Abstract
Ability grouping in mathematics is an ongoing subject of debate that has elicited different reactions from academic experts and all education stakeholders. Ability grouping in mathematics during primary and secondary education raises the question of equity, negative, and positive effects on children due to this practice. Many studies have found out that streaming system being beneficial to learners of all levels (Wiliam * & Bartholomew, 2004). Tracking in mathematics is an objective initiative based on the aptitude of a group which aims to improve student’s capability in understanding maths. It is easier to teach in a streamed class because students are able to make contributions equally and can easily discuss an idea as a group (Betts &Shkolnik, 2000). Therefore, this paper aims to analyse the circumstances streaming in mathematics can be justified. The study will provide a literature review on ability grouping in mathematics in the education system.
This paper will discuss the background information on ability grouping in mathematics within-class grouping and between-class grouping as well as answer the question on whether ability grouping can help educators achieve higher standards. Positive and negative effects of ability grouping in mathematics will be analysed and the conditions necessary for grouping. The impacts of ability grouping in mathematics in the education system and students social needs will be addressed to justify ability grouping. Finally, the paper will have a discussion on ability grouping in mathematics, implications, circumstances necessary for ability grouping and conclusion.
Introduction
The commonly used word “streaming” or “ability grouping” refers to the student’s ability as perceived by the teacher, or the ability to achievement in taking a standardised test. This paper considers ability grouping as all forms of the homogenous classroom tracking and especially in mathematics. When the students are grouped in a homogeneous class with certain abilities is known as streaming while in setting, students are grouped by subjects. Achievement tracking is applicable to either system. Many schools in the UK group students only for mathematics lessons (Boaler, Wiliam, & Brown, 2000). This trend is a common practice in Britain which leads to ability grouping towards setting. In the United States of America, students are commonly grouped in subjects rather than streaming. However, ability grouping is prohibited in France, and it is not permitted. his practice has been fully endorsed by the Britain government for the past few decades. The opposite of homogeneous groping is the mixed capacity system or the heterogeneous classes.
Background Information
Ability grouping is a traditional practice in the UK which is founded on the idea that different students have relatively fixed abilities levels, and they need to be taught according to their capabilities. In the early 1950s, most schools in Britain were streamed, which means students were placed in different physical classes according to their “ability” to take a standardized test for all subjects in the same class. According to Jackson (1964), 96% of all teachers in the UK were teaching in streamed groups. Jackson (1964) found out that students with low abilities were being taught by the less experienced teachers who had low qualifications, while a students in high talented groups were taught by the most experienced and qualified teachers (Wallace, 2007). The study by Jackson created awareness in the UK of the existing inadequacies in the class streamed systems, and it was supported by other research studies which provided evidence for inequitable nature of the streaming system. Studies by Wilkinson & Penney, (2013) argued that streaming and ability grouping are the same and students should be organised to a mixed ability class.
Education equality became a general public concern in the 1970s and 80s in support of mixed ability teaching. However, education equity concern eclipsed back in the 1990s where most schools were in support of streaming practice (Oromaner& Oakes, 1986).It is evident that ability grouping is now a widespread practice in the UK now at all levels of education, that is, in secondary, primary and with young children in maths and science lessons. Students are, on the whole, grouped according to their abilities and maths lessons are taught in different classrooms, using different curriculum and taught by different teachers. This practice came back due to the introduction of the national curriculum and structured national assessment by the government in 1988 through the Education Reform Act (ERA). The ERA, according to various studies, was found to be incompatible with mixed ability teaching since teachers were pressured to compete at national level. Therefore, the education system has shifted to a “marketplace” where schools want to attract children from working class parents who favour setting because of they believe it leads to excellence (PITT, 1990) The Labour Government also passed the White Paper ‘Excellence in Schools’ (DFEE, 1997) in support of setting (Oromaner & Oakes, 1986).
Mathematics is largely taught in a streamed class, and it has remained as the main practice in selection criteria used for admission in various schools. According to The Guardian (1996), 96% of schools in the UK taught mathematics in ability-grouped classes.
