Parental Beliefs About the Fixedness of Ability - Muenks Et Al (2015)

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Parental beliefs about the xedness of ability

Katherine Muenks a,⁎, David B. Miele b, Geetha B. Ramani a, Laura M. Stapleton a, Meredith L. Rowe a

a Department of Human Development and Quantitative Methodology, 3304 Benjamin Building, University of Maryland, College Park, MD 20782, USAb Counseling, Developmental, and Educational Psychology Department, 239E Campion Hall, Boston College, Chestnut Hill, MA 02467, USA

a b s t r a c ta r t i c l e i n f o

Article history:

Received 5 June 2014

Received in revised form 6 May 2015

Accepted 30 August 2015Available online 28 October 2015

Editor: Kimberly Anne Schonert-Reichl

Keywords:

Parents

Beliefs

Ability

Questionnaire

Motivation

The present studies examined whether parents' beliefs about the xedness of ability predict their self-reported

interactions with their children. Parents' xedness beliefs were measured at two levels of specicity: their gen-

eral beliefs about intelligence andtheirbeliefs about their children'smath andverbal abilities. Study 1, conducted

with an online sampleof 300parents, showed that the moreparents believed that abilities were xed, the more

likely they were to endorse controlling and performance-oriented behaviors and the less likely they were to en-

dorse autonomy-supportive and mastery-oriented behaviors. Study 2, conductedwith 86 parents froma univer-

sity database, partially replicated the results of Study 1 and also showed that parents' beliefs predicted the self-

reported frequency with which they engagedin math- andreading-relatedactivities with their children at home.

Specically, the more parents believed that abilities were xed, the less frequently they reported engaging in

math- and reading-related activities.

© 2015 Elsevier Inc. All rights reserved.

Prior to formal schooling, parents play a critical role in the develop-

ment of their children's foundational math and literacy skills by provid-ing them with opportunities to learn in their early home environment.

However, parents vary widely in the amount and type of math- and

reading-related activities they engage in with their children at home

(Baker & Scher, 2002; LeFevre et al., 2009). They also vary in the quality

of their interactions during these activities. At times parents may em-

phasize learning and mastery of skills, while other times they may

focus on improving their children's performance. In addition, some-

times parents act in ways that promote their children's autonomy,

while other times they attempt to control their children's behavior

(Pomerantz, Moorman, & Litwack, 2007). Both the quantity and quality

of parent–child interactions have important implications for children's

motivation and achievement in school (Pomerantz et al., 2007).

Given that the quality of parents' interactions inuences the devel-

opment of children's skills and motivation, it is important to examine

factors that mayunderlie differences in parents' behavior. One potential

factor is parents' beliefs about the xedness or malleability of their

children's abilities (i.e., whether they believe that their children's

abilities are innate and stable over time, or can be improved through

effort and practice). Although these beliefs have been successfully

manipulated in a laboratory context and shown to be causally related

to parents' behavior toward their children (Moorman & Pomerantz,2010), no studies have examined whether parents' naturally occurring

(i.e., non-manipulated) beliefs about the xedness of intelligence or

ability predict the type of behavior they report engaging in outside of

the lab. Furthermore, some studies that have measured parents' xed-

ness beliefs (but looked at different outcomes; e.g., Jose & Bellamy,

2012; Pomerantz & Dong, 2006; cf. Karkkainen, Raty, & Kasanen,

2011;Wentzel, 1998) have focused on what parents believe about intel-

ligence in general. However, considering that people vary in terms of

their lay beliefs about critical periods in development (e.g., whether

ability is malleable at some ages but not others; Worden, Hinton, &

Fischer, 2011), it seems likely that what parents believe about their

own children's abilities in particular domains differs from what they be-

lieve about intelligence more generally. Therefore, in the present stud-

ies, we measured parents' beliefs about ability at two levels of

specicity: 1) their general beliefs about the xedness of intelligence;

and 2) their specic beliefs about the xedness of their child's math

and verbal abilities. We then examined whether these beliefs predict

(a) the quality of the behaviors (mastery- vs. performance-oriented)

they use to help their young children complete challenging academic

tasks, and (b) the frequency with which they engage in math- and

reading-related home activities that are thought to improve children's

abilities in these domains. Finally, we measured parental ef cacy

(i.e., the extent to which parents' believe they are capable of improving

their children's abilities) and examined whether it mediated the effect

of parents' xedness beliefs on their parenting behavior.

Journal of Applied Developmental Psychology 41 (2015) 78–89

⁎ Corresponding author. Tel.: +1 301 405 2825; fax: +1 301 405 2891.

E-mail addresses: [email protected] (K. Muenks), [email protected] (D.B. Miele),

[email protected] (G.B. Ramani), [email protected] (L.M. Stapleton), [email protected]

(M.L. Rowe).

http://dx.doi.org/10.1016/j.appdev.2015.08.002

0193-3973/© 2015 Elsevier Inc. All rights reserved.

Contents lists available at ScienceDirect

Journal of Applied Developmental Psychology

http://dx.doi.org/10.1016/j.appdev.2015.08.002http://dx.doi.org/10.1016/j.appdev.2015.08.002http://dx.doi.org/10.1016/j.appdev.2015.08.002mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.appdev.2015.08.002http://www.sciencedirect.com/science/journal/01933973http://www.sciencedirect.com/science/journal/01933973http://dx.doi.org/10.1016/j.appdev.2015.08.002mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.appdev.2015.08.002http://crossmark.crossref.org/dialog/?doi=10.1016/j.appdev.2015.08.002&domain=pdf


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The quality of parents' interactions

One of the central aims of the current studies was to examine

whether parents' beliefs about the xedness of their children's math

and verbal abilities predict the quality of self-reported parent–child

interactions. In dening “quality of interactions,” we draw from both

self-determination theory (Deci & Ryan, 2000) and achievement goal

theory (Maehr & Zusho, 2009).

Self-determination theory: Autonomy-supportive versus controlling parenting

One dimension of parenting style that can impact children's devel-

opment is the extent to which parents interact with their children in

an autonomy-supportive versus a controlling manner. Autonomy sup-

port involves encouraging children to explore their environment,

solve problems independently, and make their own decisions. In con-

trast, controlling behavior involves tightly regulating children's actions

by issuing commands, providing external incentives, and modulating

affection(Pomerantzet al., 2007). It is importantto notethat controlling

behavior is more likely to emerge when there is a threat in the environ-

ment, such as when parents feel there is a possibility that their children

may not do well on a task (Gurland & Grolnick, 2005), and is associated

with expressions of negative affect, such as frustration (Moorman &

Pomerantz, 2010).

Research hasshownthat autonomy support hasa positive long-term

inuence on children's academic performance, whereas controlling be-

havior has a negative inuence (see Pomerantz et al., 2007, for a re-

view). Hess and McDevitt (1984) showed that the self-reported

tendency of certain mothers to control the behavior of their 4-year-

old children was associated with these children exhibiting lower levels

of verbal ability at age 4 and lower verbal and math achievement at age

12. Grolnick, Gurland, DeCourcey, and Jacob (2002)found thatthe more

autonomy-supportive and less controlling mothers were when helping

their third-grade children complete twohomework-like tasks in thelab,

the better the children performed on these tasks.

Achievement goal theory: Mastery- versus performance-oriented parenting

behavior

Another important dimension of parenting style is the extent to

which parents exhibit mastery- versus performance-oriented behavior

when interacting with their children. Mastery-oriented parenting

involves teaching children to value the process of learning and to appre-

ciatethe importanceof effort. In contrast, performance-orientedparent-

ing involves encouraging or helping children demonstrate high levelsof

performance with little effort, even if thiscomes at the expense of actual

learning (Gottfried, Fleming, & Gottfried, 1994). Research suggests that

mastery-oriented parenting leadsto positive academic outcomes. In one

study, the self-reported frequency with which mothers engaged in

mastery-oriented practices with their 9-year-old children, such as en-

couragement of curiosity, positively predicted these children's concur-

rent intrinsic motivation, which in turn predicted their math andreading performance on a standardized test at age 10 ( Gottfried et al.,

1994). In another set of studies by Mueller and Dweck (1998), fth-

grade children who initially received positive feedback from an experi-

menter about their effort (a typical mastery-oriented parenting

behavior) exhibited greater task persistence, enjoyment, and perfor-

mance in response to a later failure compared to children who received

positive feedback about their ability (see also Gunderson et al., 2013;

Pomerantz & Kempner, 2013).

