Bethany Rittle-Johnson

Vanderbilt University | Vander Bilt · Department of Psychology and Human Development

Math experiences during the preschool years play an important role in children’s later math learning. Preschool teachers exhibit considerable variability in the amount and types of mathematics activities they engage in with their students; one potentially important source of these individual differences is adults’ knowledge of early math developmen...

The current study is a conceptual replication of the influence of an advanced educational opportunity and several student propensities to learn on a college-readiness assessment for mathematics (ACT scores) among an important and under-studied group of students. We focused on a sample of predominantly Black students from economically-disadvantaged...

This study evaluated the effect of two light-touch home math environment (HME) interventions on parental math support, knowledge about early math development, and expectations for their child's math development, with attention to both numeracy and repeating patterns. Participants were 107 parents (74% college educated, 53% high income, 54% White, 3...

Understanding how marginalized students experience and perceive mathematics is critical to achieving the goal of inclusive and equitable math pedagogy. We report on 67 focus groups with 251 predominantly Black high schoolers experiencing economic marginalization in the Southern United States and attended to their achievement level and race-gender i...

Parents vary substantially in the frequency and complexity of the math support that they provide to their children, and this variability is often related to their children's math knowledge. We hypothesized that parents' knowledge about the development of two critical early math topics would help explain some of this variability in their early math...

Background To accurately measure students' science, technology, engineering and mathematics (STEM) career interest, researchers must get inside the ‘black box’ to understand students' conceptualizations of STEM careers. Aims The aim of Study 1 was to explore whether students' conceptualizations of STEM included medical careers. The aim of Study 2...

The math children are exposed to at home is a crucial source of early math knowledge, but little is known about parents’ general approaches for supporting their children’s math development at home. The current study examined what general pedagogical approaches parents believed to be most important to use in their home and if these beliefs aligned w...

Parents’ knowledge about the math skills that most preschool-aged children can develop might be an important component of the Home Math Environment (HME) as it might shape their math beliefs and efforts to support their preschoolers’ math development. This study aimed to systematically develop measures of parents’ knowledge about two critical early...

CDMS is a routine that allows teachers to organize instruction around students’ mathematical discussions and multiple problem-solving methods.

Preschoolers’ repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current study was to examine the causal effects of repeating patterning and numeracy tutoring on repeating patterning, numerac...

Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16 Al...

Children’s early repeating and growing patterning skills play an important role in their math development (Wijns et al., 2019; Zippert et al., 2020). However, little is understood about the developmental trajectory of patterning skills in relation to varying pattern rules and patterning tasks (e.g. Rittle-Johnson et al., 2013). The current study ai...

Math knowledge develops rapidly in the preschool years, varies substantially, and is strongly predictive of later math achievement (Duncan et al., 2007; Starkey & Klein, 2004). While theory, research, and education standards on math development have concentrated primarily on the contributions of numeracy skills (Sarama & Clements, 2004, Common Core...

Parents' academic beliefs influence the academic support they provide to their children. In this chapter, we review the published literature on empirical studies conducted with parents of preschoolers and propose a conceptual model for how different parental numeracy beliefs uniquely and differentially influence parents' early numeracy support and...

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns—predictable sequences that follow a rule—are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, foc...

The current article focuses on efforts to understand how a basic learning process—comparison—can be harnessed to improve learning, especially mathematics learning in schools. To harness the power of comparison in instruction, we must investigate three core decisions: what, when, and how to compare. Comparing different strategies for solving the sam...

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns—predictable sequences that follow a rule—are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, foc...

The current study modified and evaluated the validity and reliability of a measure of early geometry knowledge. Preschoolers (n = 252) were administered geometry items from a measure of broad math skills along with measures of their spatial, numeracy, and patterning skills. The geometry items’ psychometric properties including their reliability and...

The current study continues efforts to identify effective ways to promote parents’ early numeracy input. Parents (n = 60) played two card games with their preschooler, completed surveys about their academic beliefs, and received information about an important numeracy skill. Parents rated the skill (magnitude comparison) as significantly more impor...

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., person‐presentation). However, there are indicators that person‐presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked examples during ext...

Marginalized students face a range of gaps in experience, highlighting the importance of understanding these students’ perspectives on their opportunities to learn. The current study contributes to this effort by reporting on marginalized students’ experiences and liking of mathematics instructional strategies in middle-school mathematics classroom...

Background: Committing errors is a common part of the learning process, and adults are more likely to correct errors that they can recall. However, preadolescent children's recall of previous errors (i.e., memory for errors) may be limited. Aims: We examined children's ability to recall their past errors and tested whether recalling an error aid...

The current study broadens our understanding of preschoolers’ early math experiences with parents, recognizing that math knowledge and experiences are inclusive of numeracy as well as non-numeracy domains. Parents and preschoolers (N = 45) were observed exploring three domains of early mathematics knowledge (i.e., number, space, and pattern) during...