Ability grouping in the UK has been considered to be important approach because it reduces the range of attainment and it is believed that it is easier to teach in a setting classroom. Students are grouped according to their capability, attainment, achievement, and motivation (Slavin, 1987).
In France, ability grouping was challenged on the basis of disability, language, and gender. Ability grouping was legally challenged since it could end up creating segregation and discrimination. It was prohibited since it would have sacrificed equity for all students in prioritizing excellences (Hadermann, 1976). Also, President George W. Bush signed into law No Child Left Behind Act (NCLB) in 2001 which ensures no child is discriminated in term of their ability, gender, race or background. The law demands accountability to ensure that disadvantaged students are not left behind, and they achieve academic proficiency (“No Child Left Behind Act of 2001”, 2017)
Literature review
Introduction
Ability grouping for mathematics teaching raises different questions about equity as well as higher expectation. Streaming has been found to have effects on student’s achievement, self-concept, and academic growth. Studies have claimed that student’s achievement depend on the impacts of professional development and classroom instructions. The educational stakeholders and educators have determined various ways to group, sort as well as schedule students to minimise achievements gaps in different capability groups. The ultimate teacher goal is to provide effective instruction to all students in a positive environment which is conducive to learning.
The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics claims that excellence in mathematics education can be achieved through equity, setting high expectation as well as strong support for all student from teachers. The principle of equity states that all students must have access to rigorous and coherent curriculum that is taught by a well-trained teacher (Chionidou-Moskofoglou& PREMA Consortium 2008). Since students come from the different background when joining the school and possess the different type of knowledge requires them to be assigned to different levels of classes. Students can be grouped according to demographic composition, as well as rigor and the quality of instruction. The equity principle has been used in school for instructional programs in mathematics due to set expectation, available resources, accommodation, and support for all students.
However, Fuligni, Eccles, and Barber (1995) argued that when a student without learning disabilities is placed in a low achieving student’s class, they tend to do worse than students in a mixed class. According to Oakes (2000), streamed classes for mathematics receive different types of instruction as well as different instructional content and different classroom environment. Students in low-level classes have lower set expectations to achieve, and they are placed in an environment that mostly focuses on discipline and behaviour rather that academic achievement. However, when a student is grouped in a class with abilities beyond his or her level, they tend to perform better and achievement increases significantly (Fuligni, Eccles, & Barber, 1995). Students in such classes respond to higher teacher expectations and challenges provided to them. On the other hand, a student in high-level classes is encouraged to focus on achievement rather than discipline. Therefore, grouping students according to Oakes (2000) reinforces beliefs and attitude that students in low-achieving classes are not able to learn and the society expects them to do less in comparison to others. This type of society expectation tends to favour the high-achiever class, and they benefit from more instruction from the best-qualified teacher. Therefore, introduction on ability grouping class placement at a younger age is an act of sorting out students which will affect their life throughout because it sets them in different developmental trajectories (Fuligni, Eccles, & Barber, 1995).
Studies in support of ability grouping in mathematics
Kulik & Kulik (1992) conducted a meta-analysis of the effects of streamed programs, and he claimed that these programs offers the basic curriculum and do not affect students achievement. The differentiated programs for different capability groups for aptitude test are beneficial to all students of all skill levels. The study found out that the streaming program is an overall self-concept often diminishes the ability of above average pupil and it improves the ability for low capability students (Kulik&Kulik, 1992). According to Ireson, Hallam &Plewis (2001) study found out that self-concept was very high in 45 schools in the UK with moderate ability grouping levels than the tightly un-streamed or streamed schools. Self-concept is a self constructed idea that one holds about oneself and how one respond to others. The study revealed that mathematical self-concept is not at all related to students’ ability grouping in mathematics (Ireson, Hallam, &Plewis, 2001). Ireson, Hallam &Plewis (2001) study claimed that 75% of students benefit from the ability grouping program that is customised to accelerate the student learning.
