Show me the data: Constrained K-5 reading and math skills
Exploring growth patterns of constrained reading and math skills.
Note: Unconstrained Kids unpacks, translates, and integrates academic research and data about constrained and unconstrained skills for people that run, fund, and assist organizations that teach and serve kids. This post presents a series of charts I created from among four nationally representative datasets to illustrate proficiency patterns in representative groups of constrained and unconstrained reading and math skills, unconstrained nonacademic skills, and unconstrained general knowledge. For reference, see this working list of constrained and unconstrained skills. Like everything on this Substack, this post is a work-in-progress. I will make updates as needed. A list of the skills included in these charts is included at the end. Questions, comments, and suggestions are welcome.
Last updated: March 15, 2025
Three big ideas
There are significant and meaningful early proficiency gaps in constrained reading and math skills across socioeconomic groups. These gaps largely narrow between third and fifth grade.
The exception is multiplication and division. There are significant proficiency gaps across socioeconomic groups through elementary school. This gap doesn’t appear to narrow significantly until the end of middle school.
NAEP data for nine-year-olds before and after the outbreak of the pandemic show only a small difference in constrained math skill proficiency between socioeconomic groups. NAEP doesn’t provide similar information about constrained reading skills.
About these data
The data in these charts come from two sources: the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K) and the National Assessment of Educational Progress Long-Term Trend Assessment (NAEP LTT). You can read an overview of these and other datasets. The ECLS-K data were collected between Fall 1998 and Spring 2007. It’s the best dataset I’ve found to dig deep into differentiable K-8 reading and math skills. I used the EdSurvey R package to analyze the data. The NAEP LTT data were collected in 2020 and 2022. I used the NAEP Data Explorer to analyze the data. The data are organized by either household socioeconomic status or eligibility for free and reduced-price meals (a proxy for household income). In the ECLS-K dataset, socioeconomic status is defined using a combination of household income, parental education level, and parental occupation. The charts in this post focus on constrained reading and math skills in elementary and middle school.1
Early gaps in constrained skills tend to close in elementary school
A key difference between constrained and unconstrained skills is opportunity. Constrained skills involve acquisition of limited amounts of information (e.g. alphabet, numbers, etc.). In the American education system, there is more opportunity to develop proficiency in constrained reading and math skills. Kids generally have relatively equal access to this information. Mastery is clearly defined and is the same for everyone. Constrained skills can be readily taught and assessed in schools. Explicit and systematic instruction is important as well as extra support for children with learning differences.2
Example 1: Letter-sound correspondence (ending sounds)
This first chart covers kindergarten through third grade. The constrained skill is letter-sound correspondence at the end of words. There are 26 letters in the English alphabet and 44 sounds in the English language. Kids need to learn the different ways that sounds in oral language (phonemes) are represented by written language (graphemes). Kids start school with wide gaps in proficiency on this constrained skill. These gaps significantly narrow by the end of first grade. Across socioeconomic levels, kids are highly proficient in this constrained early literacy skill by the end of third grade. (Mouse over the chart.)
Figure 1. Ability to associate letters with sounds (letter-sound correspondence) at the end of words.
Example 2: Sight words
The next chart shows the growth pattern for another constrained reading skill over the same period — sight words. This skill is not as highly constrained as letter-sound correspondence. Kids need to learn to recognize 100-200 words by sight to be proficient readers (Snow & Matthews, 2016). We don’t expect kids to start school recognizing common sight words. A small percentage do, however, with a larger percentage coming from higher socioeconomic households. This relatively small disparity in fall kindergarten grows significantly by the end of first grade. But the initial advantages in this constrained reading skill largely closes by the end of third grade as other kids catch up.3 The gap eventually fully closes by eighth grade.
Figure 2. Ability to recognize common words by sight.
Example 3: Addition and subtraction
This chart shows growth patterns for two constrained math skills—addition and subtraction—from kindergarten through fifth grade. (These skills were combined in this study.) The growth patterns from kindergarten through fifth grade look remarkably similar to those for sight words. Kids from higher socioeconomic households have clear advantages during in the first two years of school. These gaps are largely erased by the end of elementary school.
Figure 3. Ability to solve simple addition and subtraction problems.
