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Issues Related to Ability Grouping In Mathematics

Mary-Angela Tombs

In large New Zealand primary schools, end of year student-class placement follows a selection process that involves consideration of the academic, social and practical needs of the students, and their potential classes and teachers. In my experience, a debate may ensue, regarding whether students should be placed with students of like ability or in mixed classes. Likewise, when planning the learning programme, there is potential for re-grouping the students again, either within or between classes for Mathematics instruction. Once again there can be differing perspectives on the best choices regarding this regrouping. Literature related to Mathematics grouping fuels this debate, with some literature advocating grouping according to academic ability, and other literature criticising this practice.

The purpose of this essay is to critically explore current debate associated with the grouping of students, both homogeneously (ability-based) and heterogeneously (non-selective), for Mathematics instruction. Literature from New Zealand and abroad that investigates how grouping decisions impact on individual students’ academic outcomes, self-esteem and participation in discourse, as well as the impact on the community of learners as a whole, is explored, contrasted and compared. Perspectives from research are evaluated in relation to the writer’s professional experience in order to highlight the strengths and limitations of this literature. Finally, implications for practitioners in the New Zealand education system are detailed.

Discourse for Learning

Sociocultural Theory, as posed by Vygotsky (1978) and later by Bruner (1996) proposes that higher order functions grow within a social interface. This theory asserts that the social connection an individual has with those around them, impacts on the development of that individual and their ability to learn. Developing a social interface necessitates discourse in one form or another, in that learners communicate with one another while working together.

Current literature related to teaching and learning also promotes the importance of creating a learning environment where discourse is encouraged, in order to promote learning. According to this literature, conversations about learning in Mathematics, where students explain their methods, justify their points of view and challenge others’ ideas respectfully, significantly increase the likelihood of enhanced learning (Saleh, Lazonder & De Jong, 2004; Hunter, 2010, n.d.; Walshaw & Anthony, n.d.). The New Zealand Ministry of Education (MOE) indicates that the ability to communicate within social contexts is a fundamental competency that underpins all learning: “Opportunities to develop the [key] competencies occur in social contexts.  People adopt and adapt practices that they see used and valued by those closest to them, and they make these practices part of their own identity and expertise” (MOE, 2007a, p.12).

A context where discourse, or communication between individuals, is active allows a community of learners to grow. In such a community the support generated between individuals can be reciprocal, mutually supportive. This, in turn, helps to build a learning community that is culturally responsive (Macfarlane, 2004; 2007; 2012; MOE, 2007). In a Māori world view, reciprocity is referred to as Ako, and is fundamental to any learning situation. Reciprocity is also important to many Pacific Island peoples represented in New Zealand classrooms, referred to in Tongan as tauhi vaha’a , and in Samoan as fetausia’i (Te Ara, 2012).

However, it is argued by Walshaw & Anthony (n.d.) and Alton-Lee (2003) that it is not enough for students to be left to have a conversation about learning without the explicit guidance and support of their ever-watchful teacher. Students need to be supported to learn the language and the skills associated with Mathematical discourse, so that they can be full participants in a meaningful discussion. This is particularly challenging in classes where students speak English as a second language.

Further to this challenge, in a culturally diverse setting, some students are reluctant to share and justify their views, as well as questioning the views of others, as this could be seen as insensitive or disrespectful. According to one Pasifika Education Adviser, this is especially relevant for children from Pacific nations, who are taught not to question learning or be involved in debate in class as this could be seen as highlighting teacher inadequacies (T. Taleni, personal communication, March 26, 2012).

Keeping in mind the need to build a culturally responsive community where learners feel supported to participate actively in Mathematics-related discourse to ensure learning, the attention now turns to literature related to grouping with the intention of investigating how discourse can be optimised through Mathematics grouping arrangements.

Homogeneous Versus Heterogeneous Grouping

Proponents for homogeneous, or ability-based, grouping in Mathematics connect this practice to better academic outcomes. Some research shows that students achieve better results in classes when their grouping is based on ability (Diezmann and Watters, 2001; Kulik, 1992; Saunders, 2005). In stark contrast a good deal of literature supports the opposite view, claiming that homogeneous grouping is detrimental to students’ academic achievement (Green, 2003; Kunick, Blatchford & Baines, 2002). Upon closer inspection, research often highlights variation of impact in relation to different students.