Students within an ability group are able to participate equally in a group work as well as discussing ideas together easily. On the other hand, teachers struggle when they are teaching a complex heterogeneous class and find it much easier when dealing with a streamed class. The teacher always prefers to teach up to the average point during class time to average children. Therefore, capability grouping achieves higher results in students’ aptitudes and learning tasks. A study conducted in America cited that 8th-grade algebra students with different abilities did better in the ability grouped classes (Kalchman & Case, 1999). According to Ireson, Hallam & Plewis (2001), study of 1139 students in Michigan revealed that 7th-grade students in higher and medium ability gain long-term benefit when they are placed in an ability group for mathematics, and there is no significant difference for the students with low-ability. Teachers tend to enjoy and feel more positive when they are teaching the same ability grouped mathematics class than in mixed-ability class even if they had previous experience in a well supportive environment.
Studies in support of mixed ability mathematics classes
According to Slavin (1987) ability grouping has no significant positive effect on learning mathematics. It has minimal influence in the acceleration of gifted students’ performance in mathematics. He did not base his study from ability grouping programs that offer different curriculum for different ability levels. There are several studies that have shown negative effects of ability grouping claiming that students of low-ability are put in a disadvantaged position because they are usually assigned the less qualified staffs and cover less curriculum work when compared to the higher-ability groups and therefore, they suffer the loss of motivation as well as self-image. Boaler et al. (2000) conducted research in three English secondary schools and found out that negative effects on the ability grouping are presumed in the highest set of students in mathematics class. Ability grouping negatively affects students in higher-ability groups because they are taught at a pace which is too fast for the student to have a comprehensive understanding of the curriculum and they are taught in a prescriptive way. Teachers have very high expectation of the ability-grouped class members to work at the same pace attain high marks. The study found out that student in high ability grouped class has a negative attitude towards maths because they believe that memorization in mathematics was more important than thinking compared to students in lower and mixed ability classes. Boaler & William (2000) conducted a research of 1000 students in six different schools in Britain and reported several disadvantages of ability grouping. They found that students placed in lower class ability had a lower expectation in mathematics, taught on a limited curriculum; they were around to copy from one another; route learning was emphasized as well as being taught by the least qualified teachers or non-specialist teachers (Koshy, 2014). However, students at mixed ability classes were around to work at their own pace, and they were given a differentiated task, and the teachers expected variable outcomes.
Linchevski& Kutscher (1998) took a study to compare students from same-ability to mixed capability classes in seventh and eighth-grade mathematics in an Israeli school, and they found out that there were significant losses for the students in low capacity and middle ability classes, while there was little gain for the students with high-ability (Linchevski& Kutscher, 1998). The study also revealed that high-achieving students gain a lot when they are placed in different streams of classes and low –achieving students suffered only a slight loss. Koshy (2014) conducted an international study and pointed out that Japanese mathematics classes were taught in mixed ability classes from the elementary to the middle school due to social diversity.
Ability grouping and learning
The streaming practice is not a reflection on the students’ ability all the time. The educational psychologists have been looking for the factors that contribute to the courses of placement and mathematics achievements. Betts &Skolnik (2000) claimed that mathematical achievement by a student is influenced by level of motivation, and the parental participation in the learning process as well as the allocation of teachers and resources. Teachers and the higher educated parents are for ability grouping for mathematics in classrooms compared to uneducated parents (Betts &Shkolnik, 2000).
Burns & Mason (1998) explored literature review on the German school system which has maintained homogeneous class and ability grouping for students. He revealed the ability grouping education system which is common in the European nation has large achievements gap, especially in the secondary school. He found out that placing a student in a high capability class is closely associated with the increased achievements. The ability grouping in mathematics and using differentiated curriculum or students attending separate schools increases that achievement gap which favours that higher level students as well as the advanced level schools. He found out that there is a link between the students’ achievement and social background in the school system where background plays a major role in students’ performance in mathematics (Burns & Mason, 1998).
