Colleen Vale

Victoria University of Technology

Introduction and background

With the current emphasis on numeracy standards the Catholic Education Commission of Victoria implemented an action research project, "Supporting Numeracy Learning in Victorian Catholic Schools", to inform the development of strategies to support numeracy learning. The project involved six teams of teachers and facilitators and this paper is a report on the work of the only team in the project that focussed on numeracy learning and teaching in the middle years of schooling.

Innovation in the middle years of schooling, defined as year 5 in primary school to year 8 in secondary schools, was initially promoted by The Schools Council (Berkeley, 1994). The subsequent attention to the middle years is a result of the recognition of the particular needs of young adolescents (Eyres, 1992), stagnation of student achievement (Hill, 1994) and the fall in student attitudes and enjoyment of learning during these years (Snapshots of the middle years, 1997). Student alienation in the middle years is reported to derive from a curriculum that does not recognise the personal and social context of young adolescents (Cumming, 1996; Eyres, 1997). The curriculum is disconnected from students' experience (Eyres, 1997) and is geared toward basic skills in primary schools and work credentials in secondary school (Stringer, 1997). Eyres (1992) identified a range of needs for young adolescents that included growing toward independence, gaining experience in decision-making and developing self identity and self-confidence, whilst adjusting to profound changes.

Teachers who have been researching this issue in their classrooms have reported a number of strategies that have been successful in the middle years. These generally embrace principles of more flexibility and democracy in the classroom and a holistic approach to curriculum and teams of teachers (Cumming, 1996; Scott, 1997). Particular strategies have been advocated. These include the use of an integrated curriculum approach to learning (Beane, 1991; Roberts, 1997), student autonomy through participation in decision making about learning, practical activities related to real life problems and varied approaches to create interest and reduce boredom (Cumming, 1996).

Research on middle school mathematics teaching is not prevalent. Bodin and Capponi (1996) conducted a review of international practices and noted a variety of practice around the world and an absence of a common approaches within countries. They did note however, an evolution toward more student centred approaches that typically involved a problem based lessons, to address the needs of greater autonomy for young adolescents. The use of other autonomous learning approaches was not discussed in their report. It is not surprising then that, approaches for addressing the needs of young adolescents within the context of mathematics curriculum and numeracy learning are not evident in the literature that informs teachers. Therefore, this action research project set out to investigate effective teaching and learning strategies for students in the middle years that would also enhance and improve numeracy outcomes.

Structure and organisation of the action research project

The action research team consisted of seven teachers drawn from four schools and a university facilitator. Three of the schools were primary schools and one a P-10 school. As a result only one secondary mathematics teacher participated in the project. Three of the schools were located in regional Victoria, the fourth on the outskirts Melbourne.

The project involved an initial two days of professional development and two months of action research as the teachers trialed ideas designed to effect positive change for their students. During this period the facilitator visited each of the schools to discuss the project, offered support and advice, and provided guidance on data collection and report writing. A final two days brought the teachers together to share experiences within the middle years team and to generalise and theorise their findings. Experiences were also shared with teacher researchers in the other numeracy teams and recommendations were prepared.

During the first two days the teachers shared their experiences of teaching mathematics in the middle years, identified issues of concern, engaged in some professional reading and reflection, and identified the main problem for their research and a strategy to implement. The teachers were encouraged to collect a range of data and to write cases (Wasserman, 1993) for their report. These reports formed the basis of the sharing activities on the final two days of the project. The teachers read each other's reports and wrote commentaries (Teachers Write, 1997). Findings were therefore more easily generalised through discussion.

Determining a direction for the action research.

During an initial discussion about their experiences of teaching mathematics in the middle years, consistency emerged as an issue of concern for the teachers in the action research team. They reported that the divide between primary and secondary schooling was characterised by differences in curriculum planning, teaching and learning, language as well as algorithms and methods. The primary teachers in the group were concerned that numeracy for their middle year students was usually concerned with students demonstrating basic skills in number and the regurgitation of algorithms rather than demonstration of understanding. They further believed that group work and problem solving got lost or squeezed out, especially as grade 6 teachers tried to make sure that their students had the necessary knowledge for secondary mathematics. The desire to deal with structural issues concerning transition between primary and secondary school was evident within the group.

When reflecting upon a selection of articles concerning the middle years of schooling (Cumming, 1996; Eyres, 1997; Roberts, 1997; Scott, 1997; Snapshots of the middle years, 1997) the teachers agreed that many of the findings concurred with their experiences. They were excited by some of the ideas proposed in the literature as they clearly related to positive experiences that they had enjoyed in their middle years classrooms when teaching other areas of the curriculum.

