Gender Differences in Computation Strategies: Evidence Across Adolescent and Adult Samples

Abstract

Background:

On computation items, young girls tend to use algorithmic approaches more than do boys. However, it is unclear whether these patterns persist as students progress into adulthood.

Aims:

In two independent studies using different measures, we examine gender differences in computation strategy use in adolescents (Study 1) and adults (Study 2). We explore factors that might explain differences, and whether they relate to gender differences in math performance.

Samples:

Study 1 uses data from students at a U.S. public high school (n=213; 54.5% female). Study 2 uses data from U.S. adults (n=810; 58.6% women).

Methods:

Participants completed computation items, math performance measures, and measures commonly found to relate to both gender and math. The unique relations between algorithm use, gender, and math performance were examined, while accounting for key covariates.

Results:

Girls and women used an algorithm more often than their male counterparts, as did people with lower mental rotation skills and higher teacher-pleasing tendencies (Study 1), and higher test anxiety (Study 2). After including covariates, the gender difference in algorithm use decreased in Study 1 but not in Study 2. Across both studies, girls and women and those who use algorithms more had lower performance on problem-solving measures, as did those with higher teacher-pleasing tendencies and lower confidence (Study 1) and lower math anxiety (Study 2).

Conclusions:

Gendered patterns in algorithm use within older samples and the negative relation of algorithm use with math performance point to the need for renewed focus on developing children’s computational approaches.

Introduction

Despite significant progress in weakening gendered¹ patterns in math performance in the U.S. (Hyde et al., 2008), achievement differences favoring boys persist in national samples (Cimpian et al., 2016). Moreover, gendered patterns in the pursuit of high-status, math-intensive careers, such as Computer Science and Engineering, remain stark (National Center for Science and Engineering Statistics, 2023).

Research shows that girls tend to perform as well as boys on basic computation (Fennema et al., 1998; Shen et al., 2016), but several studies have found differences in approaches, with girls more often using concrete, taught strategies (counting blocks, standard algorithms), and boys more often using mental and invented strategies, such as fact retrieval and decomposition (e.g., Carr & Jessup, 1997; Fennema et al., 1998; Shen et al., 2016; Sunde et al., 2020). Though familiar, taught strategies can produce correct solutions, more inventive approaches may pay off when students face nonroutine problems on high-stakes tests or in STEM coursework. However, evidence is lacking on whether early gendered patterns in computation strategies diminish as students age, or if such patterns persist and relate to other math outcomes.

On one hand, strategy differences might narrow during elementary grades (ages 5 to 11), as increased experience can help students align strategy choices with problem characteristics (e.g., Lemaire & Sigler, 1995; Torbeyns et al., 2009). On the other hand, researchers have identified gender differences in adolescents’ strategies on more advanced problems, including a proportional reasoning task (Che et al., 2012) and those on the SAT (Gallagher et al., 2000). If math classroom norms and instruction promote gender roles and rule-following, then gendered patterns in computation approaches could be implicitly encouraged or reinforced, persisting through high school and beyond. Such a process is consistent with Situated Expectancy Value Theory (SEVT; Eccles & Wigfield, 2020), which theorizes that achievement-related choices like strategy choice are the result of a complex web of socializing experiences and individual characteristics.

Across two independent studies, we examine gender differences in computation strategies among high school students (Study 1) and adults (Study 2). We test whether gender differences in strategy use exist in these populations, and if gender and strategy use relate to math performance even after including other variables known to relate to gender and math performance. These studies were initially conducted by two independent research teams, but we combined our studies for this article after becoming aware of key intersections in our foci and findings. While the independence of the two studies means we have different math-related variables, math performance outcomes, and assessment formats, these differences complement each other, as the parallel findings illuminate rarely examined gendered patterns in computation strategies of both adolescents and adults.

Computation Strategy Use

For multi-digit computation, traditional, standard algorithms (e.g., line up the columns, carry the “one”) and decomposition, which involves composing and decomposing numbers based on their meanings (e.g., 19 + 31 = 20 + 30), are common strategies. Decomposition has been promoted in U.S. school math standards (National Council of Teachers of Mathematics, 1989, 2000; National Governors Association Center for Best Practices, 2010), and researchers have linked using decomposition strategies to conceptual understanding of number structure (Cowen et al., 2011; Laski et al., 2014).

Still, although math standards and curricula may recommend alternate strategies, research on prior U.S. math education reforms document that moving teachers away from algorithmic instruction is difficult (e.g., Cohen, 1990). Indeed, Verschaffel and colleagues (2009) argue that standardized tests emphasizing speed and accuracy may encourage the use of routine procedures and inhibit teachers’ emphasis on flexible problem solving, or adaptively choosing among multiple known strategies (Star & Rittle-Johnson, 2008). Thus, U.S. teachers likely continue to prioritize the use of standard, algorithmic strategies when teaching computation.

Age, Strategy Choice, and Math Achievement

Recent scholarship has linked computation strategy use to children’s math performance. Sunde and colleagues (2024) demonstrated that first graders’ strategies on computation items strongly predicted fourth grade math achievement, while Jóelsdóttir and colleagues (2024) linked the use of non-algorithmic strategies on multi-digit computation items to higher math achievement on national tests for third, sixth, and eighth graders. These findings point to computation strategy use as an important indicator in mathematics learning, but do not explain why children use particular strategies.

Evidence suggests that strategy use and flexibility change over time. Scholars have demonstrated that children over time and adults compared to children have increased discrimination in choosing the most efficient strategies in their repertoire (e.g., Caviola et al., 2018; Lemaire & Callies, 2009; Lemaire & Sigler, 1995; Vasilyeva et al., 2015). For example, in a study of second through fourth graders, Torbeyns et al. (2009) found that the use of invented, decomposition computation strategies increased with grade. Similarly, Jóelsdóttir and Andrews (2024) found that sixth and eighth graders tended to exhibit more strategy flexibility than did third graders on arithmetic tasks.

However, recent work also suggests that for computation, growth in strategy flexibility might plateau (Jóelsdóttir et al., 2024) and other studies have found no clear pattern in strategy use by grade (e.g., Van Der Auwera et al., 2022), indicating there is more to understand about the relationship between age and strategy use. In a review of school children’s strategy flexibility, Verschaffel (2024) concluded that conceptual and procedural knowledge can lay the groundwork for strategy flexibility, but many factors shape strategy choice that we do not yet understand, including age and gender.

Gender Differences in Strategy Use

Studies have identified differences in how girls and boys in elementary school solve various types of math problems, in both the United States and abroad (e.g., Carr & Jessup, 1997; Fennema et al., 1998; Hornburg et al., 2017; Sunde et al., 2020; Sunde et al., 2024; Winkelmann et al., 2008). These differences may matter. Although girls tend to do as well as boys on measures of school-taught knowledge (Hyde et al., 2008; Voyer & Voyer, 2014), gender differences in math performance favoring boys are found on unfamiliar problems (Innabi & Dodeen, 2018), including those on the high stakes standardized tests (e.g., Gallagher & De Lisi, 1994).

On computation problems, girls more often use concrete (e.g., counting) procedures and standard algorithms, while boys more often use fact retrieval and decomposition (e.g., Bailey et al., 2012; Carr & Davis, 2001; Carr et al., 1999; Fennema et al., 1998; Imbo & Vandierendonck, 2007; Sunde et al., 2020). Studies with middle school students suggest similar gendered patterns in strategy use for computation to those observed in younger populations (Hickendorff, 2018; Hopkins & Bayliss, 2017; Jóelsdóttir et al., 2024).

These patterns do not mean that girls cannot perform strategies that boys use more. In a longitudinal study, Carr and Alexeev (2011) found that while second-grade boys used mental arithmetic strategies earlier, girls’ arithmetic development generally followed similar trends to boys. Shen and colleagues (2016) found that there were no gender differences in strategy choice among Taiwanese children, although U.S. and Russian boys were more likely than girls to use either decomposition or retrieval over counting on multi-digit arithmetic problems. These results, coupled with at least some evidence of changes in strategy use as students age, suggest that gender differences in strategy use are not fixed and may be shaped by cultural socialization.

