Teach Less, Learn More: Competency Over Coverage in Essential Math Outcomes

Crucial mathematics skills deserve something better than simple coverage. To improve early math outcomes and math outcomes for life, we must understand the principles of informed instruction that lead to student competency.

Competency vs. Coverage

“We covered it,” goes the familiar expression, “but they just didn’t learn it.”

For decades, American schools have been engaged in a failed experiment, attempting to cram more content than humanly possible into a typical teaching day, and asking children to learn overwhelming amounts of content at younger and younger ages without taking the time to build the foundational skills needed for learning or behavioral success. In most schools, we continue to deliver far too much content, using a rigid schedule that does not encourage teachers to adjust instruction to meet the individual needs of each student.

This is a major challenge that teachers face when it comes to math instruction and outcomes. As we cram more and more content into a typical day, we lose time to build the skills needed for learning/behavioral success. We’ve created anxiety-filled classrooms in which children are less likely to fall deeply in love with learning. We’ve done this even in the early childhood years, which is the most important learning phase in the life of a child. We’ve even raced through early math instruction, covering crucial content without ensuring student learning.

The outcome that matters is not what we covered, but rather what our students have deeply learned and can apply in their lives. It also matters whether they are falling in love with the study of math.

A Lack of Proficiency in Mathematics

Our standard math instructional practices are not working for many children, reflected in data about student competency. By the beginning of fourth grade, the point at which we can accurately predict long-term learning outcomes, only 41% of American children are at proficient math levels. Even fewer children living in poverty are proficient. By eighth grade, 34% of US students are math proficient and by twelfth grade that number drops to 24% proficiency among the students still in school. Among African American twelfth grade students in the city of Detroit, 6% of students are proficient in math.

Identifying Crucial Math Outcomes

In the world of technology, innovation, and constant change, math learning success is relevant. It matters. Our choice to race through math instruction without building basic skills and success is damaging the learning futures of our children. To begin to address this problem, we must identify crucial math outcomes. The principles of informed instruction are simple.

• Clearly identify crucial learning outcomes.
• Use systematic measurement to determine the readiness levels of your students in relation to essential outcomes.
• Offer informed instruction and carefully monitor progress until these skills/objectives are deeply understood (competency).
• Allow students to move on to more advanced learning as soon as they are ready.

With all the content teachers are asked to cover, it may seem daunting to identify which outcomes are crucial. Doug Reeves asks three questions to help determine which learning outcomes deserve all the time needed to achieve competency.

1. Does it address knowledge and skills that will endure throughout a student’s academic career and professional life?
2. Does it address knowledge and skills that will be of value in multiple content areas?
3. Does it provide the essential knowledge and skills that students need to succeed at the next grade level?

The Essential Math Skills Inventory identifies essential math outcomes for preschool through grade three. These are foundational skills that establish number sense and deep understanding of number concepts which are the foundation of math learning for life. Students who learn these skills deeply and joyfully establish a positive trajectory for math learning. They are prepared to succeed in the next grade and beyond.

The Essential Math Skills Inventory is not a framework for curriculum. Many additional skills, projects and activities should be included in the math instructional plan for young students. The inventory is a framework for assessment, a way to systematically assess and respond to student learning needs.

Understanding Competency

Without a deep understanding of these essential skills, many children learn to memorize facts and formulas to help them solve problems on paper. Without deep understanding, many students reach third or fourth grade and begin to struggle with math. Without understanding basic number sense and concepts, math turns on them and becomes a mystery. These students decide that math is hard, or that they just don’t have a talent for math. In the age of information and technology, we need better instruction in math to avoid these patterns of disengagement and avoidance of math.

Student competency means being able to demonstrate these skills over a period, and with many different sets of learning materials or learning contexts. Student competency means understanding and applying these skills even on days when you are distracted, not at your best. Student competency means understanding in a way that will stay with the learner for life.

If we race through non-viable content expectations, some of these crucial math outcomes may not be developed to student competency.

In my analysis of many struggling middle and high school math students, I have found that they lack competency in some of these basic first- and second-grade skills. It is not because these skills were not “covered” in one or more lessons. Lacking specific knowledge of each child’s math learning needs, however, a well-intentioned teacher “moved on” to keep up with the expectation for coverage. And one more math student was left behind. 

A Student Competency-Based Approach

Let’s consider a different approach. A rich and interesting math curriculum should include projects and activities, allow students to move to higher levels of challenge as soon as they are ready, and provide children all the time needed to develop essential skills. To teach this way, teachers cannot race through the same lesson each day with all students. There needs to be time for re-teaching and extra practice until students are fully competent in identified essential skills.

Competency-based learning begins with the identification of crucial skills or knowledge, which you need for ongoing success. In one example of competency-based learning, the Essential Math Skills Inventory for kindergarten identifies four essential math outcomes: Demonstrates counting to 100; Has one-to-one correspondence for numbers 1–30; Understands combinations (to 10); Recognizes number groups without counting (2–10). These are examples of the non-negotiable skills that every child can develop if we give teachers permission to quit racing through ridiculous lists of non-viable content objectives. Some students may need months of practice and play to develop full proficiency in these skills. Some may be ready to move on more quickly. Good teaching makes accommodations for these differences, and gives students what they need at their level, to help them achieve essential outcomes while helping them fall in love with learning.

Building crucial learning skills is not a race. By slowing down the pace of instruction and allowing every young child to fully develop essential skills, we could improve the learning future of our children. This student competency over coverage approach is used in the higher-performing school systems in the world. With these skills in place, our children will have the capacity to be great learners throughout their entire lives.