## Abstract

International studies in inclusive education in mathematics point out that students have unequal access to learn and participate (Cin & Cifti 2017; Reinholz & Shah 2018; Rubel 2016; Lambert 2015). In the most dominant form of math education, teachers explain the task and give a few examples, after which the students work individually. Lambert (2015) and Schmidt (2016) argue that the academic norms in mathematics – like remembering rules and working individually without hesitating – favours certain students, while students with a more creative and problem-solving approach are excluded. Lim et al. (2015) state that learning and the sense of belonging is promoted, when the teacher develops classroom norms and establishes a learning environment in which students recognize divergent thinking.

As a contribution to the international studies this paper presents some of the results from a three-year research project in a Danish context. The project investigates how an intervention (SYKL) with reciprocal peer tutoring in mathematics and science in 4th grade affects the students' engagement, participation and learning outcomes. In contrast to most international peer tutoring projects, SYKL focus on both social relations and academic inclusion at the same time.

SYKL is based on a sociocultural perspective in learning (Vygotsky, 2019) and emphasize the importance of inquiry-based learning (Blomhøj, 2021). In SYKL students are specifically taught how to help each other and engage in academic conversations when working in pairs. SYKL is inspired by interventions with peer tutoring, where students take on different roles (Thurston et al., 2007; Thurston et al., 2020). The students are assigned one of two positions, either as tutor or tutee. To fulfill the role of ‘coach’ or ‘helper’, the tutor receives prompt cards with generic questions and academic hints for solving the specific task. During a lesson students switch roles so that both can participate in meaning making and commit to the relation.

The purpose of this paper is to investigate students’ assisting strategies in SYKL and explore how these strategies promote or inhibit inclusion. In the paper inclusion is understood as “maximizing the participation of all children” (Allan, 2008:33), and participation is understood as learning in collaboration with others, while students are involved in the academic field and accepted for who they are (Booth, 2011). To create knowledge about students’ participation we use Wenger’s (2004) terms and ask: To what extent do we see "legitimate peripheral participation" that can potentially lead to full participation, and to what extent do we see "marginalized non-participation" that potentially leads to full exclusion from the student community?

Whether students are included in the student community is related to the different strategies they bring into play. This phenomenon can be explained with the concept of social capital (Bourdieu & Wacquant, 1996), which is the aggregate of the resources linked to being part of a group. Bourdieu emphasizes that people tend to acknowledge one another and affirm group membership through rituals, and he refers to these activities as investment strategies. Inspired by Bourdieu, we ask: Which "cards" do the students play to become legitimate participants in SYKL. What counts as trump?

Schmidt (2015) shows that students use different strategies to be included, and that these strategies are both academically and socially grounded at the same time. Thus, there is a close connection between acceptance, participation, and performance. In the presentation this is understood as a socio-academic inclusion, which is a lens we use when analyzing the students’ socio-academic investment strategies.

Thus, the driving research questions are:

What kind of conversational actions characterize the students’ different assisting strategies in SYKL?

How does different assisting strategies affect the socio-academic inclusion?

Methodology, Methods, Research Instruments or Sources Used

The research project reported investigated a 13-week intervention with SYKL. It involved 25 Danish primary school teachers and approximately 570 students from 4th grade. The total empirical data consists of pre- and post-tests, pre- and post-questionnaires, teacher- and student interviews, and video observations. This paper will focus on 15 video recorded dialogues and investigate the socio-academic patterns of participation. We have closely studied each video several times and we have transcribed each dialogue (Anderson & Tvingstedt, 2009).

As the ambition was to create knowledge about the students' assisting strategies, we have analyzed how the students used social and academic conversational actions (verbal as well as non-verbal) when they were in the role of tutor. In that regard we draw on Rasmussen and Schmidt (2022), who have categorized a number of social conversational actions (e.g., ‘expressing confidence in other’) and academic conversational actions (e.g., ‘suggesting possible solutions’), that constitute the socio-academic norms of a subject (in this case mathematics).

At the same time, we have investigated how these conversational actions are related to processes of inclusion and exclusion; to the students' opportunities to become legitimate participants in SYKL.

Based on the performed conversational actions, we have drawn up a typology that shows the students' assisting strategies. In this way, we have selected typical features of the assistance with the aim of creating a meaningful unit, so that a coherent figure or "archetype" emerges. Naming the figures is a fictionalization of analytical points that serve a communicative purpose (Kofoed & Søndergaard, 2008). By naming the assisting strategies, it is our hope that it will be easier to talk about what happens in the relation between the tutor and the one who gets help (tutee). Not with the intention of pointing out right and wrong ways of being a student, but with the intention of creating a language for the dynamics that can otherwise go unnoticed in peer tutoring.

Conclusions, Expected Outcomes or Findings

As a result of the analysis, we have constructed four ideal typical assisting strategies which relate to patterns in the students' different ways of using social and academic conversational actions when they act in the role of tutor.

