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I find differentiation to be one of the most difficult parts of teaching, and is the thing I am asked most about by teachers of all ages and experiences. Before we dive into the literature, it is worth recapping a few important points we have learned from previous sections:
1) Learning styles are not as important as many of us have been led to believe, and what is more important is that material is presented to students in its most appropriate form (see Cognitive Science)
2) Students are not good at judging what they understand, and so any reliance on student self-assessment as a guide to what they know is not likely to be accurate (see Cognitive Science)
3) Learning and Performance are very different things, and we should be very careful about inferring anything about learning from a student's performance (see Memory)
4) Overlearning can be beneficial (see Memory)
These all imply that we should not worry too much about differentiation in the sense of preparing lots of different materials for different students in advance of a lesson. We should instead focus on teaching all the students as well as we can, making judgements and interventions during the lesson using the principles of Formative Assessment. However, what does research specifically about differentiation have to say on the matter?

Research Paper Title:
The Feasibility of High-end Learning in a Diverse Middle School
Author(s): Catherine M. Brighton et al
My Takeaway:
I include this paper at the start of our discussion of differentiation to call into question the almost universally accepted idea that differentiation is beneficial to student learning. It is a large scale study carried out across many states in the US, and one of the authors (Carol Ann Tomlinson) is a huge proponent of differentiation. The study looked at the effectiveness of differentiated instruction and differentiated assessment. The surprising conclusion from this detailed paper is that the researchers could not get differentiation to work. This finding supports the conclusion from a large meta analysis entitled The effectiveness of universal design for learning (payment needed to access the full paper), which states with reference to differentiated instruction: "the impact on educational outcomes has not been demonstrated". Why on earth would this be the case? Well, there are two possibilities:
1) Differentiation is hard to do correctly. This is the conclusion of the authors, as can be seen in the quote below. And indeed, differentiation is incredibly difficult. It is time consuming preparing a plethora of different resources before the lesson, and it can often lead to chaotic lessons simply trying to manage, monitor and assess students working on different pieces of work.
2) Differentiation itself is not effective. This of course is a controversial view, but for the four reasons I outlined in my introduction to this section, it is certainly worth considering. I am not gong as far as to say all students should be doing all of the same work all of the time, but I think starting from an assumption before a lesson that different students will require different work is dangerous. As we will see from the paper below, it is incredibly difficult to predict how students will respond to a given concept, and once a decision is made it often takes a lot to deviate from that path, especially if you have taken time preparing the resources. I am leaning towards clear instruction for all students following the principles of Explicit Instruction and Cognitive Load Theory, followed by making decisions in the lesson using the principles of Formative Assessment. Having a well chosen, domain-specific extension activity for students who successfully complete the core work is important, and follows the findings related to Expertise Reversal Effect identified in Cognitive Load Theory and from the papers in Problem Solving section. Likewise, having supporting resources ready when needed is likely to be beneficial. Once again, following the benefits outlined in the Cognitive Load Theory section, these are likely to consist of example-problem pairs for the students to study and attempt.
My favourite quote:
Results suggest that differentiation of instruction and assessment are complex endeavors requiring extended time and concentrated effort to master. Add to these complexity current realities of school such as large class sizes, limited resource materials, lack of planning time, lack of structures in place to allow collaboration with colleagues, and ever-increasing numbers of teacher responsibilities, and the tasks become even more daunting.

