Square One: Promoting Systemic Math Reform.

Front-line experiences in Pittsburgh offer lessons on applying math standards districtwide

Systemic mathematics reform-so that every teacher in every classroom engages students in standards-based instruction and all students achieve at high levels-requires a lengthy and complex process.

Administrators often underestimate this complexity or fail to recognize policies and practices that, though well-intentioned, actually hinder reform efforts.

After a decade of math reform in the Pittsburgh Public Schools and working with colleagues in other school districts, we have learned some lessons about the key components, issues and district policies that must be addressed,

What's the Target?

* Lesson 1: High-stakes assessments must be tied to appropriate instructional targets.

What is assessed and how it is assessed communicates what is valued. High-stakes assessments-those for which principals and teachers feel accountable-have a significant impact on what and how mathematics is taught in classrooms.

High-stakes assessments are the linchpin of reform. They either promote reform and lead to increased math learning by all students or they under-mine reform and produce ill-prepared students who get high test scores. It all depends on the test that is selected and how it is used.

According to the National Council of Teachers of Mathematics' assessment standards, assessments positively affect teaching and learning when:

* assessment, curriculum and instruction are aligned;

* preparing students for "the test" is synonymous with good teaching (instead of familiarizing students with item formats and tricky wordings);

* student performance is compared to standards (instead of that of other students);

* the results provide useful information that can be used to guide instruction;

* the assessment is designed to assess important math content and the source of item difficulty is the mathematics it requires (no trick questions); and

* students and teachers know what students are expected to know and how they are expected to demonstrate that knowledge.

Assessments that meet these criteria are considered standards-based.

Reporting results by performance levels is not sufficient to make an assessment standards-based. For example, many norm-referenced tests now report results by performance levels. Yet such assessments are not standards-based according to the above criteria. Norm-referenced tests are designed to produce a normal curve of performance, not to measure progress toward performance standards. Most importantly, such tests are not intended to be teaching targets. In fact, publishers of such tests explicitly warn against using their tests in this fashion.

Shortcomings Exposed

Pittsburgh's experiences with the New Standards Reference Examination, a standards-based assessment, illustrates how assessment can promote reform. When New Standards became prominent as the district's high-stakes test in fall 1997 and staff recognized that our standards-based instructional programs prepared students to be successful on that exam, use of these programs increased dramatically as did requests for professional help implementing them.

The danger of teaching for a test that is not an appropriate teaching target, such as a norm-referenced test, is that the taught curriculum is narrowed to the content of that test. This may result in increased test scores, but it denies students the opportunity to learn important mathematical content, thus hurting their mathematics achievement in the long run.

Consider this example: In one Pittsburgh elementary school, 79 percent of 4th graders scored at or above the 51st percentile on our norm-referenced test. By this measure, the students were doing well, and the school was considered successful. However, New Standards results revealed that only 4 percent of these students met the standard in skills, 2 percent in concepts and none in problem solving.

The NSRE revealed almost all students were lacking basics like measuring in inches, converting between hours and minutes and drawing pictures or diagrams to solve problems. How could this happen? Norm-referenced test scores had long been the measure of school quality. Thus some schools, like this one, focused its instruction to do well on the test.

The result: high test scores but huge holes in students mathematical knowledge.

Can students do well on both norm-referenced and standards-based assessments? Absolutely. Several Pittsburgh schools have done just that. But only when the standards-based test has high stakes attached to it.

Clearly, the selection of high-stakes assessment tools is one of the most vital decisions affecting mathematics reform.

Beyond Buzzwords 

* Lesson 2: Standards-based instruction is more than using manipulatives and cooperative learning.

One of the biggest misconceptions about math reform is that using these practices is synonymous with standards-based mathematics instruction. While manipulatives and cooperative groups can be effective instructional tools, they also can be used ineffectively. A series of hands-on activities does not necessarily result in math learning. For learning to occur, instructional tasks must engage students in thinking about mathematical ideas. They must be organized into a purposeful series of lessons with a clear instructional goal. Depending on the activity and the goal of the lesson, cooperative groups may or may not be appropriate.

