Sciences as a part of research regarding school psychology. This page combines studies that have been conducted regarding math competence. The purpose of studying math competence is to specify math competence as a phenomenon, to find out Estonian students’ level of competence and how to support students in their development of math abilities. The projects have been funded by Republic of Estonia Ministry of Education and Research, Tallinn University and the School of Natural and Health Sciences research funds as well as by the Estonian Research Council. The projects have mainly been carried out by researchers from the School of Natural and Health Sciences under the field of psychology; however, there has been collaboration with other institutes, Republic of Estonia Education and Youth Board, and researchers from the University of Turku and the University of Helsinki. 

Three projects have been carried out with students who were in Grade three or six in 2019. The students took part in an assessment during the 2019/2020 school year as a part of the first project and during the 2021/2022 and the 2022/2023 school year as a part of the second project. A pilot intervention to support math competence development was conducted as a part of the third project during the 2022/2023 school year. The following intervention was modified based on the pilot intervention and carried out during the 2023/2024 school year with the students who were in Grade seven, which included pre-, post- and delayed post-intervention assessment. The delayed post-intervention assessment was carried out at the begging of Grade eight for both the intervention and the control group. 
 

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Theoretical background

The definition of math competence

Math competence helps people to understand their surrounding world and to successfully deal with everyday problems, thus, systematically supporting the development of math competence is vital throughout education. In the Programme for International Student Assessment (OECD, 2022) math competence has been defined as mathematical literacy i.e. competence as: “an individual’s capacity to reason mathematically and to formulate, employ and interpret mathematics to solve problems in a variety of real-world contexts,“ which comprises of concepts, procedures, facts and tools and: “It helps individuals know the role that mathematics plays in the world and make the well-founded judgements and decisions needed by constructive, engaged and reflective 21st Century citizens.” Danish researchers Niss and Højgaard (2019) have also emphasized that the problems related to math competence do not necessarily need to be clearly math-related but have to be solvable using math. Therefore, in addition to math skills math competence also involves knowledge of the subject areas where to use math and the knowledge regarding how to use math in those subject areas (Toomela et al., 2020).

In the research studies combined in the current page the definition of math competence is based on Toomela et al (2020) who define math competence as a person’s ability to notice, understand and formulate problems and to solve them by using mathematical concepts and procedures to accomplish goals, to develop one’s knowledge and abilities and to take part in society. Thus, math competence combines not only math specific knowledge but also the ability to notice and differentiate problems and to solve them by using math skills as well as problem-solving strategies. Additionally, math competence includes the understanding of how and when to use math to reach one’s goals and to take part in society. According to this framework math competence can be divided into three subparts: 1) math-related knowledge, skills and attitudes; 2) knowledge of the subject areas where to use math and 3) knowledge and skills regarding how to use math in the subject areas (see Figure 1). 

Math competence is expressed by solving different problems, thus math competence is closely related to the ability to problem solve. Problem solving (see Figure 1) is a process that consists of noticing and describing the problem, choosing a strategy to solve the problem, implementing the solution strategy and assessing the solution. Thus, it is first necessary to notice the problem and to word it as clearly as possible, after which an appropriate solution strategy should be chosen and implemented. Finally, the whole solution process should be assessed as well as if the solution corresponds to the conditions of the problem (Kikas, 2010, Wüstenberg et al., 2012). It is vital to understand the process of problem solving since it allows us to also describe the learning process (see Kikas et al., 2018, Kikas et al., 2021) and therefore the process of problem solving is also an important part of learning math. 

In addition to knowledge and skills, math-related attitudes i.e. motivation and beliefs related to learning and using math, are important. One of the most prevalent theories of learning motivation is the expectancy-value-cost theory (Eccles & Wigfield, 2020). Expectancies refer to the students’ estimation regarding how well they do in math. Values are expressed in the students’ estimations of how interesting math is as well as how significant and useful it is to be good at math. Cost refers to how time consuming, exhausting and emotionally taxing it is to learn math (Eccles et al., 1983; Eccles & Wigfield, 2020). Thus, if a student regards math to be interesting, it significant and useful to be good at math as well as it not too burdensome to learn and use math, then the student is considered to be motivated to learn math and to use math in their everyday life (Andersen & Cross, 2014; Jiang et al., 2020; Lauermann et al., 2017).  

Math skills in the research studies combined in the current page have been assessed by using, for example, calculation and conversion tasks, typical and novel real life word problems, spontaneous focusing on quantitative relations and the guided use of multiplicative relations. An intervention has been devised to support the development of math skills. All studies have also assessed students’ learning motivation i.e. expectancies and values related to math. More detailed information about the projects can be found in the corresponding subsections.

