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Edited by: Thomas J. Faulkenberry, Tarleton State University, United States

Reviewed by: Krzysztof Cipora, University of Tübingen, Germany; Delphine Sasanguie, KU Leuven Kulak, Belgium

*Correspondence: Sara Caviola

This article was submitted to Cognition, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection”) in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

Negative feelings and stressful situations can interfere to different degrees with success in mathematical tasks (Ashcraft and Kirk,

Strategic behavior (i.e., deciding between two or more available options) is used in a wide range of problem solving domains, not only in the field of education (Pillutla and Murnighan,

In the mathematical domain, a wide body of research suggests that mathematics builds on several cognitive abilities (Passolunghi et al.,

Among cognitive factors, the process most widely explored and strongly related to the successful performance on arithmetical tasks is working memory (WM; for review see Raghubar et al.,

While important for mathematical processes, WM is also highly sensitive to interference from stressors. Ashcraft and Kirk (

Stressful situations can also be induced by manipulating the context in which the problem is presented, such as punishing poor performance with social consequences, in order to interfere with cognition (Beilock and Carr,

In this review, we summarize the state of research about the relationship between cognitive stress and strategic behavior used to solve arithmetic tasks. The synthesis has been complicated by the use of different terms according to the specific line of research. In particular, studies on stress and math-related emotions each look at slightly different domains and consequently refer to them with slightly different terms. For example, “stress,” “negative emotions” and “anxiety” are labels which, in the mathematical research field, have often been used to describe similar states of mind that potentially can interfere with the execution of mathematical tasks (Stipek and Gralinski,

An electronic search was conducted on principal databases (PsychINFO, Web of Science, PubMed, EBSCO, Scopus) for English published articles. No date restriction was used, and the keywords were: time pressure/time constraint/time limit/time deadline; strategy/strategy selection/strategy choice/strategy efficiency; problem solving/arithmetic/math/mathematics/calculation; emotional factors/cognitive stress/anxiety/math anxiety. The search has been done with the following combinations of terms: (time pressure OR time limit OR time constraint OR time deadline) AND (arithmetic OR math^{*} OR calculation OR problem solving) AND (strateg^{*}) AND (emot^{*} OR stress OR anxiety). We used the wildcard ^{*} where alternative words like “strategic”/“strategy” or “emotion”/“emotional” might arise. As allowed by each database, the terms have been explored mainly in the title, abstract and keywords, and when possible through the entire full text.

Research was included in this review by following these inclusion criteria. First, since studies on this topic vary in their methodological design, we included those studies which clearly stated the manipulation of the execution time during the main task; second, if they considered how the time constraint affected participants' strategic behavior and consequently their results; and finally, if they have quantitatively measured emotional aspects related to math tasks. Studies aiming to highlight gender differences or that revealed different sample sizes according to gender were excluded, as well as research primarily focused on neuroimaging effects.

We considered papers published before December 2016. The initial inspection was independently completed by two reviewers (SC and EC): the electronic search identified 2,534 papers which matched the search terms. After deleting duplication 352 studies were selected. Titles and abstracts of the studies retrieved were then screened by two reviewers to identify studies that potentially met the criteria outlined above. The full text of the 129 remaining potentially eligible studies were then retrieved and independently assessed for eligibility by two reviewers: any disagreement between the two reviewers was resolved through discussion with a third reviewer (DS): 56 papers remained at this stage.

It is important to note that the inclusion criteria we used in the papers selection led us to exclude all the studies which applied a time limit constraint due to the experimental setting, i.e., studies which did not actually impose a direct time limit on the performance, but instead looked at results by setting a

Finally, 35 studies attained the eligibility criteria. A pre-prepared Excel spreadsheet was used to record extracted data from the included studies for assessment of study quality and data synthesis. Study quality consisted of a risk of bias assessment: quality of individual studies was evaluated in terms of sample size and type (and number) of tasks reported for each domain (time limits/mathematical tasks/emotional factors). Where there was concern over the methodological quality of any studies, sensitivity analyses were conducted: only 19 met the selection criteria and were included in the present review (see Figure

Flow chart summarizing the electronic search.