Although a distinction can be made between the autonomy-supportive

versus controlling and mastery-oriented versus performance-oriented

dimensionsof parenting, these constructsmay actuallybe interconnected

in some contexts. For example, when parents act in autonomy-

supportiveways, theyfoster mastery-oriented behavior in theirchildren

by encouraging independent attempts to master skills that promote a

sense of competence (e.g., Frodi, Bridges, & Grolnick, 1985). On the

other hand, when parents are primarily concerned with ensuring that

their children perform well on a task (i.e., performance-oriented), they

may be particularly likely to engage in controlling behaviors

(e.g., Grolnick et al., 2002). Thus, in keeping with previous research

(e.g., Moorman & Pomerantz, 2010), we examine the two parenting di-

mensions as a single construct and contrast autonomy-supportive and

mastery-oriented parenting behavior (mastery-oriented behavior for

short) with controlling and performance-oriented parenting behavior(performance-oriented behavior for short).

Parents' beliefs about the xedness of their children's abilities

One factor that likely inuences parents' mastery- versus

performance-oriented behavior is their beliefs about the xedness of

their children's abilities. According to Dweck's (1999) research on be-

liefs about intelligence, some individuals view intelligence as a xed

and stable trait, and do not believe that intelligence can be changed

(i.e., entity theorists), whereas others view intelligence as malleable

and able to improve with effort (i.e., incremental theorists). Consistent

with Dweck's (1999) distinction between xed and growth mindsets,

we used the term “xedness” to describe the continuum of beliefs

ranging from entity to incremental.

Although much research has examined how children's beliefs about

the xedness of intelligence affect the way they pursue their own goals

(see Dweck, 1999), less is known about how parents' beliefs about the

xedness of intelligence might affect the way they pursue the goals

they have for their children. Parents' beliefs about the nature of intelli-

gence may provide them with a framework for how and how often

they engage their children in school-related activities. Forexample, par-

ents who believe that their children's math or verbal abilities are rela-

tively xed may not think that it is particularly useful to frequently

engage them in math- or reading-related activities. In addition, when

their children struggle with a math or reading task, they may infer

that their children have reached thelimitsof their math or verbalability.

This inference, combined with the assumption that there is not much

they cando to improve their children's ability (i.e.,low parental ef cacy),

may lead them to assert control over their children's behavior inorder to ensure that they do not do poorly on the task. In contrast,

incremental-minded parents may believe that it is useful to frequently

engage in math- and reading-related activities with their children be-

cause working hard in these domains can substantially improve their

children's abilities. They may also be more likely than entity-minded

parents to focus on their children's learning rather than performance.

For example, they may allow their children to struggle with a problem

because they think that this affords them an opportunity to improve

their ability. Thus, parents' xedness beliefs will likely predict both the

frequency with which they engage in math- and reading-related activi-

ties within the home as well as the quality of their interactions during

those activities.

Preliminary evidence for these hypotheses comes from a recent

study (Moorman & Pomerantz, 2010) that examined the effects of mothers' theories of intelligence on the quality of their interactions

with their 6–9-year-old children during a puzzle task. Researchers in-

duced an entity or incremental mindset in mothers by telling them

that the task tapped either innate ability or intellectual potential, re-

spectively. Mothers induced to hold an entity (xed) mindset displayed

more unconstructive involvement, such as performance-oriented

teaching, control, and negative affect during the task than did mothers

induced to hold an incremental (growth) mindset. However, because

parents' beliefs were induced and their behavior was observed in the

lab, it is unclear whether parents' naturally occurring beliefs about the

xedness of ability also predict their behaviors.

The current studies seek to extend the previous literature by mea-

suring both parents' general beliefs about intelligence as well as their

more specic beliefs about their children's math and verbal abilities.

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These more specic beliefs may capture important variance associated

with parents' beliefs about their children's abilities and thus better pre-

dict parents' behaviors. Parents' specic beliefs about the xedness of

their children's abilitiesmay be uniquefor several reasons. First, parents

may think differently about their own children than other individuals;

for example, research has found that parents tend to overestimate

their own children's academic performance (Miller, 1988), which sug-

gests that they maythink about their own children differently than chil-

dren in general. Second, to the extentthat parents know about critical orsensitive periods in development (Worden et al., 2011), it is possible

that they think about the xedness of children's intellectual abilities

differently than adults' abilities (Miller, 1988; Murphey, 1992).

Thepresent studies also examine whether parents' beliefs arespecif-

ic to academic domains. Forexample,some parents maysimultaneously

hold entity beliefs about their children's math ability and incremental

beliefs about their children's verbal ability. Thus, it may be necessary

to measure ability beliefs that match the task domain (e.g., Chen,

2012; Chen, Metcalf, & Tutwiler, 2014) in order to best predict the

kinds of behaviors parents will engage in when helping their children.

Frequency of math- and reading-related activities in the home

Prior research showing that parents' beliefs about child develop-ment relate to both the quantity an d quality of their child-directed

speech(Rowe, 2008) suggest that parents'xedness beliefs may predict

the frequency with which they engage in math- and reading-related

activities at home, in addition to the quality of their parent–child inter-

actions. Previous research suggests that parents who frequently engage

in activities that support early numerical development (Huntsinger,

Jose, Larson, Balsink Krieg, & Shaligram, 2000; LeFevre et al., 2009)

and early language development (Ezell & Justice, 2000; Whitehurst &

Lonigan, 1998) have children with greater math knowledge and uen-

cy, and greater emergent literacy skills (respectively). These early

math and literacy skills are important precursors to children's learning

and achievement in elementary school and beyond (Duncan et al.,

2007; Stevenson & Newman, 1986). We hypothesize that the less par-

ents believe that their children's abilities in a particular domain arexed, the more they believe that they are capable of improving their

children's abilities (i.e., the higher their parental ef cacy) and, thus,

the more likely they are to engage their children in domain-related

activities at home.

The present studies

The present studies have several aims. The primary aim is to exam-

ine whether two measures of parental beliefs (i.e., parents' general

beliefs about thexedness of intelligence and their child-specic beliefs

about thexedness of math and verbal ability) differentially predict the

types of parenting behavior (mastery versus performance) that parents

report engaging in when helping their children with dif cult math and

reading tasks (Studies 1 and 2). As part of this aim, we also set the goalof validating a new questionnaire that measures parents' domain- and

child-specic beliefs about the xedness of ability (Study 1).

The second aim is to examine whether parents' general and specic

xedness beliefs predict the frequency withwhich they engage in math-

and reading-related activities with their children at home (Study 2).

And, thethird andnal aim isto examine parental ef cacy as a mediator

of the relation between parents' xedness beliefs and parenting

behavior (Study 2).

In addition to these three aims, we also examined whether parents'

beliefs and behaviors were related to demographic variables such as sex

(of both parent and child), parent education, and parent income. Previ-

ous research suggests that these variables may predict parents' beliefs

and behaviors as well as children's achievement (e.g., Davis-Kean,

2005; Hugh & Romney, 1991).

Study 1

Study 1 addressed our rst aim. Parents were recruited online and

asked to complete a seriesof questionnaires measuringtheir specicbe-

liefs about thexedness of their children's mathand verbal abilities and

their general beliefs about thexedness of intelligence. After they com-

pleted these questionnaires, the parents read two scenarios in which

they were asked to imagine their child (as a preschooler) struggling to

complete a dif

cult math or reading task. They were then presentedwith a list of mastery- and performance-oriented behaviors and asked

to say how likely they would be to engage in each of them.

We predicted that parents hold domain-specic beliefs about the

xedness of their children's abilities and that these beliefs would better

predict the types of behaviors they engage in when helping their chil-

dren during dif cult academic tasks than their general xedness beliefs.

More specically, we expected that the more parents believed their

children's math and verbal abilities are xed, the more likely they

would be to report engaging in performance-oriented behaviors and

the less likely they would report engaging in mastery-oriented behav-

iors during challenging tasks in those domains.

