Viability of a Grade Level in Math

When I am asked to consult or evaluate a student, often the student is years behind in math. As a result, I am often asked to determine the grade level of the student’s achievement. Regressing the math achievement to a single number is not viable. This post provides an explanation.

Common Scenario

Here is a common scenario. A school official reported out the grade level in math for a student. The 7th grade student tested at a 4th grade level. As a result, the student spent much of her 7th grade year working on 4th grade math. When I started working with her, I discovered that she was very capable of higher level math. Six months later, she was taking algebra 1.

The Math Spider Web

Unlike reading, math is not nearly as linear. It is more like a spider web of categories (called domains). For example, Geometry is not a prerequisite for Ratios and Proportions and Fractions is not a prerequisite for Expressions and Equations. Geometry and fractions may be included in problems associated with other domains but they are not foundational building blocks.

On the other hand, in reading, comprehension and decoding are essential in all grade levels. Unresolved trouble with decoding in 3rd grade causes major problems in 4th grade and beyond.

Reading Rockets

Grade Level

A student tests at a 3.2 in reading. This provides a clear picture of where the student is in the progression of reading ability. There are books written at that grade level.

If a student is reported to to test at a 3rd grade level in math, the student may have scored higher than 3rd grade in Geometry, at 3rd grade in measurement and data, and lower than 3rd grade in the other domains. True, in reading we have students who may decode at a high level and comprehend at a low level. That is more specific that sorting through 6 domains in math. Then consider that the comprehensive number of domains addressed by middle school increases to 11.

The Domains

The image below shows a breakdown of the Common Core of State Standards math domains. In a video, I use this graphic to unpack why it is more challenging to determine a single level of ability for math.

Addressing Grade Level Metric

If you are presented with a single grade level as an indicator of math ability, I recommend that you ask for a breakdown by category and how your student will be provided differentiation to address gaps. This is more appropriate than plowing through all of the math at a lower grade level.

Math Intervention is Packing a Suitcase

In working with students with special needs on math programming and services, a common and important issue is that the student is behind and there is a tension between math intervention to fill gaps and addressing ongoing grade level content.

Unpacking the situation

There is no single grade level for math, as is the case for reading. Math progression is more like a web, not a line. For example, if a student can do 5th grade geometry but only 3rd grade level fractions, do we average out the grade level math to be 4th grade? (No.) Do we identify the student as working at a 3rd grade level? (No.) 5th grade level? (No.)

Like a suitcase, there is a capacity to the daily time a student has for school services. I often encounter situations in which the services recommended involve the student working on grade level content and catching up on the gaps during support time. If the student has only been learning 75% of the math content each year, he or she needs that support time to help learn the new content to get closer to 100%. There is too much being stuffed into the suitcase. Something has to give.

The focus of the services and programming often shifts away from post-secondary plans, with a focus on the short term. Like the situation facing the man in the image below, there are long term implications.

Recommendations

There are two recommendations I make in regards to addressing the gaps, without overstuffng the suitcase.

The IRIS Center is part of the Peabody College of Vanderbilt University.
  • Use triage to shift focus to the priority topics. For example, the parents of a student in 7th grade but working on math from lower grade levels wanted to pursue a math track that would allow the student to go to community college. I mapped out a long range plan (image below) that focuses on algebra as that is the type of math most likely encountered in a math requirement. Here is another plan which was to prepare a student to possibly work in a field related to cars.