The NCTM Professional Standards for Teaching Mathematics states that teachers in standards-based instruction: engage students in appropriate, worthwhile tasks that promote conceptual understanding, skill acquisition, problem solving and reasoning; facilitate effective classroom discussion; ask meaningful questions, use tools such as manipulatives appropriately, establish a positive learning environment and analyze and reflect on their own practice.

* Lesson 3: Teachers need standards-based instructional materials.

One of the most powerful things we have done in Pittsburgh to support reform is to adopt instructional materials that truly reflect the NCTM curriculum, teaching and assessment standards. We are using programs created by the National Science Foundation for K-5 and 6-8. Now when teachers (and principals) ask what they should do to teach to our district standards or to prepare students for our district assessments, I simply say, "Teach the adopted programs."

The power of such materials is that they provide a carefully sequenced set of instructional experiences designed to support students' mathematics learning. Such materials enable teachers to focus on teaching instead of searching for activities to supplement the adopted text.

Fortunately, several standards-based instructional programs are now available, but school leaders must be wary when reviewing possible instructional materials. Almost all today claim to reflect the NCTM standards. Not all do what they claim. It also is unreasonable to expect teachers to create their own materials, given their lack of expertise, time or resources.

* Lesson 4: Teachers need substantial, continuing professional development and in-class support.

Teachers need much more and different kinds of professional development to implement standards-based programs. In Pittsburgh, we are supporting implementation of such programs through a National Science Foundation-supported local systemic change project. We learned the professional development must be directly tied to the materials. We must go through the new materials with teachers, unit by unit. We must ensure they know and are comfortable with the math and understand the pedagogy and the rationale for the structure of the activities.

We also address management and organizational issues. Each teacher participates in about 70 workshop hours in the first year. In subsequent years, we address pedagogical issues and mathematical content across grades.

Workshops alone are not enough. We provide regular, in-class support by a team of demonstration teachers. These teachers conduct demonstration lessons, observe teachers and provide feedback. They help plan instruction and assessment and conduct parent workshops. This peer-to-peer coaching and feedback is essential to implement standards-based materials.

Careful Observations

* Lesson 5: Administrators must recognize and support standards-based instruction.

Administrators, like teachers, need professional development regarding mathematics reform. They must be able to determine the extent to which standards-based programs are being implemented in their building and be able assess their site-specific needs. A teacher who is attempting to implement standards-based instruction is demoralized when a principal, observing a lesson in which the teacher is facilitating small-group work, says, "I'll come back to observe you when you're teaching."

Principals also must distinguish instruction with the trappings of reform (e.g., manipulatives, small-group work) from what is truly standards-based (e.g., worthwhile mathematical tasks, questions that promote conceptual understanding).

Principals must do more than recognize standards-based instruction. They must demand it of all teachers. The most frustrating barrier to Pittsburgh's reform efforts is the "cellophane syndrome"--teachers who refuse to open the package and even try the new instructional materials. These teachers undermine reform by interrupting the continuity of students' mathematical experiences. This hurts both the students and teachers of subsequent grades who receive students without the appropriate prerequisite experiences. If the principal does not demand that these teachers implement adopted programs, fellow teachers and support staff can do little to change their behavior.

This, in turn, implies that the administrators to whom the principals report also must be knowledgeable of and expect support for standard-based instruction in all schools so that they can effectively monitor the principals' efforts.

Selecting Texts

* Lesson 6: District policies and practices will have to change.

Sometimes, well-established policies and practices can hinder reform. For example, changes may need to be made in the areas of textbook adoption and teacher placement.

Single-year adoption processes in which teachers review all available texts and then select the one they like best probably will not result in the adoption of reform materials. As teachers riffle through the texts they will not find the familiar pages of computation practice and consequently reject the text.