The structural issues of communication and collaboration between primary and secondary teachers were not considered for the project. This was because the selected members of the team were all primary teachers except one, and the schools had no geographical relationship with each other, except for those from the one P-10 school. The time line for the project was less than a term and hence too short to engage in cross sector collaboration. The team therefore agreed to focus on their own classrooms. Through discussion the group determined that the key question for the action research team was:

The teachers were concerned not only about positive learning outcomes in mathematics but also positive outcomes in terms of confidence in mathematics learning and social skills, that would aid students' learning and their personal and social development.

The teachers argued that the teaching of numeracy in the middle years ought to: cater for individual differences and ways of knowing, promote the explaining and writing of mathematical thinking, make use of team learning and develop team skills, engage students through the use of appropriate concrete materials (manipulatives) and tools, and use assessment to identify student needs and modify their teaching program. These beliefs informed their choice of strategy for the classroom. The ideas for teaching and learning practices of particular interest to the teachers in the project were: integrated learning, problem solving, good questions, real life learning, autonomous learning, tools, concrete materials, investigations, games, open ended activities and personal experiences. Each school in the team framed a particular question and contributing questions to research and nominated a teaching and learning strategy to trial with content of their current mathematics program. "Mathematics in context" made sense as a theme for the team's proposed action research, especially since it also fitted neatly with definitions of numeracy:

• Underpinning mathematical concepts and skills from across the discipline (numerical, spatial, graphical, statistical and algebraic);
• Mathematical thinking and strategies;
• General thinking skills; and
• Grounded appreciation of context.

Two schools chose to focus on games as a context for mathematics. One of these schools was particularly interested in motivating students for a range of mathematics learning areas. The other school was also keen to motivate children, and especially boys, as well as develop skills in strategic thinking and thinking mathematically. At this school the grades 5 and 6 students had been surveyed concerning their thoughts about mathematics as part of a school review. The students reported that there was not enough fun in mathematics.

The teachers from one primary school had previously used the Bloom's Taxonomy for negotiating curriculum with students in other key learning areas and they were keen to try this more autonomous learning approach in mathematics. The grade 6 teacher negotiated contracts concerning shape with students, whilst the grade 5 students worked on fractions.

At the P-10 school the students in grades 5, 6 and 7 were scheduled to begin the topic of data. The teachers were keen to trial real life investigations that concerned personal experience and involvement. The grade 5 and 6 teachers challenged their students to pose questions for data collection that were of interest to them, whilst the year 7 students embarked on a project to discover 'the average year 7 student'.

Findings from the action research

The individual reports produced by teachers documented the actual implementation of these strategies. They also reported cases and particular learning outcomes for individual or groups of students according to the Mathematics Curriculum and Standards Framework (1995). Common features of the implementation of these strategies were the involvement of students in making decisions about their learning, students working collaboratively with others and communicating mathematics with others.

The teachers believed that their experience in the project had been beneficial and that they had developed new strategies for teaching mathematics as a result. For example one teacher wrote:

The teachers also reported that their students were open to their new teaching strategies in mathematics and were positive about the mathematics work that they had done during the project. Particular findings were identified for each strategy that was trialed. These findings are listed by strategy in Table 1 and include statements about learning and teaching.

Table 1: Findings about learning and teaching for each strategy trialed.

One theme running across the strategies was enjoyment and motivation. The teachers reported that their classrooms had been happy and productive learning environments. For example one teacher wrote:

This idea was echoed by the grade 5 teacher who personalised the data collection lessons:

The grade 6 students who had previous experience with negotiating contracts:

These statements concur with those of other teachers who have varied their approach to teaching in the middle years (Cumming, 1997) and suggests that the students' usual experience of mathematics was somewhat disconnected from their interests and needs (Eyres, 1997). Middleton (1995) found that teachers were generally poor at predicting what would motivate their students in mathematics lessons and the experience of the action research team suggests that by varying approaches teachers may learn more about what motivates their students in mathematics.

An element of the happy environment reported by the teacher above was the high degree of social interaction. This was the second theme evident in the findings reported by the teachers. One teacher argued that mathematical games may play an even more crucial role in the social development of young adolescents:

Mathematics lessons that personalise the content or context for learning and require interaction between students, can therefore these teachers suggest, provide a social context for the development of social skills and identity critical for young adolescents (Eyres, 1992).