Burris and Welner (2005) conducted a study in Long Island school district to determine the effects of heterogeneous grouping in a de-tracking program. Student tracking in the Rockville Centre School District was revealing an increasing achievement gap among students. The high-quality curriculum was being limited to the students of high classes which lead to the disproportionate representation of minority students as well as students from the low socio-economic status that are placed in the lower level classes. However, the district education board decided to implement a consistent and a rigorous curriculum and set a very high expectation for each and every student. All discussions were held in heterogeneous groups that only focused on academics enriched curriculum to reduce that achievement gaps (Burris &Welner, 2005).
A quick note on tracking
The research on the ability grouping has been going on for long, and there are variance discrepancies that have been found out in streaming practices. Burris &Welner (2005) defined tracking or ability grouping as a process where students are grouped into different classes with a differing curriculum based on the prior achievement or intelligence. Therefore, students are often set on a curricular path like academic, vocational and as general honours to advance. Mulkey, Catsambis, Steelman, & Crain (2005) defined ability grouping or tracking as the process of sorting out students and assigning them to different classes according to their ability or achievement. Classes are often sorted out using achievement on specific subjects and mathematics and reading. The student’s capability is perceived by the teacher to address the curriculum difficulties. Therefore, the teacher tailors the instructions to each group. Slavin (1987) claimed that ability grouping could be divided into high and low achievers and the other students can be heterogeneously grouped. Therefore, there are special classes for the low or high achievers in a school while the other students are placed in a heterogeneous group. Tracking can also take form on within class grouping where teachers arrange students into small groups for mathematics within a large heterogeneous grouped class depending on their performance level.
Tracking takes place in a heterogeneous achievement approach where all students are involved for the entire school day. Tracking refers to ability grouping where students are grouped as above average, average, or below average. However, tracking violates the principle of equity for students because it leads to increased achievement gaps among these different groups. In USA, The Civil Right Act of 1964 provided that students should have opportunities to move from one class to the other based on their academic progress and tracking practice almost ceased. Currently and in post-Civil Rights Act schools, tracking practice is only used to refer to homogeneous ability grouped courses. Most of the times students who are ability grouped for one subject or two end up in one class because of the class scheduling in the school.
Robert Slavin (1987) argued that tracking has various advantages for students. He found out that ability grouped students within a group in a heterogeneous group performs best. The students with lower abilities tend to benefit more when students with different flexible abilities are grouped together. The best ability grouping is dividing students into small groups and adds a little more time for students with low achievement to increase their achievement level. The learning effect on small groups was enhanced when the teacher used a differentiated instruction materials and grouped students into groups of 3-4 students, and the greatest effect was felt in the mathematic teaching. Betts &Shkolnik (2000) claims that merit of ability grouping can be attributed to teachers’ efforts to tailor make certain instructions for each and every small group with ease to cater for the needs of students with different abilities. In addition, students who are grouped in a homogeneous class must adapt to realize increased achievement. Because there are several discrepancies on the definition of tracking or ability grouping, therefore, researchers experience difficulties in identifying as well as comparing strategies used in schools. Betts &Shkolnik (2000) study conclude that homogeneous ability groups of students are beneficial to all students even the gifted students and special education students.
Boaler, Wiliam, & Brown (2000) focused on the cohorts of the Texas elementary children in grade 3-6. They collected their data which was characterized by race, age, gender, free lunches, and the reduced lunch price status to come up with a peer effect on students’ achievement and growth. Academic achievement is usually affected by the social economical factors and status and the study on peer achievement revealed that there was no evidence that affected achievement growth in a heterogeneity group. The study found out that the socio-economic status does not affect the achievement levels of the grouped students.
