Relations between Subdomains of Home Math Activities and Corresponding Math Skills in 4-Year-Old Children

Round 1

Reviewer 1 Report

Please see attached comments.

Comments for author File: Comments.pdf

Author Response

Dear Editor and Reviewer,

 

Thank you for the opportunity to revise and resubmit our paper entitled “Relations between Subdomains of Home Math Activities and Corresponding Math Skills in 4-Year-Old Children” (MS 1373638). According to Reviewers, this study is important and timely because the study addresses a critical question about specific associations between the home math environment and children’s skills and appropriately explains the methods used to answer this question. Below we outline in detail how we addressed each of the comments. The original comments are in bold, our responses follow in regular font.

 

Reviewer 1

 

1. Introduction - Patterning (p3, lines 97 - 103) doesn’t have as much background information as some of the other skills. A suggestion to strengthen this section would be to expand on the last thought where it mentions predictive math achievement in fifth grade: include another sentence or two describing why it is significant and how it can be strengthened in early childhood education. Alternatively, you could provide a statistic about the students who do not have strong patterning skills and what deficits this presents in later academic development (if one exists), and if not, it might be useful for the reader to know that in general, less is known about the predictive nature of early patterning skill for later learning and achievement.

We thank the Reviewer for encouraging us to further explain the importance of patterning and what we know about its importance for children’s math skills more generally. On page 3 (lines 109-110), we now write:

“Patterning helps children form generalizations, and this ability is foundational for algebraic thinking [24].”

2. Discussion - I would have liked to see at least a brief discussion of possible reasons why patterning is not correlated with children’s other math skills except for adding/subtracting and perhaps a weaker association with set comparison? Seems like there may be some correlation with the more advanced number skills, but I would like to hear what the authors speculate.

We agree with the Reviewer that the positive relation between children’s patterning skills and adding and subtracting (see Table 2) is interesting. As we now state on page 3 (lines 109-110), this relation might be explained via forming generalizations, which is foundational for algebraic thinking. Note that these correlational analyses (Table 2) are part of our preliminary analyses. The focus of the paper (i.e., research questions) are the relations among home math activities and their relation to children’s math skills in specific subdomains. In light of this, the discussion focuses on explaining and interpreting the results of the main research questions, not the preliminary analyses. If we add an explanation about the relation between patterning and adding/subtracting in the discussion, we will have to do the same for every one of the math subdomain skills and we are afraid that this will derail the reader from the focus of the study (i.e., research questions).

3. Likewise, do the authors have a speculation as to why female gender predicted number ID? Gender gaps in math seem to be slowly closing at the early ages, so I’d be curious if the authors think this is merely due to statistical error, or indicative of a more stable relation that exists in the population of interest.

To clarify, the association between child female and children’s number identification is negative. Thus, we found that boys were more likely to do better on the number identification task compared to girls (rather than the opposite), which fits with the most frequently observed gender differences in math. On page1 10-11 (lines 452-459) we addressed this negative relation. See our response to item #4 (below) for more details.

4. Again, patterning is emerging as an interesting skill with regard to being associated with parent education (as was arithmetic and counting/cardinality). I know I’ve requested a few explanations regarding the relations between certain math skills and certain demographic variables. I think the authors’ (even speculative) explanations for these findings would offer some explanation of the effect of “individual differences” (/children’s varying lived experiences) on math skills in the context of the study. I also think such a discussion would be interesting and valuable to readers.

We thank the Reviewer for encouraging us to explain associations between covariates (demographic variables) and child math subdomain skills.

On pages 10-11 (lines 452-459), we now state:

Demographic factors also related to children’s skills in certain math subdomains. Child age positively related to counting and cardinality, number identification and overall math. Child sex (female) negatively related to number identification skills. Parents’ education positively related to all math subdomain skills, except set comparison and number identification. Overall, these findings align with what prior research has found [11,17]. It would be important to replicate these findings with a larger and more diverse sample to further understand why some demographic factors but not others relate to certain math subdomains and not others.

 

5. I agree with the authors (P10, lines 433-435) that more work is needed in this area with ethnically, racially, linguistically, and culturally (etc) diverse populations. In future studies, if possible, I would recommend building on this strong study by replicating it with a more diverse sample.

 

We agree with the Reviewer that a charge is needed for more diverse work in this area.

 

On page 11 (lines 471-472), we have added:

 

“As a result, future studies should aim to replicate these findings with a more diverse sample.”

 

 

Additional edits

 

We included further information on Author Contributions, Funding and Acknowledgements.

We revised the Reference section accordingly.