Selecting books that best support student learning, rather than ones that look easy to teach, is a radical change. A process that provides time for professional development of committee members and for classroom trial of programs is much more likely to result in selecting nontraditional materials.

The classroom trial period must be long enough for teachers and students to become comfortable with a program and assess its effect on student learning. A month or two is not enough. A year's trial is more likely to reveal how a program really works. We've seen examples of this time and again in Pittsburgh. Some teachers were ready to abandon the trial elementary program in the first month because they found it difficult to teach, yet the same teachers were sold on it by the end of the year because their students knew and understood so much math.

With our pilot of a new algebra program, teachers found it tough going until things began to click for students in February. Trying these programs for only a month or two would not have given us an accurate view of their effectiveness.

Year-long trials also create a valuable cadre of experienced program users who can be program advocates and professional development leaders, Nothing is more powerful than teachers who attest to the effectiveness of a program and its impact on their students and speak from experience about particular lessons and activities.

Implementing new K-12 mathematics materials in a single year also can make reform more difficult. Especially in large systems, an overwhelming number of teachers need to be supported. Phasing in implementation of reform materials one or two years at a time has several advantages. Teachers have an easier time implementing the program. The district can provide teachers with all the materials by spreading the cost over several years. Lastly, with fewer teachers using a new program each year, the district can offer intensive support to smaller groups of staff.

The obvious downside to phasing in programs is the time it takes for full implementation. Key considerations in the decision are the resources available for materials and professional development, including in-class support.

In the area of teacher placement, reform programs tend to expose the weaknesses in teachers' mathematics preparation. In the past, teachers with weak math backgrounds were able to offer passable math instruction by concentrating on computational procedures. With richer programs, this is no longer possible.

This is a particular problem in districts with K-8 middle school certification. Some elementary-certified teachers have such weak mathematical backgrounds that even intensive professional development sessions cannot adequately prepare them to teach the new programs. We found an increased need for middle school teachers with secondary school certification.

* Lesson 7: Materials and services are available to support mathematics reform.

Varied materials and services, many created with funding from the National Science Foundation, are available to support reform efforts. Commercial publishers offer standards-based instructional materials, including NSF curriculum project materials, though you may have to ask explicitly to see them.

NSF also has established four national implementation centers (see resource list at left) that provide information about the NSF curricula and offer professional development to district leadership teams on how to select and implement standards-based programs.

Few standards-based assessments are commercially available, but standards-based assessment materials created by projects such as The Balanced Assessment project, published by Dale Seymour Publishing, are accessible. Such materials can be used for districtwide or classroom-based assessment. The Mathematics Assessment Resource Service at Michigan State University offers custom-designed assessments and related professional development.

The Bottom Line

* Lesson 8: Reform has a payoff for all students.

Data just now are becoming available to document the positive impact of mathematics reform initiatives on student achievement, (Data such as those from the Third International Mathematics and Science Study, gathered in 1995, reflect achievement based on traditional, not reform, programs.) Evaluation data from the NSF curriculum development projects and from state and urban systemic initiatives show that students who receive standards-based instruction outperform students in traditional mathematics programs.

In Pittsburgh, elementary students in schools with strong implementation of standards-based math significantly outperformed students in schools with weak implementation on the New Standards Reference Exam and our norm-referenced test.

Notably, the highest-achieving schools included ones from our lowest SES communities (more than 90 percent of students qualifying for free and reduced lunch; 100 percent African-American). The same was true for 6th and 7th graders. Eighth graders who have had standards-based instruction will take the NSRE for the first time this spring.

Diane Briars is director for mathematics, Pittsburgh Public Schools, 1501 Bedford Ave., Pittsburgh, Pa. 15219. She also co-directs the Pittsburgh Reform in Mathematics Education Project.