First, the ‘Let’s bond’ strategy, that is about

- Keeping track of process and time

- Having many off-topic dialogues with the peer and others

- Suggesting relatively few possible solutions

Secondly, the ‘I’ll wait for you’ strategy, that is about

- Being patiently waiting

- Expressing confidence in other

- Suggesting relatively few possible solutions

Thirdly, the ‘Think carefully’ strategy, that is about

- Being patiently waiting

- Expressing confidence in other and keeping track of process and time

- Suggesting many possible solutions and asking many reflective questions

And finally, the ‘Let’s go’ strategy, that is about

- Working at high pace

- Ensuring progress

- Suggesting many possible solutions

The four figures are analytically produced archetypes that do not exist in their "pure form" in the classroom. These are typical strategies that students draw on in different ways and combinations. It is important to emphasize that all four assisting strategies can be legitimate, and that they can all – depending on the situation – be both productive and challenging for socio-academic inclusion.

In the presentation, we use examples from the video observations to illustrate what characterizes the four strategies. We will show how the social and academic actions intertwine, and how the assisting strategies and the didactic framework that SYKL provides have an impact on the students' opportunities to participate.

The paper concludes by suggesting that insight into students' strategies can help the teacher support inclusive learning environments.

References

Allan, J. (2008). Rethinking inclusion: The philosophers of difference in practice. Dordrecht: Springer.

Anderson, L. & Tvingstedt, A. (2009). Med fokus på samspel: Att använda video i specialpedagogisk forskning (81-104). EDUCARE 2009: 4 Att infånga praxis − kvalitativa metoder i (special)pedagogisk forskning i Norden. Malmö högskola: Malmô.

Blomhøj, M. (2021). Samspil mellem fagdidaktisk forskning og udvikling af matematikundervisning – belyst gennem erfaringer fra et udviklingsprojekt i undersøgende matematikundervisning. Sammenlignende fagdidaktik, 6, 29-50.

Booth, T. (2011). The name of the rose: Inclusive values into action in teacher education. Prospects, 41(3), 303-318.

Bourdieu, P., & Wacquant, L. J. D. (1996). Refleksiv sociologi − mål og midler. Hans Reitzels Forlag.

Cin, F.M. & Ciftci, S.K. (2017). Exploring Classroom Inequalities in a Mathematics Class through a Capabilities-Based Social Justice Framework. H.U. Journal of Education 32(1).

Kofoed, J., &. Søndergaard, D. M. (2008). Blandt kønsvogtere og -udfordrere. Camouflagekaptajner og diversitetsdetektiver på spil i børnehaven. Dansk Pædagogisk Tidsskrift 2008(2), 46-55.

Lambert, R. (2015). Constructing and Resisting Disability in Mathematics Classroom: A Case Study Exploring the Impact of Different Pedagogies. Educational Studies in Mathematics 89(1).

Lim, W. et al. (2015): Celebrating Diversity by Sharing Multiple Sharing Methods. Mathematics Teacher 109(3).

Rasmussen, K., & Schmidt, M.C.S. (2022). Together in adidactic situations – Student dialogue during reciprocal peer tutoring in mathematics. International Journal of Educational Research Open, 2022(3), 1-8.

Reinholz, D.L. & Shah, N. (2018). Equity Analytics: A Methodological Approach for Quantifying Participation Patterns in Mathematics Classroom Discourse. Journal for Research in Mathematics Education 49(2).

Rubel, L.H. (2016). Equity-Directed Instructional Practices: Beyond the Dominant Perspective. Journal of Urban Mathematics Education 10(2).

Schmidt, M.C.S, (2016). ’Mathematics Difficulties and Classroom Leadership – A Case Study of Teaching Strategies and Student Participation in Inclusive Classrooms’. In: Lindenskov (ed.) Special Needs in Mathematics Education. Danish School of Education. Aarhus University.

Schmidt, M.C.S. (2015). Sociofaglig inklusion og elevfællesskaber. Til didaktiseringen af kammerathjælp i matematikundervisning på folkeskolens begyndertrin. Nordisk matematikkdidaktikk, 20(2), 27-52.

Thurston, A. et al. (2007). Peer learning in primary school science: Theoretical perspectives and implications for classroom practice. Electronic Journal of Research in Educational Psychology, 5(13), 477-496.

Thurston, A. et al. (2020). The influence of social relationships on outcomes in mathematics when using peer tutoring in elementary school. International Journal of Educational Research Open, 1, 100004.

Vygotsky, L.S. (2019). Tænkning og sprog. Akademisk Forlag.

Wenger, E. (2004). Praksisfællesskaber. Læring, mening og identitet. Hans Reitzels Forlag.

