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Regardless of their specific mathematics programs, No Child Left Behind - Blue Ribbon Schools use many similar instructional techniques. All emphasize alignment of the school’s mathematics curriculum with state standards and conduct frequent benchmark assessments to determine student mastery of the standards. All strive to allow sufficient time for math instruction each day to ensure that all students reach high levels of achievement. Assessment is formative and ongoing, and students who experience difficulty mastering math concepts receive immediate intervention and additional instructional time. Many schools use manipulatives to help students understand math concepts. Mastery of computation is balanced with problem-solving, applying mathematics, and making real-world connections.
1.
Improving Math Performance
What do you think is the single most important factor in
dramatically improving students’ math performance
in your school?
Regardless of their specific mathematics programs, No Child Left
Themes in
curriculum content Behind - Blue Ribbon Schools use many similar instructional
and standards: techniques. All emphasize alignment of the school’s mathematics
y Alignment with state curriculum with state standards and conduct frequent benchmark
frameworks assessments to determine student mastery of the standards. All
y Coherent, focused, strive to allot sufficient time for math instruction each day to ensure
demanding program
that all students reach high levels of achievement. Assessment is
y Connections to real
world formative and ongoing, and students who experience difficulty
y Year-to-year mastering math concepts receive immediate intervention and
continuity additional instructional time. Many schools use manipulatives to
y Building on prior help students understand math concepts. Mastery of computation
skills and
knowledge is balanced with problem solving, applying mathematics, and
y Use of making real world connections. As in all Blue Ribbon Schools,
manipulatives for quality teachers, parent involvement, and a coherent progression
concept
development from grade to grade are key to student success. School comments
about improved student math performance are organized below by
topic—curriculum, teaching, student support, and assessment—with
illustrations from survey responses.
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2.
A. Curriculum content and standards
Blue Ribbon Schools use coherent, focused, and demanding mathematics curriculum that
reflect the logical and sequential nature of mathematics. Students move from mastering
basic computational skills and number concepts to more complex ideas and mathematical
reasoning, including problem solving. Schools expect students to know math concepts and
be able to apply them in a variety of settings. All teaching is aligned with district and state
standards in mathematics.
Louisa May Alcott Elementary School Riverside, CA
“We present a balance between conceptual understanding, basic computational and
procedural skills, and problem solving. Students are intellectually engaged in learning by
reasoning, predicting, evaluating, concluding, and solving problems, skills that are
fundamental for life-long learning. Other key strategies include:
• A relentless focus on the California mathematics content standards.
• Use of a district pacing guide to ensure all key concepts are taught during the year.
• Reteaching students who do not learn after the initial instruction.”
Mountain View Academy
Greeley, CO
“Each lesson is organized around multiple skills
or topics, rather than around a single skill or
topic. Each skill or topic is addressed for only five
to ten minutes in any given day's lesson, but it is
revisited day after day for many lessons. . .
[which] promotes mastery rather than teaching
for exposure. Strands make sequencing and
cumulative introduction of skills feasible, and topics can be treated in depth. Concepts are
arranged in a logical scope and sequence, so that several topics can appear in one lesson.
This permits pre-skills to be taught before being integrated into more complex mathematical
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3.
Orleans Elementary School
Orleans, MA
“The adoption of the Massachusetts
Mathematics Curriculum Frameworks
required teachers to shift learning
mathematics from the process of
absorbing facts and practicing procedures
to the process of developing one's
knowledge of facts and procedures in
relation to a set of important, underlying
mathematical ideas.”
Joseph K. Lumsden Bahweting P.S.A. School Sault Saint Marie, MI
“The single most important factor in our math performance is the stressing of the foundation
of each mathematical concept. All concepts are first taught with manipulatives such as
counters of various types, Cuisenaire rods, base ten Blocks, fraction strips, and the like. This
teaches the students exactly what they are calculating and why. The algorithm is taught only
after the foundation is laid with manipulatives. Also, concepts are taught in a sequence that
enables skill scaffolding for learners.”
