Implementing Common Core Standards for Mathematics: Focus on Problem Solving
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
Utilizing action research as the methodology, this study was developed with the ultimate goal of describing and reflecting on my implementation of one aspect of the Common Core State Standards for Mathematics (CCSSM) in an algebra classroom. This implementation focused on the Problem-Solving Standard of Mathematical Practice (SMP) as described in CCSSM (Making sense of problems and persevere in solving them). The research question that guided my work was the following: How is the Common Core State Standards for Mathematics (CCSSM) Problem-Solving Mathematical Standard enacted in an algebra class while using a Standards-based curriculum to teach a quadratics unit?
I explored this by focusing on the following sub-questions:
- Q1. What opportunities to enact the components of the Problem-Solving Mathematical Standard are provided by the written curriculum?
- Q2. In what way does the teacher’s implementation of the quadratics unit diminish or enhance the opportunities to enact the components of the Problem-Solving Mathematical Standard provided by the written curriculum?
- Q3. In what ways does the teacher’s enactment of problem-solving opportunities change over the course of the unit?
Reviewing the literature related to the relevant learning theories (sociocultural theory, the situated perspective, and communities of practice), I outlined the history of CCSSM, National Council of Teachers of Mathematics (NCTM), National Research Council (NRC), and the No Child Left Behind Act of 2001. Exploring the details of CCSSM’s Standards of Mathematical Content (SMCs) and Standards of Mathematical Practice (SMPs), I discussed problem solving, the Problem Solving Components (PSCs) listed in the Problem-Solving SMP of CCSSM, teaching through problem solving, and Standards-based curricula, such as College Preparatory Mathematics (CPM) which is the algebra curricula I chose for this study.
There are many definitions of the construct problem solving. CCSSM describes this construct in unique ways specifically related to student engagement. The challenge for teachers is to not only make sense of CCSSM’s definition of problem solving and its components, but also to enact it in the classroom so that mathematical understanding is enhanced. For this reason, studies revealing how classroom teachers implemented CCSSM, especially in terms of problem solving, are necessary.
The Critical Theoretic/Action Research Paradigm is often utilized by researchers trying to improve their own practice; thus, I opted for an action research methodology because it could be conducted by the practitioner. These methods of data collection and analysis were employed in order to capture the nature of changes made in the classroom involving my teaching practice. I chose action research because this study met the key tenets of research in action, namely, a collaborative partnership concurrent with action, and a problem-solving approach.
While I knew how I wanted to change my classroom teaching style, implementing the change was harder than anticipated. From the onset, I never thought of myself as an absolute classroom authority, because I always maintained a relaxed classroom atmosphere where students were made to feel comfortable. However, this study showed me that students did view my presence as the authority and looked to me for correct answers, for approval, and/or for reassurance that they were on the right track. My own insecurities of not knowing how to respond to students in a way to get them to interact more with their group and stop looking to me for answers, while not being comfortable forcing students to talk in front of their peers, complicated this study. While it was easy to anticipate how I would handle situations in the classroom, it was hard to change in the moment.
The research revealed the following salient findings: while the written curriculum contained numerous opportunities for students to engage with the Focal PSCs, the teacher plays a crucial role in enacting the written curriculum. Through the teacher’s enactment of this curriculum, opportunities for students to engage with the Focal PSCs can be taken away, enacted as written, or enhanced all by the teacher. Additionally, change was gradual and difficult due to the complexities of teaching. Reflection and constant adapting are crucial when it comes to changing my practice.As a classroom teacher, I value the importance of the changes that need to be made in the classroom to align with CCSSM. I feel that by being both a teacher and a researcher, my work can bridge the gap between research and classroom practice.