Learning and teaching are two different phenomena occurring in the classroom, thus just improving teaching doesn't always yield great learning results.
See the star in the picture on the right? That's where effective learning happens!
The change in how we understand learning and knowledge has been widely recognized by researchers, and today we refer to a knowledgeable person as one who is aware of knowledge, knows ways to find information and is able to construct knowledge from information (critical thinking, problem solving). Simply memorizing lots of disconnected facts doesn't create strong academic competence, because understanding concepts and connections is necessary in today's world.
Student achievement depends on their engagement and interactions with the learning environment and the content to be learned.
Students' motivation to engage in learning is intrinsic or extrinsic. Classroom participation and real engagement over strategic or ritual compliance are important variables in student learning (here is an interesting infographic about engagement). In addition to interest in the subject, engagement also depends on students' aptitude and readiness to learn. To achieve excellent learning results we need to know the science behind the teaching and learning, and have a good understanding about how learning happens to support deeper learning in the classroom.
The 3C framework can help you achieve this.
This framework helps teachers to create the environment, structure and feedback systems needed for supporting students' authentic and independent learning. The framework can be adapted to any curriculum, and it can be used while teaching any subject. Basically the framework contains rules for good quality 21st century teaching and learning!
The cognitive approach combined with constructive and cooperative practices enable effective teaching and meaningful learning - with Common Core or any other approach or curriculum.
The cognitive approach creates the foundation, because students' thinking needs to change - not just their behaviour.
Cooperation guides the classroom management decision and help students engage in their own learning process.
Constructive tools focus on supporting students' learning process to make learning meaningful and increase motivation to learn.
3C framework also emphasizes using students' self-assessment in order to build feedback loops that support deeper learning. The underlying principle is to empower students to become independent life-long learners.
Here is a 2-page pdf about 3C framework.
 Martin, A. J., & Marsh, H. W. (2006). Academic resilience and its psychological and educational correlates: a construct validity approach. Psychology in the Schools, 43, 267–282.