While most research focuses on the contributions of early numeracy to mathematics development, emerging research suggests pre-K patterning skills also predict concurrent and later math knowledge. Why this link exists, however, is unclear. The current study evaluated the relation between patterning and general and specific aspects of math knowledge....

Little is known about how often preschool teachers provide instruction about specific numeracy and patterning concepts despite research indicating that some numeracy and patterning concepts are unique predictors of preschoolers’ later math achievement (Fyfe et al., 2019). Thus, 44 pre-K teachers from 5 public and 7 private schools were asked to rep...

Preschoolers’ patterning skills are predictive of their concurrent and later math knowledge; however, it is unclear if patterning is only a proxy for general intelligence, or how it might support specific math skills. The current study examined the relation between 66 preschool children’s patterning skills and their general cognitive abilities, inc...

Preschoolers whose parents provide numeracy input frequently tend to have better numeracy knowledge than their peers whose parents provide numeracy input infrequently (e.g. Elliott et al., 2017). However, very little of parents' numeracy input to their preschoolers is about advanced early numeracy concepts (Ramani et al., 2015). Additionally, paren...

Preschool children's ability to correctly compare magnitudes predict their advanced mathematical skills for up to five years later (Rittle-Johnson et al., 2017). Parents may be able to support their children's growing magnitude comparison skills during play by discussing the relative size of numbers (e.g. by identifying which of two numbers or amou...

Math skills before school entry relate to parent-child math exploration (e.g. Dearing et al., 2012). Parent-child guided math exploration may be particularly important to children’s early math development since it may enable children to benefit from aspects of play and formal instruction (Weisberg et al., 2016). The current study examines two quest...

Early math skills (i.e., patterning, numeracy and spatial) predict later math achievement; however, little work has examined parents’ home support of these skills or how support changes over time. The current study compared parents’ math support in their child’s preschool and kindergarten years, and explored its relations to parents’ math-related b...

Parent-preschooler play was observed in three contexts (card games, bead-stringing, block building) and coded for exploration of 3 math concepts (number, pattern, space). Dyads explored number most often, especially during card play, and explored space across contexts, especially during block building. Patterns were explored least often, mostly whe...

The goal of the study was to examine how the context of parent-child play and parents' math-related beliefs relate to parent-child talk about an early numeracy concept. Parents and their preschoolers (n = 46) engaged in a videotaped play session and parents were surveyed about their math-related beliefs. The findings indicate that the type of infor...

Math knowledge develops rapidly in the preschool years, varies substantially, and is strongly predictive of later math and reading achievement (Duncan et al., 2007; Starkey & Klein, 2004). While theory, research, and education standards on math development have concentrated primarily on the contributions of numeracy skills (Sarama & Clements, 2004,...

Research on home math experiences focuses primarily on how parents’ numeracy support predicts child numeracy development (e.g., Zippert, Rittle-Johnson, in press). Broader perspectives, however, suggest spatial and pattern skills are also critical to broad mathematical development (Mix & Cheng, 2012; Rittle-Johnson et al., 2015; Sarama & Clements,...

Children’s math knowledge develops early to varying degrees and predicts later math achievement (Duncan et al., 2007). While math theory and research focus on the role of number skills (Sarama & Clements, 2004), patterning also predicts concurrent and later math knowledge (Rittle-Johnson, Zippert, & Boice, 2018). This research focuses on kindergart...

The Cambridge Handbook of Cognition and Education - edited by John Dunlosky February 2019

Cambridge Core - Cognition - The Cambridge Handbook of Cognition and Education - edited by John Dunlosky

The goal of the current study is to develop a more complete understanding of the early home math environment, encompassing both numeracy and non-numeracy aspects of that environment. Parents of preschoolers (n = 63) were surveyed about their support of three components of early mathematics knowledge (i.e., numeracy, spatial, and pattern) as well as...

State-mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519 low-incom...

Initial participants were 79 children who were recruited from six preschool programs in the U.S. Full assessment data was available for 73 children (average age of 4 years 7 months), including demographic data (gender, ethnicity, financial need, language(s) spoken at home and special education status). Children׳s math, repeating patterning, spatial...

Early math knowledge is critical for later academic achievement; thus, we must identify skills that support young children’s math development. This study explored how repeating patterning skills are associated with specific math skills in preschoolers. Correlations showed that patterning skills were significantly related to math skills (i.e. magnit...

The magnitude comparison task and the number line estimation task are widely used in the literatures on numerical cognition, mathematical development and mathematics education. It has been suggested that these tasks assess a central component of mathematical competence and, thus, are useful tools for diagnosing mathematical competence and developme...

Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development. The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development: patte...

Preschoolers' math skills predict later math achievement. While the contribution of number skills to math knowledge is typically studied, early pattern and spatial skills have also been independently shown to predict concurrent and later math knowledge. However, little is known about the relations between pattern and spatial skills, or how both pre...

See the article at this link: http://rdcu.be/BI5Y The goal of the current study was to contribute to our emergent understanding of whether and how particular types of digital games can support student learning and engagement. We focused on commercially available educational apps that focused on similar content (fraction comparison and equivalence)...

