# Current Research Projects

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Webpage last updated: October 2018*

Current Projects: Pattern and Spatial Skills | Comparison | Fostering Parents' Numeracy Support | Putting it All Together | PRI Math Follow Up Project

Recently Completed Project: Early Algebraic Thinking

**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.

Click here to see recent coverage of the project and here to follow recent activity.

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Fostering Parents’ Support of Their Children’s Numeracy Development
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PI: Bethany Rittle-Johnson

Children’s early number knowledge and skills are predictive of their later academic success (Cross et al., 2009; Duncan et al., 2007; Jordan et al, 2009). However, children's number 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. Many researchers have attributed differences in children’s early numeracy to differences in the number input that they receive from their parents (Cheung & McBride, 2017; Ramani et al., 2015). For instance, some parents rarely help their children to explore some important early number concepts. This study examines whether researchers can improve the number input that parents provide their children using a practical and potentially generalizable process.

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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.

PI: Dale Farran

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.

#### Completed Projects

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Early Algebraic Thinking Studies: The Roles of Self- and Instructional Explanations
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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.