Method

Participants

Three hundred and eleven parents participated in the study through

Amazon Mechanical Turk (MTurk), a website that is accessed and used

by a large, diverse population of adults from around the world. Individ-

uals who are interested in joining MTurk can register as “workers” who

receive small payments for their participation in various surveys, exper-

iments, or other tasks (see Buhrmester,Kwang, & Gosling, 2011). Recent

research suggests that the internal consistency of self-reported demo-

graphics on MTurk is high, evidenced by the fact that thesame workers

gave the same demographic information across multiple studies

(Mason & Suri, 2012). Additionally, replication studies indicate that

MTurk participants display a similar level of consistency across self-

report surveys as is typically seen in non-Internet studies ( Buhrmester

et al., 2011; Rand, 2012). For this study, we recruited workers fromthe United States and paid them $0.75 to participate. We advertised

our online questionnaire with a short paragraph on the MTurk website.

Eleven parents were excluded from the analysis because they failed to

complete the rst questionnaire, gave nonsense responses to open-

ended reliability check items, or reported that they had participated in

a previous version of the study. The nal sample consisted of 300 par-

ents (65% female) who ranged in age from 19 to 75 years (M = 36.18,

SD = 10.95), and were primarily European American (78.5%; 7.8%

African American; 5.1% Asian American; 4.1% Hispanic; 4.5% other eth-

nicities). Forty-ve percent of parents had at least a four-year bachelor's

degree, and 41% of parents had a current household income above

$50,000 per year. Most parents (79%) had only one or two children.

Parents were asked to think about only one of their children when com-

pleting the survey; 60% of parents thought about a male child and 40%thought about a female child. The age of the child that parents thought

about ranged from 1 to 47 years at the time of the survey, with a mean

age of10.13 years (SD = 8.33) and a medianage of8 years. 28.5% ofpar-

ents thought about a childwho waspreschool aged, 39.4% thought about

a child who was elementary school aged, 8.8% thought about a child who

wasmiddle school aged, 9.6% thought about a child who was high school

aged, 10% thought about a child who was between 18 and 30 years of

age, and 3.1% thought about a child who was over 30 years of age.

Measures

Speci c ability xedness beliefs

Because no existing instruments measured parents' specic beliefs

about the xedness of their children's math and verbal abilities, we

80 K. Muenks et al. / Journal of Applied Developmental Psychology 41 (2015) 78–89


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developed and validated a questionnaire that measures these beliefs.

The rst and second authors drafted approximately 80 closed-ended

items that were originally intended to measure not only ability xed-

ness, but also seven other related constructs including effort beliefs

and parents' ef cacy to improve their children's abilities. Although the

items were designed to assess beliefs that apply to a specic academic

or intellectual domain, they were phrased in a general manner so that

this domaincould be changed without substantial rewording. Designing

a single set of items that could be used with multiple domains allowed

us to directly compare parents' beliefs across these domains (e.g., do

parents tend to believe that their child's math ability is more xed

than his or her verbal ability)?

Feedback regarding the initial set of items was gathered from

approximately four professors in the eld of human development

(who are all parents), two advanced graduate students, and at least

two parents who are not professors. The professors and graduate stu-

dents were asked to evaluate theitems based on howwell they assessed

the constructs they were intended to measure, how clear or under-

standable they were, and (for the professors who were also parents)

how relevant they were to real parents. The non-professor parents

were asked to read and respond to each item and to provide their

thoughts or feedback about the item's clarity (e.g., if the item was con-

fusingor they did not know howto answerit). Allfeedbackfrom profes-

sors, graduate students, and parents was provided individually to the

rst author, either by email or in person. Based on this feedback,

20 items were removed, and other items were modied. Oncethe ques-tionnaire was narrowed down to 60 items per domain, we conducted

three iterations of exploratory analyses (both exploratory and conr-

matory factor analyses were used for exploratory purposes) with

three samples of parents (total N = 812, after exclusions) on Amazon's

Mechanical Turk. These samples were independent from each other as

well as from thesample for Study 1. The rst iteration included 294 par-

ents (64.3% female, 78.4% European American, Mage = 36.62 years)and

resulted in the elimination of 40 items per domain based on exploratory

factor analysis (EFA). The second iteration included 200 parents (61.5%

female, 71% European American, Mage = 36.24 years) and resulted in

the modication or removalof several items based on results from con-

rmatory factor analyses (CFAs). The third iteration included 318 par-

ents (67% female, 74.5% European American, Mage = 35.68 years) and

resulted in the removal or modication of additional items based onCFAs (see supplemental materials for full description of scale construc-

tion procedures). The authors also decided at this point to focus exclu-

sively on the ability xedness construct, rather than the other seven

constructs the original scale was intended to measure. After all three it-

erations, a nal set of six items (per domain) was used for the Parental

Beliefs about Ability Fixedness (PBAF) scale (see Table 1 for all items).

The nal six items of the Parental Beliefs about Ability Fixedness

(PBAF) scale can be phrased in terms of math or verbal ability. Some

of these items assess beliefs about xedness across the lifespan

(e.g., “My child's math (verbal) ability will never change”), while

other items assess xedness in terms of a critical period in development

(e.g., “My child's math [verbal] ability can only be substantially im-

proved during a specic period of time in his/her development”; “My

child is past the age at which he/she can substantially improve his/her

math [verbal] ability”). Parents were asked to indicate the extent to

which they agreed or disagreed with each item on a 6-point Likert

scale (1 = “Strongly Disagree” to 6 = “Strongly Agree”). Before com-

pleting the items in a particular domain, parents were informed that,

“By math (verbal) ability, we mean your child's ability to learn math-

related (language-related) knowledge and skills, not his or her current

math (language) skills.” We used the term verbal ability rather than

reading ability to further reduce the possibility that parents would con-

fuse verbal ability with reading skills. The scale showed good internal

consistency for both the math (α = .85) and verbal (α = .85) sub-

scales in the current sample. After reverse coding the incremental

items, responses were averaged to calculate participants' nal PBAF

math and verbal scores.

General xedness beliefs

We used Dweck's (1999) Theories of Intelligence(TOI) scale to mea-

sure parents' general beliefs about thexedness of intelligence. The ver-

sion we used consists of eight items; e.g., “You have a certain amount of

intelligence and you can't really do much to change it” and “You can

learn new things, but you can't really change your basic intelligence.”

Parents were asked to indicate the extent to which they agreed or

disagreed with each item on a 6-point Likert scale (1 = “Strongly Dis-

agree” to 6 = “Strongly Agree”). The scale showed excellent internal

consistency in this sample (α = .96). After reverse coding the incre-

mental items, responses were averaged to calculate participants' nal

TOI scores.

Competence beliefs

We measured parents' beliefs about their children's current compe-

tence (i.e., how good they are) in math and reading and then used

this to establish the discriminant validity of the PBAF. Parents rated

their children's competence in math and reading using items adapted

from the University of Michigan's Childhood and Beyond (CAB) study

(Fredericks & Eccles, 2002). Four questions were asked per domain

with responses on a 7-point rating scale; e.g., “How good is your child

in math?” (1 = “Not good at all” to 7 = “Very good”). The scale

showed excellent internal consistency for both math (α = .91) and

reading (α = .91).1 After reverse coding some items, responses were

averaged to calculate participants' scores.

Self-reported behavior

Two hypothetical scenarios were presented in which parents were

asked to imagine their child as a preschooler struggling to complete a

challenging math or reading task (for all other parts of the survey, par-

ents were not explicitly asked to imagine their child at a particular age,

and therefore presumably thought about their child at hisor hercurrent

age; thus, child age was controlled for in the focal analyses, as discussed

in more detail below). For each scenario, parents were given a list of six

mastery-oriented and autonomy-supportive behaviors (e.g., “Explain or

Table 1

Means and standard deviations of PBAF items.

Study 1 Study 2

Math Verbal Math Verbal

1. My child's math [verbal] ability is innate and will never change. 2.27 (1.16) 2.09 (1.07) 2.12 (1.05) 1.95 (.96)

2. My child's math [verbal] ability can change signicantly from birth. (RC) 2.01 (1.07) 1.84 (.97) 1.92 (1.02) 1.77 (.94)

3. After a certain point in childhood, my child' math [verbal] ability cannot improve. 2.25 (1.16) 2.32 (1.25) 1.86 (.86) 1.97 (.79)

4. My child can always improve his/her math [verbal] ability, no matter how old he/she is. (RC) 2.14 (1.09) 2.17 (1.08) 2.06 (1.02) 1.98 (.91)

5. My child's math [verbal] ability can only be substantially improved during a specic period of time in his/her development. 2.98 (1.50) 2.90 (1.51) 2.42 (1.01) 2.48 (1.18)

6. My child is past the age at which he/she can substantially improve his/her math [verbal] ability. 2.19 (1.29) 2.28 (1.38) 1.72 (.88) 1.91 (.94)

Note. RC = reverse coded. Standard deviations are in parentheses.