 

Sincerely,

 

The Authors

 

 

 

 

 

Reviewer 2 Report

This study aimed to address the mixed findings in previous research on the association between children’s home math activities and math skills. The author(s) examined the associations between five subdomains of home math activities and math skills – specifically, counting/cardinality, set comparison, number identification, addition/subtraction, and patterning. Their results suggest weak to moderate associations in the frequency of engaging in these different subdomains of math activities, as well as significant, positive associations between the frequency of engaging in set comparison, addition/subtraction, and patterning and children’s skills in these subdomains. Overall, the study addresses an important question, the writing is clear and compelling, and the methods and analyses are appropriate. However, I do think the authors should do more to contextualize their study in light of other recent publications that address the same aims with discrepant findings (specifically Zippert & Rittle-Johnson, 2020; Purpura, King, Rolan et al., 2020; De Keyser et al., 2020).

 

Broad comments

1. The authors should explicitly acknowledge and describe how their study methods and findings differ from recent work with similar aim. In particular, the authors should be sure to include the work of Zippert & Rittle-Johnson (2020, Early Childhood Research Quarterly) which also compared the subdomains of home math activities to children’s skills, and only found a significant association with children’s numeracy (but not patterning or spatial) skills. In a similar vein, Purpura, King et al., 2020 and De Keyser et al., 2020 – both cited in the review of literature – should be acknowledged for their similar approach of comparing subdomains of math activities and children’s skills. To this end, I would disagree with the authors’ statement on p. 1, lines 39-41 (“To our knowledge, this is the first study to examine subdomain-specific relations between home math activities and children’s math skills.”)

 

 

Specific comments

1. p. 1, line 28 – consider rephrasing “actual research” as “empirical results” or something similar
2. p. 2, section 1.1.2 – Acknowledge that the set comparison literature is also mixed, with a number of studies that do not show a significant association between set comparison and early math skills. Could also reference Chen & Li, 2014; Fazio et al., 2014; Schneider et al. (2016) that showed a significant, positive (albeit small) meta-analytic effect between set comparison tasks and math achievement for young children.
3. p. 2, lines 82-83 – “Number identification skills prepare children for other early numeracy skills, even tasks that do not include numbers such as matching sets of objects…” This finding needs more explanation. Is it that the study showed a significant association between number identification and later set matching? If so, please reword – as written it sounds unidirectional and causal (as opposed to potentially bidirectional and an association).
4. p. 3, lines 109-112 – I would be okay saying your study addresses these two themes, but not that your review of other empirical literature addresses these themes, as other reviews have also described these studies to address this gap.
5. Section 1.2 – In the review of the home math activities literature, I would tone down some of the language that uses a few exemplar studies to generalize to the literature, unless this review was systematic (and if so, please note that!). Specifically p. 4 lines 162-163 – although these few featured studies have not found relations between mean frequency scores of home math activities, haven’t others?
6. p. 4 – In the discussion of conceptualizing based on types of skills fostered, you may note that this might also be how parents are more likely to think about home educational activities. For instance, a parent might more easily think about their child needing practice with counting, labeling numbers or naming shapes than they would think of all of the above as practicing math.
7. Section 2- Materials and methods. Please include the complete 30 item home math environment survey either in text or as an appendix.
8. Discussion – authors should discuss the low item reliability for counting/cardinality tasks, why they think it occurred, and how it may affect the pattern of findings.
9. p. 6, line 271 – the double negative is difficult to parse, maybe “…children were allowed (but not instructed) to count the dots to determine which set had more/less.”
10. Were these data collected during the COVID-19 pandemic? If so, can the authors describe this in the method and mention the potential effects of staying home on the associations between home math activities and children’s math achievement.
11. Discussion – In the introduction, the authors motivate several of the more basic skills (e.g., counting/cardinality, set comparison, number identification) as predicting addition and subtraction skills. With these data the authors could test whether more frequent engagement with those activities at the home predicted children’s addition/subtraction skills.
12. Discussion p. 9, lines 383-385: The finding that there is variability in the frequency with which parents engage in home math activities is a replication of many other previous studies (and should be acknowledged as such with references).
13. Section 4.1 – Limitations should also acknowledge the sample is highly educated. Moreover, this study (and much of the previous literature) is based on associations rather than designs that can allow for causal inference.

Author Response

Dear Editor and Reviewers,

 

Thank you for the opportunity to revise and resubmit our paper entitled “Relations between Subdomains of Home Math Activities and Corresponding Math Skills in 4-Year-Old Children” (MS 1373638). According to Reviewers, this study is important and timely because the study addresses a critical question about specific associations between the home math environment and children’s skills and appropriately explains the methods used to answer this question. Below we outline in detail how we addressed each of the comments. The original comments are in bold, our responses follow in regular font.