Promoting self-explanation (i.e., generating explanations for oneself in an attempt to make sense of new information) is a recommended study strategy and instructional practice. A meta-analysis of the literature on prompting self-explanation to improve mathematics learning confirmed that prompted self-explanation leads to a small to moderate improv...

Recent research highlights the potential benefits of practice without feedback on learner’s strategy knowledge. However, most prior work has been conducted in one-on-one settings with short retention intervals. We compared the effects of mathematics practice with and without correct-answer feedback on immediate and 1-week delayed performance in a c...

Comparison is a fundamental cognitive process that can support learning in a variety of domains, including mathematics. The current paper aims to summarize empirical findings that support recommendations on using comparison of multiple strategies in mathematics classrooms. We report the results of our classroom-based research on using comparison of...

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equat...

Developing strong knowledge about mathematics is important for success academically, economically, and in life, but many children fail to become proficient in math. Research on the developmental relations between conceptual and procedural knowledge of math provides insights into the development of knowledge about math. First, competency in math req...

Comparison is a fundamental cognitive process that supports learning in a variety of domains. To leverage comparison in mathematics instruction, evidence-based guidelines are needed for how to use comparison effectively. In this chapter, we review our classroom-based research on using comparison to help students learn mathematics. In five short-ter...

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math t...

Visual pattern knowledge is increasingly being shown to be a critical component of mathematical cognition (Rittle-Johnson, Fyfe, Loehr, & Miller, 2015); however, in the domain of music and elsewhere, patterns can exist in audible formats as well. Young children's’ abilities to detect patterns in sound, and the extent to which this is associated wit...

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math c...

This study aims to address potential costs of using incorrect worked examples in teaching mathematics. While such practice has been shown to be effective in educational research, previous findings in the memory literature suggest that exposure to an incorrect solution may lead students to later believe that it is correct due to increased familiarit...

Generating explanations for oneself in an attempt to make sense of new information (i.e., self-explanation) is often a powerful learning technique. Despite its general effectiveness, in a growing number of studies, prompting for self-explanation improved some aspects of learning, but reduced learning of other aspects. Drawing on this recent researc...

Education policy should aim to promote instructional methods that are easy for teachers to implement and have demonstrable, positive impact on student learning. Our research on comparison and explanation of multiple strategies illustrates the promise of this approach. In several short-term experimental, classroom-based studies, comparing different...

There is a long-standing and ongoing debate about the relations between conceptual and procedural knowledge (i.e., knowledge of concepts and procedures). Although there is broad consensus that conceptual knowledge supports procedural knowledge, there is controversy over whether procedural knowledge supports conceptual knowledge and how instruction...

Feedback can be a powerful learning tool, but its effects vary widely. Research has suggested that learners' prior knowledge may moderate the effects of feedback; however, no causal link has been established. In Experiment 1, we randomly assigned elementary schoolchildren (N = 108) to a condition based on a crossing of 2 factors: induced strategy k...

Children's knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers’ understanding of repeating patterns. 124 children between th...

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (Mage = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g., blue-red-blue-red) a...

When children practise solving problems, does this also enhance their understanding of the underlying concepts? Under what circumstances do abstract concepts help children invent or implement correct procedures? These questions tap a central research topic in the fields of cognitive development and educational psychology: the relations between conc...

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical...

Conceptual change is a gradual process that occurs as students integrate new information into their existing conceptions. Throughout this process, assessing learning requires measures to diagnose misconceptions and understand how knowledge is changing. We developed three measures of misconceptions to assess students' knowledge early in instruction...

Feedback is generally considered a beneficial learning tool, and providing feedback is a recommended instructional practice. However, there are a variety of feedback types with little guidance on how to choose the most effective one. We examined individual differences in working memory capacity as a potential moderator of feedback type. Second- and...

Patterning is an activity preschoolers commonly engage in and is considered a form of early algebraic thinking. In the current study, we explored the impact of combining two learning approaches, exploration and explicit instruction, on repeating pattern knowledge. Specifically, we focused on the effect of varying the source of explanation (the self...

The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear. We tested the...

Self-explanation, or generating explanations to oneself in an attempt to make sense of new information, can promote learning. However, self-explaining takes time, and the learning benefits of this activity need to be rigorously evaluated against alternative uses of this time. In the current study, we compared the effectiveness of self-explanation p...

Exploratory learning before instruction can benefit understanding, but can also be challenging. Individual differences in response to challenge, such as achievement motivation, may therefore moderate the benefits of exploratory learning. Higher mastery orientation generally leads to increased effort in response to challenge, whereas higher performa...

Erroneous examples are an instructional technique that hold promise to help children learn. In the study reported in this paper, sixth and seventh grade math students were presented with erroneous examples of decimal problems and were asked to explain and correct those examples. The problems were presented as interactive exercises on the Internet,...

A key learning outcome in problem-solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). However, students often fail to become flexible problem solvers in mathematics. To support flexibili...