Who should learn what mathematics and when

What are the impacts of ability grouping and tracking on student learning? 

The student should be the reference point for addressing the complex issue of who should learn what mathematics and when. The challenge of addressing diverse students’ needs encourages us to reflect upon the implications of placing students in various ability groups or tracks for mathematics instruction. Research suggests that these practices do not provide the same educational experience for all students.

Studies suggest that expectations placed on students differ according to their assigned ability group or track. Students deemed less capable experience less depth and breadth in school mathematics. Indications are that the most experienced teachers are assigned to teach high-level classes, while teachers with the least experience and mathematical background are assigned to teach the lowest-performing students in mathematics. Studies also reveal crucial differences in the kinds of instruction offered in different tracks. Instruction in the lower tracks tends to be fragmented, often requiring mostly memorization of basic facts and algorithms and the filling out of worksheets. Although some higher track classes share these traits, they are more likely to offer opportunities for making sense of mathematics, including discussion, writing, and applying mathematics to real life situations. 

Tracking and ability grouping rarely allow for upward movement between ability groups or tracks when a student makes some developmental leaps. Hence, a conflict exists between the structure of academic tracks or ability groups and the potential academic and intellectual growth of struggling students who may be late bloomers. An alternative to homogeneous strategies of tracking or ability grouping is mixed ability or heterogeneous grouping for instruction. Heterogeneous instruction emphasizes a differentiated classroom approach, in which teachers diagnose student needs and design instruction based upon their understanding of mathematics content using a variety of instructional strategies that focus on essential concepts, principles, and skills. Inherent in this practice is the opportunity for all students to receive quality mathematics instruction. As the demand for a more mathematically literate society continues, schools need to respond to this challenge and provide meaningful mathematics to all of our students, all of the time.

To effectively teach students coming from a variety of previous mathematics learning experiences and successes, teachers should thoughtfully choose instructional strategies for working with de-tracked or heterogeneous groups. The teacher must believe that all students can learn, although in different ways and at different rates. 

These instructional elements have been shown to be effective for mixed ability mathematics classes:

1.A meaningful mathematics curriculum. This means providing contexts that give facts meaning, teaching concepts that matter, and framing lessons as complex problems.

2.An emphasis on interactive endeavors that promote divergent thinking within a classroom. Students need to construct knowledge with peers, including safe and regular opportunities to take risks, exchange ideas, and revise their understanding of mathematics.

3. Diversified instructional strategies that address the needs of all types of learners. To embrace multiple intelligences is to present information in a variety of ways.

4.Assessment that is varied, ongoing, and embedded in instruction. Performance assessments, a portfolio of growth and achievements, projects demonstrating the accompanying mathematics, and solving and reporting on complex problems in varied contexts will provide evidence of student learning.

5.Focused lesson planning that, instead of emphasizing what the classroom teacher wants to teach, begins by understanding what students need to learn (outcomes) and assessing what they already know.

Employing these techniques will provide a rich classroom experience and an effective way to enhance the learning of mathematics for all students.