Collectively, the literature on computation and gender suggests that U.S. boys’ greater use of retrieval and decomposition strategies begins early and persists through middle school, despite boys and girls generally having the same teachers and math curricular materials. Cross-cultural differences suggest that gendered patterns in strategy use are not innate, so these differences could narrow with additional learning (e.g., math instruction beyond arithmetic) or experience (e.g., real world math, like finances) that come with age. If gender differences in strategy use persist among high school students and adults, and if these strategies relate to math performance in these older populations, then understanding what may influence these differences matters. With this knowledge, interventions with young students as they first develop computation strategies can better target student needs.

Factors That May Relate to Gender Differences in Strategy Use

Although several studies have examined gender differences in strategy use, much less is known about why such differences exist. SEVT (Eccles & Wigfield, 2020) suggests that an individual’s achievement-related choices (e.g., strategy choice) are the result of a complex web of socializing influences and experiences combined with individual differences in values and skills. The SEVT framework is often used to examine gendered outcomes and suggests that cultural beliefs surrounding an individual, including beliefs related to gender, inform their experiences and resultant learning. In this study, we include factors that have long-established relations with gender and math (e.g., mental rotation skills, math anxiety), as well as newer measures with emerging evidence of such relations (e.g., bold problem-solving orientation, teacher-pleasing tendency).

Mental Rotation Skills

Numerous studies have found gender differences favoring males in spatial skills (e.g., Lombardi et al., 2019) as well as relations between spatial skills and both numeric thinking (Harris et al., 2021; Hawes & Ansari, 2020) and math outcomes (Atit et al., 2022). Within spatial skills, mental rotation involves the ability to imagine object rotations in space (Linn & Petersen, 1985) and in the SEVT can be considered a person characteristic.

Researchers have examined links between spatial skills and math problem-solving approaches (Fennema & Tartre, 1985; Tartre, 1990). Computation strategies like decomposition and retrieval have been linked to higher spatial skills (Laski et al., 2013), which makes sense given the spatial nature of these techniques. In advanced math, Wittmann and colleagues (2013) found that some students treat algebraic equation components as spatial objects to be manipulated. These findings relate to Hawes and Ansari’s (2020) argument that spatial representations of numbers and their relationships can facilitate mathematical thinking.

Compared to other spatial skills, mental rotation skills tend to show particularly large gender differences (Voyer, 2011) and have been found to help explain gender differences in math performance (Casey et al., 1995). Importantly, research shows that spatial skills can be improved through instruction and practice, suggesting that though it may be a person characteristic within SEVT, skills in this area are the result of both biological propensities and environmental processes (Cheng & Mix, 2014; Sorby et al., 2013).

Bold Problem-Solving Orientation

To measure students’ tendency to approach problems in inventive ways, as opposed to adhering to more familiar procedures, Lubienski and colleagues (2021) developed a bold problem-solving orientation survey, which assesses students’ self-reported preferences and behaviors when encountering unfamiliar math problems. Given the survey’s focus on interest in, and enjoyment of “bold” approaches, a bold problem-solving orientation can be considered a subjective task value within the SEVT framework. Lubienski et al. found that bold problem-solving orientation is distinct from other constructs commonly used to examine gender differences in math. They also found that middle and high school boys reported “bolder” problem-solving orientations than did girls, and that such orientations predicted better performance on math problems. However, it remains unclear whether bold problem-solving orientations relate to students’ actual strategy choices. Additionally, it is unknown whether students’ “bolder” orientations to mathematical problem solving relate to gender differences in strategies on simpler computation items.

Teacher-Pleasing Tendency

In both the U.S. (Cimpian et. al, 2016) and the U.K. (Jones & Myhill, 2004), teachers have reported girls exhibiting more diligent, compliant classroom behaviors than boys. Scholars have linked conformity to gender stereotypes to gender differences in compliant school behavior (e.g., Heyder, et al., 2021; Willis, 1978). Specific to math, some researchers have posited that socialized expectations for girls to be compliant “good girls” could shape gendered approaches to math, with girls more often using teacher-taught strategies (Hyde & Jaffee, 1998; Lubienski et al., 2021). Thus, girls’ tendency for school compliance may drive girls’ more frequent use of school-taught strategies than boys. We view compliance with teacher expectations as a teacher-pleasing behavior, which fits within SEVT’s goals and self-schemata (e.g., desire to be perceived as a good student), which may indirectly impact students’ math achievement and achievement-related choices through the expectations for success and values it engenders.

Although both low- and high-performing girls exhibit more teacher-expected behaviors than do boys, the link between compliance in school and higher math achievement is much stronger among lower-performing students than higher-performers (Cimpian et al., 2016). Hence, girls’ classroom compliance may help them do well on basic, school-taught material (Catsambis, 1994; Hyde et al., 2008), but a tendency for compliance may have less payoff on non-routine math problems. If teacher-pleasing tendencies relate to the use of traditional computation strategies, then such tendencies could help shape gendered patterns in strategy use and math outcomes.

Math Anxiety and Test Anxiety

Math and test anxiety, which traditionally are considered a subjective task value “cost” in the SEVT framework, represent feelings of nervousness that arise in particular situations: math anxiety while doing math, test anxiety while taking tests (Richardson & Suinn, 1972; Sarason, 1984). Girls and women tend to have higher math and test anxiety than do boys and men (Devine et al., 2012; Else-Quest et al., 2010; Ganley & McGraw, 2016; Hyde et al., 1990; Imbo & Vandierendonck, 2007), and researchers have found that these types of anxieties relate to math performance across development (Barroso et al., 2021; Caviola et al., 2021; Ramirez & Beilock, 2011). Theory suggests that these anxieties may use cognitive resources during math tasks, leading to poorer performance (Carey et al., 2016; Eysenck et al., 2007).

Comparatively little work examines how these anxieties play a role in the relation between gender and strategy use, but what has been done suggests higher levels of anxiety relate to less use of decomposition and retrieval strategies (Imbo & Vandierendonck, 2007; Ramirez et al., 2016). These relationships have not been examined in adolescent and adult populations, nor has test anxiety been examined in relation to computation strategy choices.

Math Confidence

Math confidence sits within the SEVT framework as a form of “self-concept of one’s abilities.” In the United States and internationally, boys often express more math confidence than do girls (Else-Quest et al., 2010). Among U.S. students, gender differences in math confidence tend to be larger than differences in math achievement (Eccles & Wang, 2016; Ganley & Lubienski, 2016). Evidence suggests a reciprocal relationship, as achievement can lead to greater confidence, and gains in confidence can enhance achievement (Ganley & Lubienski, 2016; Marsh et al., 2005). However, it is not clear why or how confidence leads to higher achievement. Perhaps computation strategy choice is a missing link that could illuminate relations among confidence, achievement and gender.

The Present Research

Past research on gendered strategy use is primarily conducted with children. The findings of this research suggest that strategy use may evolve with experience and relate to problem solving performance. Given this, the current studies examine gender differences in multi-digit computation strategies in adolescents (Study 1) and adults (Study 2). Between the two studies, we also explore the roles of several math-related variables in understanding relations among gender, computation strategy use, and math performance. Table S1 in the Supplementary Materials provides a comparative overview of the two studies.

Although the two independent studies differ in terms of the specific measures and math-related variables used, in both studies the first research question tests if gender and the included math-related variables uniquely relate to standard algorithm use (versus primarily decomposition strategies), and if the inclusion of the math-related variables reduces the size of any gender difference in algorithm use. The second research question for both studies tests if gender and algorithm use uniquely relate to math problem-solving performance (Studies 1 and 2) and arithmetic fluency (Study 2 only) after considering the included math-related variables, and if the inclusion of algorithm use and other math-related variables reduces the size of any gender differences in math performance.

The literature review documents that girls use algorithmic-like strategies more often than do boys, that strategy choice on computation relates to math performance for children, and that gendered differences in strategy choice might be socialized preferences. Thus, for the first research question we hypothesize:

• 1a.Gender will relate to algorithm use, with girls and women using the standard algorithm more often than boys and men.
• 1b.The gender relation with algorithm use will remain significant, but diminish in size, when math-related factors are included in the models.

For the second research question, we hypothesize:

• 2a.Gender and algorithm use will uniquely relate to problem-solving performance such that girls and women and those who more often use the standard algorithm will have lower performance. However, these relations will not exist for arithmetic fluency.
• 2b.Gender differences in problem-solving performance will diminish upon inclusion of algorithm use and other math-related variables.

