# Julie BoothTemple University | TU · Departments of Teaching and Learning and Psychology

Julie Booth

Ph.D. in Psychology

## About

45

Publications

70,608

Reads

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3,496

Citations

Citations since 2017

Introduction

Additional affiliations

July 2014 - present

August 2008 - present

## Publications

Publications (45)

The current study assessed whether adding worked examples
with self-explanation prompts focused on making connections
between mathematical principles, procedures, and concepts of
rational numbers to a curriculum focused on invented strategies
improves pre-algebra students’ fraction number line acuity,
rational number concepts and procedures. Finall...

Both sketching and self‐explanation are widely believed to be effective for problem‐solving in science learning. However, it is unclear which aspects of these strategies promote learning and how they might interact. Compared to a read‐only baseline, we examined the impact of instructing 11‐year‐old students to solve science problems to sketch, self...

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination o...

Proportional reasoning failures seem to constitute most errors in probabilistic reasoning, yet there is little empirical evidence about its role for attaining probabilistic knowledge and how to effectively intervene with students who have less proportional reasoning skills. We examined the contributions of students' proportional reasoning skill and...

Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the person-centered approach of latent profile analysis to examine individual differences in middle schoolers' (N = 350) algebra performance at the end of the year (EOY). The relative i...

Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe,2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on alge...

Mathematics learning encompasses a broad range of processes and skills that change
over time. Magnitude and equivalence are two fundamental mathematical ideas that students
encounter early and often in their mathematics learning. Numerical magnitude
knowledge is knowledge of the relative sizes of numbers, including whole numbers, fractions,
and neg...

Proportional judgments are easier for children in continuous formats rather than discretized ones (e.g., liquid in a beaker vs. in a beaker with unit markings). Continuous formats tap a basic sense of approximation magnitude, whereas discretized formats evoke erroneous counting strategies. On this account, truly discrete formats with separated obje...

Psychologists and mathematics educators have long viewed flexibility as critical to students’ mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified research-base...

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students’ (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during...

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

INTRODUCTION. When explaining their reasoning, students should communicate their mathematical thinking precisely, however, it is unclear if formal terminology is necessary or if students can explain or describe mathematical concepts using everyday language. This paper reports the results of two studies. The first explores the relation between stude...

Rather than exclusively focus on mastery of procedural skills, mathematics educators are encouraged to cultivate conceptual understanding in their classrooms. However, mathematics learners hold many faulty conceptual ideas—or misconceptions—at various points in the learning process. In the present chapter, we first describe the common misconception...

We investigate the strategies used by 64 advanced secondary mathematics students to identify whether a given pair of polynomial representations (graphs, tables, or equations) corresponded to the same function on an assessment of coordinating representations. Participants also completed assessments of domain-related knowledge and background skills....

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM majors...

Students in the United States consistently underperform on state tests of mathe- matical pro ciency (e.g., Kim, Schneider, Engec, & Siskind, 2006; Pennsylvania Department of Education, 2011) and in international comparisons on the Trends in International Mathematics and Science Study (TIMSS; e.g., Mullis, Martin, Foy, & Arora, 2012) and Programme f...

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N=75) completed an equation-solving unit with reform textbooks either containing the original practice problems or in which a portion of those problems were converted into correct, i...

Middle school algebra students (N = 125) randomly assigned within classroom to a problem-solving control group, a correct worked examples control group, or an Incorrect worked examples group, completed an experimental classroom study to assess the differential effects of incorrect examples versus the two control groups on students' algebra learning...

Prior research has documented differences in both performance and motivation between students with learning disabilities (LD) and non-learning disabled (non-LD) students. However, few studies have conducted a finer grained analysis comparing students with LD with nondisabled students of varying achievement levels. The present study examines differe...

Cognitive development has yielded many findings with implications for improving classroom instruction and student learning. Improving learning in mathematics is a priority for the United States. This article describes stumbling blocks that preclude children from showing optimal learning and generalization of mathematics skills including misconcepti...

Numerous studies have demonstrated the relevance of magnitude estimation skills for mathematical proficiency, but little research has explored magnitude estimation with negative numbers. In two experiments the current study examined middle school students' magnitude knowledge of negative numbers with number line tasks. In Experiment 1, both 6th (n...

Findings from the fields of cognitive science and cognitive development propose a variety of evidence-based principles for improving learning. One such recommendation is that instead of having students practice solving long strings of problems on their own after a lesson, worked-out examples of problem solutions should be incorporated into practice...

Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the wor...

To reduce algebraic misconceptions in middle school, combine worked examples and self-explanation prompts.

Superintendents from districts in the Minority Student Achievement Network (MSAN) challenged the Strategic Education Research Partnership (SERP) to identify an approach to narrowing the minority student achievement gap in Algebra 1 without isolating minority students for intervention. SERP partnered with 8 MSAN districts and researchers from 3 univ...

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed a...

Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.

School-researcher partnerships and large in vivo experiments help focus on useful, effective, instruction.

Knowledge of fractions is thought to be crucial for success with algebra, but empirical evidence supporting this conjecture is just beginning to emerge. In the current study, Algebra 1 students completed magnitude estimation tasks on three scales (0-1 [fractions], 0-1,000,000, and 0-62,571) just before beginning their unit on equation solving. Resu...

Domain experts have two major advantages over novices with regard to problem solving: experts more accurately encode deep problem features (feature encoding) and demonstrate better conceptual understanding of critical problem features (feature knowledge). In the current study, we explore the relative contributions of encoding and knowledge of probl...

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students’ conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned...

The National Mathematics Advisory Panel (NMAP, 2008) asserts that a foundational knowledge of fractions is crucial for students’ success in algebra; however, empirical evidence for this claim is relatively nonexistent. In the present study, we examine the impact of middle school students’ fraction and whole number magnitude knowledge on various com...

High school and college students demonstrate a verbal, or textual, advantage whereby beginning algebra problems in story format are easier to solve than matched equations (Koedinger & Nathan, 2004). Adding diagrams to the stories may further facilitate solution (Hembree, 1992; Koedinger & Terao, 2002). However, diagrams may not be universally benef...

This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive...

The current study examines how holding misconceptions about key problem features affects students' ability to solve algebraic equations correctly and to learn correct procedures for problem solution. Algebra I students learning to solve simple equations using the Cognitive Tutor curriculum (Koedinger, Anderson, Hadley, & Mark, 1997) completed a pre...

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergart...

Two experiments examined kindergartners', first graders', and second graders' numerical estimation, the internal representations that gave rise to the estimates, and the general hypothesis that developmental sequences within a domain tend to repeat themselves in new contexts. Development of estimation in this age range on 0-to-100 number lines foll...

Recent research indicates that when solving algebraic story problems, adding a diagram is beneficial for seventh and eighth grade students, however, sixth graders—particularly low-achieving ones—do not benefit from the diagrams. In the present study, we further investigate the diagrammatic advantage in low-achieving pre-algebra students and examine...