1 In Studies 1 and2, parents were also asked to respond to items about howmuchtheir

child valued math and reading, but analyses pertaining to those items are not reported

here. In addition, moderator analyses were conducted with the child competence scale

forbothstudies(in keepingwithPomerantz& Dong, 2006), butare alsonotreportedhere.



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give hints about the problem without actually solving the problem”;

α = .76 math, α = .72 reading) and eight performance-oriented

and controlling behaviors (e.g., “Tell your child the correct answer”;

α = .82 math, α = .77 reading); mastery- and performance-oriented

behaviors were presented together in a random order (see online sup-

plementary materials for the full list of behaviors). Parents then indicat-

ed how likely they would be to engage in each behavior on a 6-point

Likert-type scale (1 = “Very Unlikely” to 6 = “Very Likely”). The

rst and second author created the hypothetical scenarios and listof behaviors based on previous literature (e.g., Reeve & Jang, 2006)

and expert opinion.2 Items were averaged to calculate participants'

scores.

Demographics

Parents reported on a number of demographic variables, including

their “gender” (heretofore referred to as sex), ethnicity, age, education,

income, and number of children. Education was measured as the

highest level of education completed, from 1 = “Grammar school” to

7 = “Professional degree (PhD, MD, JD, etc.)”. Income was measured

as the current household income in U.S. dollars, from 1 = “Under

$10,000” to 9 = “Over $150,000”.

Procedure

Prospective participants wererst asked whether or not they were a

parent, and were only allowed to proceed to themain survey once they

conrmed that they were. Parents then lled out a series of online ques-

tionnaires that were administered using Qualtrics Research Suite. For

the questionnaires that were child-specic, parents with multiple

children were asked to think about one particular child. They rst

completed Dweck's domain-general TOI Scale and then completed the

domain-specic PBAF in domain 1 (e.g., math), the PBAF in domain 2

(e.g., verbal), the competence questionnaire in domain 1, the compe-

tence questionnaire in domain 2, hypothetical scenarios for domain 1,

and then hypothetical scenarios for domain 2. The order of domain pre-

sentation was counterbalanced across participants. With the exception

of Dweck's TOI Scale, the order of the items within each questionnaire

was randomized. Parents were asked to report on demographic infor-mation at the end of the study.

Results

Factor structure

Because the PBAF is a new measure, we rst evaluated its structural

validity. Conrmatory factor analyses using LISREL 8.80 were conducted

on the items to determine which of the a priori hypothesized models

(based on our previous exploratory studies) best t the data. We used

listwise deletion because the missing data rate for these 12 items was

extremely small (0.01%). Three indices were used to evaluate the t of

the models: the comparative t index (CFI), the standardized root

mean square residual (SRMR), and the root mean square error of approximation (RMSEA). To retain the hypothesized model, Hu and

Bentler (1999) recommend that the CFI should be above .95, the

SRMR should be below .08, and the RMSEA should be below .06.

Two competing models were tested in order to determine whether

parents held domain-specic beliefs about the xedness of their

children's abilities: a one-factor model where all items in both domains

loaded onto one factor, and a two-factor model where items loaded

onto separate math and verbal factors (see Figure S1, included in the

online supplementary materials). Since the math and verbal items had

the same wording, we covaried the errors between similarly worded

items in both models. The two-factor model t adequately well to the

data (χ2 = 117.96, p b .001, df = 47, CFI = .98, SRMR = .04,

RMSEA = .07, N = 299) and signicantly better than the one-factor

model (χ2 = 276.88, p b .001, df = 48, CFI = .95, SRMR = .06,

RMSEA = .14, N = 299), Δχ2 = 158.92, p b .001, although even the

two-factor model had an RMSEA value that was just above Hu and

Bentler's (1999) recommended cut-off and a chi-square value that

was signicant.

Standardized factor loadings for items on the two-factor model

ranged from 0.51 to 0.84. A scale score was created for each domainby averaging parents' scores on each item. All items were retained due

to their high loadings. Means and standard deviations of the individual

PBAF items are shown in Table 1, andmeans and standard deviations of

all composite variables are shown in Table S1. The means were low, in-

dicating that overall, most parents do not view their children's abilities

as xed. However, there was suf cient variability in parents' responses

to examine relative differences in xedness beliefs. Skewness and kur-

tosis indices suggest that the distributions for both math and verbal

were approximately symmetric (skewness = .35, SE = .14 math;

skewness = .33, SE = .14 verbal) and platykurtic (kurtosis = − .57,

SE = .28 math; kurtosis = − .81, SE = .28 verbal). Mean values for

the PBAF-Verbal and PBAF-Math scales did not signicantly differ,

t (298) = .94, p = .35, d = .11, suggesting that parents viewed

children's abilities in both domains as equally xed. The PBAF-Verbal

and PBAF-Math scales were also highly correlated (r = .72, p b .001,

N = 299).

Validity

Convergent validity

Convergent validity of the scale was examined by investigating the

relation between the PBAF scale and Dweck's TOI scale for adults

(Dweck, 1999). Both scalesmeasure people's beliefs about thexedness

of ability, so we expected participants' responses on the two measures

to be correlated. However, we did not expect a perfect correlation

because the scales measure xedness beliefs at different levels of

specicity. As expected, the two measures were correlated for both

math (r = .50, p b .001, N = 299) and reading (r = .45, p b .001,

N = 299). However, the magnitude of the correlations indicates thatthey only shared about 20–25% of their variance.

Discriminant validity

Discriminant validity of the scale was examined by correlating the

PBAF with parents' reports of their children's competence level in

math and reading. We did not expect parents' beliefs about the xed-

ness of their children's abilities to be highly related to reports of their

children's competence, since it is possible to believe both that one's

child has high ability and that this ability cannot change. Consistent

with this expectation, there was no correlation between the PBAF

and the competence scale for verbal/reading (r = − .07, p = .24,

N = 297) and a small, yet statistically signicant, correlation for math

(r = − .13, p = .02, N = 297).

Relation between parents' beliefs and self-reported behavior

Correlations between all variables are shown in Table 3a; means are

shown in Table 2. Parents were much more likely to engage in mastery-

oriented as opposed to performance-oriented behaviors overall,

t s N 41.27, ps b .001, ds N 4.80.

To examine which set of parental xedness beliefs (specic or gen-

eral) predicted self-reported behavior better than general beliefs

about thexedness of intelligence, we conducted three separate regres-

sion models for each behavior typewithin each domain. Because the ac-

tual age of the child that each parent imagined as a preschooler varied

considerably, we entered child age as a control variable into Step 1 of

all three analyses. For Step 2, self-reported behavior was regressed

onto xedness (PBAF) scores in the rst model, theories of intelligence

2 In Studies 1 and 2, parents were also asked which behaviors they would be most and

least likely to use, but analyses pertaining to those items are not reported here.



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(TOI) scores in the second model, and both PBAF and TOI scores simul-

taneously in the third model. Analyses of self-reported behavior used

listwise deletion to deal with missing data (0.92%), which is reected

in the degrees of freedom for various analyses. As shown in Table 4a,

the two PBAF subscales (math and verbal), as well as the TOI scale, sig-

nicantly predicted self-reported parenting behavior for all combina-

tions of behavior type and domain. Specically, parents' xedness

beliefs were negatively related to mastery-oriented behaviors and pos-

itively related to performance-oriented behaviors. Furthermore, when

PBAF and TOI scores were entered into the same model simultaneously,

only the PBAF scores remained a signicant predictor of self-reported

parenting behavior. This, in conjunction with the greater R2 for Model

1 compared to Model 2, suggests that parents' child- and domain-

specic xedness beliefs accounted for a greater proportion of the vari-

ance in self-reported parenting behavior than general xedness beliefs.3

Although the PBAF predicted self-reported parenting behavior within

each domain (i.e., math and reading), it also predicted parenting behav-

ior in the other domain as well. That is, the PBAF-Math signicantly pre-

dicted both mastery-oriented, β = − .43, t (293) = −8.06, p b .001,

and performance-oriented, β = .35, t (293) = 6.46, p b .001, behavior

in the reading domain, and the PBAF-Verbal signicantly predicted

both the mastery-oriented, β = − .44, t (293) = −8.36, p b .001, and

performance-oriented, β = .45, t (293) = 8.68, p b .001, behavior in

the math domain. This nding suggests that even though parents may

holdseparate beliefs about thexednessof their children's mathand ver-

bal abilities, it is the shared variance of these beliefs that predicts self-reported parenting behavior in both domains (see General Discussion).