As noted previously, the two studies were conducted independently. The data for Study 1 were collected to develop and investigate a measure of students’ problem-solving orientations (Lubienski et al., 2021). Data from Study 2 were collected to investigate adults’ math anxiety (Hart & Ganley, 2019; Ganley & Hart, in preparation). The independence of the two studies means the study designs are not directly related, which is uncommon in two-study research reports. However, the differences are complementary, and, where results are consistent, provide stronger evidence of underlying relationships among gender, computation strategies, and math-related factors than either individual study could contribute.

Study 1

In Study 1, a subset of the author team examined gender differences in strategy use among high school students, with attention to the role of mental rotation skills, bold problem-solving orientation, teacher-pleasing tendencies, math anxiety, and math confidence. Full details on all measures given, as well as the analytic syntax and outputs for this study are available at https://osf.io/9t674/?view_only=e380533de8f1459caa2c683aae0a161b. All analyses were run using Stata 17/SE.

Study 1 Method

Sample

Participants were 231 students in a U.S. Midwestern public high school. Eighteen students were removed due to missing data or not following instructions, reducing the sample to 213 (116 female, 97 male) students. The final analytic sample was 51% white (non-Latinx), 19% Black, 9% Latinx, 9% Asian or Asian American, 1% Native Hawaiian, Pacific Islander or American Indian, and 11% Multiracial. Two students did not report their race or ethnicity. Students had an average age of 16.2 years (SD = 1.0; n = 9 missing) and were primarily in the first three years of high school: Grade 9 (35%), Grade 10 (24%), Grade 11 (38%), and Grade 12 (3%). Additional sample details are in the Supplementary Materials, which also contains a post-hoc power analysis.

Measures

Gender.

Students were asked to self-identify their gender as “male,” “female,” or “other,” with space to provide a descriptor. Although the terms “male” and “female” tend to be used as biological descriptors, we used these terms to indicate gender, given that “women”/“men” and “girls”/“boys” suggest either older or younger populations than our high school sample.

Item-level Algorithm Use.

Students solved three multiple-choice computation items (Figure A1). We created the items to cover the common operations of addition, subtraction and multiplication, with multi-digit numbers chosen to invite the use of different decomposition techniques or other mental strategies. The diversity of operations and possible strategies in our items means our findings will not generalize broadly to a single operation or strategy but provides more evidence of the propensity for algorithm use, independent of task characteristics.

Students later answered multiple-choice questions about how they had solved each item, with the standard algorithm and other likely strategies available as choices (Figure A2). For each item, “Other” was a choice, with space for students to describe their solution strategy. This format provided three potential sources of information on students’ computation strategies: (a) their self-reported strategy on the multiple-choice item, (b) their written work, and (c) their free-response answer to the “Other” prompt (n = 45, 29, and 45 for the three items, respectively). We identified a student as using an algorithm on an item if any of these data sources had evidence of algorithm use.²

Algorithm Use Count Variable.

We first checked whether gendered patterns in algorithm use varied substantially between the three computation items. Ranges were all within a few percentage points across items (see Figure 1). We thus combined data over the items to create an algorithm use count variable. This variable ranged from 0 to 3 for how many times an algorithm was used. The Supplementary Materials contain additional details related to strategy use, including a report of the frequency of each type of non-algorithm strategy used by gender. Decomposition was overwhelmingly the most common non-algorithm strategy used.

Figure 1. Algorithm Use Percents by Item and Gender (Study 1 & Study 2).

Note. For parsimony, Figure 1 uses male/female gender labels for both Studies 1 and 2.

Mental Rotation Skills.

To measure students’ spatial skills, we used a 3-D mental rotation test (Peters et al., 1995, based on Vandenberg & Kuse, 1978). The scale includes 24 items that students completed during two, three-minute sessions (α = .88). Each item showed a “target object” composed of cubes, and asked students to identify which two of the four other pictured objects were rotations of the target object. Students’ scores were computed by counting the total number of items for which both correct choices were selected.

Bold Problem-Solving Orientation.

We measured students’ bold problem-solving orientation using Lubienski and colleagues’ (2021) 10-item scale (α = .74), averaging across the 10 items. The scale ranges from 1 (Strongly disagree) to 5 (Strongly agree).

Teacher-Pleasing Tendency.

We included an eight-item teacher-pleasing tendency scale (α = .85), focusing on students’ motivations for doing schoolwork (based on Miller et al., 1996, as adapted by Lubienski et al., 2021). To create the final measure, we averaged students’ responses. The scale ranges from 1 (Strongly disagree) to 5 (Strongly agree).

Math Anxiety.

Math anxiety was measured using three items from Ganley and McGraw (2016). For our sample, the Cronbach’s alpha was .60, perhaps due to the low number of items. We computed students’ averages over the three items. The scale ranges from 1 (Strongly disagree) to 5 (Strongly agree).

Math Confidence.

We measured math confidence using a six-item scale (Lubienski et al., 2021) focusing on whether students view themselves as good at math (α = .90). We computed each student’s average over the six items. The scale ranges from 1 (Strongly disagree) to 5 (Strongly agree).

Problem Solving Performance.

Students took a problem-solving assessment consisting of eight multiple-choice math problems shown to have gender differences in national samples: five problems from the SAT (Gallagher, 1992; Gallagher & De Lisi, 1994) and three problems from the eighth-grade National Assessment of Educational Progress. Students had 15 minutes to complete these items. One item was removed because only 8% of students answered it correctly (we would expect 20% by chance). Hence, our final scale contained seven items (α = .65). The low alpha value is consistent with the fact that assessment items were selected because of male-female differences, rather than consistency in the assessed content. We ran a 2-parameter logistic item response theory model to estimate a theta score for each student to account for item difficulty and discrimination. Details of this analysis are in Lubienski et al. (2021).

Procedures

Prior to data collection, consent was obtained from parents and assent was obtained from student participants. During a 50-minute session, students responded to the assessments and surveys in a prescribed order: (1) the problem-solving assessment, (2) the mental rotation skills test, (3) a survey that included the bold problem-solving orientation, teacher-pleasing tendency, math anxiety and math confidence measures, and (4) the three multiple-choice computation items with strategy follow-up questions.

Study 1 Data Analysis

Test the Relation of Gender and Other Math-Related Variables and Algorithm Use

For research question 1, we used hurdle regression with algorithm use count as the dependent variable using methods described by Long and Freese (2014). Hurdle regression is a series of two dependent regressions on the sample: (1) a binary logistic regression predicting the use of an algorithm at least once over never using the algorithm and (2) a zero-truncated Poisson regression predicting students’ additional algorithm use given they have used an algorithm at least once. Hence, each model has two sets of coefficients and standard errors. Our use of hurdle regression reflected our assumption that one distribution governed the choice to use an algorithm at least once (i.e., not have a count of zero) and, once that hurdle was crossed, a different distribution may govern additional algorithm use (i.e., using algorithms 1, 2, or 3 times). Chi-squared goodness-of-fit tests confirmed that the full algorithm use count variable did not follow a Poisson distribution, while the zero-truncated count variable did.

To assess a baseline relationship, in Model 1 we regressed gender and grade (entered as a categorical variable; Grade 9 as the reference category) on algorithm use. In Model 2 we added mental rotation skills, bold problem-solving orientation, teacher-pleasing tendency, math anxiety, and math confidence. For Model 3, we added exploratory interactions with gender for our five additional math-related variables. Significant interactions were investigated by examining the marginal effects of female and male on the dependent variable. The interaction results are discussed in Supplemental Materials.

To assess change in the gender coefficient between the logistic models, we used the framework proposed by Mize and colleagues (2019) for non-linear dependent variables, such as those used in this study. This framework, rather than directly testing regression coefficients, uses marginal values of the independent variable to calculate the average discrete change (ADC) in the dependent variable. In all analyses, after running the models, we calculated the average discrete change (ADC) of the marginal values for each female coefficient, followed by a Wald test to assess whether the ADC difference between models was significant.

