• by Jack Dieckmann, M.A. • IDRA Newsletter • March 2002 • Image of Jack Dieckmann, M.A.

Developing students as flexible, fluent and resourceful mathematical thinkers, ready to compete in a global economy.

Middle school students are at a critical crossroad with mathematics. Even though math is essential for all students, it continues to be a gatekeeper for many adolescents. Students from groups under-represented in high school and college completion are also under-represented among those who succeed in learning mathematical knowledge and skills (Kilpatrick, et al., 2001).

Historically, minority and economically-disadvantaged children under-perform, especially in mathematics and science. The National Assessment for Educational Progress recently issued its National Report Cards 2000 in Math and Science. Persistent achievement gaps remain across the grades tested (Braswell, et al., 2001).

Clearly, traditional approaches to teaching and learning mathematics continue to fail too many students. With the growing demand for a scientifically- and mathematically-literate workforce, the loss of talent among our youth is unacceptable, and we must take action for solutions. IDRA’s focus on middle school math resonates with the work of other exciting and innovative efforts.

Veteran civil rights activist, Robert Moses began one such effort called the Algebra Project. The project is a reform initiative designed to help African American students obtain a high level of math competency. The Algebra Project focuses mainly on the middle school years.

Moses and his colleagues believe that African American children must be prepared to enter high school math classes, which will open the door to higher education and technical careers that require a strong math background. The new project includes curricular materials, teacher training, development of student leadership and community involvement, well beyond the scope of most educational reform efforts (Moses and Cobb, 2001; Levine, 2001).

So, in the face of what seems an insurmountable problem, there are success stories and effective practitioners who can lead the way to academic success for all students in Algebra and other challenging math courses.

Educators who have high expectations of all students, who are searching for teaching approaches that open new mathematical vistas and accelerate the learning of higher math concepts with students from all backgrounds, those educators must say, “You, my middle school student, can master math and I, your teacher, can help you get there!”

Institute for Math Educators

One way the Intercultural Development Research Association (IDRA) is helping is to host institutes for middle school math teachers. The goal of the most recent institute was to educate teachers on developing students as flexible, fluent and resourceful mathematical thinkers, ready to compete in a global economy. The Re-Energizing Teaching and Learning: Middle School Mathematics Teacher Leadership Institute was held in the fall of 2001.

Institute participants accepted the challenge of increasing student performance and closing the achievement gap for all students. Nine school instructional teams of math teachers, curriculum specialists, and administrators from seven school districts in the San Antonio area participated in the institute. The participating schools serve large numbers of ethnically and linguistically diverse and low-income students.

IDRA sponsored this innovative institute in collaboration with its projects, the South Central Collaborative for Equity and the STAR Center as part of their mission of equity and excellence in education, focusing on the critical content area of mathematics. The SCCE is the equity assistance center funded by the U.S. Department of Education to serve schools and education agencies in Arkansas, Louisiana, New Mexico, Oklahoma, and Texas. The STAR Center is the comprehensive regional assistance center funded by the U.S. Department of Education to serve Texas. It is a collaboration of IDRA, the Charles A. Dana Center at the University of Texas at Austin, and RMC Research Corporation.

The institute engaged campus improvement teams of middle school math teachers and specialists. Together they developed teaching and learning strategies to significantly accelerate math achievement for all their students.

First, participants gained information on effective programs and teaching of the state’s curriculum standards for mathematics in grades six through eight and Algebra I by linking current research with best practices. Second, they learned effective teaching techniques and approaches from interactions with local math teachers, specialists, and education researchers. Finally, participants practiced capitalizing on students’ strengths and informal applications of math concepts to achieve high performance goals for all learners.

Institute Presenters

The state mathematics director at the Texas Education Agency, Paula Gustafson, participated in small group discussions, provided updates on the new assessments in mathematics (TAKS) and served as a panelist to discuss equity and excellence in mathematics.

Other key presenters and collaborators included Ms. Norma Torres-Martinez with the Alamo District Council of Teachers of Mathematics, and Dr. Kathleen Cage Mittag, president of the Texas Council of Teachers of Mathematics. Dr. Mittag gave an overview and led a discussion about the preliminary guidelines for the Master Mathematics Teacher program in development for Texas teachers.

Dr. Judy Beauford, with the University of the Incarnate Word, guided the group in interactive activities that highlight the integration of math, science and technology. Dr. Arthur Hernández of the University of Texas at San Antonio, served as an expert panelist to help teachers understand the cognitive, physical, social and emotional changes that middle school students experience, with an eye toward the instructional implications.