Sex, SES, and age analyses

There were no signicant differences on any measures between par-

ents of boys andgirls. There were also no signicantdifferences between

mothers and fathers on their PBAF scores for math or verbal. However,

there were parent sex differences in self-reported parenting behavior;

mothers were more likely to engage in mastery-oriented behavior,

t (292) = −2.26, p = .03, d = − .26 [math], t (292) = −2.60, p =

.01, d = − .30 [reading], and less likely to endorse performance behav-

ior, t (292) = 3.12, p = .002, d = .37 [math], t (292) = 2.60, p = .01,

d = .30 [reading], than fathers in both domains. However, sex did notmoderate the relation between PBAF and parenting behavior.

Parent education, transformed into an ordinal variable as years of

education, was negatively related to use of mastery-oriented behavior

in the math domain (r s = − .13, p = .02), but was not signicantly

related to any other variables. Parent income and child age were not

related to any variables included in these analyses.4

Discussion

Study 1 established that parents' general beliefs about the xedness

of intelligence, as well as their child-specic beliefs about the xedness

of their children's math and verbal abilities, predict their self-reported

likelihood of engaging in mastery- and performance-oriented behaviors

when helping their children complete a dif cult math or reading task.

Specically, the more parents believed that intelligence, math ability,

or verbal ability is

xed, the more likely they were to engage inperformance-oriented parenting behaviors and the less likely they

were to engage in mastery-oriented behaviors. Importantly, parents'

child-speci c xedness beliefs did not completely overlap with their

general xedness beliefs and proved a better predictor of their self-

reported parenting behavior in both academic domains than their gen-

eral beliefs about the xedness of intelligence. An important caveat is

that parents' child-specic xedness beliefs were not uniquely predic-

tive of their parentingbehaviors withina particular domain. That is, par-

ents' beliefs about the xedness of verbal ability predicted their math

behaviors, and vice versa. This suggests that it is the child specicity of

the PBAFquestionnaire, not the domain specicity, that made it a better

predictor of parenting behavior than the general theories of intelligence

questionnaire (see General Discussion).

The study also served to validate the Parental Beliefs about Ability

Fixedness scale (PBAF), a new questionnaire created to measure par-

ents' specic beliefs about the xedness of their children's abilities.

The questionnaire showed good internal consistency as well as strong

content, convergent, and discriminant validity. And, most importantly,

the two-factor model t adequately well to the data (and better than

the one-factor model). This suggests that the parents held separate be-

liefs about their children's math and verbal abilities, although these be-

liefswere highly correlatedand equally predictive of parenting behavior

across domains.

Although Study 1 provides strong evidence for the association be-

tween parents' xedness beliefs and self-reported parenting behavior,

onepotentialweakness of the study is that it used a sample that was re-

cruited via the Internet, thus making it dif cult to validate participants'

status as parents. This weakness was addressed in Study 2, which also

served to replicate and extend the ndings of Study 1.

Study 2

Although replication studies indicate that Amazon Mechanical Turk

(MTurk) participants display a similar level of consistency across self-

report surveys as is typically seen in non-Internet studies ( Buhrmester

et al., 2011; Mason & Suri, 2012; Rand, 2012),we sought to address con-

cerns about the Study 1 sample by recruiting from a population of local

parents who are members of a university database. Parents in this pop-

ulation frequently travel to campus to participate in research studies

with their children, which helped increase our condence that they

are actually parents and that their responses on the questionnaires

accurately reected the perspective of parents.Beyond replicating the results of Study 1 with a more reliable sam-

ple, the aim of Study 2 wasto examine the association between parents'

xedness beliefs and the frequency with which parents engage in math-

and reading-related activities in the home. As previously mentioned,

parents who frequently engage in activities that support early numeri-

cal development (Huntsinger et al., 2000; LeFevre et al., 2009) and

early language development (Ezell & Justice, 2000; Whitehurst &

Lonigan, 1998) tend to have children with relatively high math and lit-

eracy skills, respectively. To the best of our knowledge, there are no

existing studies that have looked at the relation between xedness be-

liefs (whether they be general or specic) and activity frequency. We

predict that parents who believe that their children's ability in a partic-

ular domain is xed will less frequently engage their children in math-

and reading-related activities at home.

3 We also conducted these analyses with parent sex, child sex, child age, parent educa-

tion, and parent income entered as covariates into each model.The addition of the covar-

iates did not change the signicance of the TOI and PBAF as predictors.4 We alsoexamined moderation effects of agefor Studies 1 and2. Althoughsome inter-

action terms were statistically signicant, the overall pattern of results did not change.

Some effects just tended to be stronger for parents of older or younger children (depend-

ing on the outcome).

Table 2

Means and standard deviations of all composite variables.

Study 1 Study 2

Math Reading Math Reading

PBAF 2.31 (0.92) 2.27 (0.92) 2.02 (0.76) 2.01 (0.73)

Child competence 4.73 (1.35) 5.31 (1.45) 5.24 (1.03) 5.51 (1.43)

Mastery behaviors 5.12 (0.70) 5.16 (0.72) 5.08 (0.57) 5.05 (0.61)

Performance behaviors 1.99 (0.78) 2.17 (0.75) 1.95 (0.75) 1.98 (0.60)

Parental ef cacy – – 4.63 (0.69) 5.00 (0.74)

Parenting activities – – 3.25 (1.00) 4.14 (0.90)

Dweck's TOI scale 3.06 (1.16) 3.01 (1.10)



7/12

Thenal aim of Study 2 was to examine parental ef cacy as a poten-

tialmediatorof therelation betweenxedness beliefs and parenting be-

havior. We predict that the less parents believe that their children's

ability in a particular domain is xed, the more they will think of them-

selves as capable of helping their child to learn and perform well in this

domain (i.e., the higher their parental ef cacy) and, thus, the more like-

ly they will be to engage in mastery-oriented parenting behavior and

the less likely they will be to engage in performance-oriented behavior.

Furthermore, parents with low xedness beliefs and high parental ef -

cacy should be relatively likely to participate in math- and reading-

related activities with their children at home.

Method

Participants

One hundred and nine parents were recruited from a large database

housed at a mid-Atlantic university. The database consists of thousands

of local families who have volunteered to be contacted to participate in

research studies with their children. For the present study, we recruited

parents of children ages 6–12 years through email. We did not recruit

parents of children under the age of 6 because it conicted with recruit-

ment of another study we were conducting. We asked parents to ll out

an online questionnaire at home on their computer. Of the 109 parentswho initially participated, 23 were excluded from the analysis because

they failed to complete the rst questionnaire or gave nonsense re-

sponses to open-ended reliability check items. The nal sample thus

consisted of 86 parents (94.2% female). Parents ranged in age from 26

to 50 years (M = 41.0), and were primarily European American

(67.4%; 23.3% African American; 2.3% Asian American; 3.5% Hispanic;

3.5% other ethnicities). Eighty eight percent of parents had at least a

four-year bachelor's degree, and 79.1% of parents had a current house-

hold income above $50,000 per year. Most parents (79.1%) had only

one or two children. Parents were asked to think about only one of

their children when completing the survey; 54.7% of parents thought

about a male child and 45.3% thought about a female child. Although

we sought to recruit parents of children ages 6–12 years, we also

included one parent of a 4-year old child and one parent of a 14-year

old child. Thus, the age of the child parents thought about ranged

from 4 to 14 years at the time of the survey, with a mean age of 8.12

years (SD = 1.45) and a median age of 8 years, with 1.2% of parents

thinking about a child who was preschool aged, 95.4% thinking about

a child who was elementary school aged, and 3.5% thinking about a

child who was middle school aged.

Measures

The measures were the same as in Study 1 with the addition of a

questionnaire measuring parental ef cacy and an inventory that mea-

sured how frequently parents did math- and reading-related activities

with their children.

