Contributed by Ted H. Hull
Mathematical rigor is the meticulous blending of well-developed content and effective instruction designed to increase students’ thinking, reasoning, and understanding of skills and concepts. In far too many classrooms, the degree of mathematical rigor is inadequate. In order to teach with rigorous instruction, change is required. Clearly, this is no easy task.
Teaching is an extremely difficult and demanding job. Paving the way for students to learn the identified content takes years of experience. As a result, once certain instructional approaches have been adopted, they are rather difficult to give up. Nonetheless, societal shifts such as advances in technology-based assessments, demands for rigor, requirements for students to think and reason, and elevated content standards demand instructional methodology changes in mathematics. Using mathematics coaches is a highly effective way to encourage and support the essential changes in teaching.
Mathematics coaches either are, or have been, classroom teachers who demonstrated effectiveness teaching students the required mathematical content. To be effective they adopted, adapted, and formulated their own instructional methodologies. But herein lie some of the difficulties many mathematics coaches encounter when shifting from teaching students to working with adults. Furthermore, mathematical rigor was not a priority for most coaches when they were teaching.
Mathematics coaches need to build a vast array of talents and skills that support working with teachers. This takes time and experience – luxuries most coaches do not have. Here are some suggestions for mathematics coaches for when they work with teachers to support change toward mathematical rigor without burning any bridges.
1. Students, not teachers, are the focus and beneficiaries of change efforts.
Mathematics coaches work with teachers to improve learning. In this effort to change teacher actions, it is easy to forget the true purpose: to increase student understanding and learning of mathematical skills and concepts. In order to increase mathematical rigor, students must be highly engaged in activities that greatly increase thinking, reasoning, and understanding. In order to gauge success, coaches and teachers assess student’s actions with an emphasis upon student discourse.
2. Accept that the teacher is not you.
One of the easiest traps for mathematics coaches to become entangled in is trying to create mirror images of themselves. As previously mentioned, coaches’ methodologies and approaches were adopted and ingrained when they were teaching. A logical assumption for coaches to make is that the teachers just need to adopt the coaches’ instructional techniques and styles. Essentially, this approach and attitude demeans teachers and certainly erodes necessary collegial relationship. Coaches and teachers are partners in instructional change, and both are learners.
3. Build from the teacher’s strengths, not yours.
Mathematics coaches need to identify individual teacher’s strengths. Because the teacher’s approach is different from what the coaches may have done does not mean the technique is not effective. Mathematics coaches want to facilitate change in areas so that teachers build their confidence, not insecurities. Teachers need to be able to observe shifts in students’ degree of engagement in the mathematics lessons early on to believe their effort is worthwhile.
4. Understand the relationship between materials and instruction.
Materials used in the classroom greatly influence the instructional techniques and methods used by teachers. In order to change instruction, the materials must be redesigned to fit the desired instructional change. In most cases, when initiating teaching for mathematical rigor, it is easier to redesign materials rather than create new materials. Teachers and students must be prepared to successfully teach and learn with the newly created lessons.
5. Keep change expectations reasonable.
Change is difficult. Change is also a process over time. The amount of change to undertake is a balancing act. The amount of change must be significant enough to make a difference in student learning, yet small enough to be manageable for all involved. Change is initiated with support from the coach, but the change must be sustained by the teacher. Coaches, in all likelihood, cannot be present for every lesson.
6. Co-teach, do not demonstrate teach.
Supporting instructional change is far more complex than merely showing a teacher or group of teachers “how it is done.” Demonstrating a lesson means coaches are responsible, while co-teaching means teachers and coaches are both responsible. Ownership of an instructional technique or approach comes from a sense of responsibility. Co-teaching means the teacher and the coaches are doing their utmost to ensure the changes are working; co-teaching provides a feeling of collegiality; and, finally, co-teaching means teachers and coaches share both successes and failures and work together to fine-tune instruction.
7. Co-plan lessons as frequently as possible.
Adapting instructional materials, identifying change initiatives, and co-teaching all require co-planning. Ideally, co-planning is routinely accomplished through learning communities. Co-planning clarifies expectations and provides an opportunity to anticipate potential difficulties within the content or within instructional transitions.
These seven tips for mathematics coaches work in unison to support both the roles of teachers and coaches in increasing students’ mathematical comprehension. Regardless of one’s experience, there is tremendous power in the process of reflection. By reviewing these seven suggestions, mathematics coaches can revisit their own strengths and weaknesses, and thereby empower and reinvigorate their efforts toward achieving mathematical rigor in teaching.
Ted H. Hull completed 32 years of service in public education before retiring and opening Hull Educational Consulting. He served as a mathematics teacher, K-12 mathematics coordinator, middle school principal, director of curriculum and instruction, and a project director for the Charles A. Dana Center at the University of Texas in Austin. He is the co-author of five Corwin books, including the most recent, Realizing Rigor in the Mathematics Classroom. Schedule an on-site or virtual consultation, seminar, or workshop with Ted Hull today!