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Cited by 16Communication in Education and HealthcareEducation, Achievement, and GiftednessInnovative Teaching and Learning Methods

How vocal and silent forms of participation in combination relate to student achievement

Open access
Sedova, Klara, Sedlacek, Martin·2023·Instructional Science
DOI 10.1007/s11251-022-09609-1
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Abstract

We adopted a person-oriented approach to identify patterns of how classroom talk and internal behavioral engagement are combined in students. The research was conducted on a sample of 639 ninth-grade students (32 classes). We measured the duration of classroom talk for each individual student during Czech language and language arts lessons. The students completed an inventory to determine their internal behavioral engagement. Student achievement was measured using the results from standardized reading literacy tests. We also inquired about the socioeconomic backgrounds of the students. We identified five distinct participation profiles (eager, chatty, diligent, aloof, and disconnected) and analyzed whether the profiles could predict student achievement. We found that the profile with high talk and high internal behavioral engagement performed best, and the profile with low talk and low internal behavioral engagement performed worst. Analyzing the inconsistent profiles, we found that high internal behavioral engagement did not guarantee student achievement if the engagement was not accompanied by talk. Our findings thus highlight the important role of classroom talk in relation to student learning.

AI snapshot

Written from the paper’s full text.

TL;DR

Using a person-oriented approach with 639 Czech ninth graders, the study identifies five profiles combining classroom talk time and internal behavioral engagement. The high-talk/high-engagement “eager” profile performed best and the low-talk/low-engagement “disconnected” profile worst, while silent-but-engaged students did not achieve as well as vocal peers.

Key findings

  • Five participation profiles emerged: eager (high talk/high engagement; n = 18), chatty (high talk/low engagement; n = 45), diligent (low talk/high engagement; n = 150), aloof (low talk/below-average engagement; n = 216), and disconnected (low talk/low engagement; n = 97); reported prevalence was 3%, 9%, 29%, 41%, and 18%, respectively.
  • Reading literacy differed across profiles (ANOVA F = 2.47, p < 0.05), but the only significant pairwise difference was eager > disconnected. Mean reading literacy scores were eager 53.08%, chatty 46.10%, diligent 43.46%, aloof 44.48%, and disconnected 41.16%.
  • Talk time and internal behavioral engagement were only weakly correlated (r = 0.09), while reading literacy correlated with talk time (r = 0.18, p < 0.01) and socioeconomic background/HISEI (r = 0.20, p < 0.01).
  • The diligent profile (high internal engagement, low talk) ranked fourth in achievement, whereas the chatty profile (high talk, low internal engagement) ranked second, suggesting internal behavioral engagement without talk did not guarantee achievement.

Methods

  • Person-oriented design using k-means cluster analysis on standardized talk time and self-reported internal behavioral engagement; AIC/BIC informed cluster number, and a five-cluster solution was selected because smaller solutions had insufficiently populated groups.
  • Sample: 639 ninth-grade students (52% boys, 48% girls; ages 14–15) in 32 classes from 21 Czech lower secondary schools; observations occurred in two Czech language/language arts lessons per class (2 × 45 min; 64 lessons total).
  • Measures: talk time recorded via tablet app during whole-class discussion; behavioral engagement from Fredricks et al. (2016) inventory (8 items, α = 0.71); achievement from Czech School Inspectorate standardized reading literacy test (16 tasks, success rate); HISEI as socioeconomic control. Analyses included Pearson correlations, ANOVA, chi-square tests, and pairwise comparisons.

Limitations

  • Stated by the authors: participation was measured only in Czech language/language arts; only two lessons per class were observed; talk was operationalized as quantity (talk time), not quality; the k-means procedure has limitations in deciding profile number, and the five-profile model slightly distorts reality; variables on different scales were standardized.
  • Evident from the text: only the behavioral engagement dimension was examined, not cognitive, emotional, or social engagement; the design is cross-sectional and cannot establish causality; the profile analysis included 526 students because of missing measurements and students not fitting identified profiles; the sample came from three Czech municipalities.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/s11251-022-09609-1

Cites

50 of 50 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

5 of 38 cited sources checked · 3 supported · 1 flagged · accuracy not yet measured

  • Findingown data

    Class-level behavioral engagement was an insignificant factor.

    “Class-level behavioral engagement turned out to be an insignificant factor.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Sedova et al., 2019 source

      The Results section (page unavailable) treats class-level talk time—the amount of time students actively participated in talk—as a significant predictor of achievement, not an insignificant one. The paper reports that a different class-level measure, utterances with reasoning, was not significant; that does not support the unqualified claim about class-level behavioral engagement. (LLM, conf=0.87)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
  • Findingown data

    The participation profile with high classroom talk and high internal behavioral engagement had the best student achievement.

    “We found that the profile with high talk and high internal behavioral engagement performed best”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.
  • Findingown data

    The participation profile with low classroom talk and low internal behavioral engagement had the worst student achievement.

    “and the profile with low talk and low internal behavioral engagement performed worst.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.
  • Findingown data

    High internal behavioral engagement did not guarantee student achievement when it was not accompanied by classroom talk.

    “we found that high internal behavioral engagement did not guarantee student achievement if the engagement was not accompanied by talk.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.
  • Findingown data

    The study identified five distinct participation profiles: eager, chatty, diligent, aloof, and disconnected.

    “We identified five distinct participation profiles (eager, chatty, diligent, aloof, and disconnected) and analyzed whether the profiles could predict student achievement.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.
  • Classified as probably not a substantial claim. 26
  • May combine two claims. 13

  • Classified as probably not a substantial claim.

    Premisecitation

    Students who intensely verbally participate in class achieve better results than their less vocal schoolmates.

    “Some studies have indicated that students who intensely verbally participate in class achieve better results than their less vocal schoolmates”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Sedova et al., 2019 source
    • cites Ing et al., 2015 source
    • cites Larrain et al., 2019 source

  • May combine two claims.

    Premisecitation

    How long a student spoke and how many utterances with argument that student contributed were linked to the student's individual test results.

    “The analysis showed a link between how long a particular student spoke and how many utterances with argument that student contributed with the student's individual test results.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Sedova et al., 2019 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingcitation

    Class-level talk time had little impact on achievement score.

    “Class-level talk time had little impact on achievement score.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Sedova et al., 2019 source

      Table 2 reports a modest class-level talk-time coefficient (0.018 score points per second in Model 4), which lends some support to “little impact.” But the Results section says aggregate talk time predicted achievement and confirms its significance in Model 5; the paper’s description of a “negligible” effect refers to an interaction, not class-level talk time itself. Pages are unavailable in our copy. (LLM, conf=0.83)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Interpretationcitation

    Individual student talk matters, and vocal participation contributes more than silent participation.

    “Individual student talk matters (see Ing et al., 2015;Larrain et al., 2019;Sedova et al., 2019;Webb et al., 2014), and vocal participation contributes more than silent participation.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Ing et al., 2015 source
    • cites Larrain et al., 2019 source
    • cites Sedova et al., 2019 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    On average, students' talk time in one lesson was approximately 12 s.

    “their talk time in one lesson was approximately 12 s.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    On average, students had test scores of approximately 44%.

    “On average, students enrolled in our study had test scores of approximately 44%”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.
    • Rests on an assumption: Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    The average individual HISEI was 45.88 (SD = 15.31).

    “The average individual HISEI measured through the higher parent employment status was 45.88 (SD = 15.31).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Two profiles were inconsistent - chatty with high vocal and low silent participation, and diligent with low vocal and high silent participation.

    “Two profiles were inconsistent -chatty with high vocal and low silent participation, and diligent with low vocal and high silent participation.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    The total number of students included in the profiles of the selected model is 526.

    “The total number of students included in the profiles of the selected model is 526.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Eager students perform best and disconnected ones perform worst in literacy tests.

    “Not surprisingly, we found eager students to perform best and disconnected ones to perform worst in literacy tests.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    No link was proven between the quantity of student verbal engagement in the lesson and student test scores; silent and vocal students performed equally well.

    “No link was proven between the quantity of student verbal engagement in the lesson and student test scores.Both silent and vocal students performed equally well.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites O'Connor et al., 2017 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Schultz noted that students who think quickly and formulate articulate responses are often acknowledged by the teacher, but their speed does not necessarily mean they think more productively than their silent peers.

    “Schultz (2010) noted that students who think quickly and formulate their ideas into articulate responses are often acknowledged by the teacher, but their speed does not necessarily mean that they think more productively than their silent peers.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Schultz, 2010 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation

    The engagement inventory was adapted for Czech following principles of cross-cultural adaptation of self-reported measures using back translation and a monolingual test in the target language.

    “In adapting the engagement inventory for the Czech language, we followed principles of cross-cultural adaptation of self-reported measures (Beaton et al., 2000) using back translation and a monolingual test in the target language.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Beaton et al., 2000 source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Study design and conductnone given

    Altered student behavior is possible, especially under the specific circumstances of observers in the classroom.