Regarding the experimental designs, we preferred not to use any restrictive classification of the mathematical tasks reported, but due to high heterogeneity, we report a description of the task itself. Specifically related to the “pressure” aspect, we tried to classify how pressure was induced in the experimental design, in particular whether (i) it was provided by inducing a time limit or by means of other manipulations (e.g., monetary incentives), (ii) in the case of time limits, we considered extensively the experimental methodology (e.g., number of conditions, time limit applied to stimuli presentations or response window).

The main goal of this review was to shed light on how stress induction, particularly time pressure manipulations, can interfere with or modulate strategy selection in arithmetical tasks. Additionally, we were also interested in whether this association could be moderated by emotional and cognitive factors.

The electronic search and the subsequent screening phases highlighted how stress induction or time pressure manipulation have been differentially implemented to trigger cognitive stress during math task execution. Indeed, among the 19 relevant articles identified, 8 papers applied social constraints to induce pressure. Eleven further studies implemented a time pressure manipulation to induce pressure.

In the subsequent section of this article (Social Stress Induction and Choking under Pressure Phenomenon), we first consider those papers which induce stress and “choking under pressure” via social manipulations which do not limit time available to solve tasks. In the next section (Time Pressure in Math: Strategy Selection), we consider tasks which engaged a time pressure manipulation. These two types of pressure manipulation are different in nature for a fundamental reason: regardless of “choking under pressure,” time pressure manipulations may render a previous strategy useless due to complexity. With only limited time available, rapid heuristic strategies can become optimal simply due to their speed. Finally, in Section Emotional Aspects and Stress Manipulation, we consider those studies which actually measure affective factors (such as mathematics anxiety). There is a paucity of such studies, making firm conclusions challenging: however, they are of importance in determining the role of pressure in math tasks (see Figure

Graphic summary of the three principal mechanisms/relationships discussed in different sections of the manuscript.

The outcomes of the present review only partially resolve our initial questions and they can be understood more as open questions than evidence of clear associations. Each section concludes by raising a series of aspects in which this field of research may move forward.

As noted, cognitive stress may influence cognitive resources (Mazzoni and Cornoldi,

Surveying the literature regarding stress-induced performance in mathematical domain, one of the main topics referred to is the “

Studies investigating cognitive stress and “choking under pressure” phenomenon.

1. | Beilock et al., |
Undergraduate students (Study 1: 40 and 40) | Modular arithmetic task (MA, verification task) | Monetary incentives, peer pressure, social evaluation | NA | State-Trait Anxiety Inventory (STAI) | NA |

2. | Beilock and Carr, |
Undergraduate students (93) | Modular arithmetic task (MA, verification task) and a paper-and- pencil division, subtraction and multiplication task | Monetary incentives, peer pressure, social evaluation | NA | NA | Automated Operation Span task and Reading Span task |

3. | Beilock and DeCaro, |
Undergraduate students (Study 1: 44 and 48; Study 2: 46 and 45) | Study 1: modular arithmetic task (MA, verification task). Study 2: water jug problems | Monetary incentives, peer pressure, social evaluation | Written self-report (1) Rule-based algorithm that involved a series of step-by-step computations (2) Estimation or guessing based on previous associations (3) No sense | State-Trait Anxiety Inventory (STAI) | Automated Operation Span task and Reading Span task |

4. | Beilock, |
NA | Modular arithmetic task (MA, verification task) | Monetary incentives, peer pressure, social evaluation | NA | NA | NA |

5. | DeCaro et al., |
College students (78) | Modular arithmetic task (MA, verification task): vertical and horizontal presentation | Monetary incentives, peer pressure, social evaluation | NA | Non standardized retrospective verbal report | Talk-aloud/No-talk aloud conditions |

6. | Wang and Shah, |
Third and fourth graders (53) | 3-digit mental addition problems | Videotaped and external evaluation performance | NA | NA | Automated Operation Span task |

7. | Benny and Banks, |
Undergraduate students (60) | Modular arithmetic task (MA, verification task) | Monetary incentives, videotaped and external evaluation performance | NA | State-Trait Anxiety Inventory (STAI); Need Cognition Scale (NFC); Thought Probes during the MA task | Automated Operation Span task and Reading Span task |