Figure 1. Math competence

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1st project (2019-2020): Math and language competence tests for Grades three and six

Math and language competence tests for Grades three and six were created as a part of the project I ja II kooliastme üldpädevuste hindamisvahendite rakendamine põhikoolides: matemaatilise ja funktsionaalse kirjaoskuse hindamise pilootprojekt (Using I and II school level general competence assessment tools in middle school: a pilot project to assess math and functional literacy)“ (duration of the project 1.06.2019-28.02.2020). The purpose of the study was to create electronical math and language tests for Grades three and six in both the Estonian and Russian languages. This project enabled to create math and language competence tests for Grades three and six for teachers in Estonia to use to evaluate their students’ skills and knowledge. Detailed information about the tests and the use of these tests is available on the Republic of Estonia Education and Youth Board webpage (in the Estonian and Russian languages). The project leader was professor Aaro Toomela and the project was carried out by Piret Soodla, Kaja Mädamürk and Eliis Härma

2nd project (2021-2022): Assessment of the development of mathematical competence in basic school

The project Assessment of the development of mathematical competence in basic school (project duration 1.02.2021-31.11.2022) was a continuation of evaluating math competence by creating and using math and language competence tests. The purpose of the study was to evaluate math competence development between the Grades of three and five and the Grades of six and eighth. This research enables us to evaluate how students math competence develops, how earlier skills and knowledge predict math competence in Grades five and eighth and how language competence relates to math competence development. Math and learning related anxiety and motivation were also evaluated. This project gives important insights into how students’ skills develop and what aspects may hinder or assist in the development of these skills. 

The project leader was Senior Researcher in School Psychology Kaja Mädamürk from the School of Natural and Health Sciences and the project was also carried out by doctoral students from the School of Natural and Health Sciences Triinu Kilp-Kabel and Hardi Sigus, in addition to collaboration with other researchers and students from Tallinn University and researchers from the University of Turku.

 

3rd project (2022-2025): Developing math competence in middle school: Applying math outside of the classroom

 

The project Developing math competence in middle school: Applying math outside of the classroom (project duration 1.01.2022-31.12.2025) is a continuation of the previous projects of evaluating math competence development from Grade six to Grade eight. The subjects in the project are students that participated in the first project in Grade three, who will graduate from Grade eighth by the end of this project. In addition, an intervention program was developed for Grade seven to study ways of supporting math competence and to offer teachers a supplementary tool to use alongside their regular classroom curriculum to support math competence. This research enables us to evaluate how students’ math competence subskills and motivation develop and what types of math competence profiles and developmental pathways form between Grades three and eighth. Additionally, this research enables us to find what effect a math competence intervention has on students’ math competence development compared to students that do not take part in the intervention.

The project leader is Senior Researcher in School Psychology Kaja Mädamürk from the School of Natural and Health Sciences and the project is also carried out by doctoral students from the School of Natural and Health Sciences Triinu Kilp-Kabel and Hardi Sigus and visiting researcher Serhii Petrovych. In addition to collaboration with other researchers and students from Tallinn University and researchers from the University of Turku. 

 

Intervention

During the 2022/2023 school year a pilot intervention about linear functions and math competence was conducted as a part of the third project. Students also took part in assessments based on functions, which included questions about interest and utility regarding math and functions, before and after the pilot intervention. The students in the control group learned linear functions the way they normally would, while the students in the intervention group solved at least three tasks in class and two tasks about real-life situations as homework assignments instead of regular textbook or workbook tasks. Teachers could choose between six tasks: running speed, anxiety, boiling water, hair growth, financial literacy and candle burning. 

Each task consisted of background information about the subject, finding correct lines on a graph based on descriptions, solving a linear function task from a word problem using the formula, table and graph, and questions for discussion. Following each task the students had to assess their own abilities regarding linear functions by choosing one of the three options for six statements: 1) I need to study more, because I did not understand, 2) I understand but do not know how to explain it to someone else, or 3) I understand and know how to explain it to someone else. Students could also write feedback about what they thought of the tasks inside of the intervention textbooks. 

The results of the pilot intervention showed that students in the intervention group were better at solving a real-life linear function task after the intervention when compared to the control group. More specifically, students in the intervention group were better at identifying the slope, y intercept and the linear equation when compared to the control group. Additionally, the assessments of the utility of math increased for the intervention group. 

Amendments to the intervention tasks and assessment tools were made based on the feedback from students and teachers that took part in the pilot intervention. Based on these amendments an intervention will be conducted during the 2023/2024 school year. 

