Mental math test: what a spoken arithmetic score really measures

0 The short answer

A mental math test measures quantitative skill and working memory together, and a normed one compares your result with a defined group of adults instead of reporting a bare speed count. Psychologists give mental arithmetic as a supervised subtest inside batteries such as the Wechsler and Woodcock-Johnson scales, employers use timed numerical tests that are not IQ tests, and free quizzes vary in whether they name any norm group. ACIS is one concrete option: its Arithmetic subtest presents problems as audio and is in the Full Scale form (50 dollars, about 175 minutes) or the Custom Test at 5 dollars per subtest (prices read October 29, 2026, and they can change). The decisive limit is that ACIS is online and unsupervised, so it is not a clinical or diagnostic instrument and not for hiring or school decisions.

1 What does a mental math test actually measure?

A mental math test measures acquired number skill and the working memory that holds a problem while it is solved, and the two cannot be separated by looking at one score. In the Cattell-Horn-Carroll (CHC) model, which the page on the CHC model of cognitive abilities explains, the learned part is quantitative knowledge (Gq): number facts, operations and procedures that instruction builds. The holding part is working memory (Gwm), the limited store and control system that keeps information active while it is transformed. A spoken sum such as the original example below uses both at once.

Original example, written for this page and not taken from any test: "Four friends split a bill of 36 dollars and each adds a 2 dollar tip. What does each person pay?" The arithmetic is trivial. The difficulty is that the listener must keep four numbers and an order of operations in mind while computing, because the sentence is gone once it has been spoken.

Three further abilities can enter. Reasoning with quantities in a problem never seen before is filed in CHC under fluid reasoning (Gf), as the page on quantitative reasoning tests shows. Speed of simple calculation touches processing speed (Gs), which is why the Woodcock-Johnson V brochure tags its Math Facts Fluency test with both Gs and Gq (Riverside Insights, read October 29, 2026). And attention and anxiety shape performance in ways that have nothing to do with how much mathematics a person knows.

Pearson's own description of the Wechsler Adult Intelligence Scale, Fourth Edition shows the same overlap from the publisher's side. Its CHC table lists Arithmetic under quantitative knowledge and, in the same sentence, under short term memory (Pearson Assessments, WAIS-IV product page, read October 29, 2026). One subtest, two broad abilities, and that is the honest summary of what mental arithmetic is.

The practical consequence is that a mental math score answers a narrower question than "how good at math am I". It answers "how well do I calculate when I must hold the problem in mind". Math tests in general, including written and school style ones, belong to the page on math IQ tests, and this page stays with mental arithmetic. The page on what IQ measures places that question inside the wider picture, and the page on cognitive domains shows where the quantitative and working memory domains sit in a full battery.

2 Which mental math tests exist, and which are normed?

Five kinds of mental math test are available to an adult, and they differ most in whether anyone supervises them and whether your score is compared with a named group. The table sets them side by side. Fees and norm details come only from pages and documents opened on October 29, 2026, and cells that read "not stated" mean the source that was read was silent.

Sources for the rows: the Pearson WAIS-IV page for the age range, the core status and the time; the Pearson WAIS-5 and WAIS-IV comparison flyer for Arithmetic as a secondary subtest in the WAIS-5; the Woodcock-Johnson V brochure for the test names and ability tags; the University of Warwick Careers page on selection tests for the employer format; and Loenneker and colleagues (2025) for Math4Speed. The 13 minutes is our arithmetic and is explained in the section on the ACIS subtest. Two points deserve emphasis. First, a supervised clinical test is the only option on this list where a trained person controls the room, the sound and the timing. That is a real advantage and the reason the page on where to take an IQ test puts in-person testing first for high-stakes questions. Second, an employer numerical test is built to rank applicants on a workplace skill, not to estimate intelligence. Warwick describes such tests as assessing "aptitude for numeracy by analysing and drawing conclusions from numerical data", which is a different aim from a normed cognitive score.