David Crockett Elementary School Baytown, TX
“Crockett staff realizes that student achievement that is measured in grades 3, 4, & 5 is not
just the responsibility of those grades. Not only are grades pre-K-fifth vertically aligned in
reading, but this is also consistent in the math curriculum. Teachers follow the suggested
lesson design provided by the math department which begins daily with a calendar math
lesson, a problem-solving lesson, and computation. Math facts are also part of this lesson
with emphasis on practicing the facts in ways other than just pencil and paper timed drills.
Utilizing and building on these effective strategies each year engages the student and
teacher in a high level of learning.”
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4.
Kashmere Gardens Elementary School Houston, TX
“The single most important factor is scaffolding new concepts with prior knowledge during
each lesson presentation thus building a cohesive mental picture. The stage must be set in
order for new learning concepts, ideas, and information to take place. When prior knowledge
is connected to new information, students are better prepared to comprehend new
Mount Airy Elementary School Gretna, VA
“A combination of Silver Burdett/Ginn and SAXON Math programs . . . provide an
incremental developmental and continual review of concepts/skills. . . . The skill lessons and
exercises increase in complexity with each lesson, affording sufficient time for students to
become acquainted and comfortable with the skill, therefore making the application of the
skill deliberate and uncomplicated.”
Newport High School Bellevue, WA
“Four years ago Newport implemented the Core Plus integrated math curricula. Instead of . .
. [watching and hearing] how to compute math problems, students now work collaboratively
in small groups to problem solve. Students are now forced to think deeply about their
learning and to be prepared to defend and explain responses.”
Barton Elementary School Milwaukee, WI
“Mathematics: Explorations and Applications [is a] well-rounded, highly researched math
program that aligns well with state standards and the state testing. There are multiple
components of MEA that address different standards. There are thinking stories that . . .
require deep mathematical thinking related to real life scenarios. Daily problem solving
questions also address mathematical thinking for all purposes. Mental math develops
automatic recall of mathematical equations, mastery of which are critical to higher level
functions. Games develop the strategic thinking and number sense.”
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5.
B. Teaching strategies
Differentiated classroom instruction, flexible grouping, and immediate intervention for
students who are not mastering math standards give students the individual instruction they
need to succeed in math. Teacher collaboration, within and across grade levels,
acknowledges the importance of year-to-year continuity in mathematics instruction. The
quality of math teachers, particularly with regard to their content knowledge of mathematics,
is critically important.
Richardson D. White Elementary School
Themes in teaching
Glendale, CA
strategies:
“Assessment is ongoing, allowing teachers to re-teach as
y Ongoing
assessment needed. Differentiation within the math block occurs via varied
y Differentiated instructional strategies and tools including small group
instruction
instruction.”
y Flexible grouping
y Teacher
collaboration
y Year-to-year Walnut Grove Elementary School Pleasanton, CA
continuity
y Ongoing “Our average student exits Walnut Grove (5th grade) performing
professional above the 90th percentile in Math (SAT/9, CAT/6). . . . Our staff
development
approaches the teaching of math with a heavy emphasis on the
development of strong conceptual understanding. That translates to extensive early
instruction with hands-on, manipulative materials. Number sense is heavily emphasized.
Math is treated as much as a language as a subset of skills. Mathematical reasoning,
mathematical communication, and mathematical application are clearly identified as
schoolwide goals and staff training, collaboration, and reflection are aligned accordingly.”
Dennison Elementary School Lakewood, CO
“Teachers use assessment for learning, engage in ongoing staff development to improve
their own effectiveness, and plan with one another to ensure consistency and high
expectations. Teachers analyze the data available to them and make adjustments as
necessary to be sure students are learning what is necessary to meet standards.”
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6.
Holy Name of Jesus School Indialantic, FL
“The most important factor is the involvement of a high quality teacher who will ascertain
that students master a concept before moving on, work with struggling students, and provide
a strong foundation in basic facts.”
Lyon Elementary School
Glenview, IL
“The district has established a
consistent program for mathematics
for all of the schools utilizing the
University of Chicago School
Mathematics program. The district
was involved in the original pilot of
this instructional approach and has
been using the program for over ten
years. Our teachers are well trained in its instructional strategies and how to implementation
daily lessons. They also understand the need to supplement the program in certain areas,
as well as the value of the hands on learning components. Finally, the ‘Home Links’
program allows for a connection between school and home, so that the parents are involved
and have an understanding of the program.”