8. | Sattizahn et al., |
Adults (85) | Modular arithmetic task (MA, verification task) | Monetary incentives, peer pressure, social evaluation | NA | State-Trait Anxiety Inventory (STAI) | Arrow-based flanker task; Automated Operation Span task and Reading Span task |

The main hypothesis of this research field is that contextual pressure interferes with limited WM resources (Miyake and Shah,

In subsequent research, Beilock and DeCaro (

Recently, Sattizahn et al. (

Although the above studies seem to answer a distinctive question (how can pressure influence math performance?), they differ in so many aspects, making it difficult to reach a certain answer. For example, all the above research aimed to analyze the effect of pressure on math, but none of them implemented a quantifiable manipulation of pressure with controlled conditions. Instead, they engaged social scenarios which could differentially affect each participant. Similarly, the mathematical tasks and cognitive measures considered vary widely across studies. In order to clarify findings in this domain it is important to systematically consider the role of task difficulty, the nature of the tasks themselves (those that allow for multiple strategies vs. those that do not), and the type of pressure manipulation used in the different studies. This leads to another question: how else can cognitive stress be induced in the math domain?

A large amount of literature from the decision-making field suggests that manipulating the time limit/pressure associated with a task has a very strong effect on the stressful nature of that particular task (e.g., Kerstholt,

One of the first studies on this topic attempted to simulate a computational model of automated and controlled processing during the execution of addition problems in trinary notation: Richardson and Hunt (

Studies investigating strategy selection (positions 1–8) and emotional aspects (position 9–11) with time condition manipulation.

1. | Richardson and Hunt, |
College students (4) | Addition problems in trinary notation | From time to time the arithmetic task was interrupted and then resumed | NA | NA | NA |

2. | Schunn et al., |
Graduates and undergraduates students (25) | Arithmetic problems (half multiplication, and half invented operator) | Time constraints linked to the strategy choose (2 s vs. 20 s) | Participants chose between retrieval and calculation strategy | NA | NA |

3. | Campbell and Austin, |
Undergraduate students (48) | Simple addition problems | Time limit: 750 ms for the fast deadline; 2,500 ms for the slow deadline | After each problem participants chose one among 4 alternatives: Transformation, Counting, Remember, Other | NA | NA |

4. | Luwel and Verschaffel, |
Sixth-grade children (81) | Numerosity judgment task | Time pressure: manipulation of the stimuli presentation time (3 conditions: severe (5 s), moderate (10 s) and low (20 s) time pressure condition) | The three strategies (addition, subtraction and estimation) applied were identified by fitting the individual response-time pattern | NA | NA |

5. | Gillard et al., |
Study 1: undergraduate students (167) | Proportional and non-proportional (additive) word problems | Time limit: 17 s for the fast deadline; no time limit for the control condition | NA | NA | Study 2: Dot memory task as secondary task |

6. | McNeil et al., |
Undergraduate students (184) | Addition facts and equations ( |
Study 1–3: timed presentation of the equations (1000–1500ms); study 4: untimed presentation | Add-all and add-to-Equal Sign strategies (indirectly assessed) | NA | NA |

7. | Chesney et al., |
Undergraduate students (64) | Equations (a+b+c = d+__) | Half trials were timed (half were untimed): equation remained on the screen for 2 s | Responses were coded as reflecting a particular strategy: Correct; Add-all; Add-to-equal; Add-two; Carry; Repeat; Other | NA | NA |

8. | Agus et al., |
Undergraduate students (676) | Probabilistic reasoning | Time limit condition: 30 min | NA | Statistical Anxiety Scale (SAS) | Visuo-spatial and numerical scales (Primary Mental Abilities—PMA); Attitudes Toward Statistics (SATS-28) |

9. | Plass and Hill, |
Third- and fourth-grade children (155) | Test booklets with 15 arithmetic word problems with multiple-choice answers | Time-pressure condition: when 2 of the children in any group had finished, the experimenter stopped the time | NA | Test Anxiety Scale for Children (TASC): Lie Scale for Children (LSC) | NA |