Engagement Process

Participants worked in small groups to analyze approaches to math tasks in a relevant context involving ratios and proportions, a key organizing theme in the middle school curriculum. They were asked to connect to what they know, use multiple representations (numbers, tables, graphs, pictures, words, equations, and models) to solve them, and provide convincing arguments for their solutions. The teachers, as learners, experienced a process to use in their teaching.

Through this intensive process, participants were given a much wider and deeper understanding of mathematical proficiency, moving beyond simply getting the “right” answer (Kilpatrick, et al., 2001).

At the end of the first day, teams designed a mathematical task for their students. They were asked to give the task to their classes and to bring back the completed task for a guided analysis on the second day of the institute, held a month later. The goal of this activity was to look at student work from the perspective of what the student brings to the task rather than simply whether the answer was correct.

By using these assessment strategies, teachers can identify and activate students’ untapped informal knowledge of mathematics and connect it to school mathematics. By connecting professional development to classroom practice, this experience was a powerful teacher development tool.

Teachers reported being surprised and excited about interesting and complex ways their students approached the given tasks. One teacher stated, “I’m going to think about using a variety of strategies rather than just pictorial and numerical, my preferences.”

Technology and Mathematics

During the second day of the institute, technology was explored as a classroom tool that can deepen the way mathematics is taught and learned. Participants worked in hands-on technology activity groups to see how scientific probeware and real-time data collectors using graphing calculators and computers can be used to let students play a more active role in learning mathematics.

In particular, a motion detector was featured because of the many content connections available (slope, linear functions, and mathematical modeling). Representatives from Texas Instruments, Casio, and Pasco Scientific attended and shared information at the institute.

Bonnie McNemar, a recognized leader in mathematics, facilitated the session for Texas Instruments. With each technology presentation participants were given an assessment form, which included questions such as, “How might this technology help the struggling math learner?” and “What language considerations might you as a teacher need to take into account in using this technology?”

Some of the teachers had experience with these technologies and were able to assist others. Experienced teachers shared strategies for using technology in the classroom with novice users, once again validating the usefulness of peer networking for changing teacher practice. One teacher reported, “We must have this technology for our students!”

Building Networks of Leaders

Many of the participants did not have supervisory positions, so they did not consider themselves leaders. Because of this narrow view of leadership, some of the participants found it confusing to be working in a leadership conference. IDRA led the group in a discussion about an alternative view of leadership around the premise: “If you can make a difference, you can be a leader.”

Math teachers in particular can have a profound impact on students’ short-term and long-term success. Teachers whose students succeed academically in math are directly affecting their students’ potential career paths, quality of life and participation in society.

Teachers, administrators, parents and community are key to helping all students thrive in mathematics. This institute promoted equity and excellence by connecting content, pedagogy, assessment, technology and a valuing-of-student thinking. It is an important step toward reaching that goal.

Both the content and the process were critical for engaging participants. Each of the two days was highly interactive. The institute process included panel presentations, small group discussions, work circles, technology demonstrations, use of readings and task sheets, and application of strategies in participants’ classrooms between sessions. The theme of equity and excellence unified the experience as the group considered instructional strategies, math content, adolescent development, state assessments and technology.

One teacher commented that he learned “[to] keep equity in the foremost of my mind.”

Follow-up topics suggested by participants included: math strategies for English language learners, technology planning, training, curricular alignment, classroom demonstrations, and motivating struggling learners.

The initial dialogue established in this institute continues to be extended through an interactive, online network, with plans for an “action conference for mathematics” in 2002. The participants established a personal connection because of the face-to-face interaction with a variety of researchers and practitioners that continues to live in a network of sharing and communication.

Along with discussion, ideas, readings, notebook and online resources for effective math teaching at the middle school level, participants are forming a network of math leaders and practitioners to continue to share information and best practices in teaching and learning of mathematics in middle grades and Algebra I. This ongoing communication validates the research in professional development that highlights the importance of teacher networking to support teacher growth and powerful changes in instructional practices (Loucks-Horsley, et al., 1998).

With so much at stake, IDRA is committed to long-term support of meaningful change in mathematics instruction.

Talking About Equity…

“If we are interested in equity, we’ll want to offer as many different ways of learning as possible.”

– Tim Erickson

“Developments in science wait on new questions being asked in new ways and using new tools. Often this means waiting for new scientists – different scientists.”

