According to Robyn Jackson, author of ASCD's How to Plan Rigorous Instruction (2011), "Rigorous instruction asks students to create their own meaning... and use what they have learned to solve real-world problems, even when the 'correct' answer is unclear..." Jackson explains that rigorous instruction helps to develop students' capacity to consider multiple meanings and interpretation, take and support a position, tolerate uncertainty, and adjust their approach when presented with new constraints. These approaches are consistent with the best of CCSS' approaches. Consider for example, the CCSS expectations that students compare and contrast. That skill is useful in considering multiple meanings and interpretation, a skill that demands that students review how various interpretations are similar and different.

Linda Gojak, President of the National Council of Teachers of Mathematics, has discussed what is needed to incorporate rigor into mathematics instruction. Following are five of the principles she recommends, including instruction that:

• Challenges students
• Requires "effort and tenacity" by students
• May result in multiple paths to problem-solving
• Provides connection among concepts
• Expects students to be actively involved in their own learning (Gojak, 2013)

As described by Gojak, rigorous instruction may be "messy," resulting in different ways to approach problems and seek solutions-this is in direct contrast to traditional ways of finding the "one correct mathematical solution." Rigorous instruction is also "rich" - it is quality instruction that encourages deep understanding and rich discourse among students. According to Gojak, with rigor, students are directly involved in finding their own pathways to learning. With rigor, students are urged to ask clarifying questions and reflect on their own thinking and progress.

Gojak's recommendations appear to be applicable for rigor in all instruction, with implications beyond the study of mathematics. Whether studying English/Language Arts, social studies, science, or math, the principles of challenging students, engaging in rich discussion, and expecting students to reflect on and monitor their own learning seem equally applicable. To further rigor in instruction, it is necessary then to ask how--to ask how teachers will know that students are challenged, how they will know that students are considering multiple pathways or solutions, and how teachers will know that students are actively monitoring their own learning.

In a rigor rubric developed as a tool for principals and teachers to use in planning for and implementing rigor in classrooms, Oakes, Conway, and Mason (2013) provide a 4-point scale for considering the how's (the how's of teachers and students) in implementing rigor. To develop this rubric for the National Association of Elementary School Principals, Oakes et al. reviewed over 45 diverse sources to identify ways that teachers and students can engage in rigorous interactions. For example they cite:

• Evertson and Neal 's (2006) description of learning-centered environments that promote student self-direction and ownership for learning
• Wolf, Crosson, and Resnick's (2006) review of ways teachers can increase rigor by the quality of questioning and dialogue with students
• Biemuller and Meichenbaum's (1992) early work on the value of self-regulated learning

In this rigor rubric, Oakes et al. (2013) suggested that rigor can be planned for and monitored through a focus on metacognition (student awareness of their own learning), deep understanding, higher order thinking, and problem solving. For example, the rubric relates rigor to text complexity, cross-curricular instruction, addressing misconceptions, reflective feedback, student goal setting, 21^st Century instruction, and justifying responses. Oakes et al. provide a 12-page rubric that provides a roadmap for strengthening rigor in classrooms through careful planning, reflection, monitoring, and continuous improvement.

From CEI's review of rigor, many practices that have been incorporated into the CCSS approach to learning are compatible with research on promoting rigor in classrooms. However, it is unclear whether frequent student assessment using standardized assessments is essential to promotion of rigor. The research we have reviewed suggests that practices such as student reflection on learning, self-regulation, and a myriad of effective instructional strategies are associated with increases in deep conceptual understanding, problem solving, and higher order thinking. During the next few years, as we enter into a time of implementing and refining assessments, we urge districts and schools to continue to promote rigor, incorporating instruction that is supported by an evidenced-based approach, even as we rethink standardized assessments.

References

Biemiller, A. & Meichenbaum, D. (1992 October). The nature and nurture of the self-directed learner. Educational Leadership, 50(2) 75-80. Retrieved from http://www.ascd.org/publications/educational_leadership/oct92/vol50/num02/

The_Nature_and_Nurture_of_the_Self-Directed_Learner.aspx

Evertson, C.M. & Neal, K.W. (2006 July). Looking into learning-centered classrooms: Implications for classroom management. Washington, DC: National Education Association Research Department. Retrieved from http://www.nea.org/tools/44455.htm

Gojak, L.M. (2013). What's all this talk about rigor? President's Corner, NCTM Summing up. Retrieved from http://www.nctm.org/about/content.aspx?id=35428   

Jackson, R. (2011 January). Introduction: Understanding the mastery principle. In How to plan rigorous instruction http://www.ascd.org/publications/books/110077.aspx

Oakes, A. Conway, P. & Mason, C. (2013). A roadmap to rigor: A resource for principals. Alexandria, VA: National Association of Elementary School Principals.