Williams Middle School Longmeadow, MA
“For the last three years, coordinators have led teacher efforts to map their math curriculum,
using the Heidi Hayes Jacobs model. During the summers and professional development
days, coordinators and teaching teams have worked to align individual teacher curriculum
maps with the state frameworks by identifying gaps and weaknesses or repetitions and
redundancies across the grade levels. Readjustments in curriculum were made to cover all
framework topics. All district teachers were involved in developing consensus district maps
for each curriculum.”
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7.
Eugene Field Accelerated School St. Joseph, MO
“We at Eugene Field attribute our high math scores to rigorous, hands-on instruction that
involves higher order thinking skills. Students are taught that a planned procedure is helpful
in solving a problem and that process is emphasized in each math topic and unit. Students
are required to communicate—first orally and later in writing—the process that was used or
the reasoning used to arrive at the correct answer. Math games and manipulatives are used
to enhance instruction and application of concepts.”
Mt. Pleasant Academy Elementary School Mt. Pleasant, SC
“Good teachers use direct instruction to model the learning, require and provide for time on
task, have high expectations, and do not give up on any child.”
Steenrod Elementary School Wheeling, WV
“The teachers provide opportunities to apply problem-solving skills to relevant, everyday
experiences. Manipulatives, computers, and calculators are part of math instruction at all
levels to assure understanding of concepts, and daily math drills provide practice in
mathematical communication and use of algorithms. Integration with other curricular areas is
managed through thematic units and projects. Students use a variety of measuring,
estimating, graphing, and problem-solving techniques. All teachers are aware that the
concepts in math are like a set of stairs--one cannot reach the top by skipping too many
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8.
C. Student support
Blue Ribbon Schools support their students in mathematics instruction through a variety of
techniques, including keeping parents informed about student performance and involved in
their children’s educations.
Themes in student Forest Park Elementary School Fremont, CA
support:
y “The school uses multiple measures for data analysis to
y Early intervention determine areas of mathematical competencies in need of
y Frequent parent- emphasis for identified students. There is a lot of collaboration
teacher
conferences and discussion about identified students in order to determine
y Home strategies the best avenues for effecting progress. The school also
y Extended day intervenes as early as possible and makes every attempt to
programs
y Tutoring involve parents in every aspect of the student's educational
y Summer process.”
workshops
Village Christian Schools Sun Valley, CA
“We did a grade-by-grade item analysis of the standardized test score data [and] identified
areas of strength and weakness. We designed specific instructional interventions and
adopted new curricula to address those areas of weakness. Each year, we continue to
identify areas where continued growth is needed and modify the instructional program to
produce that growth. A key strategy in improving scores was to target the lowest performing
students (stanines 1-3) and to build interventions for these students. The major intervention
was to develop a peer tutoring program that would help lower performing students build
foundational skills in math.”
Sumner Academy of Arts and Sciences Kansas City, KS
“The math department has designed several interventions to assist students who are
struggling with math. They provide summer workshops to incoming students free of charge,
they provide tutoring periods during activity periods, and they meet with students regularly
before school, after school and on Saturdays. This year they have begun a new class which
requires struggling students to have 90 minutes of math instruction every day.”
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9.
Benjamin Franklin High School New Orleans, LA
“Mathematics teachers articulate the curriculum across grade levels, using frequent
assessments to ensure that students are building the necessary foundation for higher-level
mathematics. Keenly aware of student data, mathematics teachers address evident student
weaknesses, build into their courses time for tutoring students during the school day, and
staff a Saturday program for students who need to work on their mathematics skills.”
Summit Park Elementary School Baltimore, MD
“We offer advanced, compacted math curricula for students who demonstrate readiness.
Grade level students all participate in rigorous programs with high expectations. Teachers
regroup students based on their needs for each unit. Teachers work in teams to evaluate
students' work and their own instructional effectiveness.”