Critical Analysis
There is a lot of contradicting evidence about the positives and negatives of tracking which makes the situation very complex. Some researchers are clearly in support of ability grouping in mathematics while others oppose it. It is not only the ability grouping system seem to have a contradicting stands but also classes size are different, different teaching approaches, ability range within the class is different as well as teacher competence. Also, students attitude towards mathematics differ from one place to the other, the curriculum vary and resources are not equal everywhere. However, it is acceptable that there is a wide range of students’ ability and there are even gifted students in mathematics class. Since there is no concrete way or evidence in favour of either mixed-ability or same capability grouping that can warrant long-term or large-scale studies. Different researchers have passion about tracking and support each side with impending clarity, and further discussion is needed to come up with the best way of ability grouping for mathematics. The mixed ability case is only being supported by many others because it addresses the issue of equity in the school but its effectiveness aspect to address the needs with different abilities is yet to be comprehensively discussed.
There is common evidence found in many studies supporting tracking practices as well as heterogeneous grouping. Most of the studies support that high-ability students usually benefit when that is working together with other students of high-ability when the teaching approach is developed to address their needs. The researchers who are in favour of the ability grouping practices cite that the main reason for embracing ability grouping is to allow teacher explore different teaching approaches to allow them to address the needs of each group of students with different abilities. The streaming system has been criticised by many studies pointing out that it has a negative effect on the low-ability students who are associated with very low expectation from both parent and teachers. The teaching approaches in the streaming system have been questioned on the matter that less qualified teacher are assigned to students with low-ability as well as negative social effect suffered by students who are subjected to the streaming system since they are ridiculed and labelled as low achievers. Students in low-ability classes behave in a manner that makes teacher have a very hard time in teaching, and it is very difficult to teach effectively in these classes due to students’ behaviour.
Homogeneous grouping and heterogeneous grouping debaters take sides to expose that weakness of the other side to present their side as the best practice. However, it is evident that students from the low streaming having poor performance in mathematics can be directly associated with the factors such as school administration, behavioural, attitudinal and other social factors. There is theoretical justification on the advantages of streaming students according to their abilities so that to make the teacher work easier lack merit since teachers can lack the willingness to work hand and met each student needs according to their ability level. However, there is a lot of evidence from either side of the debate on the best mode of ability grouping for mathematics. Therefore, the complex situation that surrounds ability grouping must be taken beyond that point so that it can be justified as a reputable practice. Researchers have to step beyond the ability grouping debate to build consensus on factors that makes ability grouping ineffective or effective within the classroom.
Teaching Approaches and Implications
Teachers do not have freedom to choose whether to teach in un-streamed or streamed classes. Teachers adapt to the system that runs the school where they work. It is important to involve the teacher and change the ability grouping system in schools since the existing grouping is facing many unresolved challenges. Slavin (1987) argues that the teacher must be involved since they recognise that every class has a student with a different range of abilities and they should adopt a system that world address the range of abilities in the class. Therefore, some instructional approaches that are independent of grouping can be put forward to cater for the needs of student’s ability range to be implemented in the school system. The instructional practices will prevent schools from improving that same tracking system in either the same or mixed classes. Considering that there have been several decades of debates that have failed to address the ability grouping in teaching mathematics, it is time to come up with improved ways of teaching mathematics in any given class. Researchers have developed several effective instructional approached to help cater for the needs of different ability range in class.
It is my opinion that ability grouping for mathematics can only be justified if it follows these three instructional approaches: that is within-class grouping, fostering mathematically creative thinking and differentiation.
Within-class grouping
Students can be grouped into small groups to work as a team within classes purely based on random distribution or their ability. A meta-analysis of within the class grouping was conducted and found out that students grouped into groups of 3-5 students had better outcomes in mathematics, but this was found to be credible only in traditional class settings where individual students had to master learning (Kulik&Kulik, 1992). However, there were no determined benefits within class grouping. The high ability students performed better in both homogeneous classes as well as in heterogeneous class and therefore there were no overall differences. It was evident that the medium ability students perform much better in homogeneous groups rather that the time they are placed in the low-ability group. When the high ability students are placed in a heterogeneous group, they tend do most of the class work and deny the average students an opportunity to think and learn at their pace. Studies have confirmed that there are positive benefits for grouping students in heterogeneous within-class grouping since there is improved communication among the group members which creates cohesiveness. However, the high capability students perform better in mathematics in a homogeneous class and perform poorly in heterogeneous class.