Math4Speed is worth knowing about because it shows what an open, research grade fluency measure looks like and what it does not claim. Its authors describe a measure of 50 addition, 50 subtraction, 50 multiplication and 50 division problems, each operation limited to 2 minutes, evaluated on convenience samples of young adults who were mainly university students from six European countries. They report that reliability and validity were satisfactory and they invite researchers to contribute more representative samples. It is a written fluency screen for research comparison, not a mental arithmetic test in the sense of holding spoken terms, and not a norm for the general adult population.

The page on free IQ tests covers the wider market of online options. For mental arithmetic specifically, the question to ask of any online quiz is simple: does the page name the group your score is compared with?

3 What does research show about working memory in mental arithmetic?

Research on mental arithmetic points to the same conclusion from several directions: calculating in your head draws on working memory, including its executive control, even for simple problems. The clearest single summary is the review by DeStefano and LeFevre (2004). They reviewed the literature on the role of working memory in solving problems such as single-digit and multi-digit sums, and they state that the literature was neither comprehensive nor systematic, so their conclusions are tentative. Within that caution they conclude that all three components of Baddeley's working memory system (the central executive, the phonological loop and the visual-spatial sketchpad) play a role in mental arithmetic, under different conditions, and that mental arithmetic requires central executive resources even for single-digit problems (DeStefano and LeFevre, 2004).

Experiments that load working memory with a second task show how this works in practice. Fürst and Hitch (2000) used dual-task methods and found that suppressing articulation impaired the ability to add a pair of briefly presented three-digit numbers, but had no effect when the numbers stayed visible throughout the calculation. Making people do a concurrent Trails task, by contrast, impaired addition even when the numbers remained visible, and the number of carry operations in the addition predicted the damage to Trails performance. The authors concluded that carrying places substantial demands on executive processes, while retaining the problem information is handled by the phonological loop (Fürst and Hitch, 2000).

That result has a direct meaning for test design. Two different demands hide inside the phrase "mental arithmetic". One is storage: keeping the numbers available, which the phonological loop supports when the numbers are heard and not displayed. The other is control: sequencing the steps, carrying a value, and inhibiting a habitual wrong move, which draws on the central executive.

Imbo and Vandierendonck (2007) added a finding about strategy. In experiments on simple addition and subtraction, the central executive was involved in both retrieval and procedural strategies but played a larger role in procedural ones, active phonological processes mattered for procedural strategies only, and working memory load had no effect on which strategy people chose (Imbo and Vandierendonck, 2007). Put plainly, a person who solves a sum by recalling a stored fact leans less on working memory than a person who counts or works it out step by step, and which route they take depends partly on how well the fact is learned.

At the level of whole populations the association is moderate. A meta-analysis by Peng, Namkung, Barnes and Sun (2016) of 110 studies and 829 effect sizes found a medium correlation of r = .35 between mathematics and working memory, with a 95 percent confidence interval of .32 to .37. The association was comparable for verbal, numerical and visuospatial working memory, and whole-number calculation and word-problem solving showed the strongest relation, while geometry showed the weakest (Peng and colleagues, 2016). Squaring .35 gives about .12, which is our arithmetic and not the authors' statement: roughly an eighth of the variation in math performance is shared with working memory in that pooled estimate, and most of it is not.

The two numbers should be held together. Working memory matters for mental calculation, as the experiments show, yet working memory does not determine math skill, as the meta-analysis shows. The page on math ability and IQ sorts the wider evidence by study design, and the page on working memory tests explains how working memory itself is measured.

4 Why does hearing the problem change what the test measures?

A problem that is heard and then gone loads working memory more than the same problem left on screen, which is why spoken arithmetic and written arithmetic are different measures. The experiment that shows this most directly is by Logie, Gilhooly and Wynn (1994). They studied mental addition of two-digit numbers with dual-task methods. When the numbers were presented auditorily, mental addition was significantly disrupted by concurrent random letter generation and, to a lesser extent, by articulatory suppression, and it was unimpaired by hand movement or by irrelevant pictures. When the numbers were presented visually, random generation again produced the largest disruption, but the authors report that overall performance was better and that the absolute size of the disruptive effects was very small compared with auditory presentation (Logie and colleagues, 1994).

