Numeracy gaps and literacy gaps are the two main academic hurdles in elementary schools, especially Title 1 campuses. Moreover, the origination of the arithmetic ‘numeracy gap’ should be compared to that of the ‘literacy gap’ to analyze how each adversely impacts student learning in their content area. Once the central factors and origination of each type of academic gap are clearly understood, then and only then, can a solution be formulated and implemented in the public schools to eradicate both.

The ‘literacy gap’ between low income and more affluent children occurs before either student arrives for their first day of public school. In short, extensive sociological research conducted over the last 60 years indicates that middle-income and high-income students’ parents read and speak more to their preschool-aged children (e.g., ages 1 to 4) in comparison to lower income familial environments. Thus, low-income children arrive at school with a significant word recognition gap than their more affluent counterparts. If the reader desires more in-depth discussion and understanding of the literacy word gap and its effects on student learning, please read “Fix Fluency --- Or Comprehension Breaks Down.”

Inequitable Arithmetic Skill Ability is Independent of a Student’s Socioeconomics

It is highly likely that low-income children in comparison to their more affluent peer’s numeracy ability is not that appreciably different. Why? Prior to school age, most young children ages 1 to 4 are not consistently engaged in extensive arithmetic operations that produce a long-term impact on a child’s math ability. It is the author’s experience that significant and repeated levels of pattern recognition, logical thinking, analytical activities and arithmetic operations predominately occur and are developed much more readily in structured school classrooms. Thus, if a numeracy gap foments it will occur in the primary grades (i.e., kindergarten through 2nd grade). Moreover, if an arithmetic numeracy skill gap forms and is uncorrected, it widens during and after third grade as more intermediate grade level (i.e., 3rd through 5th grade) math skills are introduced. At that time, intermediate students are unable to master many (intermediate) grade level math skills that have dependent and unmastered prior grade math skills.

After a typical review of standardized test data each school year, it is empirically fair and justified to conclude that Title 1 elementary schools in comparison to non-Title 1 campuses produce greater levels of numeracy disparities that lead to poor student math performance over time. However, it is also fair to state that there are significant numbers of middle- and high-income students who exhibit similar poor math ability as low-income students for the exact same reasons.

Although a numeracy gap can occur at either Title 1 or non-Title 1 elementary schools, it is important to note that a parent with financial resources can more readily solve their child’s math issues with home support or money – since they can afford to pay for outside afterschool or nightly tutorial services from commercial vendors. A good commercial vendor understands the students’ underlying innumeracy issues occurring in the elementary schools as does the author, and they directly address them. Why? The commercial vendors have real accountability associated with results from their services. If they are not effective in their work with the child, the parent will likely not continue to pay for non-performance. Conversely, low-income students – generally – possess much lower levels of home academic support as well as their parents’ inability to afford expensive commercial afterschool tutoring. If their academic gaps are not addressed at school, then it is highly probable they will not be rectified as needed in subsequent grade levels.

Modern Teaching Failure Philosophy

As stated above, numeracy gaps lead to poor student math performance, and they may occur in either socioeconomic school setting. Clearly, it is not a teacher’s intention to provide poor daily mathematics lesson or instruction. It is a lack of knowing what and how to teach so the vast majority of students learn and master grade level mathematical content.

In a sentence, it is not the classroom teachers that are to blame for poor math performance, for they are instructing students to the best of their ability – as they were trained at university or via emulating their colleagues’ math instruction. However, the education community – teacher colleges and universities failed to provide teachers with an instructional methodology and thinking that ensures mastery by all children in arithmetic skill areas. Additionally, campus and central office administrators do not implement simple numeracy systems to rectify the situation – as stated below. In short, classroom teachers have not been provided a simple strategy to address prior grade level numeracy gaps, or shown a methodology to prevent them from forming in the primary grades. This confusion results in pedagogical and instructional mediocrity with too many elementary classroom teachers following what the author coins as the ‘Modern Teaching Failure Philosophy:’ “If a student gets it, they get it. If they do not, they do not! Teacher moves on to the next core lesson.” When there is no mastery of skills or there is no system that ensures the mastery of basic arithmetic skills, there is only one possible outcome – student math incompetence awaits at a later grade level. Of course, it will become obvious when these students are unable to pass a grade level standardized math test beginning in third grade.

The Arithmetic NUMERACY FIX – No Current and Prior Grade Level Gaps

The solution is obvious and straightforward: Do NOT let the arithmetic numeracy gaps form in the first place. The challenge is implementing an instructional and curricular resource system to accomplish this objective. A system must be implemented in the primary grades that prevent numeracy gaps from mushrooming as the child progresses into the intermediate grades.

First, the infamous achievement gap is really a skill gap. So, an effective Tier 1 curriculum must include adequate focus on arithmetic skill mastery. Primary students must be well versed in place value meaning, even-odd numbers, multiple towers (up and down), addition and subtraction math fact automaticity as well as the other state standards associated with PK – second grade.

Second, a daily spaced repetition session must be in place to provide threshold repetitions for ALL students – so ALL students ‘GET IT.’ This is a dynamic short-session of five to ten minutes each day with the rapid review of math skills from previous core lessons or grade levels. Download the 'Math Spaced Repetition Guide/Outline' for each grade level first through fifth under the "Expertise Tab" at the The New 3Rs Academic Transformation.

Third, each teacher should employ a structured math problem solving resource that puts into application current and mastered arithmetic skills. (Note: Write me an email, and first and second grade fall/spring resources will be made available for free). The teacher can also implement Problem Based Learning (PBL); however, the structured problem-solving curricular resource (15 to 20 minutes a day) ensures that there is specific application of the tier 1 curricular resource and core lessons in a sequential and accountable manner.

Fourth, a daily numeracy-based skill program (Formative Loop) should be implemented school-wide that targets each student individually, so it can be monitored in real time by both the classroom teacher and the administrator. Thus, numeracy skill gaps never should form for any student at the campus, if school personnel are attentive to the daily formative assessments of Formative Loop.

Lastly, if the students possess arithmetic numeracy gaps in the intermediate grade level years (e.g., third through sixth grades), an intervention ‘bridge’ must be constructed to ensure grade level skill mastery of a state’s standards. Thus, simply repeat steps one through four above in the intermediate grades; however, it will require more effort from classroom teachers and the instructional coaches and/or administration.

Note: If a good, accountable math and daily numeracy system is implemented in the primary grades as described above, then, again, repeat steps one through four in the intermediate grades. However, the task entails ensuring that all intermediate grade level standards are taught to mastery - as was done in the primary grades. As expected, it is a much easier instructional process because it is a current grade level issue WITHOUT prior grade level gaps bogging the classroom teacher down. As previously stated, each student must be individually targeted for accountability for the mastery of grade level numeracy skills. Transition from paper-pencil classroom work to online testing environments as referenced in the blog, 'Transitioning to On-Line Testing.'

Final Thoughts

The consequences of ignoring academic numeracy gaps are more than evident over the last 60 years. In fact, the outcome is chronically low grade-level standardized testing results beginning in third grade since significant numbers of primary aged students have been passed on with arithmetic skills or academic numeracy gaps. Unless the numeracy skill gaps are corrected, they widen, and poor student mathematics performance continues unabated.

Finally, there is absolute certitude if students possess academic skill gaps, and it does not matter if it is a literacy or numeracy gap – it is not going to fix itself. If stellar academic literacy and mathematics performance is important and a priority to the school's administration, there must be a systematic and rational plan of implementation (with consistent daily effort) in order to produce student outcomes similar to those expected of commercial vendors!