The Common Core State Standards for Mathematics
In its Myths versus Facts section, the CORE Initiative (http://corestandards.org/resources/myths-vs-facts) states that the standards “...are not a curriculum. They are a clear set of shared goals and expectations for what knowledge and skills will help our students succeed.” With this in mind, educational leaders need to ensure that teachers have a clear understanding of these goals and expectations. Districts that have pulled together teams of coaches, teachers and math experts to go through the standards and develop a curriculum document for the teachers have been able to implement the CCSSM more fully and with more fidelity than those that leave it up to the individual teacher to figure it out. Students are the reason for the Common Core mathematics standards (Hull, Balka, and Miles, SEEN, Winter 2012) lays out six steps for transforming mathematics at the classroom level that will aid educational leaders in their implementation.
The Standards for Mathematical Practice
According to the Common Core State Standards for Mathematics, “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.” The National Council of Teachers of Mathematics (NCTM), in its Principles and Standards for School Mathematics, states that “the ﬁve Process Standards highlight ways of acquiring and applying content knowledge.” The Standards for Mathematical Practice are at the heart of students developing the deeper understanding required by the CCSSM. The creators of the CCSSM took the perspective that the Standards for Mathematical Practice are “observable indicators of student understanding.” They even argue “that a lack of understanding in the mathematical content effectively prevents students from engaging in the mathematical practices.”
In the forthcoming series “Strategies for Common Core Mathematics: Implementing the Standards for Mathematical Practice” (Jones and Texas, 2013, Eye on Education) it is stated that “...it is the practices themselves that help develop that understanding. So connecting the content to the mathematical practices is critical if teachers want to develop solid mathematical proficiency in their students. The processes are how a student gains proficiency in the content that allows them to develop the practices that ultimately carry them through their mathematical journey. The CCSSM are a collection of processes, proficiency, and practices that produces students who are ready for successful transition into the workplace or college. Expertise is generated in practice but implemented through process.”
Many educators today are unsure of how these practices look at their particular grade level or in their particular subject. How the practices are developed in students with special needs is another challenge for educators. The practices do look differently in different grades since students are at different places on their mathematical journey. This is one area where a professional organization such as The National Council of Teachers of Mathematics can provide much support.
The Content Standards
The CCSSM content standards offer their own challenges for teachers. Some of the content that occurs in specific grades or subjects may be new for those teachers. They may feel a lack of content knowledge for a specific domain or cluster. Also, there are domains and clusters that support other domains and clusters. Teachers may not immediately know how to integrate the standards as support for associated standards as well as a context for applying the mathematical topic to a real world situation. The Partnership for Assessment of Readiness for College and Careers (PARCC) Content Framework for Mathematics notes that “opportunities for in-depth work on key concepts and connections to critical practices . . . intend to support . . . efforts to deliver instruction that connects content and practices while achieving the standards’ balance of conceptual understanding, procedural skill and fluency, and application.”
The CCSSM content standards also present another challenge for teachers. Teachers can no longer be familiar with just the standards for their grade or subject. Teachers need to understand from where their students came mathematically and what fluency they should have developed as well as how what they are teaching builds and connects to the prior learning. This especially impacts teachers of students with special needs who may have larger gaps in knowledge than some of their classmates. Teachers need to be able to understand to how the content they are presenting will develop as their students continue their mathematical journey.
One of our editors at Eye on Education made the statement that it “seems odd to use the same example in books about kindergartners and high-school seniors.” Our reply, “That was the very reason we started the project. It was to show teachers how what they teach in kindergarten ultimately impacts what students do in high school.” Too often primary teachers, our most important mathematics teachers, do not see where the foundation they are laying for the road upon which their students will journey will ultimately end. Educational leaders need to provide an environment in which teachers have the freedom to ask for support as needed on understanding the mathematical content and the learning progressions within it. States, districts, and schools also need to have a plan to provide on-going high quality mathematics support for teachers.
It is not enough to have content knowledge. Teachers also need the pedagogical knowledge of how to most effectively teach mathematics to a variety of learners. Teacher preparation programs struggle with the challenge of how to better prepare pre-service teachers for their future classroom assignments. One of the biggest challenges is how to cover the amount of content needed as well as the pedagogy required, given that in most teacher preparation programs only two or three courses are dedicated to this task. Add to this the additional challenge of training pre-service teachers on the latest technologies that are available, working with inclusion teachers and students, and providing pre-service teachers more classroom experience and one can sense why almost half of new teachers leave the classroom within the first five years.
What about in-service teachers? What preparation are they getting or have they received for implementing the CCSSM? Some states and districts are using the train-the-trainer model. For that model to be effective, the primary trainers need to be experts in the material on which they are training. Often this is not the case. The trainees need to implement what they have learned and be willing to share in their professional learning community. This needs to be done with fidelity. There are several challenges inherent in this model. Many times the teacher, who is now the trainer, changes class assignments or subjects, or they do not implement what they have learned with fidelity, if at all. Providing support for teachers through coaching and modeling has proved to be a more effective method for creating a true transformational change in instruction, student learning and student achievement.
Successfully implementing the CCSSM typically requires some changes in the structure and environment of the mathematics classroom. Many mathematics classrooms today tend to look like classrooms of the past. Teachers are at the board giving a list of steps to a procedure or algorithm; students are at their desk filling out worksheets of problems like the ones the teacher has just modeled; and all of this is done with little, if any, mathematical discourse or inductive investigation.
The Standards for Mathematical Practice require students to be engaged in mathematics. Mathematics is experiential! Students need time to investigate, discover, conjecture, model, and tinker with the mathematics they are studying. Facilitating this type of community of learning is a different role than most teachers have traditionally assumed. Students need to be trained as well. Mathematical discourse and writing about mathematics does not naturally occur in most classrooms. An environment rich in challenging tasks, engaging questioning and conversations, and relevant investigations needs to be the norm for successful implementation of the content found in the CCSSM. Having a classroom environment such as this will challenge and meet the needs of most all students.
Assessments do drive instruction. Until PARCC and the Smarter Balanced Assessment Consortium produce their first round of assessments, educators will be left to their own interpretations of how a certain standard will look in an assessment. States that have given assessments that provided a list of sample questions have unfortunately trained some teachers to “teach to the test.” Comparing scores on tests such as the Explore Test®, PLAN®, ACT®, PSAT®, and SAT® to scores on comparable grade level tests can show the disparity in classroom instruction that prepares students to use and apply the mathematical knowledge they have acquired to new situations and that instruction that simply teaches problems to be learned. Benchmarking students to see where they are in that snapshot of time, what they have maintained, or what they have lost, will be a new experience for some educators. Grading philosophies will have to be revisited.
Standards based grading and progressive grading are some examples of alternative grading methods that may need to be studied by districts. Formative instruction strategies become more important to teachers as they are charged with diagnosing, prescribing, and remediating students as needed on a daily or weekly basis. Teachers may require additional training in how formative instruction fits in to their daily classroom experiences and what supportive role pre-assessments and formative assessments offer in successfully implementing the CCSSM.
Successfully implementing the CCSSM can be a challenge for educators at all levels who are left without effective support. It is up to states, districts, schools, and teachers to study, plan, and prepare for continued support for classroom teachers as well as district and building leaders to ensure that our students of today can best be prepared to be productive citizens of tomorrow. Successfully implementing the CCSSM is a journey that will take careful study, planning, preparation, on going support, and time. After all, the expected end of this journey is the development of students who have been successful mathematically and are ready to enter post-secondary education and the workforce.