Reference to competition is also made in relation to higher ability students by Kulik, (1992), who states that high ability students benefit from competition in homogeneously grouped settings. Diezmann & Watters (2001), whose more recent research establishes that gifted and talented students significantly enhance their knowledge construction when Mathematics class grouping is based on ability, support this view. However, high achievers were found subsequently by Saleh, Lazonder & De Jong (2004) to be relatively unaffected by the composition of a group. These researchers argue that high achieving students tended to make good progress regardless of the students they worked with. In my practical experience as a teacher and school leader, this is indeed the case. I usually find high ability students to be intrinsically motivated in class. However, I find that their own parents sometimes place a good deal of pressure on them academically. Boaler (2005) make reference to the long-term negative emotional impact that ability grouping has on high ability students because of pressure to succeed.

Saleh, Lazonder & De Jong’s (2004) assert that students of average ability achieve better results when grouped with students of like ability. These researchers link this result to discourse between students and their teacher, claiming that within homogeneous groups, students of average ability receive more explanations than when their group is of mixed ability, where they tended to fall into the background behind students of low or high ability. This is a cause for concern, as by definition, the average ability students make up the bulk of students within any given class. Saleh, Lazonder & De Jong make the suggestion to group low and high ability students together, given their finding that low ability students benefit from working with students of higher ability, and high achieving students can achieve good results in most settings. This method would allow the average ability students to be grouped as one, separately. In theory, this appears to be a reasonable suggestion, but in reality it would quite possibly result in uneven group sizes and, in the writer’s experience, a school community that has previously grouped high ability students in Mathematics classes away from those of low ability may find that combining these two groups intentionally, opens them up to criticism from their school community – a risk not worth taking without solid evidence for change. However this suggestion may be more easily applied within one heterogeneous class, when grouping the students for independent activities.

Kulik’s (1992) research found advantages for low ability students in homogeneous groups. Kulik qualified this finding by stating that students with low ability do not need to compete with other students, when in an ability-based group, therefore can progress at their own pace. However, this finding is contrasted by more recent research. Kunick, Blatchford and Baines (2002) argue that ability grouping, while common practice within heterogeneous classrooms, is detrimental to low ability students, particularly boys. Saleh, Lazonder & De Jong (2004), corroborate this finding as they also found a negative academic impact of homogeneous grouping on students of low ability.

Much of the research providing evidence to support homogeneous grouping relates success to academic achievement. However research carried out in the United Kingdom, where the practice of grouping students according to ability is practiced widely, demonstrates that homogeneous grouping results in lower academic scores in standardised tests than heterogeneous grouping (Green, 2003). Green compared the practices of heterogeneously and homogeneously grouping students in secondary schools in the United Kingdom in relation to standardised testing. The students who were grouped heterogeneously remained this way until close to external assessment time so that students could be given ‘just in time’ targeted teaching to prepare them for external testing. At this time, there was minimal movement between groups to align instruction to ability. Other students had remained homogeneously grouped for the whole year. When comparing results between schools and groups, those students who were grouped latest and least achieved the best outcome in external testing, better than those who had remained homogeneously grouped for the whole year.

There are obvious discrepancies when it comes to the academic benefits of homogeneous and heterogeneous grouping practice, but what about the impact on the teacher?

Kulik (1992) argues that when students are grouped according to ability, there is less pressure on teachers and they can differentiate the curriculum to suit the ability of the students. In contrast, differentiation in the hands of a teacher with a poor understanding of pedagogy has the potential to ‘dumb down’ the curriculum by limiting experiences. Boaler (2005) found that students grouped according to lower ability have lower expectations placed on them by their teachers. This finding mirrors research by Anthony and Walshaw, who argue that, “Teachers who teach lower streamed classes tend to follow a protracted curriculum and offer less varied teaching strategies” (2007, p.2). However Kunick, Blatchford and Baines identified that within typical classroom settings, the classroom teacher is more likely to work alongside groups with higher ability students, than low ability.

The huge variance in results of the various studies referred to so far within this paper regarding the benefits and downfalls of ability grouping may be an indication that teacher competence, more than group make-up per se, has the most potential to impact academic results. As previously mentioned, teachers in New Zealand also have an obligation to consider the social, cultural and emotional impact that their practice has on the learning community. 