Parental ef cacy

Parents reported on how ef cacious they felt helping their children

learn math and reading. They were given ve items per domain and

asked to indicate their agreement with them on a 6-point Likert scale;

e.g., “I know how to help my child do well in math ”; “I don't know

how to help my child learn math” (from 1 = “Strongly Disagree” to

6 = “Strongly Agree”). Some items were drafted at the same time as

the initial PBAF items and were included as a separate subscale during

the exploratory analyses (see Study 1). Minor wording changes weremade to the original items (e.g., in order to make them shorteror easier

to understand), and a few items were added and adapted (e.g., made

domain-specic instead of domain-general) from the Parent Percep-

tions of Parent Ef cacy Scale (Hoover-Dempsey, Bassler, & Brissie,

1992). See supplementary materials for a list of all items. The scale

showed good internal consistency for math (α = .80) and reading

(α = .86) in this sample. After reverse coding items that were phrased

in terms of low ef cacy, responses were averaged to calculate partici-

pants' parental ef cacy scores in each domain.

Parenting activity inventory

Parents indicated the frequency with which they engaged with their

child in 9 math-related(i.e.,“Usinga calculator”) and 13 reading-related

Table 3a

Correlations of all variables—Study 1.

1 2 3 4 5 6 7 8

1. TOI

2. PBAF Math .50**

3. PBAF Verbal .45** .72**

4. Comp Math − .06 − .13* −.08

5. Comp Read − .07 − .04 −.07 .36**

6. Mastery Math − .27** − .45** −.44** .10 .17**

7. Mastery Read −

.24** −

.42** −

.42** .09 .18** .79**8. Perf Math .19** .43** .45** − .09 −.16** − .39** −.45**

9. Perf Read .19** .35** .47** − .08 −.20** − .36** −.44** .80**

* p b .05; ** p b .01. N = 300.

Table 3b

Correlations of all variables—Study 2.

1 2 3 4 5 6 7 8 9 10

1. TOI

2. PBAF math .53**

3. PBAF verbal .53** .75**

4. Mastery math − .51** − .40** −.42**

5. Mastery read − .41** − .22* −.36** .62**

6. Perf math .09 .27* .21* .01 − .03

7. Perf read .10 .16 .13 .09 .13 .81**

8. Ef cacy math − .46** − .52** −.46** .27* .14 −.23* − .26*

9. Ef cacy read − .45** − .52** −.61** .31** .25* −.18 − .22* .65**

10. Activities math − .17 − .22* −.17 .31** .18 −.07 − .02 .32** .18

11. Activities read − .31** − .35** −.21 .33** .26* −.14 −.05 .40** .24* .73**

* p b

.05; ** p b

.01. N = 86.



8/12

(i.e., “Telling stories”) activities in the past month (math and reading

activities were presented together in a random order; see online sup-

plementary materials for a full list of activities). Parents responded on

a 6-point Likert scale from “Did not occur” (coded as 1) to “Daily”

(coded as 6). Items were averaged to calculate participants' scores.

Math-related and literacy activities from this scale came from the

Frequency of Literacy and Numeracy Activities scale used by LeFevre,

Polyzoi, Skwarchuk, Fast, and Sowinski (2010), which included three lit-

eracy items and twelve math-related items; three math-related activities

from LeFevre et al. (2010) were not included because we were most in-

terested in activities that mainly engaged children's numeracy skills and

eliminated items that did not (e.g., making/sorting collections). One of

the authors withexpertise in literacy development created the additional

reading activities by examining each math-related activity and develop-

ing a corresponding reading activity (e.g., “Memorizing math facts” and

“Memorizing letters/sounds or sight words”), as well as adding some ad-

ditional activities. The reading activities were designed to capture all

areas of literacy (i.e., vocabulary, phonemic awareness, writing) relevant

to children of preschoolages based on research on earlylanguage and lit-

eracy development. All activities (for both math and reading) were simi-lar in terms of scope and function. We included activities that were both

directly related to numeracy and literacy (e.g., learning simple sums and

spelling words) and indirectly related to numeracy and literacy

(e.g., measuring ingredients and telling stories; see LeFevre et al., 2010).

The scale showed good internal consistency for math (α = .83) and

reading (α = .85) in this sample. 5

Procedure

Participants lled out a series of questionnaires online. They rst

completed Dweck's (1999) Theories of Intelligence (TOI) scale and

then completed the Parental Beliefs about Ability Fixedness (PBAF)

scale and ef cacy scale for domain 1 (i.e., math), the PBAF and ef cacyscale for domain 2 (i.e., verbal/reading), the competence questionnaire

in domain 1, the competence questionnaire in domain 2, the hypothet-

ical scenario for domain 1, the hypothetical scenarios for domain 2, and

the parent activity inventory. The order of domain presentation was

counterbalanced across participants. With the exception of Dweck's

TOIScale, the order of theitemswithin each questionnaire wasrandom-

ized. Parents were asked to report on demographic information at the

end of the study.

Results

Meansand standard deviations of thePBAF areshownin Table 1.The

math and verbal scales of the PBAF were combined to create separate

scores for each domain (α = .87 for math; α = .85 for verbal). There

was no missing data. Means for the PBAF subscales did not differ,

meaning that parents tended to believe that math and reading abilities

were equallyxed, t (85) = .14, p = .89, d = .03. Subscale scores were

highly correlated (r = .75, p b .001).

Relation between parents' beliefs and self-reported behavior

Parents were much more likely to engage in mastery-oriented as op-

posed to performance-oriented behaviors overall, t s N 31.08, ps b .001,

ds N 6.73. Correlations between all variables are shown in Table 3b;

means are shown in Table 2.

To examine whether PBAF scores predicted self-reported parent-

ing behavior better than a general measure of beliefs about thexed-

ness of intelligence, we conducted the same set of regressionanalyses as in Study 1. Again, child age was controlled for in Step 1

of each regression analysis. As shown in Table 4b, the PBAF subscales

signicantly predicted parenting behaviorfor all combinations of be-

havior type and domain except for performance-oriented behavior

in the reading domain. Like the PBAF, the TOI scale (which served

as the more general measure of xedness beliefs) predicted

mastery-oriented behavior in both domains; in fact, it was actually

a stronger predictor of parenting behavior in these cases. However,

the TOI scale did not predict performance-oriented behavior in ei-

ther domain, whereas the PBAF predicted performance-oriented be-

havior in math. This suggests that, although the PBAF was not as

strong a predictor of mastery-oriented parenting strategies (in con-

trast to Study 1), it predicted a broader array of parenting behavior

than the more general xedness measure.6Once again, the PBAF subscales also predicted self-reported parent-

ingbehavior acrossdomains.That is,the PBAF-Mathmarginally predict-

ed mastery-oriented parenting behavior, β = − .21, t (85) = −1.95,

p = .06, in the reading domain, and the PBAF-Verbal signicantly pre-

dicted both mastery-oriented, β = − .42, t (85) = −4.20, p b .001,

and performance-oriented, β = .21, t (85) = 1.97, p = .05, behavior

in the math domain.

5 Participants were also asked to rate how important they perceived particular math-

and reading-related activities to be, but analyses pertaining to this questionnaire are not

reported here.

Table 4b

Regression analyses predicting self-reported parenting behavior from Theories of Intelli-

gence (TOI) scale and PBAF questionnaire—Study 2.

Type of parenting behavior

Math mastery Math

performance

Reading

mastery

Reading

performance

R 2 β R 2 β R 2 β R 2 β

Model 1 .16** .07* .14** .02

PBAF −

40** .27* −

.36** .13Model 2 .26** .01 .18** .01

TOI −.51** .09 − .41** .10

Model 3 .28** .08* .21** .02

PBAF −.18 .31* − .20† .10

TOI −.41** −.07 − .30* .04

† p b .10, * p b .05, ** p b .01

Note: β s arestandardized.N = 86.Child agewas entered as a control variable into Step 1

of each model.

6 We also conducted theseanalyses with parent sex, child sex, child age, parent educa-

tion, andparent incomeenteredas covariates into each model.The signicance ofthe TOI

and PBAF as predictors did not change, except for Model 3: the betas for both predictors

(TOI and PBAF) drop down to marginal signicance when the covariates were added.

Table 4a

Regression analyses predicting self-reported parenting behavior from Theories of Intelli-

gence (TOI) scale and PBAF questionnaire—Study 1.

