## About

63

Publications

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Introduction

I study cognitive development with a focus on the development of mathematics knowledge and problem solving. My primary goal is to understand how children think and learn about mathematics, both independently and with instructional guidance. My research not only helps identify basic cognitive processes that support the construction of knowledge, but also examines how to use that information to design effective instructional techniques.

Additional affiliations

August 2015 - present

August 2010 - August 2015

August 2006 - August 2010

## Publications

Publications (63)

While it is well established that multimedia materials presented during instruction often increase learning, prior research has mostly incorporated only text in the feedback. The current experiment tests whether multimedia materials in feedback benefit student learning. We randomly assigned undergraduate students (N = 129) to one of four conditions...

Previous research suggests that negative emotions invoked by failure feedback might lead people to tune out from the task, which is detrimental to their learning. However, failure feedback is pervasive in the real world and we need to identify ways we can learn from it optimally. In the current study, the participants' (n = 218) task expectations w...

Theories of learning emphasize the importance of both the cognitive and affective state of the learner. The current study focused on children's affective reactions to corrective feedback during mathematics problem solving. Eighty-seven elementary school children (M age = 7.6 years, 41% female, 68% White) solved mathematical equivalence problems dur...

Previous research indicates that failure feedback leads people to tune out from the task, which is detrimental to their learning (Eskreis-Winkler & Fishbach, 2019; Keith et al., 2022). The current work aims to identify ways to optimize learning from failure feedback. We conducted five preregistered experiments (N = 1,061) to replicate the findings...

Students’ expectations for whether a task will be easy or hard can influence their learning outcomes. In the current study, we experimentally tested whether students’ expectations of task difficulty changed how much they learned from receiving success feedback (“you answered the question correct!”) versus failure feedback (“you answered the questio...

This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; Mage = 79.5 months; 55% female; 88% White) and adults (N = 93; Mage = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged: (1) repeating pattern ta...

Research in psychology and education indicates that corrective feedback can be a powerful learning tool. We provide a developmental perspective to focus specifically on how corrective feedback influences learning in childhood (∼ages 3–11). Based on a systematic search, we review 44 empirical papers published between 1990 and 2022 examining the effe...

General Audience Summary
Helping students learn to think critically is an important priority across education levels, but there is currently no clear consensus on how to teach critical thinking. Many proposed teaching strategies are very elaborate and involve extensive discussion and analysis, which makes it difficult for teachers to incorporate cr...

Instructional gestures can influence children's comprehension and learning. One potential reason is that gesturing encourages children to mimic the movements they observe. The current study examined the role of gesture mimicry for 100 four-to six-year-old children (86% White; 53% female) on learning patterning skills. Children received a lesson on...

Decades of feedback research have suggested that feedback is more effective in correcting errors than confirming the right responses. A study conducted by Eskreis-Winkler and Fishbach (2019) challenged this notion by showing that people learn less from feedback that indicates their answer is incorrect (failure feedback) than feedback that indicates...

Children often learn abstract mathematics concepts with concrete
manipulatives. The current study compared different ways of
using specific manipulatives – base-ten blocks – to support children’s
place value knowledge. Children (N¼112, M age ¼
6.88 years) engaged in place value learning activities in one of
four randomly assigned conditions in a on...

We focused on how children and adults in the U.S. solved pattern tasks and whether strategies and errors changed with age. In Study 1, 90 children (Mage = 5.4 years; 52% female; 88% White) solved a series of pattern abstraction tasks with repeating patterns that varied on 2 dimensions (shape and size). A subset of children (n = 30) also completed a...

Children often struggle to solve mathematical equivalence problems correctly. The change-resistance theory offers an explanation for children’s difficulties and suggests that some incorrect strategies represent the overgeneralization of children’s narrow arithmetic experience. The current research considered children’s metacognitive abilities to te...

Emphasizing the predictive success and practical utility of psychological science is an admirable goal but it will require a substantive shift in how we design research. Applied research often assumes that findings are transferable to all practices, insensitive to variation between implementations. We describe efforts to quantify and close this pra...

Metacognition is theorized to play a central role in children’s mathematics learning. The primary goal of the current study was to provide experimental evidence in support of this role with elementary school students learning about mathematical equivalence. The final sample included 135 children (59 first graders and 76 second graders) who particip...

Participants performed a categorization training task, where each trial presented an example scenario in which an individual makes a claim based on an observation, and participants marked which fallacy or bias, if any, the individual in the scenario was committing. In two studies, we measure the effect of this training task on critical thinking, me...

Psychology researchers have long attempted to identify educational practices that improve student learning. However, experimental research on these practices is often conducted in laboratory contexts or in a single course, which threatens the external validity of the results. In this article, we establish an experimental paradigm for evaluating the...

Teachers often produce gestures, and, in some cases, students mimic their teachers’ gestures and adopt them into their own repertoires. However, little research has explored the role of gesture mimicry in technology-based learning contexts. In this research, we examined variations in the rate and form of students’ gestures when learning from a comp...