10. | Kellogg et al., |
Undergraduate students (30) | 10-page arithmetic questionnaires (simple and complex problems) | Timed condition: 70% of the mean response time for each page | NA | Abbreviated Math Anxiety Rating Scale (sMARS) | NA |

11. | Tsui and Mazzocco, |
Sixth grade gifted children (36) | Math calculations involving fractions, decimals, calculus, and trigonometry (similar to the calculation test, Woodcock-Johnson III) | Timed condition: 10-min time limit to finish the math calculation task | NA | The Mathematics Anxiety Rating Scale Elementary (MARS-E); the Screen for Child Anxiety Related Emotional Disorders (SCARED); the Multidimensional Perfectionism Scale (MPS) | NA |

As in the decision-making domain, time pressure in mathematics has been manipulated primarily by limiting available time for each decision or choice. Several studies have shown that time pressure interferes with decision-making by altering strategy selection. The presence of a time constraint in any math or problem-solving situation can affect performance: the presence of time limits could either encourage students' engagement with the task or increase choice of the wrong strategy for that task (Beilock and DeCaro,

Thus, time pressure is one factor that influencing which strategy people select to deal with a particular math problem situation (Young et al.,

A similar pattern of results has been found by Luwel and Verschaffel (

The overall results highlight that time pressure adjusts the strategy decision process generating a sort of strategy costs and benefits trade-off: when the available time is short and the task complexity is substantial (i.e., Campbell and Austin,

The negative emotional state and discomfort felt during performance of mathematical tasks is commonly referred to as math anxiety (Hembree,

Although it seems to be widely recognized that providing a reasonable time for the accomplishment of a math test should be effective in reducing at least some of the disadvantage experienced by math anxious subjects (Faust et al.,

Plass and Hill (

Tsui and Mazzocco (

These outcomes do not converge with Kellogg et al. (

In sum, there is some evidence that math anxiety interacts with timed or high-stakes conditions to cause a further performance decrement than usual. However, due to the paucity and heterogeneity of research both in terms of sample and tasks considered, these results do not allow us to conclude that increasing time pressure has a differential effect depending on math anxiety. Similarly, assuming causal relations between time pressure and inducing math anxiety currently does not have evidential support.

This literature overview of the past 30 years focuses on the effect of stress and/or time pressure on math proficiency. It has revealed that, generally speaking, pressure has a great influence on both strategic and emotional aspects of task execution.

Research on choking and excelling under pressure has focused on tasks that demand many cognitive resources, especially working memory (Miyake and Shah,

It has been widely assumed that people are equipped with a range of cognitive strategies which they adaptively select and apply according to the specific task and situation. Within this framework, pressure represents one factor that can influence which strategy people select to deal with a particular situation. Relatively little research has focused on the impact of time pressure on strategy selection in mathematics, principally aiming to show how time pressure interferes with the decision process in terms of strategy selection in mathematical domain. Results seem to suggest that time pressure generally acts as a stressor, causing suboptimal strategy selection. However, the causal mechanism of this is still unclear. It is not clear whether time pressure interferes with strategy

Further research is needed to address this question, taking into account the huge variability of execution time linked to task type (e.g., simple vs. complex calculation or even verification vs. production task; Ashcraft,

Similar considerations can be drawn regarding the relationship between time pressure and emotional aspects within the mathematical learning framework, leaving space for several open questions. Among them is whether time pressure can be always considered as a negative factor in terms of proficiency and math anxiety. To date the literature does not clearly answer this issue. Decreased performance under time pressure is not consistently observed in high or low math anxiety individuals. Previous problem-solving studies suggest that time constraints inhibit creative thinking; but more recent research indicates that time constraints can sometimes prove beneficial (Medeiros et al.,

To sum, the present review demonstrates the need for a broader view of the effects of time pressure on math performance. Future research should systematically examine the effects of time pressure on math performance and strategy selection to develop a fuller framework of phenomena that drive choking or excelling under pressure.

SC and DS developed the study concept. Literature review was conducted by SC and EC. SC and IM drafted the manuscript. DS provided critical revisions. All authors approved the final version of the manuscript for submission.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.