    “However, altered student behavior is possible, especially under the specific circumstances of observers in the classroom.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    Similar results might not be found in non-linguistic subjects.

    “Similar results might not be found in non-linguistic subjects.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    O'Connor et al. interpreted their findings as the consequence of students' long-standing enculturation in classroom norms of active listening.

    “Similarly, O'Connor et al. (2017) interpreted their findings as the consequence of students' long-standing enculturation in classroom norms of active listening.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites O'Connor et al., 2017 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    According to Ollin, the notion of classroom participation should be revised to encompass silent thinking as something different from passivity.

    “Thus, according to Ollin (2008) the notion of classroom participation should be revised to encompass silent thinking as something different from passivity.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ollin, 2008 source

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationreasoning

    It could be appropriate not to participate in classroom talk if students stay engaged in another way.

    “This perspective implies that it could be appropriate not to participate in classroom talk if the students stay engaged in another way.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Jaworski and Sachdev emphasized the positive impact of silence in the classroom, as it offers room for undisturbed thinking.

    “Jaworski and Sachdev (1998) emphasized the positive impact of silence in the classroom, as it offers room for undisturbed thinking.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Jaworski and Sachdev, 1998 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    No one withdrew during the study.

    “No one withdrew during the study.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

    Premisecitation

    Silent students may be both engaged and disengaged; those who closely follow the discussion with interest but do not make verbal contributions are silently participating.

    “O'Connor et al. (2017) claimed that silent students may be both engaged and disengaged.Those who closely follow the discussion with interest, but do not make verbal contributions, are silently participating according to these authors.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites O'Connor et al., 2017 source

  • Classified as probably not a substantial claim.

    Premisecitation

    Student engagement is positively linked to student achievement and academic success.

    “finding a positive link between engagement and student achievement and academic success”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Fredricks et al., 2004 source
    • cites Chang et al., 2016

      Not checked in the free run.

    • cites Wang & Eccles, 2012 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    There was no statistically significant difference between the vocal students who contributed to the discussion and the students who did not.

    “There was no statistically significant difference between the vocal students who contributed to the discussion and the students who did not.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Inagaki et al., 1998 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductreasoning

    The five-profile model used in the study slightly distorts reality.

    “The five-profile model used in this respect also slightly distorts reality.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Goldin et al. identified three kinds of student learning practices central to participation in class: listening, speaking publicly, and making and using records.

    “Goldin et al. (2019) identified three kinds of student learning practices central to participation in class: listening, speaking publicly, and making and using records.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Goldin et al., 2019 source

  • May combine two claims.

    Study design and conductown data

    The CFA model fit indices were RMSEA = 0.042, CFI = 0.901, TLI = 0.893, and SRMR = 0.018.

    “root mean square error of approximation (RMSEA) = 0.042, comparative fit index (CFI) = 0.901, Tucker-Lewis Index (TLI) = 0.893, and standardized root mean square residual (SRMR) = 0.018.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The significance of chi-squared was not in conformity with the required parameters, but this was due to the sample size rather than a substantial discrepancy between the model and the data.

    “only the significance of chi-squared (χ 2 ) was not in conformity with the parameters required.However, this was due to the sample size rather than a substantial discrepancy between the model and the data.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    Participation in classroom talk and internal behavioral engagement were measured only for Czech language and language arts.

    “Participation in classroom talk and internal behavioral engagement were measured only for Czech language and language arts.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    Student achievement in Czech schools depends on socioeconomic status.

    “Given that the dependence of student achievement in Czech schools on socioeconomic status is evident from international surveys (Blažek & Příhodová, 2017)”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Blažek & Příhodová, 2017

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Study design and conductown data

    Confirmatory factor analysis confirmed the consistency of the engagement scales and the model proved to be a good fit to the data.

    “The results of the confirmatory factor analysis (CFA) outlined in Table 1 confirmed the consistency of the engagement scales.The model proved to be a good fit to the data.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Kline, 2005

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Hu & Bentler, 1999 source

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    Student participation was operationalized only in terms of the quantity of student talk (talk time), not in terms of quality (e.g., incidence of reasoning or argument).

    “we operationalized the student participation only in terms of the quantity of student talk (talk time), not in terms of the quality (e.g., incidence of reasoning or argument).”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Japanese sociocultural norms ensured that all students carefully listened during discussions and were thus able to utilize the discussion for learning even when they did not personally take the floor.

