How many times do educators read in the media that their students suffer from gaps in their basic understanding of reading, writing, and arithmetic? Learning gaps are unsuccessful or incomplete learning of content, concepts, and skills that are required building blocks for future learning. It is like seeing a picture of a smiling person missing two front teeth and wondering how that person chews food. Gaps in learning, like missing teeth, make it hard if not impossible for children to “bite into” more complex instruction.
Learning gaps are becoming a standard fixture of educational reports. They beg the questions – when we know something is a significant problem, why don’t we fix it? What keeps us from doing what we know we should do?
What do we know?
To understand learning gaps, I do what most of us do today; I make an AI search of “gaps in K-12 student learning achievement in the United States and in Wisconsin (my state)” to get a rough portrait of learning gap problem areas. In a quick summary of student learning gaps, and as a generalization about all K-12 students, a high percentage of school children today show gaps in
- Automaticity of basic arithmetic skills, understanding conceptual concepts in algebra, fractions, and math reasoning and the application of math skills to their real-world experiences.
- Decoding of words leading to struggles with fluency and comprehension, vocabulary development, understanding complex texts, using what they have
- Organizing their thoughts into writing or spoken conversation, constructing written or spoken arguments based upon evidence, understanding of grammar and language mechanics.
- Understanding and applying scientific theories and practices to their real-world experiences, development of inquiry skills to investigate their real world, and the interpretation and understanding of data to interpret the patterns and trends in the world.
- Knowing and understanding governmental rights, responsibilities, and organization, looking at historical and current events from multiple perspectives, understanding patterns and trends in global issues, and having a clear understanding of global geography and socio-economic-cultural differences.
We recognize the above gaps by taking a 1,000-foot overhead view of K-12 education and considering student achievement from a multi-year analysis of data. The National Assessment of Educational Progress (NAEP) makes national studies and points to these shortcomings for Wisconsin 4th and 8th graders.
NAEP Reading: 32.6 of 4th graders achieved proficiency (67.4% were not proficient) and 32.4% of 8th graders achieved proficiency (67.6 were not proficient)
NAEP Math: 42.9% of 4th graders achieved proficiency (57.1were not proficient) and 33.2% of 8th graders achieved proficiency (66.8 were not proficient)
From a ground level view of statewide assessments, children in Wisconsin demonstrated more pointed gaps in learning in 2024.
- Math – 42% of 4th grade students achieved proficiency in math and this falls to 37% for 8th graders.
- Reading – 31% of 4th grade students achieved proficiency in reading and the same percentage (31%) were proficient readers in 8th grade.
When learning gaps are disaggregated by race and special learning needs, children of color and children receiving special education services score 30 to 45 points below white children and white children without special learning needs.
We attempt non-instructional for instructional challenges.
School districts annually respond to the educational reports with a variety of actions to address learning gaps. Actions range from
- Identifying students with gaps using formative assessments and standardized test data and grouping these children for targeted instruction.
- Small group instruction that personalizes the focus on each student’s gap needs.
- Response-To-Intervention protocols that increases instructional supports based on student needs.
- Tutoring.
- Culturally sensitive instruction.
- After school programs.
- Saturday instruction.
- Summer school.
- Community partnerships that support families and provide additional tutoring.
- Professional development to strengthen teachers’ instruction.
- Social-emotional support for students.
Yet gaps persist. The effectiveness of these outcomes mirrors the proverbial Dutch boy trying to plug leaks in a dam wall with fingers.
Mastery learning for core outcomes.
We need to teach children differently if we want to achieve different outcomes.
Mastery learning is not a new concept education. To generalize, mastery learning makes learning achievement the instructional constant and time an instructional variable. All children successfully learn all core outcomes no matter how long it takes. Repeat – mastery learning teaches until all students meet the outcomes of success.
In contrast, most classes in our schools are organized using traditional instruction practices. In traditional instruction time is the constant and achieving successful is a variable – in the time allowed, many children cannot achieve successful learning. Repeat – children run out of time to successfully learn their lessons.
What does this look like?
We identify the core outcomes every child must learn in their grade level or course curriculum. The core outcomes are the building blocks that allow the child to continue learning in their grade level or course and be ready for success in the next grade or course. There is a lot of content knowledge and curricular activities in each grade level and course curriculum that add value to the core, are good for children to know and experience but are not core. The non-core lessons in each lesson take time for planning and teaching.
