Institute of Education Sciences (IES) Project
Recruiting spatial-numerical representations to enhance the use of advanced math strategies in low-income students
Mediocre math achievement has been a persistent problem of K-12 education in the US and math scores have dipped even further following the COVID-19 pandemic. The problem is particularly pronounced among students from under-resourced communities who begin elementary school with less math experience and knowledge than more advantaged children. This project aims to identify ways to more effectively promote early arithmetic learning, which is foundational for subsequent math achievement. It focuses on children’s learning of advanced arithmetic strategies, such as retrieval and decomposition. Based on evidence from cognitive science, we hypothesized that incorporating spatial representations of magnitude into instruction might support children’s learning of these strategies.
The project includes 3 studies that have the same design: Pretest (assessment of initial skills) -> Instruction (teaching sessions) -> Posttest (assessment of changes in skills). The instruction is conducted in small groups over the course of multiple sessions.
- Study 1: 8 sessions focused on retrieval strategy for problems within 10
- Study 2: 8 sessions focused on decomposition strategy for problems within 20
- Study 3: 16 sessions focused on both strategies
Instructional Sessions:
Studies 1 and 2:
Children in each classroom are assigned to one of four conditions that vary only in the kinds of materials used to model numbers in the instructional sessions.
In two spatial conditions, the materials used in training have embedded spatial information about numerical magnitude: each number is printed on a strip whose length is proportional to the magnitude of that number (e.g., 5 is half as long as 10). In the Spatial-Continuous condition, the strips provide only continuous spatial cues (length). In the Spatial-Discrete condition, the strips are demarcated into individual units, providing cues about both spatial extent and discrete quantity.
In two nonspatial conditions, the materials used in training do not provide spatial cues: numbers are printed on equal-sized square tiles so there is no association between the size of the tile and the magnitude of the depicted number. In the Nonspatial-Verbal condition, children receive verbal cues about magnitude (e.g., “5 is more than 3”). In the Nonspatial-Nonverbal condition, children receive neither spatial nor verbal cues about number magnitude.
Study 3:
Children in each classroom are assigned to one of two instructional conditions— experimental (using the most effective materials identified in Studies 1 and 2) and business-as-usual control (using current instructional practices for teaching 1st grade math). The two conditions will provide children with math instruction for the same amount of time.
Evaluation:
Across studies, children’s improvement in four types of skills is assessed to compare learning across the four instructional conditions:
- Arithmetic fluency: accuracy and speed of carrying out basic computations
- Arithmetic strategy use: the frequency of using different types of strategies (e.g., retrieval, decomposition, counting) for solving addition and subtraction problems
- Numerical magnitude understanding: accuracy of placing a number on a number line with only the ends marked (0-100) and accuracy of identifying the bigger of two numbers within limited time
- Broad math achievement: score on a standardized math task
Primary Investigators:
Drs. Beth Casey, Elida Laski, and Marina Vasilyeva
Project duration:
4 years (2020-2024)
Participants:
550 first graders from racially and ethnically diverse families in under-resourced communities in Massachusetts
Setting:
Studies are conducted in schools
Grant funded by: