The premise on which our synthesis is based is the fragmentation of research focused on teaching and learning in mathematics. Our intention is to build an aggregate synthesis from these sources in the context of school education and meaningful learning. Our research targets the links between the different approaches used in teaching, interaction during the teaching-learning process and learning outcomes. Methodologically, our dataset consists of qualitative, quantitative, and mixed-methods studies and meta-analyses. An EBSCO search produced 69 analysis-eligible publications from 2007-2019. According to our findings, the use of contextual, concrete and social approaches promotes meaningful learning in mathematics, although with certain refinements. The analyses revealed that high-quality learning in mathematics requires guidance during student activities and evaluation with immediate feedback during the teaching-learning process. It also requires the skill among teachers to choose suitable contexts and learning tools, and to focus the students' communication on what is relevant. Additional significant factors in a meaningful learning process include an affectively favourable classroom atmosphere and teachers who treat their students as individuals.

Synteesitutkimuksemme tarkoituksena on rakentaa laaja-alainen koonti niistä yhteyksistä, jotka kohdentuvat matematiikan kouluopetukseen ja mielekkään oppimisen kontekstiin. Tutkimusmetodologisesti synteesi koostuu kvalitatiivisista, kvantitatiivisista ja mixed methods –lähestymistapaan perustuvista alkuperäistutkimuksista ja muutamista meta-analyyseistä. Lopullinen Ebsco-haku tuotti 50 analyysiin soveltuvaa julkaisua vuosilta 2007–2017. Aineiston analyysin alkuperäisenä kehikkona toimi aikaisemmin laadittu käsitteellinen malli (Koskinen, 2016). Aineistostamme ei löytynyt yhtään tutkimusta, jossa olisi tutkittu edellä mainittua kokonaisuutta. Tutkimustulosten mukaan matemaattiseen ymmärtämiseen tähtäävät opetuksen lähestymistavat – kontekstuaaliset, konkreettiset ja sosiaaliset – edistävät mielekästä oppimista. Niiden onnistunut soveltaminen edellyttää kuitenkin opettajan taitoa valita sopivat välineet ja käyttää niitä sekä oppilaan toiminnan vuorovaikutteista ohjaamista. Näiden lähestymistapojen yhdistäminen opetuksessa parantaa entisestään niiden vaikuttavuutta. Teaching mathematics to promote meaningful learning: Towards an integrative model Abstract The purpose of this research synthesis is to build a comprehensive entity with links that focus on school education in mathematics and the context of meaningful learning. The synthesis consists of qualitative, quantitative and mixed methods studies, and a few meta-analyzes. The final Ebsco-search produced 50 publications that met our criteria (for years 2007-2017). The tentative framework for the analysis of a data was the previously presented conceptual model (Koskinen, 2016). Our research synthesis did not find any studies that examined the above mentioned entity. According to research findings, analysis suggests that teaching approaches to mathematical understanding – contextual, concrete, and social – support meaningful learning. However, their successful application requires that the teacher has the skill to select and use the appropriate tools and the interactive guidance of the pupil's activities. Combining these approaches in teaching will further enhance their effectiveness. Keywords: mathematics, teaching, learning, research synthesis, holistic approach

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