## Implementing Common Core Standards for Mathematics: Focus on Problem Solving

#### thesis

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.

*CCSSM*. I feel that by being both a teacher and a researcher, my work can bridge the gap between research and classroom practice.