“Mathematics rightly viewed, possesses not only truth, but supreme beauty.” – Bertrand Russell
A Civil Right
Mastery of mathematics is evading many of our students; an appreciation for mathematics is evading many more. Students and many educators have experienced anxiety or frustration with mathematics. Comfort and confidence with mathematics have been compromised by experiences dependent upon abstract, procedural, and computationally-based lessons. The mathematical memories of many adults in North America include extensive experiences with worksheets, textbook pages, and timed assessments. While elements of those instructional practices continue to have value in mathematical learning, the over-dependence on these practices likely contributed to many students and adults’ lack of confidence with mathematics.
During the past decade, an examination of international perspectives has contributed to a new understanding and appreciation of mathematical learning. Teachers and students throughout North America have begun to develop a greater appreciation of mathematics through learning experiences that include inquiry, collaboration, and hands-on learning.
For our students to develop the depth of mathematical knowledge we recognize is imperative, we must integrate innovative instructional strategies into a balanced mathematics program that promotes conceptual understanding and effective, efficient problem solving.
An International Perspective: The Critical Need for Mathematics
The education we are providing our students must prepare them to be citizens in a global economy. We can longer accept the perception that being a literate adult is defined primarily by elements of written and spoken language; mathematical reasoning and problem solving skills are equally essential for today’s students. Multiple international organizations that promote educational reform emphasize the critical importance of mathematical learning (e.g., The Partnership for 21st Century Skills, 21st Century Learning Initiative).
The international perspective reinforces our recognition that high levels of mathematical competency will unquestionably be a significant factor in our students’ personal success and our global community’s ability to solve some of the critical challenges we are facing economically, environmentally, and socially. Analyses of international studies, such as Trends in International Mathematics and Science Studies (TIMSS) and the Program for International Student Assessment (PISA) reveal two key improvements that must be made to North American teaching and learning of mathematics – greater focus and superior instruction.
Mathematically Redefining What We Teach and How We Teach
In order to address these areas for improvement, educational systems across North America have invested significant time and resources in the revision of curriculum standards in order to promote more rigorous understanding and application of mathematical concepts. Educators have recognized that extensive lists of curricular outcomes have impaired teachers’ ability to ensure high levels of learning for students. The primary purpose of mathematics instruction in many classrooms has been reduced to the covering of content, as opposed to developing mathematical learning that encompasses conceptual understanding, procedural fluency, and problem solving, as recommended by the National Mathematics Advisory Panel’s report in 2008.
Redefining the quantity and quality of what we teach through revisions to standards and outcomes is a critical first step to promoting understanding and application of mathematical learning. However, the revision of standards alone will do little to increase actual student achievement. As educational systems identify more cohesive, rigorous standards relevant to today’s learners, the investment of time and resources must shift to instructional approaches that will connect the standards to increased student achievement in the area of mathematics.
What Do Educators Need to Significantly Improve Students’ Mathematical Learning?
As we recognize the need for our students to be more confident with mathematical competencies, we also recognize the need to increase our understanding of mathematics and to increase our repertoire of evidence-based instructional practices. We also accept that richer learning experiences are necessary to engage today’s students in new and innovative ways. While a greater focus and coherence of content is necessary, we must also attend to how we teach.
Despite the recognition of the increasingly critical need to for high-quality mathematics instruction, much less investment has been made to providing teachers professional development and practical, implementable resources to support their mathematics learning or instruction than has been made to the areas associated with language arts.
Relying primarily on teacher education programs to address this need is impractical at best. While we recognize that teacher education programs are critical partners in this work, it is equally imperative that school systems invest in supporting current educators. School systems must support teachers in developing a deeper understanding of the mathematics they teach and providing classroom teachers with practical instructional and intervention practices to meet the diverse needs of their learners.
How to Meet the Challenge
Civil rights leader Robert Moses calls mastery of mathematics a civil rights issue. We must ensure that today’s learners will engage in mathematical learning that is rich, exciting and prepares them for their individual and collective futures. We recommend that all educators engage in dialogue and action research that address:
- An overview of the most critical (essential) mathematical standards explicitly connected to a Response to Intervention model (Tier 1, 2, 3).
- The conceptual understandings of critical mathematics that will enhance their flexibility and “real-time” responsiveness to students’ mathematical thinking and learning.
- An understanding of the connections between the critical components of number sense including quantity, equality, proportional reasoning, place value, and pre-algebraic thinking.
- Well-designed open-ended assessments (including CFAs, diagnostic interviews, universal screening probes, and progress monitoring tools) in the critical areas of mathematics that will promote identification of instructional needs for Tier 1, 2, 3 and will measure the students’ response to interventions.
- Evidence-based instructional practices that promote conceptual understanding, procedural fluency, and problem solving for high, quality Tier 1 instruction.
- Intervention strategies to promote student learning of the identified essential mathematical concepts.
No single course is failed by more high school students than Algebra. Students who do not pass Algebra will not graduate from high school; if they pass it after several attempts at taking the course, they will likely not directly attend a four-year university, since acceptance requires that students take and pass mathematics courses beyond Algebra. Success in mathematics is a civil rights issue. We look forward to further work and progress toward securing this right for all.