice in a supportive environment.10 The consensus
based curricula is on using numbers in a way that is is that “teachers who have participated in professional
meaningful to students and that allows students to development on the use of particular instructional
see the real impact of numbers. In practice, however, materials and are using the materials as designed are
“We’re not going to be several teachers have noted that math is the most much more effective than those who either had not
doing math worksheets on difficult subject to integrate into interdisciplinary proj- received professional development or who attempt to
future jobs. Here, we cre- ects and that the discipline is not as fully integrated modify the materials.”11
ate things; we use math.” as it should be. Some projects lack mathematical rigor,
according to interviewed teachers. Additionally, the On-site support. Several foundation-supported
— A student recurrent problem of students with weak math skills is schools are providing on-site support for math teach-
sometimes exacerbated with interdisciplinary projects ers. The support varies depending upon the size and
because students do not receive direct instruction in needs of the math departments, although the theme
fundamental mathematical principles. To address these of collaboration is a constant. Some schools have
issues, some schools that are almost entirely project designated lead math teachers who serve as mentors
based are now offering math seminars several times a and supporters for other math teachers in the school.
week. These seminars focus on basic math skills as a These lead teachers host meetings on instructional
supplement and support for project-based work. topics, observe teachers or conduct demonstration les-
sons in teachers’ classrooms.
In the search for projects that incorporate grade-level
math, teachers both post to and pull from Internet A few foundation-supported schools have hired out-
Web sites. One example, produced by NCTM, is a side consultants to provide on-site support using
Web site that seeks to engage students interactively funds from grantees’ professional development
while delivering content that conforms to NCTM accounts and grant money from private sources. The
standards (http://illuminations.nctm.org/swr/list. consultants’ routines vary, with some serving full
asp?Ref=0&Grd=9). The Center for Innovation in time at a school for an entire year while others come
Engineering and Science Education also provides to schools intermittently, holding workshops. Some
an online source of free interdisciplinary projects schools have partnered with local universities to
(http://k12science.org/currichome.html). The math hire professors to work with their staff as a whole or
skills required in these projects are linked to NCTM one on one with math teachers. While the particular
standards. Other sites of interest that provide high mechanism for providing on-site support varies from
school-level math projects or project ideas are listed school to school, the shared goal across campuses is
in the resources section at the end of this brief. to provide teachers with on-site development that fits
their particular needs.
Providing Support and Professional
Development for Teachers Professional development and common planning
time. Support for teachers is not limited to coach-
One compendium of best practices strongly advocates ing on pedagogy. Some school leaders have engaged
providing a quality professional support mechanism as the entire school staff in math professional develop-
teachers transition from traditional methods of teach- ment workshops or curriculum training to encourage
ing math to problem-based learning and interdisciplin- interdisciplinary collaboration and project design.
ary projects.9 Without appropriate teacher training, Furthermore, conscious of the need to give teachers
schools run the risk that only a veneer of problem- time to improve their curricula and lesson plans, some
based learning will be practiced around the edges of a schools’ math departments have instituted common
9
Teacher Education Materials Project: A Database for K–12 Mathematics and Science Professional Development Providers (2005).
Building on Current Knowledge About Professional Development. Retrieved Nov. 7, 2005, from www.te-mat.org/building.
10
The Urban Institute (2005). What Do We Know? Retrieved Nov. 9, 2005, from www.urban.org/url.cfm?ID=311150.
Weiss, I., Gellatly, G., Montgomery, D., Ridgway, C., Templeton, C., Whittington, D. (1999). Local Systemic Change through Teacher
11
Enhancement, Year Four Cross-Site Report. Retrieved Nov. 11, 2005, from www.horizon-research.com/reports/1999/year4.php.
5.
planning time for teachers. During this common plan- impossible for math teachers at smaller schools, where
ning time, math teachers come together to ensure an entire department may consist of as few as one or
that they are integrating concepts across instructional two teachers.13
years or that they are interpreting the curriculum in
similar ways. Interviewed teachers noted that com- Conclusion
mon planning time was a key enabler to helping them
Creating a mathematically literate citizenry is as im-
teach effectively. Institutionalizing such interactions
portant today as it ever has been. Between 2004 and
also fosters a culture of collaboration and experimen-
2014, for example, employment growth in technology-
tation for teachers on the campus.
related fields is projected to far outstrip the overall
Support from grantee organizations. In many cases, projected rate of job growth (see Figure 2).
the grantee organizations that serve as intermediaries
Additionally, independent of any individual’s occupa- Creating a mathemati-
between the foundation and the foundation-
tion, the policy and financial decisions made by an edu- cally literate citizenry is
supported schools have created support systems for
cated populace require an ever greater understanding
math teachers. Some grantees, for example, host as important today as
of fundamental mathematical concepts. And yet, large
annual conferences to share best practices with teach- it ever has been. ... And
ers from their affiliated schools. These conferences yet, large portions of the
often have sessions designed around mathematics Figure 2. Projected Percentage Increases country’s youth currently
content and various instructional supports for in-ser- in Employment for Select Occupations, are passing into adult-
2004–201414
vice teachers. Additionally, some grantees have hired hood with minimal math
math coaches for their affiliated schools. The coaches sophistication.
Total, all occupations
have several years of math teaching experience and 13.0%
provide direct professional development to teachers Total, computer and
mathematical 30.7%
science occupations
in the form of weekly or monthly workshops, curricu-
Computer specialists 31.4%
lum support, observations, or departmental meetings.
