• by Kathryn A. Brown • IDRA Newsletter • August 2008 • 

Experiencing transformations in mathematics is as beautiful as listening to Beethoven’s Für Elis as a performer strokes each key on the piano in your living room, and it is as intricate as listening to Eddie Van Halen’s hammer-ons in Eruption while sitting in the front row at a concert. Transformation is a prevalent concept studied from pre-kindergarten when students describe locations and sizes of objects in relation to each other, to middle school when students reflect shapes across a line in a coordinate plane, to algebra and pre-calculus where students transform a myriad of parent functions, and to calculus where students take it up a notch to transform the derivatives of these functions.

It is easy to apply a change in parameters to a math function and then readily see the resulting graph using a graphing calculator or an online applet. What would happen to the graph showing my distance over time if I decided to drive faster to work that day? How does it compare to the graph from the day before?

We live and breathe transformations every day. The world around us is in a continuous state of transformation. It is absolutely awesome once we take a moment to notice this. The invention of new technologies is transforming how we communicate and shifting how we play, how we engage with others and how we even listen to music!

But, when we talk about changes in teaching instruction, the chord sounds loudly with a negative note. Change is called upon when schools do not perform. Teachers often are first to be required to change what they are doing in the classroom to meet adequate yearly progress, and many students are left with fading opportunities.

IDRA proposes a new way of looking at change and that is through transformation. The word change implies exchanging one set of instructional strategies for an entirely new set. We do not exchange one parent function for another or one shape for another in mathematics when the image is under a transformation. Instead, the function or pre-image is carried through a process that could entail a reflection, translation and rotation that results in the new image.

Webster’s Dictionary defines transformation as an act, process or instance of transforming or being transformed. Through IDRA’s Math Smart! professional development model, teachers are transforming their instruction and impacting student achievement in mathematics through a process that is supportive, grounded in research and strategies that value students and what they bring to the classroom.

For example, in light of Texas’ state-mandated test, Texas Assessment of Knowledge and Skills (TAKS), was at the time just over a month away, teachers and students at Socorro High School in El Paso and George Sanchez Charter School in Houston already are experiencing the benefits of transforming teacher practice and learning in their mathematics classrooms. How does this happen?

This article focuses on teacher experiences in transforming practice and key elements that have to be in place so this process can occur. It is the first of a series of articles that focus on transformations in teaching practice for secondary mathematics teachers and schools through IDRA’s Math Smart! professional development model. Future articles will discuss the key players involved and their roles and ways that transformation in instruction impacts student learning and success.

Teachers’ Experiences in Transforming Practice

Leticia Monsivais teaches geometry, pre-calculus, and Algebra 1 at Socorro High School in El Paso. In a recent interview, Ms. Monsivais gave insight into transformations in her practice that she has made and how this has impacted student learning (a video of this interview can be seen on IDRA’s Newsletter Plus online). These transformations include going from teaching in rows to teaching in groups and including cooperative learning strategies. This is not periodically or just for hands-on activities but a strategy she incorporates consistently, daily. This setting has changed learning from being teacher-dependent for answers and guidance to facilitating student peer-exchange and problem solving.

Ms. Monsivais credits IDRA’s professional development as a supporting parameter in this transformation through on-site assistance that includes coaching and mentoring, co-planning and co-development of activities, co-teaching and debriefing – all elements of IDRA’s Math Smart! model.

One key component that she credits is the peer exchange of strategies and activities that have worked in her colleagues’ classes. Another key element is having the freedom to take risks in the classroom.

She states: “I consider myself always a risk taker because I want to do the best for my students. When I see something interesting for the students I try it, and if it doesn’t work, it doesn’t work. At first, I didn’t like the idea of groups because I tried cooperative learning when I first started teaching, it was a disaster.”

Ms. Monsivais integrates cooperative learning management strategies that have made this successful in her classroom. Cooperative learning gives students the opportunity for the social interaction important for learning (Borko, 2000). Through discussion, interaction and shared experiences, students form meaning and conceptual connections.

Ms. Monsivais’ students are doing just that through group interaction and through the use of interactive white boards that also have added a new dimension to her instruction. All math teachers at Socorro High School have interactive white boards and projectors as tools for engaging students and deepening understanding. Students are more apt to get up and use technology to justify their thinking. They have virtual tools that afford them the opportunity to illustrate their reasoning and explanations.