Example 4: Multiplication and division
This next chart shows growth patterns for multiplication and division from first grade through eighth grade. (These skills were combined in this study.) There is a 33 percentage point gap between the highest and lowest socioeconomic groups at the end of first grade. This mirrors the 36 point gap for addition and subtraction in Figure 3. While this gap does not close by third grade, it does begin to narrow by the end of elementary school. Kids from lower socioeconomic households continued to increase mastery of these skills in middle school.
Figure 4. Ability to solve simple multiplication and division problems.
A clear pattern emerges across these four examples. On average, kids across socioeconomic groups master constrained reading and math skills between elementary and middle school. Gaps between socioeconomic groups vary in how quickly they close. In some cases, early gaps are closed by the end of first grade. In other cases, the narrowing doesn’t occur until late elementary or middle school.
Example 5: Simple arithmetic facts
These data from the ECLS-K study are from more than 20 years ago. A great deal has occurred in education and society since 2007. Do we continue to see similar patterns today? To answer this question, we turn to the NAEP Long-Term Trend Assessment. We use data collected in 2020 and 2022 before and after school closures caused by the pandemic. The NAEP LTT assessed a nationally representative sample of about 7,400 9-year-olds in reading and math.
This next chart shows proficiency of U.S. nine-year-olds on simple arithmetic facts. This largely centers on addition and subtraction. (See skill definition at the end of this post.) Data are organized by eligibility for free and reduced-price meals. The chart compares proficiency between these two groups of kids before and after the outbreak of the pandemic.
Figure 5. Ability to solve simple math problems involving adding and subtraction.
Most 9-year-olds are proficient in this constrained math skill. There is a small two percentage point gap before the pandemic and a four-point gap after schools were reopened. For comparison, this roughly tracks with the gaps between socioeconomic groups for third and fifth graders in the ECLS-K study in spring 2002 and 2004.
Of course, we expect children to be proficient in much more than basic arithmetic and recognize sight words by the end of elementary school. We expect them to be able to comprehend what they read and think and solve problems as mathematicians. To understand ability in these more complex skills, we need to look to their unconstrained skills.
But wait, there’s more
If you’d like to see more data about constrained and unconstrained skills, check out these other posts on Unconstrained Kids:
Skill definitions
ECLS-K Reading and Math Skills
The ECLS-K assessed elementary and middle school students on a range of constrained and unconstrained reading and math skills. The skills were considered hierarchical, i.e. one has to master the lower levels in the sequence before one could learn the material at the next higher level. The skills included in the charts in this post:
Ending sounds. Associating letters with sounds at the end of words. This is a constrained reading skill.
Sight words. Recognizing common words by sight. This is a constrained reading skill.
Addition and subtraction. Solving simple addition and subtraction problems. This is a constrained math skill.
Multiplication and division. Solving simple multiplication and division problems and recognizing more complex number patterns. This is a constrained math skill.
NAEP Long-Term Assessment Math Performance Levels
The math NAEP LTT has five performance levels that involve a mix of constrained and unconstrained math skills. Each skill level involves successively greater degrees of unconstrained skills. The skills included in the charts in this post:
Simple arithmetic facts. Students at this level know some basic addition and subtraction facts, and most can add two-digit numbers without regrouping. They recognize simple situations in which addition and subtraction apply. They also are developing rudimentary classification skills. This is a constrained set of math skills.
Works Cited
Snow, C. E., & Matthews, T. J. (2016). Reading and language in the early grades. The Future of Children, 57-74.
ECLS-K researchers used a statistical method called “differential item functioning” to determine there was no bias in the K-8 reading and math assessments by socioeconomic status.
Some children of course have learning challenges with constrained reading skills (dyslexia) and constrained math skills (dyscalculia). Good systematic instruction can help children develop these skills, particularly if challenges are diagnosed and addressed early.
Some readers will object that recognition of common sight words is not the same as decoding or reading fluency. Indeed, reading fluency is the highest level constrained word reading skill. The ECLS-K did not include measures of either of these reading skills. The next highest skill level assessed is word comprehension—kids were asked to fill in missing words in simple sentences (a cloze test). This is an unconstrained skill. But the specific task is dependent upon proficient word reading skill. In third grade, proficiency levels across socioeconomic groups ranged from 80% to 97% on this skill. By eighth grade, the range narrowed to 96% to 100%.