Fostering Parents' Numeracy and Patterning Support
Recently Completed Projects:
PRI Math Follow Up Project
PI: Dale Farran
This project will use a longitudinal research design and link rich data from previous projects to track growth in math knowledge from preschool through 12th grade and make connections to postsecondary readiness in STEM. By identifying pathways and predictors of postsecondary readiness in math for low-income and minority students, the proposed project can identify factors that may be changed to broaden future participation in STEM fields.
The study participants will include at least 450 of the 519 students previously consented in 5th grade and followed in middle school in a large urban school district in Tennessee.
Our research goals are to: (1) examine students’ growth in math achievement across high school and relate high school growth to previous patterns, (2) identify predictors of math achievement and other indicators of postsecondary readiness, and (3) describe marginalized students’ beliefs about careers in STEM in high school, including how their beliefs have changed since middle school.
For more information, go to: https://my.vanderbilt.edu/mathfollowup
Fostering Parents’ Support of Their Children’s Numeracy and Patterning Development
PI: Bethany Rittle-Johnson; co-PI: Ashli-Ann Douglas
Parents' early math support is important because children's math knowledge and skills vary significantly at school entry and children who start school with poorer knowledge and skills tend to do worse at math throughout their school years than their peers who began formal schooling with better math skills. Most research on parents’ support of their children’s early mathematics knowledge focuses exclusively on parental support of number knowledge. However, early math knowledge extends beyond number knowledge and includes a wider range of skills (National Research Council, 2009; Sarama & Clements, 2004). For instance, very little research has focused on parents’ support of their children’s patterning knowledge, despite evidence suggesting that it is an important contributor to early mathematics development (e.g. Sarama & Clements, 2004; Zippert et al., 2020). The current study focuses on parents’ support of two aspects of their children’s math development: patterning knowledge and numeracy knowledge. Specifically, it focuses on understanding how parent and child characteristics relate to parents’ patterning and numeracy support and the malleability of these characteristics for promoting parents’ patterning and numeracy support. For more information, visit the project webpage.
Completed Projects
Exploring the Roles of Pattern and Spatial Skills in Early Mathematics Development
PI: Bethany Rittle-Johnson
Research indicates that preschool and kindergarten math knowledge is predictive of later math and reading outcomes; however, research is still needed to identify the specific early math skills that are linked to math achievement (Duncan et al., 2007; Jordan, Kaplan, Ramineni, & Locuniak, 2009; Watts, Duncan, Siegler, & Davis-Kean, 2014). This project explores the predictive and causal contributions of two early skills - pattern and spatial skills - to early mathematics development. Pattern skills include identifying, extending, and describing predictable sequences in objects or numbers. Whether pattern skills are important for mathematics achievement is under debate (National Mathematics Advisory Panel, 2008). However, recent research indicates that improving pattern skills improves mathematics achievement (Kidd, et al., 2013, 2014). In addition, there is increasing evidence that spatial skills are related to math knowledge (Mix & Cheng, 2012; NRC, 2009), with some limited evidence that improving spatial skills improves math knowledge (Cheng & Mix, 2013). Pattern and spatial skills have been studied independently, but they share overlapping characteristics and likely tap overlapping skills. Our goal is to elucidate the contributions of these skills to early math development, as this knowledge can inform the development of innovative programs to improve student education outcomes. For more information, visit the project webpage.
Comparison Studies: Contrasting Cases
PI's: Bethany Rittle-Johnson; Jon Star, Harvard University; Kelley Durkin, Peabody Research Institute
We theorize that productive learning of algebra is supported by reflection on multiple solution strategies through comparison and explanation of the reasons behind the strategies (Comparison and Explanation of Multiple Strategies: CEMS). Existing theories of algebra learning focus on building conceptual knowledge and place less emphasis on how students gain expertise with symbolic strategies. Working with symbolic strategies is essential in algebra learning. Students need to develop procedural flexibility - knowing multiple strategies for solving a problem and selecting the most appropriate strategy for a given problem - and understand the conceptual rationale behind commonly used strategies. Knowledge of strategies (procedural knowledge) supports gains in both procedural flexibility and conceptual knowledge of algebra (Schneider, Star & Rittle-Johnson, 2011). In small-scale studies, redesigning lessons on equation solving to integrate a CEMS approach supported greater procedural knowledge, flexibility and/or conceptual knowledge than completing the lessons without a CEMS approach (Rittle-Johnson & Star, 2007, 2009; Rittle-Johnson, Star, & Durkin, 2009, 2012; Star & Rittle-Johnson, 2009). A preliminary set of supplemental materials to support a CEMS approach across the Algebra I curriculum has been developed, with evidence that classroom teachers can implement the materials with good fidelity (Star, Pollack, et al., 2015).