There is considerable diversity in the same achievement class, and therefore, there is a need to utilise homogeneously as well as a heterogeneous grouping within ability grouping classes. The use of corporative learning is important in tracking for mathematics because students are grouped together, encouraged to corporate and be responsible for their learning. Therefore, co-operative learning rewards the group that has done best and call for individual accountability within class groups to ensure increased achievement. The co-operative learning is an effective ability grouping for mathematics, and it can be used in both heterogeneous and homogenous groups in a classroom.
Differentiation
There are several problems that students experience in the ability grouping for mathematics class when the teacher fails to differentiate students’ ability. Teachers who teach in the high ability class, according to the literature, expect all students to learn at the same pace. Therefore, there is a need to introduce some form of differentiation even in the high achievement class through cluster groups, enrichment as well as curriculum compacting and acceleration. According to Kulik &Kulik, (1992) they advocate for the formation of mixed-achievement classes argues that the enrichment programs that characterize gifted students call can actually be beneficial to all students. The highly differentiated teaching approaches in important for all students and since all teachers will take considerable time to for professional development and proper planning and lesson preparation is taken seriously.
Therefore, differentiation in terms of different curricula, teaching approaches, assessment and resources to different students is important in tracking in mathematics teaching. Mathematical talented students require instructions and modified learning material to meet their needs. Cluster grouping is one of the differentiation groupings where 3-6 students of the same capacity are grouped together within the mixed ability classroom. The student enjoys the opportunity to work together and enables the teacher to address the needs of lower ability students as well as high ability students. Differentiation occurs when the teacher clusters students into groups individualise the mathematics program by special issue projects to a cluster group.
Differentiation is the very useful approach in acceleration and completion of the standard curriculum in school. Curriculum compacting issues pre-test to students to determine which areas need to be emphasized on and create time other learning. The enrichment programs are additional curriculum features to help student gain breadth and depth of learning the regular and extra curriculum. The enrichment programs enhance students’ critical thinking, general achievement as well as improved creativity.
Mathematically creative thinking
Mathematics curriculum emphasizes the need to incorporate creativity in mathematics. Several researches into the Japanese education system shows that students in Japan have higher mathematical ability than the western nations. The Japan education system encourages creativity in mathematics and emphasis on thinking as the main objective in learning mathematics whiles the western nation’s emphasis on the learning skills. Therefore, Japanese students in the middle and primary level spend most of the mathematics class analyzing, thinking and inventing while the western nations spend most of the class time practicing skills. The Japanese class system is entirely mixed ability group. Therefore, teaching mathematics need creativity as well as thinking to improve the learning ability in disregard of the grouping, (KOSHY, 2014).
Conclusion
There is a lot of divergence among the factors that have been found to contribute and benefit students in learning mathematics. The western nations and Japan use different approaches even though mathematical excellence has been achieved in Japan (Hirano, 1996). Ability grouping in mathematics during primary and secondary education raises the question of equity, negative, and positive effects on children due to this practice. Many studies have found out that tracking system being beneficial to learners of all levels (Boaler, Wiliam, & Brown, 2000). The results from Japan studies reveal that focusing on streaming is only important when people are interested in improving mathematics achievement. However, this paper has built that case for as well as the case against tracking using relevant literature. But further studies need to be done to compare each side with the other. Tracking can be justified when it aims to improve the overall performance of every student in the class without discrimination the low capability students. Learning in a heterogeneous class is beneficial to the middle-level ability students while homogenous grouping benefits the high-achievement students only because teacher pay more attention to them to satisfy the demand of a “marketplace” education system. On the other hand, low achievement student is neglected by teachers and less is expected from them. It is unfortunate that low capability students are taught by the less qualified teachers who focus on discipline most of the time. Therefore, ability grouping can be justified in mixed within class grouping where the teacher individualizes the mathematics curriculum to address the needs of each student.
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