Two details matter for reading a score. The first is that the central executive was implicated in both conditions, so even the written version is not free of working memory demands. The second is that incorrect responses tended to be quite close to the correct answer, which suggests that an overloaded calculation tends to drift and not to collapse into a random guess. A person who misses a spoken item by a small margin has often held most of the problem and lost a piece of it.

Fürst and Hitch (2000), described above, point the same way from another direction. When the numbers stayed visible, suppressing articulation did nothing, which means the phonological storage was not needed. When the numbers were briefly presented, it hurt. Reading that result alongside Logie and colleagues, a reasonable inference (ours, not a claim either paper makes about any commercial test) is that a spoken test with nothing left on screen makes storage a real part of the demand, whereas a written test with the problem in view mostly tests calculation and control.

DeStefano and LeFevre (2004) make the same methodological point in their conclusions. They urge researchers to manipulate presentation conditions such as operand duration and format, and response requirements such as spoken versus written, because these change which parts of the working memory system a problem uses. In other words, two mental math tests with the same arithmetic content can measure somewhat different things if one is heard and the other is read.

This is also why mental arithmetic sits near, but not at, the working memory tests. The page on digit span describes a task that holds and repeats numbers with no calculation. Spoken arithmetic adds a calculation on top of that holding, and the sibling page on the auditory memory test is the place to follow heard material further.

5 How does mental arithmetic differ from written math achievement?

Mental arithmetic is scored on efficient manipulation of quantities held in mind, while written math achievement is scored on learned procedures applied with the work visible, and the ACIS technical manual treats the two as complementary rather than interchangeable. The ACIS pages on Arithmetic and Mathematical Achievement divide the territory the same way. Mathematical Achievement is described as acquired quantitative knowledge and the application of learned procedures, sitting closer to educational attainment than to novel reasoning. Arithmetic is described as mental quantitative problem solving that is both quantitative and memory loaded, especially when problems must be solved without external working space.

The manual adds a reading rule for the pair. Arithmetic is less purely achievement based than Mathematical Achievement because it emphasizes active manipulation and efficient problem solving, though it still depends on learned number concepts, and it is sensitive to attention, anxiety, working memory and calculation fluency. A low Arithmetic score with adequate Mathematical Achievement may indicate that the person understands mathematics but performs less efficiently under working memory demands. A high Arithmetic score with lower Mathematical Achievement may indicate strong quantitative manipulation with narrower formal math exposure (ACIS technical manual, read October 29, 2026). The technical manual holds the full descriptions.

Why would people differ in how they solve a simple sum at all? Campbell and Xue (2001) studied adults who solved simple arithmetic problems in the four basic operations and reported their strategies. Canadian university students of Chinese origin and Chinese students educated in Asia did equally well on simple arithmetic, and both did better than students of non-Asian origin, while on a standardized test of more complex multistep arithmetic the Asia-educated group outperformed both Canadian groups. The authors interpreted the simple-arithmetic advantage as due to culture-specific extracurricular factors and not to differences in formal education, and they found that all three groups reported using procedures for the larger simple subtraction and division problems (Campbell and Xue, 2001).

That is a laboratory result about particular student groups, so it should not be generalized into claims about any nationality. What it does show is that fluency on simple sums depends on how those facts were learned and practiced, and that adults reach the same answer by different routes. It is one more reason a mental arithmetic score is a mixed signal.

A related distinction concerns the whole battery. The page on IQ tests without math covers how Wechsler scales place Arithmetic differently from edition to edition: according to Pearson's comparison flyer, Arithmetic is a core subtest in the WAIS-IV, whose Full Scale IQ uses ten subtests, and a secondary subtest in the WAIS-5, whose Full Scale IQ uses seven. The ACIS Arithmetic page notes that the Wechsler scales place arithmetic under working memory, whereas ACIS reports it with Mathematical Achievement in the Quantitative Reasoning Index. Neither placement is a mistake. They reflect different answers to the question of what mental arithmetic mostly is.

