Tracking is a process often used in many schools in United States where students are placed into tracked groups in seventh grade. These separate classes provide higher- or lower-level content to students.
Opportunities to Learn
One key factor in student achievement is known as “opportunity to learn” (OTL). Put simply, if students spend time in classes where they are given access to high-level content, they achieve at higher levels.
We cannot know what a 4- or 14 year old is capable of, and the very best environments we can give to students are those in which they can learn high-level content and in which their interest can be piqued and nurtured, with teachers who are ready to recognize, cultivate and develop their potential at any time.
Teaching Heterogeneous Groups Effectively: The Mathematics Tasks
- Providing Open-Ended Tasks
- Offering a Choice of Tasks
- Individualised Pathways (SMILE – http://www.nationalstemcentre.org.uk/elibrary/collection/44/smile-cards)
Teaching Heterogeneous Groups Effectively: Complex Instruction
Experienced teachers know that group work can fail when students participate unequally in groups. If students are left to their own devices and they are not encouraged to develop productive norms, this is fairly likely to happen: some students will do most of the work, some will sit back and relax, some may be left out of the work because they do not have the social status with other students.
In complex instruction (CI) classrooms, teachers value, and assess students on, the many different dimensions of mathematics. The mantra of the CI approach:
No one is good at all of these ways of working, but everyone is good at some of them
When students were interviewed in traditional mathematics classrooms as part of the study in the US, they were asked: “What does it take to be successful in mathematics?” A stunning 97% of students said the same thing: “Pay careful attention.” This is a passive learning act that is associated with low achievement (Bransford, Brown, & Cocking, 1999). At the CI classroom when students were asked the same question they came up with a range of ways of working, such as:
- Asking good questions
- Rephrasing problems
- Using logic
- Justifying methods
- Using manipulatives
- Connecting ideas
- Helping others
Students when faced with mathematics problems are encouraged to read questions out loud, and when they are stuck, to ask each other questions such as:
- What is the question asking us?
- How could we rephrase this question?
- What are the key parts of the problem?
The students’ engagement was due to many factors:
- The work of the teacher, who had carefully set up the problem and circulated around the room asking students questions
- The task itself, which was sufficiently open and challenging to allow different students to contribute ideas
- The multidimensionality of the classroom: different ways to work mathematically, such as asking questions, drawing diagrams, and making conjectures were valued and encouraged
- The request to deal with a real-world object or idea
- The high levels of communication among students who had learned to support each other by asking each other questions.
Teaching students to be responsible for each other’s learning