– Cecily Cannan Selby

“Every day, every educator makes decisions that affect equity. Each decision carries implications for educational outcomes. If decisions are thoughtful and knowledge-based, we stand a much better chance of creating classrooms and settings in which all children believe themselves to be learners.”

– Nancy Kreinberg

“Experience can change beliefs. Skeptics can become believers. Even in areas of poverty, some schools perform well above average. If some can do it, why can’t others? Because most people do not really believe that is possible for all students to learn algebra and geometry. That’s where equity begins: with strong beliefs in high expectations for all.”

– Susan L. Forman and Lynn Arthur Steen

Source: Mathematics for All: A Source Book of Essential Information for Leaders in Mathematics Equity (Reston, Va.: National Council of Teachers of Mathematics, 1999).

IDRA Re-Energizing Teaching and Learning:
Middle School Mathematics Teacher Leadership Institute, Fall 2001

Objectives for Day 1

  • Engage in mathematical reasoning using multiple representations to illustrate informal, intuitive, and invented mathematics
  • Experience, articulate and analyze the following components of mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, analytic reasoning, and productive disposition
  • Integrate adolescent development, the content and pedagogy of mathematics, and equity for all students
  • Create an assessment tool based on the principles of mathematical reasoning presented in the institute and commit to bringing the results to the next session

Objectives for Day 2 (held one month after Day 1)

  • Analyze and share student work and discuss implications for instruction
  • Interact with a panel of principals and math education researchers about supporting effective practices, latest findings and trends in middle school math
  • Draft a document “Planning for Mathematical Excellence and Equity” as a support document for campus improvement plans
  • Sample technology with dynamic software to illustrate the connection to mathematical proficiency and engaged mathematical thinking
  • Plan follow-up networking activities

Texas Essential Knowledge and Skills for Mathematics Selections for Illustration of Activities during the Institute

Strand: Patterns, Relationships, and Algebraic Thinking

6.3 Proportional reasoning: Use ratios to describe proportional situations; represent ratios and percents with models, fractions and decimals; use ratios to make predictions.

7.4 Proportional reasoning: Expressing relationships and making predictions; generate formulas and graft data; describe relationship between terms in a sequence.

7.5 Equations: Solve equations with models and symbols; formulate problems from equations.

Key Principles of the IDRA Re-Energizing Teaching and Learning: Middle School Mathematics Teacher Leadership Institute

  • The learning and mastery of mathematics directly impacts students’ well-being, both short term and long term. Potential career pathways, quality of life and participation in society are all affected by how math is taught and learned in schools.
  • All students come to school with a substantial amount of untapped informal mathematics. With training and support, teachers can identify students’ informal knowledge and intuition and use them to promote success in school mathematics.
  • Campus math departments represent a powerful unit of change and can form dynamic learning communities to meet the challenges of creating and sustaining quality mathematics learning environments for every student in every classroom.
  • Teachers who are flexible, fluent and resourceful mathematical thinkers are better able to develop such qualities in students.
  • Teacher networks are valuable opportunities for teachers to grow professionally, share and reflect together about best practices, and receive key information in a timely manner. Investment in teachers’ learning gives them more powerful tools to use with students in their classrooms.
  • The process of re-energizing teaching and learning mathematics so that all students succeed can occur when it is supported by campus and district-level leadership, which include periodic communication, resource allocation, and parent and community involvement


Braswell, J.S., and A.D. Lutkus, W.S. Grigg, S.L. Santapau, H. Tay-Lim, M.S. Johnson. The Nation’s Report Card: Mathematics 2000 (Washington, D.C.: U.S. Department of Education, NCES, 2001).

Kilpatrick, J., and J. Swafford, B. Findell. Adding It Up: Helping Children Learn Mathematics (Washington, D.C.: National Academy Press, 2001).

Levine, D. “Radical Equations,” Rethinking Schools (Summer 2001).

Loucks-Horsley, S., and P. Hewson, N. Love, K. Stiles. Designing Professional Development for Teachers of Science and Mathematics (Thousand Oaks, Calif.: Corwin Press, Inc., 1998).

Moses, R.P., and C. Cobb.?Radical Equations: Math Literacy and Civil Rights (Boston, Mass.: Beacon Press, 2001).

Jack Dieckmann, M.A., is a senior associate in the IDRA Division of Professional Development. Comments and questions may be directed to him via e-mail at feedback@idra.org.

[©2002, IDRA. This article originally appeared in the March 2002 IDRA Newsletter by the Intercultural Development Research Association.  Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]