High School Longitudinal Study of 2009 (HSLS:09)

3. KEY CONCEPTS

Key Concepts

Assessment of Algebraic Reasoning. Several different types of scores are used in HSLS:09 to describe students’ algebraic reasoning skills: theta, estimated number right, standardized T–scores, quintile, and proficiency probability scores. Each score is derived from Item Response Theory (IRT) models. The theta (ability) estimate provides a summary measure of achievement useful for correlational analysis with status variables, such as demographic characteristics, school type, or behavioral measures, and may be used in multivariate models as well. IRT scores from HSLS:09 first follow–up can be equated to the scale of HSLS:09 base year so that scores may be compared longitudinally. The common items between the HSLS:09 base year and first follow–up allowed for this. The tests were equated using the Stocking and Lord procedure. The procedure allowed the base–year thetas to remain unchanged while the first follow–up thetas were equated to the existing base–year scale.

The estimated number–right score represents the number of items that students would have answered correctly had they answered all 72 items in the item pool. Similar to the theta scores above, the estimated number–right score provides a measure of achievement useful for correlational analysis with status variables and may be used in multivariate models.

Standardized T–scores provide norm–referenced measurements of achievement relative to the HSLS:09 student population (i.e., fall 2009 grade 9 students). A change in mean T–scores over time reflects a change in the individual’s or group’s relative status in the distribution of achievement scores. (Note that these scores do not indicate whether students have mastered a particular algebraic skill or concept, but represent students’ standing in relation to others.) For the first follow–up, the standardized scores provide a norm–referenced measurement of achievement, that is, an estimate of achievement relative to the HSLS:09 first follow–up student population. They provide overall measures of status at a point in time compared with those of peers, as distinguished from the criterion–referenced scores, which represent status with respect to achievement on a particular criterion set of test items. The norm–referenced standardized scores do not answer the question “What skills do students have?” but rather, “How do they compare with their peers?”  Because the scores are standardized within assessment, the base–year standardized T–score is not comparable to the first follow–up standardized T–score.

The mathematics quintile score is a norm–referenced measure of achievement. The quintile score divides the weighted (population estimate) achievement distributions into five equal groups based on the standardized T–scores. Quintile 1 corresponds to the lowest achieving one–fifth of the population and quintile 5 to the highest achieving one–fifth of the population. Quintile scores are convenient for analysts interested in examining associations between variables for students at different achievement levels.

Proficiency probability scores provide a continuous measure of students’ mastery of the five levels of algebraic reasoning (i.e., algebraic expressions, multiplicative and proportional thinking, algebraic equivalents, systems of equations, and linear functions). The probability of proficiency for a given student at a given level is calculated as the probability of getting correct at least three of the four items in a given cluster marking a proficiency level. Proficiency at a higher level is indicative of proficiency at a lower level, and these scores are also useful as longitudinal measures of change because they show the extent of gains, as well as the skill sets in which gains are taking place.

In the base–year assessment, five mastery or proficiency levels were identified. With the addition of more difficult items in the first follow–up assessment, two additional levels were identified. Thus five levels are calculated for the baseline and seven proficiency levels are calculated for its longitudinal follow–up.

Plans, transitions, and evolutions. Core research questions for HSLS:09 explore students’ secondary to postsecondary plans and transitions, and how they evolve over time. Additionally, HSLS:09 brings a new and special emphasis to the study of youth transitions by exploring the path that leads students to pursue and persist in courses and careers in STEM fields. Specifically, HSLS:09 collects data on when, why, and how students make decisions about high school courses and postsecondary options, including what factors, from parental input to considerations of financial aid for postsecondary education, enter into them. In later waves, questions will be asked regarding students’ follow–through on their plans as well as the academic and social factors that contribute to their completion or evolution.

Contextual Influences. The HSLS:09 design acknowledges the importance of social context–families, teachers, peers, and the wider community–to students' experiences. As such, information was collected from parents, teachers (math and science), school principals, and school counselors to provide contextual information that can be attached to students' records for analysis.

Dropping out of School. Due to the grade level of students during the first data collection period (fall semester, ninth grade), HSLS:09, similar to NELS:88, will be able to identify and study “early” and “late” dropouts. Early dropouts are defined as individuals who leave school without graduating or receiving an alternative credential by the spring of 10th grade. Overall, the dropout data from HSLS:09 will be comparable with dropout data from the four previous education longitudinal studies, but the distinction between early and late dropouts is shared by only HSLS:09 and NELS:88.  

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