Test the Relations Among Gender, Algorithm Use, and Math Performance

To examine the first part of the second research question, which asks whether gender and algorithm use uniquely relate to math performance, we performed Ordinary Least Squares (OLS) regression analysis with robust standard errors using students’ problem-solving performance as the dependent variable. Grade was included in all models. We first entered gender (Model 1) and algorithm use count (Model 2; 0 as the reference category) individually. To examine the unique contributions of these two variables when included together, Model 3 included both variables. To assess whether any relationship between students’ gender and algorithm use to problem-solving performance persisted after including additional explanatory variables, Model 4 included our full set of independent variables. In Model 5 we added the exploratory interactions of female with the five math-related covariates. Significant interactions were examined in the same way as for the first research question. Interaction results are presented in Supplemental Materials. To assess the change in the female regression coefficient between models, we again used the ADC method.

Study 1 Results

Preliminary Analysis

Figure 1 highlights raw gender differences in algorithm use for the three computation items, with 32-35% of males using the standard algorithm on each item, and females over twice as likely to do so (68-72%). In addition, 18% of males used an algorithm on all three problems, while 52% of females did so (Figure 2).

Figure 2.

Study 1: Algorithm Use Count Percent by Gender

Table 1 presents descriptive statistics for the analytic sample on all included variables. Table 2 reports the pairwise correlations between the variables used in these analyses. Consistent with prior research, female students were more likely to use an algorithm, have lower mental rotation skills, bold problem-solving orientation, math confidence, and problem-solving performance, and have higher teacher-pleasing tendency and math anxiety. Algorithm use correlated with lower mental rotation skills, lower problem-solving performance, and higher teacher-pleasing tendency, but did not correlate with bold problem-solving orientation, math anxiety, or math confidence. All of the variables correlated with problem-solving performance. Neither algorithm use nor gender related to the number of computation items answered correctly.

Table 1.

Study 1 Descriptive Statistics

	Mean	SD	Min	Max	Skew	Kurtosis
Algorithm use count	1.61	1.26	0	3	−0.17	1.60
Mental rotation skills	9.58	5.35	0	24	0.51	2.53
Bold problem-solving orientation	3.00	0.52	1.6	4.3	−0.02	2.85
Teacher-pleasing tendency	3.57	0.67	1	5	−0.88	4.67
Math anxiety	3.11	0.86	1	5	0.00	2.52
Math confidence	3.11	0.88	1	5	−0.29	0.77
Problem-solving performance	0.01	0.75	−1.20	1.67	0.36	2.52
Computation items correct	2.70	0.67	0	3	−2.42	8.47

Table 2.

Study 1 Pairwise Correlations with Algorithm Use Count Variable

	Female†	Algorithm use count	Mental rotation skills	Bold problem-solving orientation	Teacher-pleasing tendency	Math anxiety	Math confidence	Problem-solving performance	Grade
Female†	1
Algorithm use count	.43***	1
Mental rotation skills	−.27***	−.30***	1
Bold problem-solving orientation	−.18**	−.10	.22**	1
Teacher-pleasing tendency	.19**	.20**	−.20**	−.13	1
Math anxiety	.21**	.10	−.11	−.08	.20**	1
Math confidence	−.21**	−.09	.19**	.36***	.01	−.53***	1
Problem-solving performance	−.26***	−.35***	.30***	.19**	−.20**	−.19**	.30***	1
Computation items correct	−.08	.04	.17*	.06	−.05	−.09	.17*	.23***	1
Grade	.005	.01	−.12	−.08	−.002	.09	−.05	.0003	−.01

Note. The pairwise sample size is 213 for each correlation. Correlations between female and mental rotation, bold problem-solving orientation, teacher-pleasing tendency, math anxiety, math confidence, and problem-solving theta score and the respective pairwise correlations have been previously reported in Lubienski et al. (2021) for a related sample.;

^†Female is a binary coded indicator taking on a value of 1 for students who chose “Female” on the survey and 0 for those who chose “Male”.

^*p < .05,

^**p < .01,

^***p < .001

Test the Relation of Gender and Other Math-Related Variables and Algorithm Use

Table 3 reports results from the hurdle models for algorithm use. The logistic coefficients represent the change in log odds of using the algorithm at least once versus never using an algorithm for each one-unit change in the associated independent variable. The count coefficients represent the results from the zero-truncated Poisson model. We also report the odds ratios (OR) for the logistic models and the incident rate ratios (IRR) for the zero-truncated Poisson models.

Table 3.

Study 1 Hurdle Models Using Algorithm Use Count as Dependent Variable

	Model 1		Model 2
	Logistic	Count	Logistic	Count
Constant	1.09 (0.29)***	0.79 (0.05) ***	1.20 (0.30)***	0.78 (0.05)***
	OR: 2.97	IRR: 2.20	OR: 3.33	IRR: 2.18
Grade (reference: Grade 9)
10	−0.33 (0.42)	0.09 (0.07)	−0.39 (0.43)	0.10 (0.07)
	OR: 0.72	IRR: 1.09	OR: 0.68	IRR: 1.10
11	−0.21 (0.39)	0.05 (0.06)	−0.30 (0.42)	0.05 (0.07)
	OR: 0.81	IRR: 1.05	OR: 0.74	IRR: 1.06
12	0.23 (0.87)	−0.01 (0.17)	0.01 (0.82)	−0.04 (0.17)
	OR: 1.25	IRR: 0.99	OR: 1.01	IRR: 0.96
Female†	1.83 (0.33) ***	0.17 (0.06) **	1.59 (0.39) ***	0.15 (0.07) *
	OR: 6.23	IRR: 1.18	OR: 4.93	IRR: 1.16
Mental rotation			−0.08 (0.03) *	−0.01 (0.01) *
			OR: 0.92	IRR: 0.99
Bold problem-solving orientation			0.02 (0.41)	−0.01 (0.06)
			OR: 1.02	IRR: 0.99
Teacher-pleasing tendency			0.78 (0.30) **	−0.07 (0.05)
			OR: 2.18	IRR: 0.93
Math anxiety			−0.07 (0.25)	0.02 (0.04)
			OR: 0.93	IRR: 1.02
Math confidence			0.07 (0.26)	0.02 (0.04)
			OR: 1.07	IRR: 1.02

^*p < .05,

^**p < .01,

^***p < .001;

^†Female is a binary coded indicator taking on a value of 1 for students who chose “Female” on the survey and 0 for those who chose “Male”.

In logistic Model 1, the odds a female student used the algorithm at least once were 6.23 times the odds of a male student using the algorithm at least once. The unique relation between gender and using an algorithm at least once remained when all potential explanatory variables were included (Model 2), with the odds a female used an algorithm at least once becoming 4.93 times the odds of a male doing so. Lower mental rotation skills and a higher teacher-pleasing tendency also predicted algorithm use in Model 2. The reduction of the ADC for female between Models 1 and 2 was significant (ADC difference = 0.070, p = .016).

Results from the zero-truncated Poisson models indicate that being female uniquely related to using the algorithm additional times given an algorithm had been used at least once, and this relation did not significantly change between Models 1 and 2 (ADC difference = 0.031, p = .631). Higher mental rotation skills negatively related to using the algorithm additional times. The results of Model 3 with gender interactions are in the Supplementary Materials (Table S4).

Test the Relations Among Gender, Algorithm Use, and Math Performance

Table 4 reports regression results examining the relation between gender, algorithm use count, and problem-solving performance. Individually, both gender (Model 1) and increased use of the algorithm (Model 2) significantly related to lower problem-solving performance. The frequency of algorithm use mattered: compared to never using the algorithm, using the algorithm once did not relate to problem solving performance, but using it twice or three times related to lower problem-solving performance. When included together, using an algorithm three times uniquely, negatively related to problem solving performance, but gender was no longer significant (Model 3). The 46% reduction between Model 1 and 3 in the relation between female and problem-solving performance was statistically significant (ADC difference = −0.178, p = .002).

Table 4.