 

 

Reviewer 2

 

1. The authors should explicitly acknowledge and describe how their study methods and findings differ from recent work with similar aim. In particular, the authors should be sure to include the work of Zippert & Rittle-Johnson (2020, Early Childhood Research Quarterly) which also compared the subdomains of home math activities to children’s skills, and only found a significant association with children’s numeracy (but not patterning or spatial) skills. In a similar vein, Purpura, King et al., 2020 and De Keyser et al., 2020 – both cited in the review of literature – should be acknowledged for their similar approach of comparing subdomains of math activities and children’s skills. To this end, I would disagree with the authors’ statement on p. 1, lines 39-41 (“To our knowledge, this is the first study to examine subdomain-specific relations between home math activities and children’s math skills.”)

We thank the Reviewer for alerting us about this research and for encouraging us to include it in our paper. We have deleted the statement that our study is the first to examine subdomain-specific relations. In addition, we reference the three papers suggested by the Reviewer.

On page 1 (lines 39-43), we now state:

Three prior studies have examined math subdomain relations [11,16,17]. However, these studies have grouped several skills (i.e., counting and cardinality, set comparison, adding and subtracting, number identification) into a single “numeracy” cluster. To our knowledge, this is the first study to “unpack” the numeracy cluster and examine subdomain-specific relations between home math activities and children’s math skills.

On page 5 (line 1970198), we now state:

“Others have called for similar nuanced approaches [11,16,17].”

On page 10 (lines 457-459), we now state:

“In prior research, no associations have been found between the frequency of home math activities and children’s patterning skills [11,12,16].”

On page 10 (lines 435-444), we now state:

Importantly, in some prior research [11,12] a composite measure of home math activities (across subdomains of math skills) was used, which might have prevented researchers from finding associations to children’s patterning skills. In other prior research [16], items administered to parents included both patterning activities (which tend to happen once per week) and other activities such as watching TV shows involving patterns (which tend to happen several times per week) [52]. This clustering of activities that happen at different frequencies and across different formats (e.g., active vs passive engagement) might have prevented researchers from finding associations. In our study, we focused only on the former (i.e., patterning activities).

 

2. p. 1, line 28 – consider rephrasing “actual research” as “empirical results” or something similar

 

We thank the Reviewer for this recommendation.

 

On page 1 (lines 26-29), we now say:

 

“Despite the wide-spread notion that home math activities are beneficial for children’s early math development, empirical studies on the relations between home math activities and children’s math skills reveal mixed results [3].”

 

3. p. 2, section 1.1.2 – Acknowledge that the set comparison literature is also mixed, with a number of studies that do not show a significant association between set comparison and early math skills. Could also reference Chen & Li, 2014; Fazio et al., 2014; Schneider et al. (2016) that showed a significant, positive (albeit small) meta-analytic effect between set comparison tasks and math achievement for young children.

 

We thank the Reviewer for pointing out the mixed results in this literature and for directing us to key meta-analytic reviews.

 

On page 2 (lines 80-82), we now write:

 

“Though studies associating children’s comparison skills with general math skills are mixed, meta-analytic reviews have found small but significant effects between these factors [28,29].”

 

4. p. 2, lines 82-83 – “Number identification skills prepare children for other early numeracy skills, even tasks that do not include numbers such as matching sets of objects…” This finding needs more explanation. Is it that the study showed a significant association between number identification and later set matching? If so, please reword – as written it sounds unidirectional and causal (as opposed to potentially bidirectional and an association).

 

We agree with the Reviewer that the original phrasing was confusing.

 

On page 2 (lines 87-89), we now write:

 

“Number identification skills are related to other early numeracy skills, even tasks that do not include numbers such as matching sets of objects with equivalent quantities [31].”

 

5. p. 3, lines 109-112 – I would be okay saying your study addresses these two themes, but not that your review of other empirical literature addresses these themes, as other reviews have also described these studies to address this gap.

 

We thank the Reviewer for expressing their confusion about the way we have presented these two themes.

 

On page 3 (lines 116-118), we now state:

 

“Our study aims to address these two themes by paying closer attention to specific subdomains of math in both surveys of home math activities and children’s math assessments instead of primarily targeting math broadly [15].”

 

6. Section 1.2 – In the review of the home math activities literature, I would tone down some of the language that uses a few exemplar studies to generalize to the literature, unless this review was systematic (and if so, please note that!). Specifically p. 4 lines 162-163 – although these few featured studies have not found relations between mean frequency scores of home math activities, haven’t others?

On page 4 (lines 168-176), we now state:

“Some of these studies have found no relations between mean frequency scores of home math activities and a composite measure of children’s math skills (4- to 6-year-olds in the U.S.: [9]; 2- to 4-year-olds in the U.S.: [10]; 3- to 5-year-olds in the U.S.: [12]; 5- to 6-year-olds in Belgium: [11]). Others have found positive relations. For example, one study of 5- to 7-year-olds in Germany conceptualized home math activities as a sum score (3 items; frequency of playing games involving dice, counting, and calculation) and found positive associations to children’s math skills, a sum score of several tasks assessing counting, number identification, set comparison and adding/subtracting [7].”