As a contribution to the international studies this paper presents some of the results from a three-year research project in a Danish context. The project investigates how an intervention (SYKL) with reciprocal peer tutoring in mathematics and science in 4th grade affects the students' engagement, participation and learning outcomes. In contrast to most international peer tutoring projects, SYKL focus on both social relations and academic inclusion at the same time.

SYKL is based on a sociocultural perspective in learning (Vygotsky, 2019) and emphasize the importance of inquiry-based learning (Blomhøj, 2021). In SYKL students are specifically taught how to help each other and engage in academic conversations when working in pairs. SYKL is inspired by interventions with peer tutoring, where students take on different roles (Thurston et al., 2007; Thurston et al., 2020). The students are assigned one of two positions, either as tutor or tutee. To fulfill the role of ‘coach’ or ‘helper’, the tutor receives prompt cards with generic questions and academic hints for solving the specific task. During a lesson students switch roles so that both can participate in meaning making and commit to the relation.

The purpose of this paper is to investigate students’ assisting strategies in SYKL and explore how these strategies promote or inhibit inclusion. In the paper inclusion is understood as “maximizing the participation of all children” (Allan, 2008:33), and participation is understood as learning in collaboration with others, while students are involved in the academic field and accepted for who they are (Booth, 2011). To create knowledge about students’ participation we use Wenger’s (2004) terms and ask: To what extent do we see "legitimate peripheral participation" that can potentially lead to full participation, and to what extent do we see "marginalized non-participation" that potentially leads to full exclusion from the student community?

Whether students are included in the student community is related to the different strategies they bring into play. This phenomenon can be explained with the concept of social capital (Bourdieu & Wacquant, 1996), which is the aggregate of the resources linked to being part of a group. Bourdieu emphasizes that people tend to acknowledge one another and affirm group membership through rituals, and he refers to these activities as investment strategies. Inspired by Bourdieu, we ask: Which "cards" do the students play to become legitimate participants in SYKL. What counts as trump?

Schmidt (2015) shows that students use different strategies to be included, and that these strategies are both academically and socially grounded at the same time. Thus, there is a close connection between acceptance, participation, and performance. In the presentation this is understood as a socio-academic inclusion, which is a lens we use when analyzing the students’ socio-academic investment strategies.

Thus, the driving research questions are:

What kind of conversational actions characterize the students’ different assisting strategies in SYKL?

How does different assisting strategies affect the socio-academic inclusion?

Methodology, Methods, Research Instruments or Sources Used

The research project reported investigated a 13-week intervention with SYKL. It involved 25 Danish primary school teachers and approximately 570 students from 4th grade. The total empirical data consists of pre- and post-tests, pre- and post-questionnaires, teacher- and student interviews, and video observations. This paper will focus on 15 video recorded dialogues and investigate the socio-academic patterns of participation. We have closely studied each video several times and we have transcribed each dialogue (Anderson & Tvingstedt, 2009).

As the ambition was to create knowledge about the students' assisting strategies, we have analyzed how the students used social and academic conversational actions (verbal as well as non-verbal) when they were in the role of tutor. In that regard we draw on Rasmussen and Schmidt (2022), who have categorized a number of social conversational actions (e.g., ‘expressing confidence in other’) and academic conversational actions (e.g., ‘suggesting possible solutions’), that constitute the socio-academic norms of a subject (in this case mathematics).

At the same time, we have investigated how these conversational actions are related to processes of inclusion and exclusion; to the students' opportunities to become legitimate participants in SYKL.

Based on the performed conversational actions, we have drawn up a typology that shows the students' assisting strategies. In this way, we have selected typical features of the assistance with the aim of creating a meaningful unit, so that a coherent figure or "archetype" emerges. Naming the figures is a fictionalization of analytical points that serve a communicative purpose (Kofoed & Søndergaard, 2008). By naming the assisting strategies, it is our hope that it will be easier to talk about what happens in the relation between the tutor and the one who gets help (tutee). Not with the intention of pointing out right and wrong ways of being a student, but with the intention of creating a language for the dynamics that can otherwise go unnoticed in peer tutoring.

Conclusions, Expected Outcomes or Findings

As a result of the analysis, we have constructed four ideal typical assisting strategies which relate to patterns in the students' different ways of using social and academic conversational actions when they act in the role of tutor.

First, the ‘Let’s bond’ strategy, that is about

- Keeping track of process and time

- Having many off-topic dialogues with the peer and others

- Suggesting relatively few possible solutions

Secondly, the ‘I’ll wait for you’ strategy, that is about

- Being patiently waiting

- Expressing confidence in other

- Suggesting relatively few possible solutions

Thirdly, the ‘Think carefully’ strategy, that is about

- Being patiently waiting

- Expressing confidence in other and keeping track of process and time

- Suggesting many possible solutions and asking many reflective questions

And finally, the ‘Let’s go’ strategy, that is about

- Working at high pace

- Ensuring progress

- Suggesting many possible solutions

The four figures are analytically produced archetypes that do not exist in their "pure form" in the classroom. These are typical strategies that students draw on in different ways and combinations. It is important to emphasize that all four assisting strategies can be legitimate, and that they can all – depending on the situation – be both productive and challenging for socio-academic inclusion.

