- iSeeNumbers

# What have we found out so far?

The data collection ended around a year ago, in spring -21, and during the past year we have mainly focused on reporting and presenting the findings from our studies in the project. Here comes a list of published work so far with some key findings and links to the publications. The preliminary results have been presented in many scientific conferences (see __presentations__), both online and finally this year also face to face. During the past three years, there have been many students doing their master thesis work connected to the project (see all completed __master's theses__). Most of them could see the different steps of research work – starting from working as a research assistant and collecting data, and finally doing data analyses to be able to answer the research questions of their thesis work.

Good math skills and motivation do not always go hand-in-hand

Our first publication was part of the Psykologia journal's special issue, which focused on math learning and motivation. Here we reported findings of what kind of profiles of math skills and motivation could be found among first graders. Four different profiles were identified: (1) students with relatively better math skills but a bit lower interest in math (46 %), (2) students with relatively good skills and motivation (22 %), (3) students with relatively weak math skills and negative motivation (21%), and (4) students with relatively weak skills but positive motivation, especially high interest (12 %). Boys and girls were equally represented in the groups. As good skills and motivation do not seem to go always hand-in-hand, the practical implication of this study is that it is important to identify those students who need intensified support in either learning math skills, increasing motivation in math, or in both. A more detailed blog post about this study is available in Finnish __here__.

Publication: *Tuominen, H., Niemivirta, M., Korhonen, J., Tapola, A., & Mononen, R. (2021). Matemaattisten taitojen ja motivaation profiilit ensimmäisen luokan oppilailla. Psykologia, 56(6), 548–566. *

Low level of math anxiety in early grades

Our second publication focused on "Developmental relations between mathematics anxiety, symbolic numerical magnitude processing, and arithmetic skills from first to second grade." This study is among the first ones reporting longitudinal results concerning math anxiety and math skills in this age group. The main findings were that in this age group students in general did not really experience math anxiety (which is nice, of course!), but there were some individual differences. Change in math anxiety was more connected to change in arithmetic skills than to symbolic numerical processing. As a practical implication, there are some children who experience math anxiety already in early grades, and teachers should be aware of this. Creating a positive and motivating math learning environment may help, but we still need more research in the future about the effective interventions for mitigating math anxiety, so that the level of math anxiety could be decreased. You can read the main findings also from this __infograph__.

This publication is open access:* Mononen, R., Niemivirta, M., Korhonen, J., Lindskog, M., & Tapola, A. (2021). Developmental relations between mathematics anxiety, symbolic numerical magnitude processing, and arithmetic skills from first to second grade. Cognition and Emotion. Advance online publication. **https://doi.org/10.1080/02699931.2021.2015296*

What predicts math learning difficulties?

In the third article, and the first published article in year 2022, we were finally able to use the data from the first to third grade. In this study, we aimed to find out which domain-general and domain-specific skills measured in the first grade predict the status of having math learning difficulties (MLD) in the third grade. We used different cut-off criteria and measured of math performance for defining the math learning difficulties status. We found, for example, that especially symbolic numerical magnitude processing, verbal counting, and rapid automatized naming were good predictors when math learning difficulties were defined based on arithmetic fluency performance, whereas verbal counting skills and nonverbal reasoning predicted the status based on curriculum-based math performance. Different cut-off scores and mathematics measures used for the definition of MLD status are important to acknowledge, as those seem to lead to different early domain-specific and domain-general predictors of MLD.

This publication is open access: *Mononen, R., Niemivirta, M., & Korhonen, J. (2022). Predicting mathematical learning difficulties status: The role of domain-specific and domain-general skills. International Electronic Journal of Elementary Education, 4(3), 335–352. Retrieved from **https://www.iejee.com/index.php/IEJEE/article/view/1731*

Symbolic numerical processing and working memory matter

Our fourth article used again the first grade data, and investigated the patterns of symbolic numerical magnitude processing (SNMP) and working memory (WM) as predictors of early mathematics performance. Although the roles of SNMP and WM in mathematics performance are well acknowledged, studies examining their joint effects are few. We identified four groups of children with different patterns of SNMP and WM performance (1) weak SNMP (33.6%), (2) strong SNMP (25.8%), (3) weak SNMP and WM (23.4%) and (4) strong WM (17.2%). As an implication for practice, screening SNMP skills already in the first grade might be an effective and feasible approach to identify children with potential problems in mathematics learning and at risk for mathematical learning difficulties later on.

This publication is open access:* Mononen, R., & Niemivirta, M. (2022). Patterns of symbolic numerical magnitude processing and working memory as predictors of early mathematics performance. European Journal of Psychology of Education. **https://doi.org/10.1007/s10212-021-00596-4*

What does a pupil size tell us about the math problem difficulty?

The first eye-tracking study from the project had older students involved, as we first needed to explore how our developed eye-tracking math measures work with older students before trying similar ones with younger students. This study aimed to find out does mathematics anxiety moderate the effect of problem difficulty on cognitive effort. The analyses showed that the difficulty level of the multiplication problems affected the cognitive effort so that the pupil dilated more with harder multiplication problems. However, we did not find a moderating effect of MA on cognitive effort, when controlling for arithmetic competence, general intelligence, and working memory. This suggests that MA does not contribute to cognitive effort when solving multiplication problems.

This publication is open acces*s: Throndsen, T. U., Lindskog, M., Niemivirta, M., & Mononen, R. (2022). Does mathematics anxiety moderate the effect of problem difficulty on cognitive effort? Scandinavian Journal of Psychology. Advance online publication, **https://doi.org/10.1111/sjop.12852*

Enjoyment in math decreases from first to third grade

Our latest article, just submitted for peer-review but already accessible as a preprint, aimed to find out the developmental trajectories and interrelationships of mathematics-related achievement emotions (enjoyment, anxiety, and boredom) and arithmetic fluency (addition and subtraction) from first to third grade, and the effects of these on third grade mathematics performance. This is again one of the first longitudinal studies in this field and in this age group. __Preprint__ means that the article still needs to go through the peer-review process. We will modify the article based on the feedback and suggestions from the reviewers, and hopefully have the article accepted for publication later on. Fingers crossed!

You can access the preprint here:* **Rawlings, A. M., Niemivirta, M., Korhonen, J., Lindskog, M., Tuominen, H., & Mononen, R. (2022). Achievement emotions and arithmetic fluency – Development and parallel processes during the early school years. Preprint available at PsyArXiv: **https://doi.org/10.31234/osf.io/ufr32*

Looking forward to reporting the remaining results from the project later on!

*Have a nice and sunny summer!*

Posted by Riikka