Students in Grade seven from six schools participated in the intervention (5 intervention classes and 8 control classes). An observation of a function task similar to the intervention linear function task was conducted to ensure that the tasks are conducted similarly by all teachers in the study. Additionally, an observation of a linear function intervention task was conducted to check if the teachers followed the intervention procedure in all intervention classes. Students completed a test regarding function prior to learning linear functions. A linear function test was conducted immediately after learning linear functions as well as at the beginning of the 2024/2025 school year prior to any repetition of the last years subjects in math. The tests also included questions regarding the utility and self-efficacy regarding math and functions. A more thorough analysis of the intervention results will be done during the fall of 2024/2025 school year and at the end of the study the intervention tasks will be published to use for free. 

Both the pilot intervention and the intervention were lead by Senior Researcher in School Psychology Kaja Mädamürk from the School of Natural and Health Sciences and carried out by doctoral students from the School of Natural and Health Sciences Triinu Kilp-Kabel and Hardi Sigus

Research team

KAJA MÄDAMÜRK

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Position: Senior Researcher in School Psychology

Research interests: 

  • Development of key competencies
  • Learning motivation
  • Intervention studies of math skills

E-mail: kaja.madamurk@tlu.ee 

CV in the Estonian Research Information System

 

TRIINU KILP-KABEL

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Ph.D. Candidate in Psychology

E-mail: triinu.kilp-kabel@tlu.ee

Research interests: 

  • Math competence development in middle school
  • Achievement motivation in math
  • Development of an evidence-based math skill intervention

CV in the Estonian Research Information System

 

HARDI SIGUS

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Ph.D Candidate in Psychology

E-mail: hardi.sigus@tlu.ee

Research interests: 

  • Developing real-life math problems
  • Researching mathematics motivation of elementary school students
  • Mathematics intervention research

CV in the Estonian Research Information System

 

SERHII PETROVYCH

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Position: Researcher

Research interests: 

  • Pedagogy and didactics
  • Math competence 
  • Technology in Teaching and Learning

E-mail: politex2013@gmail.com

CV in the Estonian Research Information System

 

Research articles

 

  1. Mädamürk, K., Upadyaya, K., Hietajärvi, L., Lonka, K., & Salmela-Aro, K. (2025). The importance of socio-emotional skills obtained before the COVID-19 pandemic in supporting study engagement during the pandemic and transition to higher education. European Journal of Psychology of Education, 40(1). https://doi.org/10.1007/s10212-024-00898-3 
  2. Kilp-Kabel, T., Mädamürk, K. Expectancies, values, and task persistence can alleviate the negative effects of math anxiety on math performance. European Journal of Psychology of Education, 40, 17 (2025). https://doi.org/10.1007/s10212-024-00928-0 
  3. Mädamürk, K., & Kikas, E. (2024). The development of math skills from grades 1 to 12: Novel findingsusing person-oriented approach. Developmental Psychology. Advance online publication. https://doi.org/10.1037/dev0001813 
  4. Sigus, H., & Mädamürk, K. (2024). Context matters: The importance of extra-mathematical knowledge in solving mathematical problems. Frontiers in Education, 9, 1334034.  https://doi.org/10.3389/feduc.2024.1334034 
  5. Kilp-Kabel, T., & Mädamürk, K. (2024). The developmental trajectories of math skills and its relation to math interest in Grades three and five. European Journal of Psychology of Education, 1-19.  https://doi.org/10.1007/s10212-024-00807-8
  6. Kilp-Kabel, Triinu; Mädamürk, Kaja (2023). A pilot intervention using real life linear function tasks and its relation to self-reported math and function interest and utility. ICERI2023 Proceedings.  ICERI2023 Proceedings, 2601−2610. (ICERI2023 Proceedings; 1). Doi: 10.21125/iceri.2023.0696
  7. Petrovych, Serhii; Mädamürk, Kaja (2023). Math motivation, anxiety, and teachers’ emotional support related to calculation and word problem solving skills in middle school. ICERI2023 Proceedings.  IATED, 3408−3413. (ICERI2023 Proceedings; 1). Doi: 10.21125/iceri.2023.0881
  8. Sigus, H.; Soodla, P.; Mädamürk, K. (2023). Tava- ja eriklassis õppivate hariduslike erivajadustega õpilaste lugemis- ja matemaatikaoskused. Eesti Haridusteaduste Ajakiri = Estonian Journal of Education, 11 (1), 159−186. Doi:  https://doi.org/10.12697/eha.2023.11.1.07
  1. Kikas, Eve; Mädamürk, Kaja; Silinskas, Gintautas (2022). Parental homework-help profiles throughout grades 6-9: Relations to motivation and mathematics skills. Frontiers in Education, 7, ARTN 914992. Doi: https://doi.org/10.3389/feduc.2022.914992