A Tactic for Educating Parents

Parents clearly play an important, influential role in mathematics reform. Our experiences in Pittsburgh (and those of other districts) dramatically illustrate the need to provide substantial information to parents as well as the consequences when they are not kept informed.

How can we enlist parents as allies rather than opponents to reform? Here are four suggestions.

* Make basic skills visible.

Research by the Public Agenda Foundation shows that parents do want their students to reason mathematically and develop problem-solving skills. But first they want to be assured that their children will learn the basics--the number facts and fundamental computation skills. Ironically, math reform programs also expect students to learn the basics. In fact, most programs expect more mental math capabilities than traditional programs.

The problem is one of public relations. In their zeal to extol the virtues and importance of problem solving, reformers stopped mentioning the basics. We assumed that parents knew they would still be there. This is a costly mistake! The basics must be clearly visible to parents and the public.

* Provide specific information about how parents can help their children.

Most parents, especially parents of elementary students, want to help their children learn math. Unfortunately, traditional ways of helping (e.g., showing them how to do specific procedures) are not applicable to standards-based programs.

Many reform programs are activity-based. Students keep journals instead of using traditional textbooks. Thus parents do not have access to the regular, specific information about what is going on in class that they got from textbooks. Even if books do come home, their content often is so different from parents' experiences that most are at a loss about how to help their children.

Parents need specific direction about things they can do and ideas on how to do it. Basic facts practice can certainly be a parental responsibility. Even better, schools can offer a packet of games to reinforce basic facts (and other concepts) in fun ways. Schools can provide glossaries of mathematics terms, send notes to explain homework activities that might be unfamiliar and conduct frequent parent meetings to facilitate two-way communication.

* Provide information on assessment as well as curriculum and instruction.

If we want parents and the public to accept and value standards-based assessments, we must inform them about the topic. Pittsburgh's director of public relations, Pat Crawford, created a successful way to provide such information.

During "Take the Test Night," parents answered sample questions from our state and district tests, including the New Standards Reference Exam, had dinner, then scored their own tests and discussed the results. Parents were surprised at the level of questions on the NSRE and clearly recognized it as a good test of their children's knowledge. The news media gave good coverage to this event, so the public was also informed.

* Listen to parents.

Parental concerns and complaints are often well-founded. With appropriate follow-up, they can provide valuable information about faulty implementation of programs. The most common complaint I hear about our elementary program is that students aren't learning their basic facts.

When I ask parents if they have seen games coming home or if their children mention playing games in school, and they say "no," the problem is clear. Games are the primary vehicle for basic fact practice in that program. By eliminating games, the teacher has eliminated the basic fact practice from the program! The problem is implementation, not the program and not the parents.

Many parents had terrible mathematics experiences when they were in school so they want a better experience for their children. Most parents are positive about standards-based reform once they understand it, see it works and recognize they have a productive role to play.

Additional Resources

Educators can obtain useful materials about math reform from the following implementation centers funded by the National Science Foundation.

* Elementary Mathematics: The ARC Center, COMAP Inc., 57 Bedford Sr., Suite 210, Lexington, Mass. 02420, 800-772-6627 ext. 50 or 781-862-7878, www.arccenter.comap.com. Contact: Sheila Sconiers

* Middle School Mathematics: The Show-Me Center, University of Missouri, 104 Stewart Hall, Columbia, Mo. 65211, 573-884-2099, showmecenter.missouri.edu. Contact: Barbara Reys

* High School Mathematics: COMPASS, Ithaca College, 306 Williams Hall, Ithaca, N.Y. 14850, 800-688-1829 or 607-274-1513, www.ithaca.edu/compass. Contact: Eric Robinson 

* K-12 Mathematics: The K-12 Mathematics Curriculum Center, Education Development Center, 55 Chapel St., Newton, Mass. 02458, 800-332-2429 or 617-969-7100, www.edc.org/mcc. Contacts: June Mark, Deborah Bryant