Current Projects:
Leveraging Numerical Patterns in a Modified Board Game to Improve Numeracy Knowledge in Primary School Students
Leveraging Exit Tickets to Enhance Students' Self-Regulated Learning and Mathematics Knowledge
ManyNumbers
Data Science Challenge to Model Math Misconceptions
Graduate Student Projects
Completed Projects:
Fostering Parents' Numeracy and Patterning Support
Current Projects
Leveraging Numerical Patterns in a Modified Board Game to Improve Numeracy Knowledge in Primary School Students
PI: Bethany Rittle-Johnson
Many children in the U.S. struggle to understand place value and calculate with two-digit numbers (11-99). This difficulty hinders math achievement. Playing number board games is a fun and effective way to improve children’s numeracy knowledge. This project explores use of a 0-100 number board game to help children learn key math standards related to place value and arithmetic. It tests whether modifying the game board’s layout to support children in using a patterning lens - to look for and make use of predictable patterns in numbers - promotes greater numeracy learning. In the experimental condition, children play with a 0-100 game board with the numbers increasing from bottom-to-top and left-to-right, such that decades are in the far-right column and numbers ending in the same ones digit are in the same column (similar to a hundreds chart). Implicit support for a patterning lens is provided further by using visual cues to highlight numeric patterns. The research will advance understanding of a feature of games that can enhance learning and provide evidence for the benefits of a hundreds chart as a tool for promoting numeracy learning.
Leveraging Exit Tickets to Enhance Students' Self-Regulated Learning and Mathematics Knowledge
PI: Kelley Durkin
An exit ticket (i.e., ticket to leave, or exit slip) is a recommended and widely used way to end a lesson. A common exit ticket format is for students to solve a few problems related to the day’s lesson and to turn it in when they exit the classroom. We are exploring two potential enhancements to exit tickets, with the goal of improving high-school students’ mathematics knowledge and self-regulated learning (SRL). A student’s ability to regulate their own learning processes is critical for successful learning and academic achievement, and students face increasing demands on regulating their own learning when they enter high school. We identified two evidence-based enhancements that could be implemented easily by teachers in the context of exit tickets to support students’ self-reflection. In particular, we will explore the impact of enhancements for supporting students in (1) determining how well they know material via confidence calibration, and (2) evaluating their strategy use and answers using metacognitive evaluation strategies. We hypothesize that these enhancements will improve students’ confidence calibration (i.e., metacognitive knowledge of what they know and do not know) and use of metacognitive evaluation strategies (e.g., strategies for checking their work and making sure their answers make sense), which in turn should support students’ mathematics self-efficacy (i.e., confidence in their abilities to succeed in their current mathematics course) and mastery-approach goals (i.e., goals to develop their understanding and competence). In turn, the enhancements should benefit students’ mathematics performance on content assessments. We will work with Integrated Mathematics I teachers to add enhancements to their exit tickets for one curriculum unit.
ManyNumbers
PIs at Vanderbilt: Bethany Rittle-Johnson & Eric Wilkey
The ManyNumbers network is a research consortium of over 100 sites worldwide, interested in the conceptual foundations of early numeracy. ManyNumbers aims to expand the investigation of early numeracy to a diverse global network, while promoting new and innovative exploratory projects. Our lab, in collaboration with Prof. Eric Wilkey’s Number Lab, is participating. The study examines 2.5-6 year old children’s understanding of numbers, and we will include a parent survey on the Home Numeracy Environment.
Data Science Challenge to Model Math Misconceptions
PIs: Bethany Rittle-Johnson & Scott Crossley
We will lead a data science challenge focused on modeling students’ math misconceptions. We are identifying large datasets with students' open-ended responses to math questions and coding responses for potential misconceptions (by humans). Teams will then compete to develop AI models that can detect potential math misconceptions in students’ written work. The aim is to provide teachers and students with early feedback on probable misconceptions, including via digital learning platforms.
Read press release here.
Graduate Student Projects
Graduate students in the lab lead their own research projects. Projects focus on topics such as self-regulated studying of mathematics and helping young children learn about patterns.
Self-regulated Learning (SRL) While Studying (led by Rebecca Adler)
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.
Click here to see recent coverage of the project and here to follow recent activity.
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.
To find out more about these studies, visit the project webpage (archived).