Conference presentations

 

  1. Mädamürk, Kaja; Silinskas, Gintautas; Kikas, Eve. (2024). Motivation and worry profiles related to math skills before, during, and after the COVID-19 pandemic. In: ICM2024 International Conference on Motivation and Emotion, Bern, Switzerland, 28-30 August, 2024.
  2. Kilp-Kabel, Triinu; Mädamürk, Kaja. (2024). Expectancy-value motivation profiles and their relation to specific math skills. In: ICM2024 International Conference on Motivation and Emotion, Bern, Switzerland, 28-30 August, 2024.
  3. Sigus, Hardi; Mädamürk, Kaja. (2024). Students’ motivation as a mediator between extra-mathematical knowledge and word problem-solving. In: ICM2024 International Conference on Motivation and Emotion, Bern, Switzerland, 28-30 August, 2024.
  4. Kilp-Kabel, Triinu; Mädamürk, Kaja. (2023). A pilot intervention using real life linear function tasks and its relation to self-reported math and function interest and utility. In:  ICERI2023 16th annual International Conference of Education, Research and Innovation, Seville, Spain, 13-15 November 2023.
  5. Petrovych, Serhii; Mädamürk, Kaja (2023). Math motivation, anxiety, and teachers’ emotional support related to calculation and word problem solving skills in middle school. ICERI2023 Proceedings.  IATED, 3408−3413. (ICERI2023 Proceedings; 1). DOI: 10.21125/iceri.2023.0881.
  6. Mädamürk, Kaja; Kurvits, Jüri; Kikas, Eve (2023). Profiles of mathematical relational reasoning and students’ motivation in fifth grade. In: (302). EARLI  2023 The 20th Biennial EARLI Conference for Research on Learning and Instruction, Thessaloniki, Greece, 22-26 August 2023.
  7. Kilp-Kabel, Triinu; Mädamürk, Kaja (2023). The development of math competence and its relation to math interest. In:  EARLI 2023 The 20th Biennial EARLI Conference for Research on Learning and Instruction, Thessaloniki, Greece, 22-26 August 2023.
  8. Mädamürk, Kaja; Kikas, Eve (2023). Development of Mathematical Skills: Variable- and Person-Oriented Approaches. In:  2023 AERA Annual Meeting, Chicago, 13.04-16.04.2023.

Courses and other presentations

As a part of the research highlighted on this webpage students’ math-related motivation has been assessed, including math anxiety. Thus, a math anxiety course has been created as a collaboration between Tallinn University and the University of Tartu. The target group of the course are primary school teachers, math teachers, special educators, school psychologists etc. The course gives a theoretical overview of math anxiety and offers practical advice to help prevent the development of math anxiety and to support students who experience math anxiety. 

The course is taught by Kaja Mädamürk and Triinu Kilp-Kabel from Tallinn University and by Karin Täht and Getriin Aaviste from the University of Tartu.  More information can be found on the course website (in Estonian): https://www.tlu.ee/koolitused/matemaatikaarevus 

An article regarding alleviating math anxiety was written by Kaja Mädamürk for the Estonian newspaper Postimees (in Estonian): https://www.postimees.ee/7597091/ak-fookus-kaja-madamurk-matemaatikaarevuse-leevendamisel-on-oluline-roll-nii-opetajal-kui-ka-psuhholoogil

A short blogpost regarding math anxiety was written by Triinu Kilp-Kabel for the Tallinn University education blog (in Estonian): https://www.tlu.ee/hti/meediavarav/blogid/mis-matemaatikaarevus-ja-kuidas-sellega-toime-tulla 

Karin Täht has spoken on the positive and negative emotions regarding learning math for the Kuku radio podcast (in Estonian): https://kuku.pleier.ee/podcast/kuue-samba-taga/173115

An interview conducted with Triinu Kilp-Kabel on the relationship between math anxiety and other motivational aspects can be read from Novaator (in Estonian) https://novaator.err.ee/1609588487/matemaatikaarevus-halvendab-laste-opitulemusi-ja-ahendab-tulevikuvalikuid and an interview with Triinu Kilp-Kabel can be listened to from Terevisioon (in Estonian) https://jupiter.err.ee/1609591103/arevus-matemaatikatunnis-toob-kehvema-hinde