Giselle Easton is a second-year teacher at George Sanchez Charter School in Houston. She teaches eighth grade Algebra I, Algebra II, math models and pre-calculus. Transformation comes early for Ms. Easton as she has already seen growth in her practice from last year to this year. Ms. Easton’s insights into transformation in her instruction include making mathematics relevant to her students’ lives, structuring learning through mathematics learning stations, and structuring meaningful and engaging hands-on activities. (See a video of Ms. Easton’s Algebra I class with English language learners in IDRA’s Newsletter Plus online.)

She perfectly orchestrates engaging learning stations for her students where students work cooperatively at stations, including a station for solving equations, a station for writing equations for problem situations, a teacher-guided station at the white board where she is able to see student misconceptions on a more individual basis, and a Sudoku station for building logical thinking skills.

Students work eagerly during the 90-minute class where a timer that is displayed from her computer through the projector counts down the allotted time for each station. Students move seamlessly, and management is in place.

Ms. Easton, like Ms. Monsivais, is open to taking risks. Her reply e-mails to suggestions from her IDRA trainer often read, “Let’s try it!” Their time in the classroom is a partnership that involves coaching, co-teaching, immediate debriefing and reflection. Once a strategy is implemented, debriefing is important, so reflection becomes part of the transformation process.

A component that she has come to demonstrate fluently is the ability to modify instruction and draw from a variety of engagement-based instructional strategies that support her English language learners and traditionally underserved students.

The impact is students experiencing mathematics and expressing their mathematical thinking without hesitancy. When asked what has supported her growth, Ms. Easton replies, “IDRA!” It was during the initial Math Smart! two-day institute that she was able to be a “learner outside of her classroom” (Putnam, 2000) and visualize the framework in creating meaningful learning experiences for students through relevant and engaging activities.

Ms. Easton has great vision for her students and already sees the next transformation that will take place for the next school year. Transformation does not come without challenges or obstacles. Access to technology for her math models class is limited, and the “learning noise” created by being in a portable disturbs other classes during activities that measure the height and vertical distance that you can jump as part of a data collection survey she has students fill out so the data may be used for upcoming activities.

Elements of Teacher Experience for Transformation

Although Ms. Monsivais and Ms. Easton are at two different campuses in two different cities and have varied years of experience, they share common experiences in transforming instruction. These elements are:

  • Having a vision for future growth grounded in their desire for student success in mathematics and their true love of the discipline and teaching.
  • Understanding that implementing tools does not merely enhance learning but transforms student learning. These tools include manipulatives, hands-on activities for exploring math concepts and technology.
  • Creating learning situations that exhibit high expectations of learning rigorous content.
  • Risk-taking that is supported by an administration, colleagues and themselves is integral to the process. Taking instructional risks followed by reflection becomes second-nature and ongoing.
  • Attending professional development sessions that model situated learning.
  • Building a trusting relationship with colleagues and coaches.
  • Feeling valued as an educator and learner by colleagues, coaches and administrators.

Seeing the transformation of instruction as continuous and ongoing is critical for student success, proficiency and achievement in mathematics (Putnam, 2000). This is a multidimensional and dynamic process. It is imperative for our students to have real opportunities that go beyond passing state-mandated tests.


Dieckmann, J. “Teachers Pressing for Quality Teaching – Lessons from Content Teachers of English Language Learners,” IDRA Newsletter (San Antonio, Texas: Intercultural Development Research Association, May 2004).

Merriam-Webster Online Dictionary. B., and J. Butcher, E. Bird. Leading Professional Development in Education (New York, NY: RoutledgeFalmer, 2000).

Putnam, R., and H. Borko. “What do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning?” Educational Researcher (2000) Vol. 29, No. 1, pp. 4-15.

Zmuda, A., and R. Kuklis, E. Kline. Transforming Schools: Creating a Culture of Continuous Improvement (Alexandria, Va.: Association for Supervision and Curriculum Development).

Kathryn A. Brown is an education associate in IDRA Field Services. Comments and questions may be directed to her via e-mail at feedback@idra.org.

The following article originally appeared in the August 2008 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.]