6 How does the ACIS Arithmetic subtest work?

The ACIS Arithmetic subtest plays word problems as audio, leaves no written copy of the terms on screen, gives a limited time per item, and ends after three consecutive errors. The technical manual describes the task this way: the examinee hears a word problem delivered in the listening area and computes the answer mentally, and because the problem is presented aurally and no written copy remains on screen, the terms must be held while the solution is computed, so the format adds a retention demand to the arithmetic itself. It lists 26 audio problems, notes that items 1 to 5 include images, sets a response limit of 30 seconds per item, and states that the subtest ends after 3 consecutive errors (ACIS technical manual, read October 29, 2026).

The subtest page adds the conditions a test taker meets. No external aids are allowed, which the page lists as calculators, notes, scratch paper and drawing tools. Each problem must finish playing before the person responds. The instructions for the later section allow each item to be replayed one additional time, while the 30 second timer keeps running. The page does not disclose item content, scoring keys or adaptive rules, and this article does not either.

The page and manual give a few numbers that allow simple reasoning. If every one of the 26 items used its full 30 seconds, response time would total 13 minutes, which is our arithmetic and not a published testing time. In practice the subtest can end earlier because of the three consecutive error rule, and real sessions include instructions and audio playing time, so the figure is an upper bound on response time and not a duration to plan around. The Full Scale form is about 175 minutes across all 20 subtests, with breaks allowed, progress saved between subtests and 30 days to finish.

In the CHC terms of the manual, Arithmetic maps to quantitative reasoning with working memory control, and it requires quantitative manipulation, maintenance of numerical information, operation selection and accurate step execution. The subtest belongs to the Quantitative Reasoning Index (QRI), the pair with Mathematical Achievement. The manual also lists composites built from predefined subtest sets, among them the CQRI, which combines Mathematical Achievement, Figure Weights, Arithmetic and Visual Number Series, and these are available only when their subtests are.

Where it can be taken: among the standard forms Arithmetic is in the Full Scale form only, and it is also in the Custom Test, where a buyer picks subtests at 5 dollars each. The Custom Test returns a scaled score for every subtest and a full index score for any domain completed, so Arithmetic alone returns a scaled score, and Arithmetic with Mathematical Achievement returns the QRI for 10 dollars (prices read October 29, 2026, and they can change). A Full Scale IQ needs the Full Scale battery, and at 10 subtests the Full Scale form costs the same as the Custom Test, as the page with the ACIS one time prices shows.

7 What can a low or high mental arithmetic score mean?

A low mental arithmetic score has several ordinary explanations besides weak quantitative ability, so it should be read as a prompt for comparison and not as a verdict. The manual lists the main ones for Arithmetic: attention, anxiety, working memory and calculation fluency, plus the quantitative knowledge the problems rest on. The research gives two of them a closer look.

Experimental evidence indicates that anxiety about mathematics acts through working memory. Ashcraft and Kirk (2001) found that individuals with high math anxiety had smaller working memory spans, especially on a computation-based span task, and that this reduced capacity led to a pronounced increase in reaction time and errors when mental addition was performed together with a memory load. They described the effect as a transitory disruption of working memory and not a fixed trait of ability (Ashcraft and Kirk, 2001). For a test taker the implication is practical: nervousness at the start of a spoken arithmetic subtest can lower the score through the same mechanism that the test is partly measuring.

Pressure is a second route, and it has a surprising direction. Beilock and Carr (2005) examined choking under pressure in mathematical problem solving and found that only individuals high in working memory capacity were harmed by performance pressure, with the decrements limited to the math problems that made the highest demands on working memory. Their reading was that pressure consumes the working memory capacity that high performers rely on (Beilock and Carr, 2005). Both studies were laboratory experiments with students, and neither tested a self-administered online assessment, so they explain a mechanism and do not forecast what happens in a living room.

