Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper reports competently set out and analysed quantitative research. The reasoning behind carrying out such research is well set out and the conclusions that are made are supported by the evidence. There is nothing surprising or particularly novel about the research despite the authors telling the reader several times that a link between spatial anxiety and mathematics anxiety had not been established as yet. I remained unconvinced that such a thing as spatial anxiety is widespread or of particular interest and was horrified to find that these young people already showed significant mathematics anxiety. Your conclusion that spatial skills and mathematics skills grow together was of interest and I would like to see a qualitative exploration of how these results could be used in practice.

The paper would be improved by:

Remembering that not all your readers live in the USA and changing 'math' to 'mathematics' (except on line 653 where the use of 'math' is appropriate) and giving ages instead of assuming your reader knows the ages of children in grade 1.

Removing some of the repetition of the gap in knowledge you were trying to fill and of other long phrases that turn up unnecessarily often in the text

Removing the term ability in line 310 and use attainment or achievement instead. You use both these latter terms in that paragraph and I think it would be better to stick to attainment as that is all you have a measure of.

Removing conclusions about spatial anxiety after your well set out reasons for you not having a good measure of this.

Comments on the Quality of English Language

this is a very well written paper which has no syntax or grammar errors

Author Response

Dear Reviewer,

Thank you so much for the time spent reviewing our work as well as the thoughtful suggestions. Please see the attached document for our specific responses to your reviews and the comments from the other reviewers.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The submitted manuscript investigates the influence of anxiety constructs on mathematics and spatial skills in a longitudinal study. I consider this paper to be a solid piece of research. I have a few comments:

Line 39 and elsewhere: The authors refer to a “true causal nature.” The word “true” can be safely omitted, as imposed causal structures are by definition true within the model. More generally, I am not convinced that causal terminology is needed in this manuscript, as the distinction between causal and non‑causal modeling approaches is somewhat arbitrary in this context.
Section 3.1: Do the descriptive statistics refer to participants at the first wave? How does the second wave differ? Please also provide information about missing data and how it was handled.
Section 4.1: Including a graphical representation of an example item would be helpful, as the core idea may be difficult to grasp from a purely verbal description.
Section 4.1: Please clarify which IRT score is being used.
Section 4.2: The authors use EAP scores, which have reduced variance compared to the true latent variance. I recommend using weighted likelihood estimates (WLE scores) instead and applying measurement‑error corrections in the path models.
Line 334: Typo: “unidimensional.”
Section 6: Presenting a power analysis for an already completed study is unnecessary. Because standard errors and significance tests are reported, readers can already assess statistical uncertainty. A post‑hoc power analysis does not add information. I strongly recommend removing this section.
Results sections: Please include standard errors for all estimated parameters, including correlations and standardized regression coefficients.
Section 7.3: Little’s MCAR test should be removed, as it provides limited useful information. It is well known that the test has low power, meaning that data may be MAR or MNAR even when MCAR is not rejected. Moreover, FIML relies on the weaker MAR assumption, making the test unnecessary for justifying FIML.
Section 7.3 (second point): It was unclear what was meant by stating that FIML is applied in the IRT and CFA models. Please clarify.
Data availability: The article requires a statement on data availability. At minimum, the authors should provide the means and covariance matrix of all variables. If the dataset contains missing values, these statistics could be obtained using FIML (or the EM algorithm) under a saturated multivariate normal model.

Author Response

Dear Reviewer,

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript addresses an important and timely question about reciprocal longitudinal relations between spatial and mathematical skills in early elementary school, and the domain-specificity of spatial versus mathematical anxiety. The large sample, preregistered analysis plan, and explicit Wald tests comparing domain-specific and cross-domain pathways are notable strengths, and the finding that Wave 1 mathematical anxiety predicts Wave 2 mathematical achievement (controlling prior achievement) is a meaningful contribution. However, several issues substantially qualify the conclusions.

Major revisions

The spatial skills measure shows very low internal consistency across forms (α ≈ .37–.51 at Wave 1; .42–.67 at Wave 2), raising concerns about construct validity and the attenuation or instability of cross-lag estimates. Since the authors have derived IRT scores, they should report IRT model fit and appropriate IRT reliability indices (e.g., marginal reliability), examine form equivalence, and temper claims about “spatial skills” beyond mental rotation.
Because students are nested within classrooms/schools, the manuscript must state and, if not already done, re-estimate models with clustering-adjusted standard errors (or a multilevel/complex survey approach).
The manuscript should reduce causal language: a two-wave CLPM supports reciprocal prediction but cannot establish reciprocal causation or separate within-person change from stable between-person confounding.

Minor revisions

On line 240, the authors state, "we do not have a specific hypothesis." This is not true. The authors report p-values which do not make sense without a hypothesis. Furthermore, the hypothesised model clearly assumes a bidirectional relationship.

The authors should clarify the conceptual alignment between the spatial anxiety items (some task-specific, navigation/maze-like) and the mental rotation outcome.

Three references do not appear in the reference list: Kazelskis et al., 2000; Wang et al., 2014; and Codding et al., 2023. Furthermore, 11 references in the list are not cited in the text.

Author Response

Dear Reviewer,

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

thank you for making all the advised changes - I now recommend the manuscript for publication

Author Response

We wish to thank the reviewer for the time taken to review the revision of our manuscript. Attached is our response to all reviewer comments for this revision.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I still think it is strongly advised using WLE scores with measurement error correction instead of EAP scores.

Author Response

We wish to thank the reviewer for the time taken to review the revision of our manuscript. Attached is our response to all reviewer comments for this revision.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors addressed all issues raised by the reviewers in an excellent way. I have no further comments,

Author Response

We wish to thank the reviewer for the time taken to review the revision of our manuscript. Attached is our response to all reviewer comments for this revision.

Author Response File: Author Response.pdf

Review Reports

Major revisions

Minor revisions