Study 1 Linear Regressions Predicting Problem Solving Performance

	Model
	1	2	3	4
Constant	0.01 (0.09)	0.31* (0.12)	0.24 (0.13)	0.16 (0.13)
Grade (reference: Grade 9)
10	0.004 (0.13)	0.02 (0.14)	0.02 (0.13)	0.01 (0.13)
11	0.05 (0.12)	0.05 (0.11)	0.06 (0.11)	0.11 (0.10)
12	−0.41 (0.26)	−0.37 (0.28)	−0.39 (0.28)	−0.29 (0.30)
Female†	−0.40*** (0.10)		−0.22 (0.12)	−0.09 (0.11)
Algorithm use count (reference: 0 uses)
One		−0.15 (0.17)	−0.10 (0.18)	0.01 (0.18)
Two		−0.34* (0.13)	−0.26 (0.14)	−0.19 (0.14)
Three		−0.61*** (0.12)	−0.49*** (0.14)	−0.38** (0.14)
Mental rotation				0.02 (0.01)
Bold problem-solving orientation				0.05 (0.11)
Teacher-pleasing tendency				−0.14* (0.07)
Math anxiety				0.01 (0.07)
Math confidence				0.21** (0.07)
	213	213	213	213
	.08	.13	.14	.24

^*p < .05,

^**p < .01,

^***p < .001;

^†Female is a binary coded indicator taking on a value of 1 for students who chose “Female” on the survey and 0 for those who chose “Male”.

These patterns largely remained with the inclusion of our additional explanatory variables: using an algorithm three times retained a unique negative relation with problem-solving performance while gender remained non-significant (Model 4). The reduction in the relation between female and problem-solving performance between Models 3 and 4 was significant (ADC difference = −0.131, p = .002). In addition, higher confidence and lower teacher-pleasing tendency related to higher problem-solving performance. The results of Model 5, which included interactions with gender, are in the Supplementary Materials (Table S5).

Study 1 Discussion

Consistent with Hypothesis 1a, the findings show a persistent positive relationship between gender and algorithm use. Consistent with Hypothesis 1b, lower mental rotation skills uniquely predicted both use of an algorithm at all and additional algorithm use, while higher teacher-pleasing tendencies uniquely predicted using the algorithm at least once. Additionally, inclusion of the math-related variables significantly reduced the strength of the relation between gender and algorithm use, with the odds of a female student using the algorithm at least once changing from 6.23 times the odds of a male to 4.93. The fact that the findings differed for predicting use of an algorithm at all versus additional use of the algorithm suggest that our theoretical assumption that different factors govern these processes was correct.

Consistent with Hypothesis 2a, more frequent algorithm use related to lower problem-solving performance, primarily when comparing students who always used the algorithm to those who never used an algorithm. As predicted, algorithm use maintained a unique negative relation with problem-solving performance and this unique relation persisted after the inclusion of algorithm use and other math-related variables in subsequent models. Consistent with Hypothesis 2b, the relation between gender and problem-solving performance diminished after including other math-related variables. In the final models, lower math confidence, higher teacher-pleasing tendency, and using the algorithm three times compared to never were uniquely related to lower problem-solving performance.

Overall, females in Study 1 used algorithms far more often than did males, and algorithm use persistently predicted lower problem-solving performance. However, there are limitations to what we can conclude. Some students in this relatively modest sample may have used algorithmic strategies learned in school due to the school setting in which assessments were administered and their limited real-world computational experiences. Additionally, the computation items were on paper, which may have prompted more students to use an algorithm, and the items were multiple choice which might have prompted some students to guess instead of computing the answer. In light of these limitations, Study 2 provides a useful complement to Study 1.

Study 2

Study 2 addresses the same questions as Study 1, but with a large sample of adults and different math-related variables, math performance outcomes, and assessment format. In this study we (a subset of the author team) examined two potential related factors, math anxiety and test anxiety, and included a problem-solving measure and a fluency measure. By testing similar questions in this study, we can assess whether the same gendered patterns hold despite different design elements.

The design and analysis for Study 2 were not preregistered, but the data are from a preregistered data collection, with details available in Hart and Ganley (2019). Analytic syntax, information on the assessments administered and data that we have permission to share are available at https://osf.io/9t674/. All analyses were conducted in R, except the tests of differences in the effect of gender between models, which were conducted in Stata 17/SE.

Study 2 Method

Sample

We recruited 1,000 online survey participants using two strategies: (a) 875 participants from Amazon’s Mechanical Turk (MTurk) and (b) 125 participants from social media. Recruitment via both methods took place over the same two-week period. The Supplementary Materials include additional details on the recruitment of the sample.

A total of 190 participants were removed for having missing data on at least one analytic variable, resulting in an analytic sample of 810 individuals. Of those removed, 185 were missing on algorithm use (explained in the next section). In the analytic sample, 59% of participants identified as women and 41% identified as men. Participants had an average age of 37.1 years (SD = 12.2). In regard to ethnicity, 5% of participants identified as Hispanic/Latino. In regard to race, 1% identified as American Indian or Alaska Native, 6% identified as Asian, 9% identified as Black or African American, less than 1% identified as Native Hawaiian or Other Pacific Islander, 82% identified as White, and 2.1% identified as Multirace. For highest education level, 56% had a bachelors degree or higher. Additional education details and demographic information for the full sample are in the Supplementary Materials.

Measures

Gender.

Participants indicated whether they were a man or a woman. They could also select Prefer not to answer, which was coded as missing for this study (n = 2).

Algorithm Use.

Participants were asked to solve 125 + 238 using mental math and to describe their solution strategy in a text box within the survey. We chose this item to support use of a variety of strategies as (a) 125 is an “easier” number to work with given how U.S. currency is structured, and (b) the sum requires regrouping, which makes visualizing the standard algorithm more challenging, thus incentivizing alternative methods. That said, addition is a simpler algorithm than those for other operations, so standard algorithm use remained a likely strategy.

Responses were coded for the strategy used. After an iterative coding process, each response was ultimately assigned one of four possible strategies: (a) standard algorithm (non-ambiguous), (b) standard algorithm (probable), (c) decomposition, or (d) missing. Of the 185 participants coded as missing, 9 had a missing explanation, 12 ignored instructions, and 164 had insufficient information. These codes were mutually exclusive. Details of the coding process and scheme, including examples, can be found in the Supplementary Materials.

After coding was complete, we created an algorithm use variable called standard algorithm use indicator to use in analyses wherein a value of 1 was given if the reported strategy was identified as standard algorithm (non-ambiguous) or standard algorithm (probable), and 0 if the reported strategy was decomposition.

Math Anxiety.

Participants completed the 12-item Math Anxiety Rating Scale-Revised (Hopko, 2003; α = .94), responding to each item from 1 (low anxiety) to 5 (high anxiety). We computed the average of the items for each participant.

Test Anxiety.

Participants completed four items from the Cognitive Test Anxiety scale (Cassady & Finch, 2014; α = .92). Responses were on a scale from 1 (not at all typical of me) to 4 (very typical of me). We averaged the items for each participant.

Arithmetic Fluency.

Participants were given one minute to complete as many of 48 arithmetic items as they could. These items required participants to add, subtract, or multiply two one-digit numbers. The items were developed for this project through a random number generator, which selected from numbers 0 to 9. Items were designed such that no subtraction items resulted in a negative value. Each participant’s score was the number of the 48 items answered correctly (α = .96).

Probability Knowledge.

Participants completed the adaptive, two- to three-item Berlin Numeracy Test, involving probability and proportional reasoning (e.g., dice chances; Cokely et al., 2012). This measure was administered and scored according to the directions of the measure, to create four leveled groups given values of 1, 2, 3, and 4, with 1 being the lowest performing group and 4 being the highest.

Covariates.

We used self-reported age (in years) and educational attainment (categories outlined in Participants) as continuous covariates. Given educational attainment could be argued to be categorical, we also ran analyses with a series of dummy codes and present those results in the Supplementary Materials (Tables S17 to S20). Any differences in findings are mentioned in the Results.

Procedure

The online survey took 32 minutes to complete, on average. The questions were in a set order: informed consent, the computation problem, arithmetic fluency assessment, probability knowledge test, math anxiety survey, and demographic questions.

Study 2 Analysis

Test the Relation of Gender and Other Math-Related Variables with Algorithm Use

To examine which variables uniquely relate to using the standard algorithm, we conducted a series of binary logistic regressions with the standard algorithm use indicator as the outcome. Age and educational attainment were included as covariates in all models. Model 1 tested the association between gender and standard algorithm use. Model 2 included gender and both math and test anxiety. Model 3 included exploratory gender interactions with math anxiety and test anxiety. To assess whether the relation between gender and algorithm use was significantly reduced when math and test anxiety were included, we used the same methods described in Study 1.