A high score deserves the same care. It can reflect strong working memory, well-learned number facts, an efficient strategy, or practice with similar problems. The manual's pairing rule helps here: a high Arithmetic score next to a lower Mathematical Achievement score points to manipulation outrunning formal exposure, while the reverse suggests knowledge without the holding efficiency. The page on index score differences explains why gaps between indices are common enough to need their own interpretation, and the page on processing speed tests separates calculation speed from the reasoning that the other indices sample.

Knowledge matters too, and not only mathematical knowledge. The problems are spoken English word problems, so listening comprehension and English proficiency play a part, and ACIS is English only. Language based acquired knowledge, grouped in CHC under crystallized intelligence (Gc), is the topic of the sibling page on the crystallized intelligence test.

8 How should a mental arithmetic score be read?

A mental arithmetic score is a scaled score for one subtest, and it is less precise than an index or a Full Scale IQ, so read it as a range and compare it with its neighbors. In ACIS, scaled subtest scores run from 1 to 19 with a mean of 10 and a standard deviation of 3, while indices and the Full Scale IQ use a mean of 100 and a standard deviation of 15, and the report adds percentiles and a 95 percent confidence interval. The page on how IQ scores are normed explains what a norm group is and why adult norms matter, and the page on the standard deviation of 15 explains why those numbers were chosen.

Converting between scales is simple on a normal curve. A scaled score of 13 sits one standard deviation above the mean, which is about the 84th percentile. That is our arithmetic on the stated mean and standard deviation, and it assumes the scores follow the normal curve. The page on IQ score versus percentile explains why scores and percentiles cannot be averaged, and a percentile calculator does the conversion for any score.

Precision is the part people skip. The Standards for Educational and Psychological Testing state that estimates of reliability and precision should be reported for each total score, subscore or combination of scores that is to be interpreted, and the comment to that standard adds that total scores can be acceptably consistent while subscores have unacceptably low reliability, depending on how they are defined and used (AERA, APA and NCME, 2014, Standard 2.3). To see why that matters, take a hypothetical subtest score with a reliability of .80. The standard formula gives a standard error of measurement of 3 times the square root of .20, about 1.3 scaled points, so a 95 percent range is roughly 2.6 points either side of the observed score. This is our arithmetic on an invented reliability, not an ACIS figure. The lesson is only that a single subtest score carries a band wide enough to matter.

That is why the Quantitative Reasoning Index, which combines Arithmetic with Mathematical Achievement, is the better unit for a question about quantitative ability, and why a Full Scale IQ rests on all 20 subtests. The page on reliability and validity explains the two ideas in plain terms, and the manual documents how ACIS reports its scores. For a view of how mental arithmetic fits into a broad estimate, the manual's General Ability Index is a composite that reduces the influence of working memory and processing speed.

9 Can you improve at mental math, and does it change an IQ score?

Practice improves the specific skill of calculating in your head, but there is no convincing evidence that training working memory itself transfers to broader abilities such as arithmetic. The strongest summary on the second point is the meta-analysis by Melby-Lervåg, Redick and Hulme (2016) of 87 publications and 145 experimental comparisons. Working memory training produced reliable improvements on measures of intermediate transfer, meaning verbal and visuospatial working memory tasks, but for far transfer measures, which included arithmetic as well as nonverbal ability, verbal ability, word decoding and reading comprehension, the authors found no convincing evidence of reliable improvement when training was compared with a treated control condition (Melby-Lervåg and colleagues, 2016).

The first point is an inference from the findings above and not a result of a single study. Imbo and Vandierendonck (2007) showed that retrieval strategies load the central executive less than procedural ones, and Campbell and Xue (2001) showed that adults differ in how much they retrieve facts and how much they compute them. Together these suggest that practicing number facts until they are recalled rather than computed should lower the working memory cost of a sum. That is a reasonable expectation. It is not a promise about a score, and it would be learning a skill, not raising general ability.

For a person planning to take a test, two sensible habits follow. Do not cram arithmetic drills in the hour before, because the aim of a normed score is to compare your usual performance with a group and not your best sprint. And do not expect a memory app to lift a quantitative score, since the transfer evidence is weak. The page on short term memory tests is the sibling to read for the memory side of this question.

