Students are the reason for the COMMON CORE mathematics standards

curricucommon core

The Common Core Mathematics Standards and the Standards for Mathematical Practice are at our doorsteps. Opportunity for serious change, a change that is purposeful, meaningful and that positively impacts students and their learning of mathematics, is knocking. The ultimate question is “Will leaders open their doors?”

Attempting change initiatives alone is generally unproductive. Isolation of teachers and leaders is most likely the greatest single factor undermining change eff orts.

Our experiences allow us to understand both challenges and opportunities that Common Core Standards present for mathematics leaders. Among the three of us are more than 100 years of combined knowledge in K-12 mathematics teaching and leadership. We have written numerous books supporting mathematics change. Our latest book, The Common Core Mathematics Standards: Transforming Practice Through Team Leadership (Corwin, 2012), describes how leadership teams can open the door to seek real transformation in mathematics classrooms.

Common Core Mathematics Standards and the Standards for Mathematical Practice will not enter schools unbidden. After all the reforms, programs, reports, and mandates tossed at schools over the last several decades, nothing compares to this chance to make substantive changes. As mathematics leaders, our challenge is clear — open the door and embrace the opportunity to make a difference for every student.

Transforming Steps

If this door is opened, what can leaders do to promote change in mathematics classrooms? The answer resides in six integrated, sequential, iterative steps. They are integrated in the sense that the steps interact and support one another. They are sequential in the sense that they logically flow one to the next. They are iterative in the sense that they constantly shift higher and deeper as improvements are made, the process sustained, and the steps are repeated.

The steps are:

  • Build teams
  • Articulate the CCSS mathematics curriculum
  • Focus on students
  • Focus on adoption
  • Build coherence and a critical mass
  • Establish a feedback loop

These steps are not some alchemist’s magic elixir recently blended for the Common Core, but are founded on research and are well established. The significant difference is that now a structure for action has arrived.

With leadership, determination, and belief, mathematics classrooms are transformed, and students are successfully learning mathematics. At every step, focus is on students’ success – every student, every day.

Building Teams

Leaders need to share responsibility, ownership, and success. Teachers need to participate as team partners to implement the Common Core Standards. Teams are more than just artificially designated groups. They provide collective brainpower, motivation, and courage to make a difference by trying new strategies and techniques. Attempting change initiatives alone is generally unproductive. Isolation of teachers and leaders is most likely the greatest single factor undermining change efforts.

While there are wonderful resources and recommendations for creative team structures, leaders must work within constraints of schools or school systems. Leadership teams assigned to identify and resolve an issue often find more creative solutions. Conversations within teams and among teams are about student success. Communication flows must be multi-dimensional.

As an example, actions leaders might take to build teams include locating and recruiting influential power players within a school or district. Teachers, administrators, and central office staff must be included.

Articulating the Curriculum

Teachers need to know what they are responsible for teaching. A successful curriculum document, with appropriate supplementary materials, evolves over time. Data-informed decisions need to be made to ensure the content is taught reliably and accurately. Alignment among the written, taught, and tested curriculum is a hallmark of effective school research.

Students must be taught mathematics content contained within the Common Core Standards. This point is so obviously self-evident, yet it is a significant problem faced by mathematics leaders and teachers. Far too often, the mathematics that is already taught and materials already used to teach mathematics are rationalized as being aligned. Leaders and teachers that make this assumption of alignment have already failed to successfully implement the Common Core Standards. Alignment must be constantly monitored and dogmatically reaffirmed by leadership teams.

As an example of articulating the curriculum, grade level and subject area teachers are provided time to study in depth the content standards for their grades or courses and those of grades or courses above and below.

Focusing on Students

Actions teachers take inside classrooms are obviously very important. Research has been consistent on this point. However, the focus of the research has generally been on teachers to the exclusion of students. The only reason for teachers to use research-affirmed strategies is so students are actively engaged in learning. During active engagement, students carefully think about the mathematics they are learning. This thinking must be made visible to students and teachers. With this visibility occurring, two highly successful events are positioned to happen in classrooms. First, ongoing formative assessment is provided. Second, intervention-—first tier RTI—is available. Ongoing formative assessment and intervention mean that teachers and students are constantly aware of their thinking and understanding during instruction. This process allows continual feedback upon correct understandings, and immediate opportunities for correcting misunderstandings.