The teachers were also pleased that the strategies that they had trialed enabled all the students some experience of success in mathematics. This was the third theme evident from their findings. The students recognised success through self-evaluation of their mathematics projects, as reported by the following teacher:

The teachers also observed success since they noted the high levels of engagement of their students with the various tasks, as well as, the bridging of differences between high mathematics achieving and low mathematics achieving students. Students were successful because they were able to build on their own understandings:

And games also provided a means of shifting the competition evident in the classroom away from mathematics to the game itself:

The flexibility and democracy advocated by Cumming (1997) and Scott (1997) and trialed by these teachers lead to particular mathematics learning outcomes as well as increased levels of self esteem in mathematics lessons in these brief classroom trials. The relationship between confidence in mathematics and continued participation and achievement in mathematics has been well documented (see for example, Kloosterman, 1988). Positive experiences of schooling contribute to a positive sense of self worth critical to young adolescents (Eyres, 1992).

So why did these trials of teaching strategies in middle years mathematics lessons yield such positive outcomes as expressed by the teachers in their individual and collective reports? The common theme that emerged from discussion between the teachers about their experiences was the notion that mathematics needs to be meaningful for students in the middle years. When given the option, students in these classrooms selected real life contexts for learning mathematics and demonstrated numeracy skills:

And:

One teacher spoke about two boys in one class who were competent mathematically and knew all the mathematics before starting their contract:

The task designed by the students themselves therefore generated mathematical meaning for these students through an experience of situated learning. Similarly the secondary teacher reported the conceptual understanding developed through the personalised data collection project:

One teacher summed up the action research team's conclusion that 'meaningfulness' was the main recommendation that they wanted make about the teaching and learning of mathematics in the middle years in her report:

The strategies employed by this group of teachers therefore provided meaning on a personal level as well as in a numeracy sense, that is an understanding of mathematics that enabled them to use their knowledge and skills in a way that was relevant to their daily lives. A relevant curriculum was a goal articulated by Cumming (1996) for the middle years of schooling.

Alongside the positive outcomes the teachers also expressed some dilemmas. For example, the teachers raised concerns about the content of the student negotiated learning:

The teachers discussed how to encourage students to challenge themselves and move beyond what they feel comfortable with. Examples of students extending themselves during the project were identified. The teachers believed that the mathematics program needed to provide time for students to explore a topic in depth, even when the pressure may be to cover more learning outcomes. The management of assessment was also an issue within this context:

These themes of concern, echoed the difficulties faced by middle school teachers as reported by Bodin and Capponi (1996).

The team seriously discussed the reflection made by one teacher during this project. This teacher had written about her changing role in the classroom:

They agreed that striking a balance between student directed learning and teacher directed learning was difficult to achieve, but worthwhile striving for.

Conclusion

The experiences of these teachers are not new. They concur with the previous experience of teachers who have conducted action research in the middle years (Cumming, 1997) or in negotiating mathematics curriculum (Boomer, 1982). These teachers have however, established links for themselves between these practices and the needs of young adolescents in particular. Through the project the teachers listened to young adolescents and reflected on their own practice. As a result these teachers have been inspired to repeat the strategies that were trialed, to improve on this practice, and to endeavour to use a variety of teaching and learning approaches in their teaching of mathematics in the middle years of schooling. The challenge for making mathematics meaningful in the middle years of schooling for young adolescents is ongoing and expressed by one teacher in the following commentary:

The teachers expressed concern about the limitations of their brief action research project. They believed that reform in the middle years of schooling also meant tackling the problem of consistency through communication between the sectors and structural change. A mathematics curriculum appropriate for the middle years would be more effectively researched through a cross sector project that brought together teachers working with students on both sides of the transition 'gulf' in local communities. The teachers also argued that further research by teachers in their classrooms, and by other researchers was required in order to confirm and understand the notion of meaningful mathematics, and to improve the practice of teaching and learning for young adolescents.

Acknowledgments

The author sincerely thanks and acknowledges the academic contribution made by the teachers working on the project: Lidia Goodwin, Robyn Henott, Mick Scully, Rebecca Rohde, Katrina O'Brien, Robyn Weinbergs and Chris Dickson, and would also like to thank the Catholic Education Office and Jill Cheeseman for the opportunity to work collaboratively with teachers on this project. Please note that the views expressed in this paper are not necessarily those of the Catholic Education Commission of Victoria.

References

Wasserman, S. (1993) Getting Down to Cases. New York: Teachers College Press.