Granville Middle School Granville, OH
“The students at Granville Middle School are permitted to advance to upper levels of math at
their own pace. Many of those students need some extra support from teachers because
they are in class with high school pupils. At the same time, it is necessary to support
struggling students with individual help. The math department holds individual help sessions
for students called ‘Monday math help.’ The Math Counts program, which has become so
popular that it has almost turned into a club, participates in daily morning math help
sessions. These are open to all students regardless of ability, and therefore draw students
who may be struggling as well as those who are advanced.”
W. W. Scarborough Elementary School Houston, TX
“Our biggest leap in math achievement came from careful analysis of disaggregated test
data. We were then able to devise focused tutoring through Math Camps during the day and
at before- and after-school tutorials. Careful data analysis gave us a focus so that we could
help more students be successful.”
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10.
Franklin Elementary School Tacoma, WA
“Some of our intermediate teachers hold math curriculum nights to help parents better
understand the curriculum and homework. We extended the day for at-risk and English as a
second language students to help them understand math exemplars and develop strategies
in solving story problems. We increased our support staff time in the area of math for grades
4 and 5. There is cross-grade tutoring. High school students from a local private school
come to tutor our students in skills they lacked.”
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11.
D. Importance of assessment
Formative, continuous assessment guides mathematics instruction. It informs instructional
planning at the specific level of individual student needs and, more broadly, suggests where
a given teacher might improve a lesson.
Themes in William Howard Taft Elementary School Boise, ID
assessment:
“Continuous classroom assessment which is focused on specific
y Diagnostic benchmarks is the one factor which allows us to:
screening
y Provide K parents with specific activities to meet the needs of
y Individual their child(ren)
instruction based
y Schedule students in small and large groups in order to meet
on assessment
their needs
y Teaching guided
y Provide paraprofessionals with specific skills/concepts to work
by assessment
with individual students
y Performance
assessment y Move students in and out of flexible small groups based on their
attainment of specific skills/concepts on a daily/weekly basis
y Ongoing
assessment y Focus our horizontal and vertical collaborative team meetings on
specific data which then drives our classroom instruction.”
Dirksen Primary School Pekin, IL
“Math district criterion-based assessments were also developed for each grade level to be
taken in the Fall, Winter, and Spring. These formative tests, along with individual student
portfolios, help staff and students monitor learning progress in meeting and exceeding the
district/state learning expectations. See http://www.pekin.net/pekin108/curr/math/math.html.”
Lone Dell Elementary School Arnold, MO
“Math instruction is provided through an individualized approach to instruction utilizing
performance tasks that are monitored through various assessments, including our district's
quarterly assessments. We focus on the results of the standardized testing as well as our
own quarterly assessments to redirect and focus on strengths and weaknesses to our
instruction. Each year may require modifications to our instructional practices depending on
the needs of the incoming students.”
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12.
Robert Seaman Elementary School Jericho, NY
“A process of continuous diagnosis and customized instruction based upon benchmarking,
coordinated by a lead Mathematics teacher, [is] supported by small group non-redundant
instructional support.”
Northwest Elementary Schoo Smithfield, OH
“[We] use weekly review sheets and [break] down the strands of the proficiency test, zeroing
in on the weakest areas of concern and providing many supplemental teaching materials for
the classroom.”
Walsingham Academy Lower School Williamsburg, VA
“[We] develop learning plans by department and grade based on the strengths and
weaknesses discovered on the previous year's tests. We review our curriculum and teaching
strategies, and new strategies are implemented if necessary. Data from student progress in
the classroom is reviewed in regularly scheduled math meetings. Math teachers met with
math teachers in the grade above them and grade below them to align curriculum and
developed a math mastery reporting instrument to be used for all students. Parents are
apprised of their students’ performance on standardized tests, and conferences are
scheduled to explain scores and develop home strategies when appropriate.”
Kenova Elementary School Kenova, WV
“Math performance at our school has been dramatically improved by doing an item analysis
of our test results from the previous year and gearing our instruction toward improving in
weak areas. Mid year we assess our students again and once again focus our efforts toward
areas that need further instruction. “
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