Emphasizing the predictive success and practical utility of psychological science is an admirable goal but it will require a substantive shift in how we design research. Applied research often assumes that findings are transferable to all practices, insensitive to variation between implementations. We describe efforts to quantify and close this pra...

Psychology researchers have long attempted to identify educational practices that improve student learning. However, experimental research on these practices is often conducted in laboratory contexts or in a single course, threatening the external validity of the results. In this paper, we establish an experimental paradigm for evaluating the benef...

How far should the results of an A/B test be expected to generalize? The answer to this question depends on how the A/B test was designed, and particularly the nature and scale of its implementation. Some A/B tests conducted across broad and diverse samples may provide better evidence to support generalizations than others. Although A/B tests can v...

Decades of research have documented young students’ misinterpretations of the equal sign and the impediments these present for children’s mathematical development. Much less is known about individual differences in adults’ knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a subse...

Students’ problem-solving success depends on more than their knowledge and abilities. One factor that may play a role is the teacher’s expectations of students. The current study focused on how a teacher’s explicitly-stated expectations influence students’ ability to learn from corrective feedback during problem solving. On the one hand, setting lo...

Emerging research demonstrates a central role of early patterning skills in supporting cognitive development. This study focused on the labels used to describe patterns. Children (N = 90; M age = 5.4 years) solved and explained 10 pattern abstraction tasks (i.e., recreated a model pattern using novel materials). Using a between-participants design,...

Metacognition is central to children’s cognitive development. However, there is conflicting evidence about children’s ability to accurately monitor their performance and subsequently control their behavior. This is of particular interest for mathematics topics on which children exhibit persistent misconceptions—that is, when children’s knowledge of...

The purpose of education research is to better understand educational phenomena to inform policy and improve practice. Forward progress within any field is based on the validity and credibility of that field’s research base - educators cannot make informed decisions based on anecdotal evidence, opaque research practices, or on studies that cannot b...

Young children often learn mathematics concepts with concrete manipulatives (e.g., blocks, counters); yet, the mere use of manipulatives does not ensure successful learning. The current study compared different ways of using manipulatives (i.e., base-ten blocks) in conjunction with written symbols. Children (N = 138, M age = 6.86) learned about pla...

Metacognition is central to children’s cognitive development. However, there is conflicting evidence about children’s ability to accurately monitor their performance and subsequently control their behavior. This is of particular interest for mathematics topics on which children exhibit persistent misconceptions—that is, when children’s knowledge of...

Embodied cognition is growing in theoretical importance and as a driving set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to attract engaged and inspired colleagues into a growing community of discou...

Previous research suggests that children with language disorders often have difficulties in mathematical tasks. In the current study, we investigated two relevant factors – working memory and pattern skills – that may underlie children's poor mathematics performance. Children with developmental language disorder (DLD, n = 18, ages 6–13) and age-mat...

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...

The effects of feedback often depend on individual learner characteristics. In the current study, we experimentally tested whether an individual's task expectations influence learning from feedback on mathematics problems. Specifically, we manipulated undergraduate students' beliefs about the difficulty of the task to influence their expectations f...

Little research has explored the role of gesture in technology-based learning contexts. This study analyzed the gestures produced by students after viewing an avatar instructed algebra lesson. Students who mimicked the gesture of the avatar instructor scored higher on a posttest suggesting gesture mimicry relates to learning.

Over the last several decades, previous research has shown that metacognition–the knowledge, monitoring, and regulation of cognition–is predictive of academic achievement across many domains and abilities. Yet, the underlying mechanism of why metacognition predicts academic achievement is not clear; we hypothesize that children’s ability to accurat...

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. Concreteness fading is a theory of instruction that offers a solution for making these connections. As originally conceived, i...

A central understanding in mathematics is knowledge of math equivalence, the relation indicating that two quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7-11) children’s (mis)understanding of math equivalence, and recent work has developed a construct map, including comprehensive assessments of...

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can...

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...

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...

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...

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...

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...

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 often struggle to gain understanding from instruction on a procedure, particularly when it is taught in the context of abstract mathematical symbols. We tested whether a “concreteness fading” technique, which begins with concrete materials and fades to abstract symbols, can help children extend their knowledge beyond a simple instructed pr...

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...

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...

Two quasi-experiments examined mental organization of addition knowledge as a potential source of individual differences in understanding math equivalence in symbolic form. We hypothesized that children who mentally organize addition knowledge around conceptually related groupings would have better understanding of math equivalence. In Quasi-experi...

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...

A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and...

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...

This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer" format (e.g...

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are " faded" into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three cond...

This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children (M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3 + 4 = 7, 2...

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain kno...

Young children have an impressive amount of mathematics knowledge, but past psychological research has focused primarily on their number knowledge. Preschoolers also spontaneously engage in a form of early algebraic thinking—patterning. In the current study, we assessed four-year-old children's knowledge of repeating patterns on two occasions (N =...

This study examined whether practice with arithmetic problems presented in a nontraditional problem format improves understanding of mathematical equivalence. Children (M age = 8;0; N = 90) were randomly assigned to practice addition in one of three conditions: (a) traditional, in which problems were presented in the traditional "operations on left...