Type of parenting behavior

Math mastery Math

performance

Reading

mastery

Reading

performance

R 2 β R 2 β R 2 β R 2 β

Model 1 .20** .19** .18** .22**

PBAF −

.45** .43** −

.43** .47**Model 2 .08** .04** .06** .04**

TOI − .27** .19** − .23** .19**

Model 3 .21** .19** .18** .22**

PBAF − .42** .46** − .40** .48**

TOI − .06 − .04 − .06 −.03

* p b .05, ** p b .01

Note: β s arestandardized.N = 294. Childage wasenteredas a control variable into Step 1

of each model.



9/12

Relation between xedness beliefs and the frequency of activities in the

home

To examine the relation between parents' xedness beliefs and the

frequency with which they engage in math- and reading-related activi-

ties with their children at home, we conducted three separate regres-

sion models for each activity type (math and reading). Child age was

controlled for in Step 1 of each regression analysis. Activity frequency

wasregressed onto PBAF scores in the

rst model, TOI scores in the sec-ond model, and both PBAF and TOI scores simultaneously in the third

model. The results showed that the two PBAF subscales predicted the

self-reported frequency of both types of activities.7 In contrast, the

more general TOI scale only predicted the frequency of reading-

related activities, although it was actually a better predictor of these

activities than the PBAF-Verbal subscale (see Table 5 for the full set of

regression coef cients).

There was some evidence that the PBAF subscales predicted parents'

self-reports across domains. In particular, the PBAF-Math subscale

signicantly predicted the frequency of reading-related activities,

β = − .38, t (85) = −3.26, p = .002,and was infacta strongerpredic-

tor than the PBAF-reading subscale. However, the PBAF-Verbal subscale

did not predict the frequency of math-related activities.

Parental ef cacy as a mediator of the relation between beliefs and behavior

As shown in Table 2b, the PBAF was negatively correlated with pa-

rental ef cacy in each domain, such that the more that parents' believed

that their child'sability wasxed, the less capable they perceived them-

selves of helping their child to learn and perform well in that domain. In

turn, parental ef cacy was positively correlated with mastery-oriented

parenting behavior and negatively correlated with performance-

oriented behavior in both domains. To formally test whether parental

ef cacy mediated the relation between xedness beliefs and parenting

behavior, we used SPSS to conduct a bootstrapping procedure with

1000 resamples. Compared to tests that assume a normal distribution

of indirect effects (e.g., the Sobel test), bootstrap methods are more ac-

curate for assessing mediation in small- to moderately-sized samples(see Shrout & Bolger, 2002). The procedure, developed by Hayes

(2013) and implemented in SPSS v20.0, allowed us to estimate the indi-

rect effects of the PBAF on behavior in both domains (with parental ef-

cacy as a mediator), as well as bias-corrected 95% condence intervals

for the estimates. Child age was entered as a covariate in all the media-

tion analyses. The intervals for the math mastery, math performance,

and reading mastery behaviors contained zero, which means that the

indirect effect was not signicant at α = .05. However, the condence

interval for reading performance behaviors (which ranged from .01 to

.27) did not include zero, so the indirect effect can be considered signif-

icant atα = .05 (Shrout & Bolger, 2002). Thus, it appears that parental

ef cacy at least partially mediated the relation between child-specic

xedness beliefs about verbal ability and performance-oriented behav-

ior in the reading domain.Parental ef cacy was also positively correlated with the self-

reported frequency with which parents engage in math- and reading-

related activities in the home (see Table 3b). Thus, we conducted an ad-

ditional set of analyses to determine if parental ef cacy also mediates

the relation between xedness beliefs and activity frequency. Thecon-

dence interval included zero for reading-relatedactivities (− .33 to .07),

but not for math-related activities (-.40 to -.01). Thus, it appears that

parental ef cacy at least partially mediated the relation between

child-specic xedness beliefs about math ability and the frequency of

math-related activities in the home.

Sex, SES, and age analyses

Parents of girls reported more frequent engagement in both math,

t (84) = −2.17, p = .03, d = − .47, and reading, t (84) = −2.05,

p = .04, d = − .45, activities at home than parents of boys. There

were not enough fathers in our sample to examine reliable differences

between mother and fathers.

Parent education, transformed into an ordinal variable as years of

education, was positively related to the TOI scale (r s = .29, p = .001),

but was not related to any other variables. Parent income, transformed

into dollars per year (by assigning a value of the median of that range to

every participant that fell within that range), was related positively to

the TOI scale (r = .24, p = .04) and negatively to engagement in

mastery-oriented behaviors in the math domain (r = − .25, p = .03),

but was not related to any other variables.

Finally, we found a negative correlation between child age and

frequency of engagement in reading-related activities (r = − .32,

p = .003). As discussed above, although parents were asked to imaginetheir child as a preschooler when completing the hypothetical scenari-

os, they were not explicitly told in the instructions to think about their

child as a preschooler when completing the rest of the survey, and

thus presumably thought about their child at his or her current age.

Parents who thought about an older child reported engaging less fre-

quently in reading activities in the home. Child age was not related to

any other variables.

Discussion

Study 2 replicated many of the results from Study 1. In particular,

parents'xedness beliefs predicted their self-reported parenting behav-

ior in both domains.Unlikein Study 1, the pattern varied in terms of the

specicity of these beliefs. The more parents believed that theirchildren's abilities were xed, the less likely they were to engage in

mastery-oriented behaviors in both the math and reading domains

and the more likely they were to engage in performance-oriented be-

haviors in the math domain (but not the reading domain, contrary to

Study 1). Interestingly, parents' general beliefs aboutthexedness of in-

telligence were more predictive of their mastery-oriented behavior in

both domains than their child-specic beliefs, although these general

beliefs did not predict performance-oriented behavior in the math do-

main. Thus, in this study, parents' child-specic beliefs signicantly pre-

dict a broader range of self-reported parenting behaviors than general

beliefs about intelligence.

The results of Study 2 extend the Study 1 ndings in two important

ways. First, they show that parents' xedness beliefs predict the self-

reported frequency with which they engage their children in math-

7 We also conducted theseanalyses with parent sex, child sex, child age, parent educa-

tion, and parent income entered as covariates into the rst step of each model.For Model

1, the PBAF-Math was no longer a signicant predictor of frequency of math activities

when the covariates were added ( p = .26). Additionally, in Model 3, the TOI dropped

down to marginal signicance ( p = .06) with the addition of the covariates.

Table 5

Regression analyses predicting frequency of engagement in math and reading activities

from Theories of Intelligence (TOI) scale and PBAF questionnaire—Study 2.

Math activities Reading activities

R 2 β R 2 β

Model 1 .05 .14**

PBAF −.23* −.20*

Model 2 .03 .20**

TOI −.17 −.31**

Model 3 .05 .20**

PBAF −.19 −.05

TOI −.07 −.29*

* p b .05, ** p b .01

Note:βs arestandardized.N = 86.Child agewas entered as a control variable into Step 1

of each model. Child age remained a signicant predictor of reading activities in all three

models.



10/12

and reading-related activities in the home. And, second, they show that

the relation between xedness beliefs and both parenting behavior and

parenting activities is, in some cases, mediated by their parental ef cacy

(i.e., the belief that they are capable of helping their children to learn

and perform well in math and reading).

General discussion

The present studies are the

rst to examine the association betweenparents' naturally occurring (i.e., non-experimentally manipulated)

beliefs about the xedness of ability and their self-reported parenting

behavior. Results of both studies suggest that parents' xedness beliefs

were negatively associated with the likelihood of engaging in

autonomy-supportive and mastery-oriented parenting behaviors and

positively associated with the likelihood of engaging in controlling

and performance-oriented behaviors when their children struggle

with a math or reading task. Study 1 also validated a new instrument,

the Parental Beliefs about Ability Fixedness (PBAF) scale, which mea-

sures parents' child-specic beliefs about the xedness of math and

verbal ability. The math and verbal factors of the scale were found to

be distinct yet highly correlated.

One explanation for our ndings is that parents who believe that

their children's abilities are relatively xed (perhaps at a low level)

also believe that their children are unlikely to benet from mastery-

oriented behavior and thus resort to performance-oriented and control-

ling behavior in order to ensure that their children do not perform poor-

ly. The same parents may also feel that engaging in math- and reading-

related activities with their children at the home is unlikely to improve

their children's math and verbal abilities. Conversely, parents who

believe that their children's abilities are relatively malleableand cande-

velop with effort may think that the best way to help their children

achieve their goals is to allow them to learn from their own mistakes.