10 What conditions does an unsupervised spoken arithmetic test need?

A spoken arithmetic test needs working sound, a quiet room and no calculator, and a failure on any of these changes what the score measures. The Standards for Educational and Psychological Testing say that the testing environment should furnish reasonable comfort with minimal distractions to avoid construct-irrelevant variance, and that technology-based administrations should avoid distractions such as equipment or internet connectivity problems (Standard 6.4). They also say test takers should be given appropriate instructions, practice and other support to reduce construct-irrelevant variance (Standard 6.5) (AERA, APA and NCME, 2014).

Applied to a spoken subtest, the checklist is short. Confirm that the sound works before starting, because the ACIS Arithmetic, Digit Span and Alphanumeric Sequencing subtests present their items as audio and need working sound. Take it in a room where noise will not mask the audio, since a missed word turns an arithmetic item into a different problem. Put calculators, notes and scratch paper out of reach, because the instructions forbid them. A hearing difficulty or weak speakers lowers a score for reasons unrelated to arithmetic, and such a result should be reported with that caveat and not as an ability estimate.

ACIS allows breaks and saves progress between subtests, with 30 days to finish a purchased form. That is an advantage for fatigue and a reason to start a subtest only when you can finish it, since the response limit runs per item. APA's Guidelines for Psychological Assessment and Evaluation (2020) ask psychologists to make test selection, scoring and administration reflect the appropriate normative comparison, situational influences, effort and standardized administration (Guideline 8), and the same logic applies to a person reading their own online score: note anything unusual about the session, and weigh the score accordingly.

11 Who should take a mental math test, and who should look elsewhere?

A mental math test suits adults who want a normed read on quantitative skill and working memory, and it does not suit decisions that need a supervised, documented assessment. If the goal is curiosity about how you calculate under memory load, a normed online option is reasonable, and the page on IQ tests for adults shows the wider set of choices. If the goal is a broad ability profile, the page on cognitive ability tests places a quantitative subtest inside a full battery, which is a better basis than one subtest alone.

Engineers and other quantitative professionals often ask whether mental arithmetic predicts anything about their work. The sibling page on the IQ test for engineers is the place to follow that question, and the note above on knowledge and fluency applies: a strong score can reflect training as well as ability. If you are preparing for an employer's numerical test, a mental arithmetic subtest is not a stand-in. Those tests, as the University of Warwick page describes them, are normally timed, run 20 to 30 minutes in many cases and ask about tables, graphs, word problems and number series, so practice with that format is the better preparation.

Some goals call for another route entirely. An ACIS score is not for hiring decisions, school accommodations or admission to high IQ societies, and ACIS is not a diagnostic instrument. Anyone concerned about persistent difficulty with numbers, or about a change in how they handle numbers, should speak with a qualified professional and not rely on any online quiz. For people aiming at the very top of the range, the page on high range IQ tests covers tests aimed at the top of the range.

12 Where ACIS sits, and what a buyer should do

ACIS offers one concrete, normed way to take spoken mental arithmetic online, and the same format also sets its limits: it is unsupervised, self-administered, English only, and not a clinical or diagnostic instrument. We sell this test, so treat this section as a disclosure and check it against the rest of the page. The ACIS Arithmetic subtest compares an adult's result with norms covering ages 16 to 90, reports a scaled score with percentile and confidence interval, and feeds the Quantitative Reasoning Index with Mathematical Achievement. It is not a substitute for a psychologist's supervised testing, for an employer's selection test, or for a society's proctored exam.

The Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) set the frame for this section. Standard 1.1 asks the test developer to set forth clearly how scores are intended to be interpreted and used, to delimit the population for which a test is intended, and to describe the construct clearly, and its comment notes that no test permits interpretations that are valid for all purposes or in all situations. APA's Guidelines for Psychological Assessment and Evaluation (2020) add that tools should show sufficient validity evidence for their uses and sufficient score reliability (Guideline 6), that results are one piece of information among multiple sources (Guideline 7), and that normative comparison, situational influences, effort and standardized administration all need attention (Guideline 8). In practice that means reading an Arithmetic score as a bounded estimate of one skill, for the purpose of understanding yourself, and not as a credential. The manual says verbal and knowledge tasks are affected by English proficiency and educational exposure, and the documentation behind the scores is on the technical manual.

A buyer's next step depends on the question. To see how the platform works before paying, the free trial needs no card, and only one trial is allowed per person. To get the Arithmetic score itself, choose the Custom Test at 5 dollars for Arithmetic, 10 dollars with Mathematical Achievement for the Quantitative Reasoning Index, or the Full Scale form at 50 dollars for a Full Scale IQ with all 20 subtests (prices read October 29, 2026, and they can change). The refund terms are quoted exactly: "Full refund within 5 days if the report does not deliver the features described at checkout or a technical issue prevents you from accessing your results." That is a conditional refund, not an unconditional money back guarantee. Example reports are available for each form, so the output can be inspected before any purchase.

13 Sources Behind This Page

Every figure above is traceable to one of the following, and each is linked at the point where it is used. The 13 minute upper bound on Arithmetic response time, the squared correlation of about .12, the 84th percentile for a scaled score of 13 and the standard error in the hypothetical example are our own arithmetic on stated figures and are labelled as such in the text. Prices and product details were read on October 29, 2026 and can change. The APA guidelines were read in an archived copy of the PDF published at the address below.

• DeStefano D, LeFevre J. The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 2004, volume 16, issue 3, pages 353 to 386.
• Fürst A, Hitch G. Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition, 2000, volume 28, issue 5, pages 774 to 782.
• Logie R, Gilhooly K, Wynn V. Counting on working memory in arithmetic problem solving. Memory & Cognition, 1994, volume 22, issue 4, pages 395 to 410.
• Imbo I, Vandierendonck A. The role of phonological and executive working memory resources in simple arithmetic strategies. European Journal of Cognitive Psychology, 2007, volume 19, issue 6, pages 910 to 933.
• Peng P, Namkung J, Barnes M, Sun C. A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 2016, volume 108, issue 4, pages 455 to 473.
• Campbell J, Xue Q. Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 2001, volume 130, issue 2, pages 299 to 315.
• Ashcraft M, Kirk E. The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 2001, volume 130, issue 2, pages 224 to 237.
• Beilock S, Carr T. When high-powered people fail: Working memory and choking under pressure in math. Psychological Science, 2005, volume 16, issue 2, pages 101 to 105.
• Melby-Lervåg M, Redick T, Hulme C. Working memory training does not improve performance on measures of intelligence or other measures of far transfer: Evidence from a meta-analytic review. Perspectives on Psychological Science, 2016, volume 11, issue 4, pages 512 to 534.
• Loenneker H, Cipora K, Artemenko C and colleagues. Math4Speed: A freely available measure of arithmetic fluency. Canadian Journal of Experimental Psychology, 2025, volume 79, issue 2, pages 212 to 220.
• Pearson Assessments. Wechsler Adult Intelligence Scale, Fourth Edition, product page (core subtests, age range, CHC constructs), read October 29, 2026.
• Pearson Assessments. WAIS-5 and WAIS-IV comparison flyer (core, primary and secondary subtests, Full Scale IQ subtest counts), read October 29, 2026.
• Riverside Insights. Woodcock-Johnson V brochure (test names and CHC ability tags), read October 29, 2026.
• University of Warwick Careers. Selection tests (format, timing and level of employer numerical tests), read October 29, 2026.
• American Educational Research Association, American Psychological Association, National Council on Measurement in Education. Standards for Educational and Psychological Testing, 2014, Standards 1.1, 2.3, 6.4 and 6.5.
• American Psychological Association. APA Guidelines for Psychological Assessment and Evaluation, approved by the APA Council of Representatives, March 2020, Guidelines 6, 7 and 8.

14 Frequently Asked Questions