In the presentation, we use examples from the video observations to illustrate what characterizes the four strategies. We will show how the social and academic actions intertwine, and how the assisting strategies and the didactic framework that SYKL provides have an impact on the students' opportunities to participate.

The paper concludes by suggesting that insight into students' strategies can help the teacher support inclusive learning environments.

References

Allan, J. (2008). Rethinking inclusion: The philosophers of difference in practice. Dordrecht: Springer.

Anderson, L. & Tvingstedt, A. (2009). Med fokus på samspel: Att använda video i specialpedagogisk forskning (81-104). EDUCARE 2009: 4 Att infånga praxis − kvalitativa metoder i (special)pedagogisk forskning i Norden. Malmö högskola: Malmô.

Blomhøj, M. (2021). Samspil mellem fagdidaktisk forskning og udvikling af matematikundervisning – belyst gennem erfaringer fra et udviklingsprojekt i undersøgende matematikundervisning. Sammenlignende fagdidaktik, 6, 29-50.

Booth, T. (2011). The name of the rose: Inclusive values into action in teacher education. Prospects, 41(3), 303-318.

Bourdieu, P., & Wacquant, L. J. D. (1996). Refleksiv sociologi − mål og midler. Hans Reitzels Forlag.

Cin, F.M. & Ciftci, S.K. (2017). Exploring Classroom Inequalities in a Mathematics Class through a Capabilities-Based Social Justice Framework. H.U. Journal of Education 32(1).

Kofoed, J., &. Søndergaard, D. M. (2008). Blandt kønsvogtere og -udfordrere. Camouflagekaptajner og diversitetsdetektiver på spil i børnehaven. Dansk Pædagogisk Tidsskrift 2008(2), 46-55.

Lambert, R. (2015). Constructing and Resisting Disability in Mathematics Classroom: A Case Study Exploring the Impact of Different Pedagogies. Educational Studies in Mathematics 89(1).

Lim, W. et al. (2015): Celebrating Diversity by Sharing Multiple Sharing Methods. Mathematics Teacher 109(3).

Rasmussen, K., & Schmidt, M.C.S. (2022). Together in adidactic situations – Student dialogue during reciprocal peer tutoring in mathematics. International Journal of Educational Research Open, 2022(3), 1-8.

Reinholz, D.L. & Shah, N. (2018). Equity Analytics: A Methodological Approach for Quantifying Participation Patterns in Mathematics Classroom Discourse. Journal for Research in Mathematics Education 49(2).

Rubel, L.H. (2016). Equity-Directed Instructional Practices: Beyond the Dominant Perspective. Journal of Urban Mathematics Education 10(2).

Schmidt, M.C.S, (2016). ’Mathematics Difficulties and Classroom Leadership – A Case Study of Teaching Strategies and Student Participation in Inclusive Classrooms’. In: Lindenskov (ed.) Special Needs in Mathematics Education. Danish School of Education. Aarhus University.

Schmidt, M.C.S. (2015). Sociofaglig inklusion og elevfællesskaber. Til didaktiseringen af kammerathjælp i matematikundervisning på folkeskolens begyndertrin. Nordisk matematikkdidaktikk, 20(2), 27-52.

Thurston, A. et al. (2007). Peer learning in primary school science: Theoretical perspectives and implications for classroom practice. Electronic Journal of Research in Educational Psychology, 5(13), 477-496.

Thurston, A. et al. (2020). The influence of social relationships on outcomes in mathematics when using peer tutoring in elementary school. International Journal of Educational Research Open, 1, 100004.

Vygotsky, L.S. (2019). Tænkning og sprog. Akademisk Forlag.

Wenger, E. (2004). Praksisfællesskaber. Læring, mening og identitet. Hans Reitzels Forlag.

Originalsprog | Engelsk |
---|---|

Publikationsdato | 2023 |

Status | Udgivet - 2023 |

Begivenhed | ECER 2023: The Value of Diversity in Education and Educational Research - University of Glasgow, Glasgow, Storbritannien Varighed: 22 aug. 2023 → 25 aug. 2023 Konferencens nummer: 2023 https://eera-ecer.de/ecer-2023-glasgow |

### Konference

Konference | ECER 2023 |
---|---|

Nummer | 2023 |

Lokation | University of Glasgow |

Land/Område | Storbritannien |

By | Glasgow |

Periode | 22/08/23 → 25/08/23 |

Internetadresse |

## Emneord

- Læring, pædagogik og undervisning
- Skoler, fag og institutioner