    “Inagaki et al. (1998) claimed that Japanese sociocultural norms ensured that all students carefully listened during discussions and were thus able to utilize the discussion for learning even when they did not personally take the floor.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Inagaki et al., 1998 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    Several students did not fit into any of the identified profiles.

    “Furthermore, several students did not fit into any of the identified profiles.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    The discrepancy with the sample size (639) is because only students who passed all measurements were included in the cluster analysis (533).

    “The discrepancy with the sample size (639) is because only students who passed all measurements were included in the cluster analysis (533).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Teaching in Czech schools is still traditional and not student-oriented, manifesting as a limited allowance of student talk during class.

    “This corresponds to the fact that teaching in Czech schools is still traditional and not student-oriented, manifesting as a limited allowance of student talk during class (Sedova et al., 2014).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Sedova et al., 2014 source
35 of 35

  • The authors state this as an assumption.

    During the observed lessons, both teachers and students behaved in a way similar to their usual conduct.

    “We therefore assume that both teachers and students behaved in a way similar to their usual conduct.”

  • The paper relies on this without support.

    Data from the two observed lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.

    “We believe that data from these two lessons represent the nature of classroom talk in the given class and the participation patterns of individual students.”
2 of 2

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Profile talk times cannot produce the reported overall mean

    Major

    Table 3 assigns 528 students to the five profiles. Weighting their Table 4 talk-time means by those profile sizes gives about 20.5 seconds per lesson, already above Table 2's 12.19-second mean for 533 students. The remaining five students cannot bring the mean down to 12.19 seconds because talk time cannot be negative.

  • HISEI descriptive statistics disagree with Table 2

    Major

    The prose reports a HISEI mean of 45.88 and SD of 15.31, whereas Table 2 reports 47.52 and 18.56 for HISEI.

  • SRMR differs between Table 1 and its description

    Major

    Table 1 reports an SRMR of 0.098, but the paragraph describing the same CFA model reports 0.018.

  • Behavioral-engagement comparison reverses two profile means

    Minor

    Table 4 reports eager students' mean engagement as 6.73 and diligent students' as 7.30, yet its pairwise comparison says eager exceeds diligent. The text also says their engagement difference was not significant.

  • Disconnected students do not have the lowest reported talk time

    Minor

    The results call disconnected students the lowest in talk time, but Table 4 gives them 10.12 seconds per lesson, compared with 9.02 seconds for aloof students.

  • Disconnected-profile count differs between text and table

    Minor

    The text gives 97 disconnected students, while Table 3 gives 99. Consequently, the stated total of 526 profiled students matches the text's counts, but Table 3's five counts total 528.

  • Reading-literacy testing is dated both October and November

    Minor

    The method says the CSI conducted the reading-literacy testing in October 2017, while the achievement measure says testing took place in November 2017.

7 of 7

Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. Blažek, R., & Příhodová, S. (2017). Mezinárodní šetření Pisa 2015. Praha: ČŠI.
  2. Chang, D. F., Chien, W. C., & Chou, W. C. (2016). Meta-analysis approach to detect the effect of student engagement on academic achievement. ICIC Express Letters, 10, 2441–2446. https://doi.org/10.24507/icicel.10.10.2441. · DOI
  3. Kline, R. B. (2005). Principles and practice of structural equation modelling. New York: The Guilford Press.

Cited by

Sorted by citations

Related

Authors
Sedova, K., & Sedlacek, M.
ORCID
Sedova, Klara
Venue
Instructional Science
Publisher
Springer Science and Business Media LLC
Published
2023-01-23
Volume
51
Issue
2
Pages
343-361
ISSN
  • 0020-4277 (ISSN-L)
  • 1573-1952
DOI
10.1007/s11251-022-09609-1
OpenAlex
W4317740052
Semantic Scholar
ab3a041e448afc4a15be8e0bc3c30c135196465f
Cited by
16
References
49
Citations by year
2026: 2 · 2025: 9 · 2024: 5
FWCI
4.58
Type
journal article
Language
en
Open access
Licence
Locations
Instructional Science (publishedVersion, cc-by)
Funders
  • Czech Science Foundation (GA21-16021S)
  • National Recovery Plan (LX22NPO5101)
Topics
  • Social Sciences › Psychology › Social Psychology › Communication in Education and Healthcare
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Education, Achievement, and Giftedness
  • Social Sciences › Psychology › Developmental and Educational Psychology › Innovative Teaching and Learning Methods
Keywords
classroom discourse, student participation, academic performance, reading literacy, ninth grade students, language arts instruction, socioeconomic background, person-oriented approach

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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-23.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-23.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

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