"There is no formula or recipe that works for all learners in all times. There is no set of lesson plans or units that engage the range of learning styles, approaches and intelligences that are likely to gather in one class."
By William Ayres, To Teach: The Journey of a Teacher
By William Ayres, To Teach: The Journey of a Teacher
There are many different ways a teacher can use differentiation in their teaching, however this site is going to focus on differentiation by task and open ended tasks to be exact. Open ended tasks are ideal for composite classes or classes that have different level of students because open ended activities create opportunities for students (Masingla 2006). These opportunities include students taking ownership in their own learning and show their thinking in explicit ways; whatever solution they come up with was the result of their construction of their understanding and meaning of the task and also allows all students to participate in the task to varying degrees (Masingla 2006). Thus open ended tasks become a logical and effective way to cater for diverse learning.
Open- ended tasks does three things in a classroom they are (Masingla 2006):
Verbalizing: where students ask questions with “how” and “why”, the use of thinking aloud creates conversation between student and teacher, this leads to a shared understanding of a topic (Masingla 2006).
Clarifying: This is where the teacher is establishing norms for what is valued in a classroom, negotiating assessment criteria and creating individual or classroom concept maps (Masingla 2006).
Recording: This is where classrooms represent their understanding through written procedures, concept maps and other work samples that include drawings, diagrams, table or charts and justification solutions to open ended tasks (Masingla 2006).
Location and Transformation
As there are many topics in mathematics, this site will use location and transformations as the framework to explain differentiation. The reason for this is because spatial sense initiates awareness of an individual’s surroundings and the objects in them, also plays an important role in interpreting and understanding the world around us (Sullivan 2003). As students develop spatial reasoning abilities they can appreciate the important role geometry plays in art, science and their everyday world.
Spatial reasoning include two spatial abilities( Sullivan 2003):
Spatial orientation- This is the ability to locate and describe objects in spaces and carries out and describes transformations .
Spatial visualization- This is the ability to imagine, describe and understand movement of two and three dimensional space.
Combining open-ended tasks and location and transformation students will all be able to participate in the task and gain an understanding of their world and in turn the learning experience they gain from these activities will assist them in other learning areas.
Why open-ended tasks benefit all students
Above grade level: the above grade levels benefit because open-ended tasks remove the barriers. These students are then able to produce their best products and to are also able to encounter self-created challenges(Sullivan 2003).
On grade level: the at grade level students benefit from open-ended tasks because they provide them with opportunities to explore and present their individualized creativity in projects. Their work cannot be compared to any other work in class because it is unique(Sullivan 2003).
Below grade level: The students who are below grade level benefit because open-ended tasks give these students opportunities to express their creativity through choices and to demonstrate where their strength lie (Sullivan 2003).
For instance the open-ended task could be drawing a birds eye view map after modelling what birds eye view looks like. The students have the freedom to choose how and what they draw, there are no barriers stopping students from sharing their thoughts. However the very task that gives students the freedom to try many different potentially successful mathematics techniques unfortunately also limits how much of what we know of those paths that students chose not to follow (Wees 2014). One possible solution is to make sure that each time students work on a task, they have the opportunity to share their different solutions with each other (Wees 2014). Below is a short video of how to apply differentiation strategies in a classroom.
Two studies have raised specific concerns:
1. Cooper and Dunne (1998) found that open-ended tasks created difficulties for low socioeconomic status students, that these students performed significantly poorer than their middle class peers (Cooper and Dunne, 1998).
2. Lubienski (2000) also found that low socio-economic pupils were worse off, even though many were capable students (Lubienski, 2000). Another criticism towards open-ended tasks is that students may not be able to differentiate what might be important, especially in areas with no prior knowledge (Sullivan, 2003).
There are possible solutions for some of the concerns raised (Sullivan, 2003):
1. Teachers can change the context of the problem to make the context more abstract.
2. Teachers can change the inherent assumptions in the problem, or at least point out that those assumptions exist.
3. Teachers can give students a pre and post test, so the teachers can target their teaching at all students.
On the next page of this website provides lesson ideas that promote open-ended tasks in classrooms that take in account of the concerns raised in research.