Test the Relations Among Gender, Algorithm Use, and Math Performance

To test whether gender and algorithm use relate to math performance on their own, and with math and test anxiety added, we conducted a series of analyses with two different measures of math performance as outcomes: arithmetic fluency and probability knowledge. As the arithmetic fluency variable is continuous, we used OLS regression when predicting this outcome. The probability knowledge measure categorizes respondents into four ordinal numeric categories, with higher numbers corresponding to better performance. Not all the model assumptions for an ordinal regression analysis were met. Therefore, we used multinomial logistic regression for models predicting probability knowledge.

Across outcomes and models, age and educational attainment were included as covariates. Model 1 includes gender, Model 2 includes algorithm use, Model 3 includes both gender and algorithm use, Model 4 includes gender, algorithm use, math anxiety, and test anxiety, and Model 5 includes exploratory interactions between gender and algorithm use, math anxiety, and test anxiety. To assess whether any relation between gender and arithmetic fluency significantly reduced after including standard algorithm use, math anxiety, and test anxiety, we used the same methods described in Study 1. Given the categorical structure of the probability knowledge outcome, we were unable to find a clear method for testing differences in the gender coefficient between models.

Study 2 Results

Preliminary Analyses

Table 5 presents descriptive statistics for the analytic sample (n = 810). Descriptives for the full sample are in Table S13 of the Supplementary Materials. The vast majority (95%) of participants obtained the correct answer for the problem regardless of their reported strategy. Figure 1 shows that females were 50% more likely than males to use an algorithm (69% of females compared to 46% of males).

Table 5.

Study 2 Descriptive Statistics for the Analytic Sample

	% Responses	Mean	SD	Skew	Kurtosis
Woman	58.5%
Strategy use
Reported strategy
Standard algorithm (non-ambiguous)	53.6%
Standard algorithm (probable)	5.8%
Decomposition	40.6%
Standard algorithm use indicator	59.4%
Correctly answered computation problem	94.6%
Math anxiety		2.26	0.94	0.62	−0.37
Test anxiety		1.77	0.83	1.03	0.22
Arithmetic fluency		31.49	10.72	−0.05	−1.01
Probability knowledge
Lowest quartile	38.6%
Second quartile	23.3%
Third quartile	14.2%
Top quartile	23.8%
Age		37.09	12.19	0.72	−0.28
Educational Attainment		5.56	1.57	0.12	−1.00

Note. n = 810 except for computation problem correct, where n = 809.

Table 6 displays correlations among variables within the analytic sample. Women were more likely to use the standard algorithm, had higher math and test anxiety, and had lower scores on the math performance measures (though there was no difference in the proportion of women in the third compared to the highest quartile of probability knowledge). Using the standard algorithm was correlated with higher math and test anxiety and lower arithmetic fluency, and those who used the standard algorithm were more likely to be in the first, second, or third quartile of probability knowledge compared to the highest. Neither gender nor standard algorithm use correlated with accuracy on the computation problem.

Table 6.

Study 2 Pairwise Correlations within Analytic Sample

	Woman	Standard algorithm use indicator	Math anxiety	Test anxiety	Arithmetic fluency	Probability knowledge – lowest quartile	Probability knowledge – 2nd quartile	Probability knowledge – 3rd quartile	Computation item correct	Age
Woman	1
Standard algorithm use indicator	.23***	1
Math anxiety	.26***	.11**	1
Test anxiety	.17***	.14***	.64***	1
Arithmetic fluency	−.11**	−.11**	−.23***	−.21***	1
Probability knowledge – lowest quartile†	.21***	.19***	.37***	.29***	−.21***	1
Probability knowledge – 2nd quartile†	.21***	.14***	.22***	.11**	−.11**	---	1
Probability knowledge – 3rd quartile†	.07	.07*	.14***	.05	−.08*	---	---	1
Computation item correct	−.06	−.02	−.09**	−.10**	.03	−.08*	−.08*	−.03
Age	.09*	.02	−.01	−.11**	−.14***	.02	.04	−.06	.05
Educational Attainment	−.04	−.06	−.15***	−.20***	.11**	−.15***	−.03	−.04	.07*	.03

Note.

^*p < .05,

^**p < .01,

^***p < .001;

Relations among woman, math anxiety, test anxiety, arithmetic fluency, and probability knowledge have been previously reported in Hart and Ganley (2019) or Ganley and Hart (in preparation) for the full sample; n = 810 for all correlations except correlations with computation problem correct where n = 809.;

^†For probability knowledge, we report partial correlations covarying out the other dummy codes using the highest (fourth) quartile as the reference group

Test the Relation of Gender and Other Math-Related Variables with Algorithm Use

Table 7 reports results from the logistic regression analyses predicting the standard algorithm use indicator. The odds of a woman using the algorithm (versus decomposition) were 2.61 times the odds of a man using the algorithm, which was statistically significant (Model 1). When math and test anxiety were added (Model 2), women and people with higher test anxiety were more likely to use the standard algorithm, but math anxiety was not a significant predictor. Between the two models, the odds of a woman reporting algorithm use (versus decomposition) went from 2.61 to 2.46 times the odds of a man using the algorithm. The inclusion of math and test anxiety in Model 2 did not significantly change the relation between gender and algorithm use (ADC difference = 0.016, p = .109). There were no significant interactions in Model 3 (Table S14 in the Supplemental Materials).

Table 7.

Study 2 Results of Logistic Regression Analysis Predicting Standard Algorithm Use Indicator

	Model
	1	2
Constant	0.20 (0.35)	−0.44 (0.43)
Age	0.0006 (0.006)	0.002 (0.006)
	OR: 1.001	OR: 1.003
Educational Attainment	−0.07 (0.05)	−0.04 (0.05)
	OR: 0.93	OR: 0.96
Woman	0.96 (0.15) ***	0.90 (0.15) ***
	OR: 2.61	OR: 2.46
Math anxiety		−0.04 (0.11)
		OR: 0.96
Test anxiety		0.30 (0.12) *
		OR: 1.35
Woman*Math anxiety
Woman*Test anxiety
Nagelkerke R2	.074 ***	.087 ***

^*p < .05,

^**p < .01,

^***p < .001

Test the Relations Among Gender, Algorithm Use, and Math Performance

Arithmetic Fluency.

In the regression analyses with arithmetic fluency as the outcome, both gender alone and the standard algorithm use indicator alone significantly related to arithmetic fluency (Table 8). Specifically, women and those who used the standard algorithm both completed about two fewer arithmetic items correctly than did men (Model 1) or decomposition users (Model 2). When included in a model together (Model 3), both gender and standard algorithm use maintained unique relations with arithmetic fluency. When math and test anxiety were added in Model 4, standard algorithm use, but not gender, still had a significant negative relation with arithmetic fluency, as did math and test anxiety, with higher scores on each associated with lower arithmetic fluency scores. Tests of the change in the ADC for woman showed a significant decrease both between Models 1 and 3 (ADC difference = −0.433, p = .023) and between Models 3 and 4 (ADC difference = −1.100, p < .001). Note that when educational attainment was modeled as a set of dummy codes, the gender difference in Model 3 and the algorithm use differences in Model 4 went from being just barely significant (ps = .049) to nonsignificant (ps = .053). There were no significant interactions in Model 5 (Table S15 in the Supplemental Materials).

Table 8.

Study 2 Regressions Predicting Arithmetic Fluency

	Model
	1	2	3	4
Constant	32.61*** (1.79)	33.06*** (1.81)	33.63*** (1.83)	40.91*** (2.13)
Age	−0.12*** (0.03)	−0.12*** (0.03)	−0.12*** (0.03)	−0.13*** (0.03)
Educational Attainment	0.78*** (0.24)	0.76** (0.24)	0.75** (0.24)	0.48* (0.24)
Woman	−1.95** (0.75)		−1.52* (0.77)	−0.42 (0.78)
Standard algorithm use indicator		−2.24** (0.75)	−1.89* (0.77)	−1.50* (0.76)
Math anxiety				−1.61** (0.51)
Test anxiety				−1.39* (0.58)
Woman*Standard algorithm use indicator
Woman*Math anxiety
Woman*Test anxiety
R2	.041***	.043**	.048**	.094***

^*p < .05,

^**p < .01,

^***p < .001

Probability Knowledge.