Several studies allude to the social impact of homogeneous grouping. Boaler (2005) connects homogeneous grouping practices to social class, stating that lower social classes tend to achieve lower results than those from more privileged backgrounds. This practice led to students of low ability giving up on learning over time, as they felt there was no point trying to work their way up the academic ladder. Boaler interestingly found that that the employment prospects of students who had been grouped homogeneously were more limited when they were older than those who had been grouped heterogeneously. In some countries, the practice of homogeneously based classes, or ‘streaming’ is banned because of the social inequities this practice perpetuates (Yui, 2001). All of this raises questions about equity and cultural responsiveness in education. Should teachers not consider the long-term social impact of their groupings, rather than focusing merely on the academic outcomes? Mulkey, Catsambis, Steelman and Crain (2005) claim that the social impact of homogeneous grouping in Mathematics far outweighs the academic achievements reported.

In summary, homogeneous grouping practices have been reported to produce better (and worse) academic outcomes for low, average and high ability students. Furthermore there is an acknowledgement by researchers (Kulik, 1992; Mulkey, Catsambis, Steelman & Crain, 2005; Saleh, Lazonder & De Jong, 2004) that academic progress comes at a price, in terms of perpetuating social norms and lowering self-confidence. While the practice of deciding how a teacher might group students for the purpose of a Mathematics lesson may seem minor, the wider picture of the long-term implications of such grouping is important to consider. Teachers have a responsibility to ensure that they are meeting the needs of the whole child, not just their academic needs.

Implications for Teachers: Taking Responsibility for Building a Community of Learners

The New Zealand education system traditionally has operated as a Eurocentric hegemony, in that a Eurocentric model places the emphasis on the needs of the individual, as opposed to the collective needs of the whole group. New Zealand’s National Standards provide only a benchmark for measuring individual success (MOE, 2012a). Yet culturally responsive teachers have a responsibility to build a community of learners, and consider the benefits of ako, reciprocity in relationships.

In Japan’s educational practice, the emphasis is on building a community of learners. The standard practice of heterogeneous grouping allows learners to work collaboratively and support one another while learning (Yui, 2001). By providing a context where those who are more capable have an obligation to support those who are not as capable, this practice makes a valuable, and inexpensive investment in social justice – a practice that can pay huge dividends for a country’s social infrastructure in the long term.

It cannot be assumed that students will be able to work collaboratively, but Saleh, Lazonder & De Jong (2004) state that collaboration should be a goal in itself. Boaler (2005) argues that while planning and teaching in Mathematics may be more challenging for teachers in a heterogeneous context, the result is more equitable. It can also be argued that by developing a culture of ako, reciprocal teaching could provide a context that eases the burden on teachers. According to Saleh, Lazonder & De Jong, when high ability students take the role of teacher, working alongside low ability students, not only are they given an opportunity to strengthen their understanding by explaining and justifying their method to a peer, but their self esteem benefits as a result.

In many of the research projects referred to previously within this essay, students within homogenous groupings were placed in such a grouping as a class, over a full year. Few refer to small groupings within a class such as numeracy strategy or knowledge-based ability groupings as recommended within the New Zealand Numeracy Project (MOE, 7007b). The Ministry of Education (2007b) recommends flexibility in student grouping within Numeracy teaching, with an emphasis on providing a context where discourse is encouraged. However, much of the research found that if a student was assigned to a particular ability grouping early on, regardless of group size, it was likely that they would remain in groups at that level throughout their schooling. Are teachers then grouping homogeneously for numeracy strategy teaching merely for academic reasons? Or to ease the burden of teaching? Is it necessary, once again, to consider the long-term social implications and the impact on current relationships in the class?

In accordance with New Zealand’s National Administration Guidelines (2012b), current research tells us that twenty-first century educators have a professional responsibility to provide a responsive learning environment built on strong relationships (De Jong, 2005; Glynn & Berryman, 2005; Villegas & Lucas, 2002; Weinstein, Tomlinson-Clarke & Curran, 2004). It follows that any decision about teaching practice must consider whether such practice will enhance relationships or undermine them. While the practice of grouping according to ability has been found by many to benefit students academically in the short term, the long term academic and social implications of such practice must be questioned.

Conclusion

The literature explored in this essay does not provide teachers with a definitive answer to the debate over ability grouping. It does, however, initiate debate about balancing the academic and social needs of students. Teachers must consider all evidence to help them make decisions about grouping. They must also be involved in complex dialogue; such as that recommended for students in Mathematics. With explanation, reasoning, justification, evidence and comparisons, effective and responsive collaborative practice can occur.

Effective pedagaogy in Mathematics creates opportunity for high quality engagement between students through dialogue and collaboration. Therefore effective practitioners must develop a learning context and environment for this to occur.

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