Across three years, we are working with teachers to integrate a CEMS approach into their teaching of four Algebra I units. In Year 1, we worked with a small number of teachers to refine our existing CEMS materials, to integrate the materials into their curriculum, and to validate outcome measures that assess multiple types of knowledge (e.g., procedural flexibility, conceptual knowledge, and procedural knowledge). In Year 2, we will evaluate the effects of teachers using our materials versus a “business as usual” control for each of the four units. In Year 3, we will study the effects of the CEMS approach versus business as usual with a larger group of teachers; we will also study the quality of implementation and impact on student outcomes after treatment teachers have gained some proficiency with the CEMS approach. Using both quantitative and qualitative analyses, we will evaluate the hypotheses that: a) Classroom teachers can successfully and consistently integrate a CEMS approach in their algebra instruction, b) Students’ procedural flexibility, procedural knowledge, and conceptual knowledge for a variety of algebra topics can be reliably assessed and each type of knowledge is positively related and predictive of one another over time, and c) Integrating a CEMS approach supports better procedural flexibility, conceptual knowledge, and procedural knowledge for a variety of algebra topics (units) than business as usual instruction. For more information, visit the project webpage.
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Putting it All Together: Developing a More Comprehensive Theory of Early Mathematics Development
PI: Bethany Rittle-Johnson; co-PI: Erica Zippert
Most research and theory on early mathematics development focuses on numeracy development (Baroody et al., 2009; Geary, 2011; Jordan et al., 2006; Kolkman, Kroesbergen, & Leseman, 2013; Purpura & Lonigan, 2013; Wright, Martland, & Stafford, 2006). Numeracy, or number knowledge, is children’s basic knowledge of whole numbers, i.e. their knowledge of the meaning of numbers and number relationships (Jordan, Kaplan, Ramineni, & Locuniak, 2009; National Research Council, 2009). However, early math knowledge extends beyond numeracy knowledge and includes a wider range of skills than is usually considered in theories of math development (National Research Council, 2009; Sarama & Clements, 2004). This research project supplements our current IES-funded project to evaluate how well children’s pattern and spatial skills at the beginning of preschool predict their mathematics knowledge at the end of preschool. It focuses on two important, but under-researched, skills that recent evidence suggests are important contributors to early mathematics development: pattern and spatial skills. Further, it focuses on the nature and influence of parental support for the development of each of these early math-related skills (i.e., pattern, spatial and number skills), as well as how parental beliefs explain variation in the nature of these parent-child math experiences. The goal of the current project is to develop a more comprehensive theory of early mathematics development, integrating a broader range of math-relevant skills and how parents support these skills. For more information, visit the project webpage.
Early Algebraic Thinking Studies: The Roles of Self- and Instructional Explanations
PI: Bethany Rittle-Johnson
We evaluated the role of explanation in mathematics learning- specifically "why" explanations, or reasoning about why something is true. Such explanations can be generated by the student to explain new content or be provided by the instructor. Although explanations are often used as a learning tool, many factors can determine whether explaining will actually benefit learning, such as the source and timing of these explanations and individual differences such as working memory capacity. My research group performed a series of studies to uncover these factors. In doing so, we hoped not only to reveal the learning mechanisms that make explanation helpful, but also to use this knowledge to inform mathematics instruction in the classroom. This research was funded by the National Science Foundation.
To explore these ideas, we investigated knowledge development in three early algebra topics: mathematical equivalence (Grades 2 - 6), functions (Grades 2 - 6) and patterns (preK). Algebra is no longer a course saved for high school; rather, fundamental components of algebraic thinking have been identified as focal points for instruction beginning in preschool (NCTM, 2006). The hope is that inculcating algebraic thinking in the early grades will reduce students' difficulty with algebra in middle and high school.
To find out more about these studies, visit the project webpage (archived).