In the multinomial regression analyses with probability knowledge as the outcome, we used the highest (fourth) quartile as the reference group. In the model with just gender (Model 1; Table 9), women were more likely than men to be in the lowest or second quartile of probability knowledge scores compared to the highest quartile, but there was no gender difference for the third versus the highest quartile. In the model with only standard algorithm use (Model 2), participants who used the standard algorithm were more likely to be in the lower three quartiles than in the highest quartile. When gender and standard algorithm use were included together (Model 3), the patterns from Models 1 and 2 remained with the exception that there was no longer a difference between the third versus highest quartile in standard algorithm use. With math and test anxiety added (Model 4), the patterns for gender and standard algorithm from Model 3 remained, and those higher in math anxiety were more likely to be in the lowest, second, and third quartiles than in the highest quartile. Those with higher test anxiety were no more or less likely to be in any quartile compared to the highest quartile. Given the modeling approach, we could not test whether including the additional variables reduced the relation between gender and performance. However, between Models 1 and 4, the coefficient for women in the lowest quartile compared to the highest quartile was essentially halved. There were no significant interactions in Model 5 (Table S16 in the Supplemental Materials).

Table 9.

Study 2 Results of Multinomial Regression Analyses for Probability Knowledge

	Model
	1	2	3	4
Highest Quartile vs. Lowest Quartile
Constant	1.24 (0.45)**	1.12 (0.46)*	0.83 (0.47)	−2.16 (0.61)***
Age	0.002 (0.008)	0.005 (0.008)	0.002 (0.008)	0.008 (0.009)
	OR: 1.002	OR: 1.004	OR: 1.002	OR: 1.01
Educational Attainment	−0.25 (0.06) ***	−0.25 (0.06) ***	−0.25 (0.06) ***	−0.17 (0.07) **
	OR: 0.78	OR: 0.78	OR: 0.78	OR: 0.84
Woman	1.07 (0.19) ***		0.91 (0.20) ***	0.52 (0.21) *
	OR: 2.94		OR: 2.50	OR: 1.68
Standard algorithm use indicator		1.00 (0.19) ***	0.82 (0.20) ***	0.79 (0.21) ***
		OR: 2.73	OR: 2.28	OR: 2.21
Math anxiety				1.06 (0.17) ***
				OR: 2.88
Test anxiety				0.19 (0.18)
				OR: 1.21
Highest Quartile vs. Second Quartile
Constant	−0.52 (0.52)	−0.42 (0.52)	−0.93 (0.19)	−2.42 (0.66)***
Age	0.005 (0.009)	0.008 (0.009)	0.005 (0.009)	0.008 (0.009)
	OR: 1.01	OR: 1.01	OR: 1.01	OR: 1.01
Educational Attainment	−0.06 (0.07)	−0.06 (0.07)	−0.06 (0.07)	−0.02 (0.07)
	OR: 0.94	OR: 0.94	OR: 0.94	OR: 0.98
Woman	1.21 (0.22) ***		1.10 (0.22) ***	0.86 (0.23) ***
	OR: 3.36		OR: 3.01	OR: 2.35
Standard algorithm use indicator		0.78 (0.21) ***	0.57 (0.22) **	0.58 (0.22) **
		OR: 2.19	OR: 1.77	OR: 1.79
Math anxiety				0.87 (0.18) ***
				OR: 2.38
Test anxiety				−0.16 (0.20)
				OR: 0.86
Highest Quartile vs. Third Quartile
Constant	0.43 (0.58)	0.33 (0.58)	−0.88 (0.19)	−0.77 (0.72)
Age	−0.02 (0.01)	−0.02 (0.01)	−0.02 (0.01)	−0.02 (0.01)
	OR: 0.98	OR: 0.98	OR: 0.98	OR: 0.98
Educational Attainment	−0.09 (0.08)	−0.08 (0.08)	−0.08 (0.08)	−0.07 (0.08)
	OR: 0.92	OR: 0.92	OR: 0.92	OR: 0.93
Woman	0.45 (0.24)		0.37 (0.24)	0.19 (0.25)
	OR: 1.58		OR: 1.45	OR: 1.20
Standard algorithm use indicator		0.48 (0.24) *	0.41 (0.24)	0.43 (0.25)
		OR: 1.62	OR: 1.51	OR: 1.54
Math anxiety				0.81 (0.20) ***
				OR: 2.24
Test anxiety				−0.36 (0.23)
				OR: 0.69

^*p < .05,

^**p < .01,

^***p < .001

Study 2 Discussion

Similar to Study 1, and consistent with Hypothesis 1a, of those who reported an interpretable strategy to compute 125 + 238, women used the standard algorithm significantly more often than did men (69% to 46% respectively). With respondents instructed to compute mentally, the fact that so many, especially women, performed the algorithm in their head is striking given the challenge of “carrying the one” mentally. When considered together, women and those with higher test anxiety were more likely to use the standard algorithm, but math anxiety did not matter. Contrary to Hypothesis 1b, the inclusion of math and test anxiety did not diminish gender differences in algorithm use.

We had anticipated that gender and algorithm use would have unique relations with probability knowledge, but not with arithmetic fluency (Hypothesis 2a), and that we would see reductions across models in the gender relation only with the probability knowledge measure (Hypothesis 2b). However, we found that men performed better than women in both arithmetic fluency and probability knowledge. Consistent with Hypothesis 2b, the unique gender relation was not persistent across covariates as it became nonsignificant either when algorithm use was added or when math and test anxiety were added depending on whether educational attainment was modeled as continuous or categorical. Standard algorithm use negatively related to arithmetic fluency across all models (except the last model but only when educational attainment was categorical), and the gender difference decreased in size when algorithm use was included and decreased further upon adding math and test anxiety. Women and those using the algorithm had lower probability knowledge, as did those with higher math anxiety, but not test anxiety.

Overall, among the adult participants in Study 2, when accounting for age, educational attainment, and math and test anxiety, women were more likely to use the standard algorithm and have lower probability knowledge, and those who used a standard algorithm had slightly lower arithmetic fluency and probability knowledge.

General Discussion

Despite different populations, variables, and data collection methods, the results from Studies 1 and 2 follow similar patterns related to strategy use for computation problems, with both adolescent girls and women using algorithmic strategies far more often than their male counterparts. For each of the three items in Study 1, the percent of males who used an algorithm ranged from 32% to 35%. Females were over twice as likely to do so (68-72%). Moreover, only 18% of males used an algorithm on all three problems, compared to 52% of females. The pattern was similar, but less pronounced in Study 2 with 46% of males versus 69% of females using the algorithm, perhaps because of the difference in age or task difficulty.

Gender differences in algorithm use persisted even after including other key factors related to gender and math. Our results are consistent with prior studies with younger students (e.g., Bailey et al., 2012; Jóelsdóttir et al., 2024; Sunde et al., 2020) and suggest these differences persist into older adolescence and adulthood despite increased time since learning computation, and despite gaining more varied math experiences. Consistent with emerging research on the link between computation strategy and math achievement in elementary and middle school students (Jóelsdóttir et al., 2024; Sunde et al., 2024), in both studies algorithm use uniquely, negatively related to problem-solving performance.

The SEVT (Eccles & Wigfield, 2020) suggests that achievement-related choices and performance, including strategy choice, are a function of socializing experiences informed and influenced by personal characteristics, internal values, and feedback loops. Given that gendered differences in math strategy use are not universal across international contexts (e.g., Shen et al., 2016), it might be that U.S. gender norms conveying math as a male domain (e.g., Leyva, 2017), contribute to the gendered patterns in algorithm use observed here. In the sections that follow we explore in more detail the patterns in our findings that point to possible explanations for our results.

Relation of Gender and Other Math-Related Variables to Algorithm Use

As discussed in the previous section, and consistent with Hypothesis 1a, females were more likely to use algorithms in both studies. We then examined the extent to which this difference diminished with the inclusion of other math-related variables (Hypothesis 1b). Our findings were mixed. In Study 1, lower mental rotation skills and higher teacher-pleasing tendencies related to algorithm use and the relation between gender and algorithm use diminished with their inclusion. In contrast, in Study 2, although increased test anxiety uniquely related to algorithm use, the relation between gender and algorithm use was not significantly diminished by its inclusion.