 

7. p. 4 – In the discussion of conceptualizing based on types of skills fostered, you may note that this might also be how parents are more likely to think about home educational activities. For instance, a parent might more easily think about their child needing practice with counting, labeling numbers or naming shapes than they would think of all of the above as practicing math.

 

We agree with the Reviewer that parents’ conceptualization of the home math environment is likely more subdomain-focused.

 

On pages 4-5 (lines 193-196), we now write:

 

“This may also be the way that parents rationalize providing math support to their child, choosing to focus on a particular activity because their child struggles with the skill rather than providing math support more generally.”

 

8. Section 2- Materials and methods. Please include the complete 30 item home math environment survey either in text or as an appendix.

 

We appreciate the Reviewer’s recommendation to include the items in the survey.

 

We have added the home math environment survey as an appendix at the end of the manuscript and on page 6 (lines 257-258), we now state:

 

“See Appendix for a full list of items.”

 

9. Discussion – authors should discuss the low item reliability for counting/cardinality tasks, why they think it occurred, and how it may affect the pattern of findings.

On page 6 (lines 268-275), we now state:

“There was high item reliability for all math subdomains (a = .80-.86), except for counting/cardinality (a = .37), which might be because we grouped counting/cardinality activities with different levels of complexity and thus very different frequencies of occurrence at home (e.g., counting using fingers is low in complexity and presumably more often practiced while counting by 2s or 5s is high in complexity and presumably less often practiced). We calculated separate average scores for each math subdomain and an overall score (mean score across five subdomains).”

We refrained from including this in the Discussion section because the lack of associations was not only found in counting/cardinality but also in number identification, which had high item reliability. Thus, item reliability does not explain the null findings. We have provided an alternative explanation about the lack of associations in these two math subdomains (emphasis in preschool curricula), which we believe is more comprehensive.

10. p. 6, line 271 – the double negative is difficult to parse, maybe “…children were allowed (but not instructed) to count the dots to determine which set had more/less.”

 

We agree with the Reviewer that the original phrase was confusing.

 

On page 6 (lines 286-288), we now write:

 

“For the Set Comparison items, the child was allowed (but not instructed) to count the dots to determine which set had more/less.”

 

11. Were these data collected during the COVID-19 pandemic? If so, can the authors describe this in the method and mention the potential effects of staying home on the associations between home math activities and children’s math achievement.

 

We thank the Reviewer for alerting us to the need to clarify the role of the COVID-19 pandemic in the data collection for this study.

 

On page 5 (lines 42-243), we now write:

 

“All data from this study were collected virtually due to restrictions to in-person research activities during the COVID-19 pandemic.”

 

On page 11 (lines 490-492), we now write:

 

“Sixth, these data were collected during the COVID-19 pandemic, which offers a unique reflection of the home numeracy environment that may not generalize to research conducted prior to the start of the pandemic and may not generalize to the future.”

 

12. Discussion – In the introduction, the authors motivate several of the more basic skills (e.g., counting/cardinality, set comparison, number identification) as predicting addition and subtraction skills. With these data the authors could test whether more frequent engagement with those activities at the home predicted children’s addition/subtraction skills.

 

We thank the Reviewer for their recommendation that we run these additional analyses.

 

On pages 9 (lines 367-371), we now say:

 

“Subsequent analyses regressing children’s adding and subtracting skills on home counting/cardinality, set comparison, and number identification activities, controlling for child age, sex, and parent education revealed no significant associations (bs ranging from -0.85 to -0.13, all ps > .10) except marginal significance for set comparison activities (b = 10.66, p = .09).”

 

13. Discussion p. 9, lines 383-385: The finding that there is variability in the frequency with which parents engage in home math activities is a replication of many other previous studies (and should be acknowledged as such with references).

 

On page 10 (lines 404-406), we now state:

 

“Together, our findings indicate that there was variability in the frequency with which parents engaged in home math activities, which replicates the results of many previous studies [4,5,8,41].”

 

14. Section 4.1 – Limitations should also acknowledge the sample is highly educated. Moreover, this study (and much of the previous literature) is based on associations rather than designs that can allow for causal inference.

 

On page 11 (lines 468-469), we now write:

 

“Our study has some limitations. First, our sample was homogeneous (mostly White, highly educated, and from middle-income backgrounds).”

 

 

Additional edits

 

We included further information on Author Contributions, Funding and Acknowledgements.

We revised the Reference section accordingly.

 

Sincerely,

 

The Authors