Thus, they are likely to prefer to engage in mastery-oriented and

autonomy-supportive behaviors. They may also believe that engaging

their children in math- and reading-related activities at home is a

good way to improve their abilities over time.

This explanation is consistent with the results of Moorman and

Pomerantz (2010), which showed that parents induced to hold anentity (xed) mindset about a task displayed more controlling and

performance-oriented behaviors when helping their children than par-

ents induced to hold an incremental (growth) mindset. However, this

study manipulated parents' beliefs about the intellectual abilities

assessed by a particular task as opposed to measuring their naturally

occurring beliefs about the xedness of intelligence (generally) and of

their children's math and verbal abilities (specically). In Study 1,

our newly constructed measure of child- and domain-specic xedness

beliefs (the Parental Beliefs about Ability Fixedness scale, or

PBAF) emerged as a stronger predictor of parents' mastery- and

performance-oriented parenting behavior in both the math and reading

domains than Dweck's (1999) general measure of xedness beliefs. Fur-

thermore, in Study 2, the PBAF signicantly predicted parenting behav-

ior in three out of four combinations of behavior type and domain,whereas the general measure predicted behavior in only two. That is,

parents' general xedness beliefs strongly predicted their mastery-

oriented behavior in both the math and reading domains (in fact,

more strongly the PBAF), but did not signicantly predict their

performance-oriented behavior in the math domain (unlike the PBAF).

Together, the results from Studies 1 and 2 suggest that, in certain con-

texts, child- and domain-specic xedness beliefs are more strongly

predictive of parenting behavior than general xedness beliefs; and, in

other contexts, may predict a broader range of behavior.

An important question is why our child- and domain-specic mea-

sure of xedness beliefs appears to be a betterpredictor of parenting be-

havior in some cases than a more general measure of xedness beliefs.

Our results suggest that the predictive power of our measure is due

more to the fact that it is child-specic rather than domain-specic.

Although our conrmatory factor analysis suggests that parents' beliefs

about the xedness of their children's math and verbal abilities are dis-

tinct, these beliefs predicted parenting behavior across domains rather

than uniquely predicting behavior within a domain. That is, beliefs

about the xedness of math ability predicted parenting behavior in

thereading domain,and beliefs about thexedness of verbalability pre-

dicted parenting behavior in the math domain. If the shared variance

between the math and verbal subscales of our measure is what predict-

ed parenting behavior (as this

nding suggests), then it is probably thefact that our measure assesses parent's beliefs about the xedness of

their children's abilities that makes it more predictive (in some cases)

than a more general measure of xedness beliefs. For instance, parents

who generally believe that intelligence is xed may still act as if their

children's intelligence is malleable, particularly if they prefer to be

optimistic about their children's futures.

It is, however, worth noting that the domain-specicity of our mea-

sure may not have contributed to its predictiveness due to measure-

ment error. That is, the fact that parents completed nearly identical

surveys (one for math and one for verbal) within the same session

may have resulted in carryover effects. A study that implemented a

between-participants design or that examined parents' actual behavior

(rather than their self-reported behavior) may have found that parents'

domain-specic beliefs uniquely predicted their behavior within that

same domain. Now that we have established the validity and reliability

of the PBAF, this possibility will be easier for researchers to explore in

the future.

Another contribution of the studies that is worth highlighting is

the negative association we found between parents' xedness

beliefs and the self-reported frequency with which they engaged in

math- and reading-related activities with their children at home. To

the best of our knowledge, this is the rst study to relate xedness be-

liefs (general or specic) to the amount of math and reading support

that parents provide to their children. We think this is an important

contribution given what is currently known about the constructive

role that math- and reading-related activities play in early numerical

development (Huntsinger et al., 2000; LeFevre et al., 2009) and early

language development (Ezell & Justice, 2000; Whitehurst & Lonigan,

1998).Finally, in order to further explore the association between xedness

beliefs and both the quality and quantity of parenting behavior, we ex-

amineda potential mediator of this association: parents' self-ef cacy for

being able to help their children learn and perform well in math and

reading. We found that the more that parents felt that their children's

verbal ability wasxed, theless capable they thought they were of help-

ing their child with reading, and the more likely they were to engage in

performance-oriented behaviors during a challenging reading task. We

also found that the more parents felt that their children's math ability

was xed, the less capable they thought they were of helping their

child with math and the less likely they were engage their children in

math-related activities at home. Together this suggests that, in some

cases, parental ef cacy may serve as a more proximal determinant of

parenting behavior than xedness beliefs. However, it should again benoted that parental ef cacy was not a consistent mediator of the rela-

tion between xedness beliefs and parental behavior. Mediation was

not found for performance-oriented behavior in the math domain, for

mastery-oriented behavior in either domain, or for the frequency of

reading-related activities (although parental ef cacy was correlated

with each of these outcomes). Additional research is needed to clarify

the conditions under whichxedness beliefs have a director indirect ef-

fect on parenting behavior.

Although the studies make important contributions to research on

parenting and motivation, they have some limitations that may need

to be addressed in future studies. First, we used hypothetical vignettes

to measure parent's self-reported behavior rather than examining

their actual behavior. Thus, our results may have been inuenced by

parents' social desirability concerns. This inuence is perhaps evident



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in the mean levels of parents' self-reported master- and performance-

oriented behavior. Parents thought they were much more likely to

engage in mastery-oriented behaviors compared to performance-

oriented behaviors (which tend to have negative connotations).

Perhaps the disparity between mastery- and performance-orientedpar-

enting behaviors would have been smaller if parents' behaviors had

been discreetly observed in a home context. Beyond social desirability

concerns, it may have also been challenging for participants to imagine

themselves within a hypothetical situation that involved interactingwith a preschool aged child, especially for the parents in Study 1,

many of whose children were well beyond preschool age. However,

we controlled for child age in all of our focal analyses, and still found a

consistent pattern of results. We also found that entering child age as

a moderator did not change the general pattern of results that we re-

ported (see Footnote 4). Another reason that relying solely on parents'

self-reports can be problematic is that it can inate relations among

measures (e.g., DeYoung, 2006). In order to address this concern, future

studies should use multi-informant methods, such as child-report of

parents' behaviors in addition to parent-report. Researchers could also

observe parents' behaviorsin thehome or thelaboratory in order to bet-

ter capture the extent to which they use mastery- or performance-

oriented strategies.

Demographically, our sample consisted of mostly mothers, although

Study 1 was much more gender balanced than Study 2. It is therefore

important to keep in mind when interpretingthe results that these pat-

terns may look different if our sample had consisted of mostly fathers.

Additionally, parents were not asked about their family composition

(i.e., whether they live in a one- or two-parent household), which

could certainly inuence their levels of autonomy supportive versus

controlling behavior. Future research could examine how these

demographic characteristics inuence the association between parents'

xedness beliefs and their behaviors.

A nal limitation is that measures of parents' beliefs and behaviors

were administered during a single testing session. Thus, it is possible

that parenting behavior actually predicts xedness beliefs and not the

other way around. However, previous research by Moorman and

Pomerantz (2010), which temporarily manipulated xedness beliefs

showed that xedness beliefs do, in some cases, lead to changes in par-enting behavior. Future research can examine the causal inuence of

parents'xedness beliefs on their parenting behavior using longitudinal

designs.

Conclusion

Children often experience challenge, dif culty, and even failure

when engaging in dif cult academic tasks. How parents respond to

their children's struggles can potentially impact children's motivation

and success in school. When parents become frustrated and controlling,

children may learn to give up on challenging tasks. In contrast, when

parents allow children to make their own decisions and mistakes, chil-

dren may learn to persist when they are confronted with challenges.

The current studies demonstrate how parents' beliefs might help to ac-count forthesedifferencesin their behavior. Specically, parents' beliefs

about the xedness of their children's math and verbalabilities appear to

be important predictors of howparents will behavewhen their children

are struggling with an academic task. The current studies introduce a

new instrument, the Parental Beliefs about Ability Fixedness (PBAF)

scale, for measuring these xedness beliefs. Ultimately, the more that

we know about what drives parents' behaviors, the better prepared

we can be to educate parents about what types of beliefs and behaviors

will enhance their children's motivation and learning.

Appendix A. Supplementary data

Supplementary data to this article can be found online at http://dx.

doi.org/10.1016/j.appdev.2015.08.002.

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