Estimated Average Annual Growth for HMH Math Inventory

This paper provides an update to the HMH Research Update publication 8334 “Estimated Average HMH Math Inventory Annual Growth” to provide estimated average growth for HMH Math Inventory^®.

There are a variety of factors (e.g., instructional time and quality) that can influence the level of academic growth demonstrated in a school year. In addition, there are several factors that influence the accuracy of how that achievement and therefore growth is measured, such as standard error, human-related factors (student’s state of mind or body), or testing environment. Although these factors exist, a thorough treatment of them is outside the scope of this paper. The purpose of this paper is to describe the average student growth on Math Inventory over the course of an academic year. Because changes in student growth in math achievement may vary by grade and initial achievement level, growth estimates were broken out across these two dimensions. As a result, average growth was computed for Grades 2 through 8 by initial performance category (Below Basic, Basic, Proficient, and Advanced).

The final average growth estimates were based on two complimentary studies; a yearlong pilot study utilizing data from multiple districts and a normative conversion of prior Math Inventory 2.7 test scores.

A sample of 11,204 students in Grades 2 through 8 taking Math Inventory during the 2018–2019 school year was used in this analysis. Each student was administered Math Inventory in the fall and spring semesters as part of his or her regular assessment program. Table 1 indicates the number of students with available data for each grade level.

Average growth was computed from two test administrations (fall and spring) in the same academic year. A fall administration was defined as the first administration occurring in the August through October testing window. A spring administration was defined as the last administration of the school year occurring in the March to June testing window. Only students with a date range greater than 180 days between administrations were used to compute growth. Scores from the school year’s fall and spring administrations were aggregated across grade and performance level to form the growth comparisons. Utilizing this data, the following procedures were followed to create the initial set of growth bands.

The average fall and spring Math Inventory score was computed for each performance category and grade. For each performance category and grade, difference scores were computed and stored with their Standard Error of Measure (SEM) and retained for later use. The standard errors were then used to compute confidence intervals around each average difference score. The confidence intervals were set to +/- 2.58 SEM. This process resulted in a set of provisional growth bands that were retained for the next stage of analysis using normative growth data from converted Math Inventory 2.7 data.

To create norms for Math Inventory, HMH^® took the 2016–2017 Math Inventory grade-level calibration data and included examinees that had 50% or more grade-level items that matched their actual grade level (e.g., students with 50% or more Grade 5 items on their test for the Level Test). The Math Inventory test design allows students to be administered items from the following: two grades down, on-grade, and one grade up. For instance, a Grade 6 student could potentially be administered items from Grades 4, 5, 6, and 7. Therefore, students with 50% or more of Grade 6–7 items on their Grade 6 test were included in the Grade 6 norms due to being considered “on-grade” for analytical purposes. Due to the methodology of creating the sample, these would be strictly considered “user norms.” The numbers of students in the norming sample was in the thousands for each grade level. For example, the Grade 6 norms had a sample comprising 29,228 fall scores, 19,696 winter scores, and 33,095 spring scores.

Utilizing the data from the initial pilot study and verifying these growth estimates with the normative data obtained from converted Math Inventory 2.7 scores, a final set of estimated growth bands were computed (see Table 2). The growth estimates presented here demonstrate a similar pattern seen in previous versions of Math Inventory where students in lower grade levels and with lower initial (fall) scores tended to demonstrate the greatest amount of growth in the spring. 

Although the growth obtained by administering Math Inventory in the fall and spring represents multiple data points, it is important to point out that these data points still come from the same assessment. When making instructional decisions about students it is always good practice to employ multiple measures to arrive at a student’s level of comprehension.

Although the growth estimates provided here may provide insights into the relative performance of students taking Math Inventory, they are descriptive and therefore should not necessarily be viewed as growth expectations. Descriptives are statistical computations used to aggregate and designate student performance and change on an assessment. Expectations can be grounded in these descriptives but may also include several other factors such as context and the goals of the school/district.