A mastery learning curriculum isolates the critical knowledge, concepts, and skills a child needs to know and be able to do to achieve success in a grade level or course. Let’s drill down. These are the math standards that are essential for success in second grade math and readiness for third grade math.
1. Operations and Algebraic Thinking (2.OA)
• Represent and solve problems involving addition and subtraction.• Solve one- and two-step word problems within 100 using addition and subtraction. • Add and subtract within 20.• Fluently add and subtract within 20 using mental strategies. By the end of second grade, know sums and differences of numbers up to 20 from memory. • Work with equal groups of objects to understand multiplication:
• Determine whether a group of objects (up to 20) is even or odd. • Use addition to find the total number of objects arranged in rectangular arrays (up to 5 rows and 5 columns) and write equations to show the total.
2. Number and Operations in Base Ten (2.NBT)
• Understand place value. • Understand that the three digits of a three-digit number represent hundreds, tens, and ones. • Count within 1000 and skip-count by 5s, 10s, and 100s. • Read and write numbers up to 1000 in numerals, words, and expanded form. • Compare two three-digit numbers using >, <, and = symbols. • Use place value understanding and properties of operations to add and subtract. • Fluently add and subtract within 100 using strategies based on place value.
• Add up to four two-digit numbers. • Add and subtract within 1000 using models, drawings, and strategies, and explain the methods used. • Mentally add or subtract 10 or 100 from a given three-digit number.
3. Measurement and Data (2.MD)
• Measure and estimate lengths. • Measure objects using standard units like inches, feet, centimeters, and meters. • Estimate lengths using appropriate units of measure. • Compare lengths of two objects and express the difference. • Relate addition and subtraction to length. • Use number lines and rulers to solve addition and subtraction problems involving lengths. • Work with time and money. • Tell and write time to the nearest five minutes, using analog and digital clocks. • Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies. • Represent and interpret data. • Generate measurement data and show it on a line plot. • Draw and interpret picture graphs and bar graphs to solve simple problems.
4. Geometry (2.G)
• Reason with shapes and their attributes. • Recognize and draw shapes like triangles, quadrilaterals, pentagons, hexagons, and cubes. • Partition shapes into equal parts and describe the parts using words like halves, thirds, and fourths.
A mastery learning teacher carves enough time out of every school day and week for daily instruction of units and lessons that teach these to all children in the class. Instruction is explicit with formative assessment to ensure students understand initial instruction and enough guided and independent practice to reinforce student learning. Summative assessments document student learning success, but if a child is not successful the child must repeat instruction until the content, concepts, or skills not met are successfully learned. Children must be proficient in each day’s lesson before they advance to the next lesson.
When learning outcomes are non-negotiable constants, there are no learning gaps. But when time and the calendar are constants, learning stops when time and the calendar tell instruction to stop and learning gaps are obvious outcomes. Reconsider the second-grade math standards. Which of these can we say, “It is okay if you do not learn this (these) standards this year?”, however in third grade we will assume you know these standards.
The following two videos display how Sal Khan and the Khan Academy perceive mastery learning and our need to change from traditional instructional models to a mastery model.
Let’s Teacher for Mastery – Sal Khan
Khan Academy View of Mastery Learning
Reality leads to learning gaps.
I have participated in this conversation repeatedly over the past decades. Many strong arguments have been made for infusing mastery learning in our schools. We examined models of direct instruction, explicit instruction, and outcome-based instruction as they are prime ingredients in mastery models. However, whenever these are discussed and even in early implementation, the issue of time and priorities arise. Predominantly, the issues boil down to –
- If some or most of the class were successful in learning the lesson, what do we do with them while we wait for those who were not successful? The logistics of management are both worrisome and tiresome. We are not willing to change our paradigms of whole class teaching.
- The time it takes to ensure mastery for all reduces the time for other curricula. Time must come from somewhere and it comes from non-core curricula. We are not willing to change our preferences for a comprehensive curriculum for all with learning gaps for some to a targeted curriculum of no learning gaps for any in the core curriculum and a reduced non-core curriculum.
While we decry learning gaps, we are not willing to let go of the traditional school day and school year or prioritize core curricula over non-core.
Hence, school boards as representatives of their community and the community’s concept of public education, abandon mastery learning in favor of traditional learning, happiness for the majority instead of success for all. And the acceptance that some children will suffer learning gaps every year and these gaps will plague them for a lifetime.
As I participated in these discussions over time as a teacher, principal, superintendent, and school board member, I always was aware of the whimsy and politics of public education. We would rather endure learning gaps of traditional teaching models than face the stresses of teaching differently.