Previous work has linked spatial skills and numeric thinking (e.g., Hawes & Ansari, 2020; Harris et al., 2021), so it makes sense that those with lower mental rotation skills would use algorithms more often. These results suggest that early work to develop spatial skills could diversify girls’ strategy choices, especially given strong evidence that spatial skills can improve with training (Cheng & Mix, 2014; Uttal et al., 2013). The results for teacher-pleasing tendencies predicting algorithm use are intriguing. The relation to algorithm use may point to a key, missing link, illuminating a potential path within the SEVT framework between socialization and gendered patterns in mathematics achievement.

Bold problem-solving orientation, math confidence, and math anxiety (in both studies), did not relate to algorithm use. The lack of relation involving bold problem-solving orientation may seem puzzling but could be due to the lack of alignment between this study’s computation items and bold problem-solving orientation’s focus on approaches to unfamiliar problems (Lubienski et al., 2021). The lack of relation between confidence and algorithm use could be due to students having diverse (including procedural) views of what it means to be “good at math.”

The math anxiety result is surprising as math anxiety has a strong relation with gender and math outcomes (e.g., Else-Quest et al., 2010; Ganley & McGraw, 2016; Imbo & Vandierendonck, 2007) and has been previously found to predict strategy use, albeit with children (e.g., Ramirez et al., 2016). Math anxiety also conceptually seems like a compelling reason why someone might use a familiar strategy like an algorithm. It might be that the math anxiety measures used, which had low reliability in Study 1 (likely due to the low number of items) and a high correlation with test anxiety in Study 2, may mask this relation in our samples. Given that a substantial part of the stark gender difference in algorithm use remains unexplained, variables not considered here likely also contribute to these differences.

Ultimately, the findings that greater test anxiety and teacher-pleasing tendency uniquely related to more algorithm use, when most of our math-specific affective factors from the SEVT’s subjective task value component did not, may indicate that algorithm use has more to do with the desire to be viewed as correct or reliable in general, rather than with math-specific affect, at least for U.S. adolescents and adults. Ultimately, in both studies, females used algorithms at a much higher rate than males even when accounting for all other variables in the models.

Relation of Gender and Algorithm Use to Math Performance

Consistent with Hypothesis 2a, in both studies, females and those using algorithms more (two or three times in Study 1; at all in Study 2) had lower math problem-solving performance, which is consistent with previous research (e.g., Innabi & Dodeen, 2018; Jóelsdóttir et al., 2024; Sunde et al., 2024). Contrary to our hypothesis, being female and greater algorithm use also negatively related to adults’ arithmetic fluency (Study 2), which differs from prior research with children finding no gender differences in computation performance (Fennema et al., 1998; Shen et al., 2016). Notably, in Study 1 the use of algorithms on all three items negatively predicted problem-solving performance, while occasional use did not. This may indicate that occasional algorithm use is a marker of strategic, flexible approaches to computation (e.g., Star & Rittle-Johnson, 2008).

Hypothesis 2b posited that gender differences in math performance would diminish upon inclusion of algorithm use and other math-related variables. Our findings in both studies were consistent with this hypothesis. In Study 1, the gender difference in performance decreased and became nonsignificant after including algorithm use, and decreased further upon the inclusion of additional variables, most notably teacher-pleasing tendency and math confidence (both uniquely related to performance). In Study 2, we found a parallel pattern for arithmetic fluency. These results suggest that some of the gender difference in these math performance measures are related to the fact that females more often use algorithms, that they had lower math confidence and higher teacher-pleasing tendencies (Study 1), and that they had higher math and test anxiety (Study 2). Results with the probability knowledge assessment in Study 2 showed a similar pattern, but gender remained a significant predictor throughout the models, suggesting a continued unique impact of gender that is unexplained by algorithm use and math and test anxiety. This contrast between the problem-solving and fluency measures in Study 2 is consistent with findings that gender disparities are larger on novel problems than on school-based assessments (Hyde et al., 2008).

One other interesting finding to consider is that in Study 2, math anxiety related to both math performance variables, but only test anxiety related to the use of algorithmic strategies (research question 1). This suggests some specificity in how these two types of anxiety relate to algorithm use and math achievement.

Overall, the results of Studies 1 and 2 suggest that algorithm use, or factors related to their use, may shape the development of students’ mathematical problem-solving skills and could have lasting effects on math performance. The studies reveal stark gender differences in computational strategies and suggest that girls’ and women’s greater use of algorithms may contribute to gender differences in arithmetic fluency and more advanced mathematical problem solving.

Limitations

The usual caution against drawing causal conclusions from correlations applies here. Additionally, caution about generalization of findings is important, given the studies’ non-random U.S. samples. Prior results suggest that some patterns found here may look different outside of the United States (Shen et al., 2016). Additional research using more representative samples from the U.S. and other countries would benefit the field, with samples sufficiently powered to test for small effects and interactions with key variables. We also did not probe gender beyond binary categories. Considering gender in more nuanced ways could shed new light on factors underlying gendered patterns in computation strategies.

Across the two studies, only four computation items were given, each involving whole-number addition, subtraction or multiplication. Gender patterns in algorithm use might differ with more complex items. Also, we did not assess whether the participants could use alternative strategies, and so the extent to which gender differences in strategy use are due to preference versus proficiency is unclear.

Finally, we must also caution against definitive conclusions about the lack of importance of variables that showed no unique relation with algorithm use here. For example, Study 1’s three-item math anxiety scale had relatively low reliability (α = .60), and Study 2’s measure of algorithm use involved only one item. More extensive measures with higher reliability might reveal relations not detected in these studies.

Implications for Future Research

Despite limitations, the striking gender differences in algorithm use among the U.S. students and adults in these studies are concerning. While there is nothing strategically incorrect about using algorithms, the use of decomposition strategies has been linked to mathematical reasoning (Casey et al., 2017), and in this research algorithm use persistently, negatively related to both math problem-solving performance and basic-fact fluency. More research is needed to determine if, indeed, the link between algorithmic approaches and problem-solving performance is causal. If it is, then then additional work to promote less reliance on algorithms and to address gender differences in strategy use is needed for improving students’ problem-solving skills and narrowing gender disparities in mathematics outcomes.

Our findings that both teacher-pleasing tendency and test anxiety uniquely related to algorithm use, suggest that future research should consider whether girls’ socialization might foster the tendencies that are manifested in these variables (Eum & Rice, 2011). For example, research should examine whether gender differences in strategy use are due to choice or proficiency differences. Such findings could inform interventions to increase girls’ strategy flexibility, including knowledge of multiple strategies and using the most appropriate method for a given problem (Star & Rittle-Johson, 2008; Verschaffel, 2024). Alternatively, perfectionist tendencies have been observed in some students while solving computation problems (e.g., Hecht, 2006; Siegler, 1988). Investigating whether girls’ fears of getting the wrong answer or of using the “wrong” strategy, contribute to their algorithm use is also a potentially rich future direction.

Lastly, given that the gender difference in algorithm use decreased after covarying mental rotation skills in Study 1, mental rotation skills may be a lever for addressing gendered patterns in problem solving. However, further research should investigate whether the relation between spatial skills and computation approaches is causal. If so, then given the malleability of spatial skills (Cheng & Mix, 2014; Uttal et al., 2013), interventions designed to enhance those skills should be pursued with young children early, before computation learning begins.

Conclusion

Despite the differences between the two studies, the results were consistent, with females markedly more likely to use algorithms than were males, in both high school and adult samples.

Our gender-focused analyses add to a small but consistent set of studies indicating that girls tend to approach computational tasks more algorithmically than boys. Additionally, our results suggest that such differences may persist into adulthood and relate to gender differences in solving mathematical problems. Given that algorithm use was persistently, negatively related to math performance in both studies, the magnitude of gender differences in strategy use found here is concerning. The unique relation of algorithm use with mental rotation skills, teacher-pleasing tendency and test anxiety point to specific gendered socialization patterns that might need to be disrupted to address gender differences in mathematics outcomes. Intervening early and deeply in this domain could be a critical lever for improving outcomes for girls and women throughout the math pipeline.

Appendix

Study 1 Computation Item and Strategy Measures

Figure A1.

Multiple Choice Computation Measure

Figure A2.

Computation Strategy Use Report Measure