Other grantees provide opportunities for teachers from Computer systems
analysts
31.4%
different schools to communicate through mini-con- Network and computer
systems administrators 38.4%
ferences or workshops. Interviewed teachers often
Computer software
referred to such grantee support as helpful for their engineers 46.1%
instruction, although the ultimate impact on student Network systems and
data communications 54.6%
analysts
achievement has yet to be determined. 0% 10% 20% 30% 40% 50% 60%
Example from overseas. Perhaps the most salient
examples of a culture of support for math teachers
come from overseas. The 2003 report of the Trends in portions of the country’s youth currently are passing
International Mathematics and Science Study describes into adulthood with minimal math sophistication.
teaching supports that are built into day-to-day inter-
Against this backdrop, educators at some foundation-
actions of Japanese mathematics teachers. The report
supported schools are reforming math education.
describes a teaching culture in which there are faculty
Specifically, they are shifting from traditional methods
meetings dedicated to math instruction, professional
of presenting mathematics in class and instead are
discussions on topics of learning and routine videotap-
embedding math instruction in projects that are
ing of classroom instruction.12 Math teachers partici-
interdisciplinary, relevant and interesting to students.
pate regularly in curriculum development meetings
This emphasis on relevance simultaneously requires
and are assigned action plans and individual research
that students master the skills necessary for higher-
assignments and follow-up tasks. In the United States,
level math and statewide assessments. The educators’
such an intense and ongoing degree of collegial inter-
ultimate goal is to educate imaginative learners who
action is rare. Indeed, without the concerted support
grasp concepts and have the ability and willingness to
of a wider network, such collaboration would be nearly
investigate ideas and solve real-life problems.
Stevenson, H.W. (1998). A TIMSS Primer: Lessons and Implications for U.S. Education. Retrieved from www.edexcellence.net/
An example of a public high school in the United States that consistently exhibits high student outcomes in mathematics is Adlai E.
Stevenson High School, a large comprehensive high school in the Chicago suburb of Lincolnshire. The school dedicates about 15 days
each year when other educators are encouraged to visit. For more information, see the school Web site at www.district125.k12.il.us.
U.S. Department of Labor, Bureau of Labor Statistics (2005). Employment by Occupation, 2004 and Projected 2014. Retrieved Feb. 7,
2006, from http://stats.bls.gov/emp/emptabapp.htm.
6.
While the experience, enthusiasm and intelligence ics skills. They can offer training in solid, innovative
of teachers and administrators at these schools go a teaching practices; they can provide access to rich,
long way toward accomplishing these goals, there is concept-oriented curricula; and they can construct for
a wider circle of interested parties with resources and teachers systems of continued feedback and support
talents that can help with this endeavor. Districts, from a network of professional peers. With such sup-
states, community organizations and higher education port, teachers and administrators may find that even
partners can fill critical training and systemic needs in the achievement score numbers start adding up in
the effort to improve the nation’s level of mathemat- their students’ favor.
Resources
The educators’ ultimate
goal is to educate imagi- Materials for teachers to use in the ment materials and allows you to search by
classroom several different criteria.
native learners who grasp
concepts and have the Education Development Center (www2.edc.org/ Background information
ability and willingness MathProblems). A searchable database of math
Creating Mathematical Futures through an
word problems, many of which are based in practi-
to investigate ideas and Equitable Mathematics Approach: The Case of
cal scenarios.
solve real-life problems. Railside School, Jo Boaler and Megan Staples,
The Illuminations Project (http://illuminations. 2005 (www.stanford.edu/~joboaler/equity.pdf). A
nctm.org/swr/list.asp?Ref=0&Grd=9). Sponsored case study that highlights one urban school that
by NCTM, materials and lesson plans aligned with increased student math achievement and engage-
NCTM standards. ment through innovative teaching strategies.
Math Forum @ Drexel (www.mathforum.org). National Center for Education Statistics Report,
Lesson plans and activities, including a problem 1999 (http://nces.ed.gov/pubs99/timssvid). The
of the week. official report on the TIMSS video study from the
National Library of Virtual Manipulatives U.S. Department of Education.
(http://nlvm.usu.edu/en/nav/index.html). An Radical Equations, Bob Moses, 2001 (http://
online library of interactive manipulatives and thealgebraproject.org). Description of Moses’ work
tutorials focused on mathematics. in founding and leading The Algebra Project, an
Web sites to support teacher innovative program that targets minority youth.
professional development The Teaching Gap, Jim Stigler, 1999 (www.
Annenberg Media Learner.org (www.learner.org). lessonlab.com/teaching-gap). Rooted in the
Fee-based courses and complimentary video librar- TIMMS video study learnings, highlights the need
ies on teaching strategies for several different for effective instructional methods to drive stu-
math concepts. dent achievement.
Lesson Lab (www.lessonlab.com). A resource A TIMSS Primer: Lessons and Implications for
geared toward administrators, offering several fee- U.S. Education, Harold W. Stevenson, 1998 (www.
based professional development courses based on edexcellence.net/FOUNDATION/publication/publi-
using textbooks and research to shape practice. cation.cfm?id=50&pubsubid=725). Lessons learned
and “best practices” from the TIMSS study.
National Council of Teachers of Mathematics
(www.nctm.org). Online workshops, materials and What Do We Know? The Urban Institute, 2005
resources. (www.urban.org/url.cfm?ID=311150). Summary
of the research that exists for dozens of popular
Teacher Education Materials Project (www.
math and science curriculum programs.
te-mat.org/home). A searchable database that
reviews math and science professional develop-
Editorial and design by KSA-
Plus Communications, Inc.,
in Arlington, VA.
+1-315-636-4485
+91 98151-74050 
