Differentiation in Mathematics

In the webcast "Differentiating Mathematics Instruction", Dr. Marian Small begins by identifying elements of successful mathematics classrooms. She recounts situations where teachers created types of tasks that had a relative sense of importance to the learner. As teachers interact with students, they have demonstrated care and knowing their learning by choosing words that would prompt learning and deeper understanding. Dr. Small recognize that effective teacher facilitation of student learning responds differently to each learning being sensitive to what they need creating a safe and inclusive environment for all learners. Throughout her observations, Dr. Small also notes that effective mathematics classrooms are lead by teachers that focus on what the learner is saying, thinking, and how they are responding to one another. From there, she examines the knowing and learning that happens and how time to answer, perseverance, appropriately built inquiry at the right challenging level for the learners, allowing for diversity in student thinking, and creating meaningful tasks all contribute to an inclusive differentiated successful mathematics classroom.

With these understandings of successful classrooms, Dr. Small builds the conceptual framework of what a differentiated mathematics classroom will comprise.

Big Ideas with Open Ended Approach -- Dr. Small feels that students need to deal with Big Ideas at different levels of sophistication to allow them to perform successfully and safely where they are in their learning. In order to do this, the teacher needs to know where students are at in their learning in the intended content area through diagnostic assessments (these can be in different forms...conferencing, performance task, paper/pencil test).  This will give a window into how well prepared the students are for the intended learning (it may turn out they are well ahead and can tackle more diverse inquiries as well).  Diffferentiation also includes focusing on inclusivity where the inquiries are open ended enough for al students to engage in meaningful ways. The entry points may look like giving students options to select their own objects, build their own designs, select their own number set, selecting their own data group for graphing, etc. where they are empowered to make as much of the inquiry safe and familiar to themselves while not detracting from the learning intention connected to the big idea.

In addition, Parallel Tasks can be incorporated to give students the responsibility of choice to select the most appropriate entry point for their engagement. The two tasks can be more structured then the open ended tasks, but are varied in levels of complexity but still meet the learning intentions of the lesson.

Differentiating Mathematical Process is something that can also contribute to deeper understanding by allowing students the power to use their understanding of concepts to decompose procedures and communicate solutions.

Reflecting on My Practice

I would begin by saying that I don't come near some of these recommendations especially with regards to parallel tasks. I am intrigued by this diversity in inquiry design and feel that this will definitely provide even more opportunity for students to engage in meaningful learning experiences. With regards to open ended inquiries, I have always felt that this kind of flexibility is always a positive accommodation for the learner as they are empowered to customize some of the elements to make it their own. This has always brought amazing results as students expand from this starting block to naturally connect other ideas and understandings they have to the task. I believe that Dr. Small's chronicle is more structured and effective as I have always just kept everything open to anyone's ideas. I will change my practice of open ended questions to purposefully build threads of openness in order to stay the focus on the intended learning.

Beyond task design, I also feel very passionate about Dr. Small's notions on treating our learners differently as to how they would respond best (public praise might not be appreciated by all learners) and on listening to our learners. I have always believed in the power of students making their own meaning and that each person might have different solutions and/or different explanations that deserve our attention. I think having students share their ideas fully can also provide an opportunity for us to facilitate their learning even further.