As a note, there is no such thing as actively engaged listening for an extended period of time, usually more than 10 minutes. A quiet and orderly classroom does not equate to student learning. Students need regular opportunities to process and think about the mathematics they are experiencing, and how new experiences relate to previous learning. Furthermore, thinking is not promoted by skill drill. For many teachers, the ideas of providing for student engagement and providing opportunities for students to process mathematics are new. Professional learning is critical at this point.

An excellent guide for teaching and learning mathematics that focuses on students is provided within the Common Core State Standards. The Standards for Mathematical Practice indicate how content is both presented by teachers and learned by students. These eight practices must be continually discussed, translated into actions, and monitored for implementation. The practices are:

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.

Over time, the practices become embedded in classrooms, as both teachers and leaders continue to understand and implement them. They are an essential part of the Common Core Initiative that are vitally important if the Initiative for change in mathematics is to succeed.

As an example of focusing on students, any initiative or change is directly linked to factors that positively impact student learning, such as research-informed instructional practices, time, and formative assessments.

Focusing on Adoption

Adopting new practices does not occur through knowledge alone. While knowledge is required, teachers and leaders need support to experience, practice, learn, and refine new strategies and techniques. Adults learn at different rates and for different reasons. Leadership teams must focus on change over time by supporting learning curves. This is done through ongoing professional learning activities, supportive monitoring, coaching, and evidence of success. Evaluating teachers or leaders while they are learning new skills, strategies, or techniques is counterproductive. Although evaluation of teachers is a necessary task, it should not be done while teachers are attempting to integrate new ideas about teaching mathematics.

Humans are amazingly resilient. They make changes to adapt when desired, and do not make changes when undesired. Although educators are occasionally frustrated by their students, they truly care about their welfare and learning. This care and concern is the leverage point for change, not threats. The general trend in society appears to be based upon compliance through threat. School leaders do not need to perpetuate or promote this trend. Teachers adopt actions that positively impact students when these actions are presented in an inclusive, caring, and supportive environment.

As an example of focusing on adoption, leaders carefully monitor change initiatives to support teachers in learning new strategies rather than evaluating their performance.

Building Coherence and a Critical Mass

This step is a critical extension of the focus on adoption. Leadership teams must emphasize improvements and change over time. This emphasis is only accomplished through routine, positive monitoring of program implementation. Teachers and leaders must consciously know how they are performing and what the next step is toward improvement.

Emphasizing the point made about adoption, constant progress in implementing change builds from success demonstrated by increased student participation and achievement. Innovation and classroom transformation grow classroom by classroom.

As an example of actions for building coherence and a critical mass, leaders see evidence of successful change by certain teachers and then use these teachers to bring additional teachers on board.

Establishing a Feedback Loop

Everyone involved in change needs affirmation that his or her efforts have value. Students must be performing better and learning more. The feedback loop also encourages steady improvement. Each of the five steps cited previously will not be, and should not be, perfected before implementation. Change is adopted by engaging in specific actions. As these actions are learned and refined, a sense of empowerment by teachers emerges.

Feedback comes in many forms. Leadership teams must find the type of feedback that serves their school best. Feedback must come regularly and in a variety of ways. Useful feedback, the kind that notes increased achievement, focuses on student learning and on instructional approaches which promote student success.

Change is supported by evidence of success. As an example of establishing a feedback loop, leaders ensure teachers receive data that indicate successful student learning is occurring.

Implementing the Common Core Standards

There are numerous opportunities for flexibility within each of the six steps. Leaders and teachers form formal and informal groups with the purpose of implementing the Common Core Mathematics Standards. Teams use these steps to focus their time and energy. The steps also assist in monitoring and gauging implementation. The important point is that the steps are integrated, sequential, and iterative. While a particular step may be the current focus issue, the greater picture of student success as a result of all six steps cannot be ignored.

Teams build coherence and critical mass in commitment to adoption. Teams also inform the curriculum and actualize data analysis into practice. Effective feedback provides leaders and teachers opportunities to refine and improve instructional strategies that impact curriculum documents. These steps increase adoption of effective strategies.

As leaders and teachers work together to open the door of opportunity for all of their students, they will renew their love for mathematics and rekindle their passion for teaching. With the Common Core Standards Initiative at our door, we are challenged as mathematics educators to use this opportunity to make a difference in the lives of our students and of ourselves.

Ted H. Hull, EdD, served for 32 years in public education before retiring and opening Hull Educational Consulting. Don S. Balka, PhD, is a noted mathematics educator who has served as a director of the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics. Ruth Harbin Miles coordinated the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years and now coaches mathematics teachers. Together they are the authors of The Common Core Mathematics Standards: Transforming Practice Through Team Leadership (Corwin, 2012).
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