Research Paper Title: Teaching to What Students Have in Common
Author(s): Daniel Willingham and David Daniel
My Takeaway:
This is a fascinating review of relevant research that reaches the clear conclusion that teaching geared to common learning characteristics can be more effective than instruction focused on individual differences. The rationale behind this is that students are in fact more similar than they are different. The authors identify two varieties of cognitive characteristics that all students share:
(1) things that the cognitive system needs to operate effectively
  • Factual knowledge
  • Practice
  • Feedback from a knowledgeable source
(2) methods that seem to work well to help most kids meet those needs
  • Distribute study over time
  • Practice recalling facts
  • Cycle between the concrete and the abstract.
The point here is that these are characteristics that all students need to learn effectively, and it is clear (to me, at least) that the three characteristics in (1) are far more easily achieved within a framework of Explicit Instruction. Sure, there will be individual differences concerning how quickly certain students comprehend a concept, or the amount of practice certain students need. But, as the authors point out, "the observation that not every student can do everything the exact same way at the exact same time should not lead to the overreaction of hyper-individualizing the curriculum". One final point really resonated with me - the most of failure. We know that students share many common cognitive characteristics, and we know how best to teach to those. But we don't know nearly as much about their cognitive differences and the best ways of teaching to those. And, as we shall see in the next paper, the issue is made even more complex given the fact that students cognitive abilities vary task by task, and day by day. So, teaching to individual differences, as well as being impractical in many large classes, may also not be as effective as we might hope. Students are more similar than they are different, and gearing teaching towards these common characteristics is likely to be more effective than an attempt to over-individualise.
My favourite quote:
Of course, students will differ with regard to how they respond to and benefit from any single instructional strategy in a given lesson. There is no doubt that students have individual differences that are both situational and preferential. And there is no doubt that effective teachers address these differences using their own experience as a guide. But when it comes to applying research to the classroom, it seems inadvisable to categorize students into more and more specialized groups on the basis of peripheral differences when education and cognitive sciences have made significant progress in describing the core competencies all students share. Teachers can make great strides in improving student achievement by leveraging this body of research and teaching to commonalities, not differences.

Research Paper Title:
What Is Developmentally Appropriate Practice?
Author(s): Daniel T. Willingham
My Takeaway:
I love this paper. Willingham begins by providing evidence against Piaget's proposed stages of development, and instead argues two key points. Firstly, development does not occur in discrete, pervasive stages. Anyone aware of this fact is likely to feel the same way I do when we are expected to show students making progress every single time data is reported. Secondly, children’s cognitive abilities vary by task and day, not just by age and individual developmental pace. And that causes a huge problem when planning for differentiation in your lesson. You simply cannot know how well students will respond to a particular task or topic until you do it. Simply assuming some students will not be up to the work denies them the opportunity to prove you wrong. Likewise, assuming other students do not require as much support and guidance risks leaving them with an incomplete understanding. With this in mind, Willingham gives four pieces of advice to teachers with regard to differentiation:
1) Use information about principles, but not in the absolute. It is useful knowing what students should know - and age related expectations are pretty good for this. They may even give you insight into how students may think and their likely misconceptions. But they should act only as a guide, and should not be taken as absolute.
2) Think about the effectiveness of tasks. Often it may not be the concept that is the problem, but the task itself. For example, I have had success introducing key concepts in algebra to Year 7s using The Border problem, whereas other tasks have failed to provide the same level of understand to older, higher achieving students. Finding good tasks, explanations or analogies for key concepts and always learning from each time you use them is crucial.
3) Think about why students do not understand. Related to the point above, if a child seems to not understand something, the issue may not be with the concept itself, but a feature of the task, or  - and I increasingly find this is a case - a missing bit of background knowledge. Effective use of Formative Assessment to assess background knowledge and resolve any misconceptions may be the key to this.
4) Recognise that no content is inherently developmentally inappropriate. This is a big claim! Willingham gives the example of probability: "the notion of probability is embedded in games that children play using dice, and this understanding can be expanded to include the notion of a distribution. Thus, one approach is to help the child gain an intuitive appreciation of a complex principle long before she is prepared to learn the formal description of it. Without trivializing them, complex ideas can be introduced by making them concrete and through reference to children’s experience." Whilst I agree to a certain extent with this, I still feel there are certain topics that should be left until students are older and more mathematically experience. Take trigonometry, for example. I would make it illegal to study trigonometry before Year 10. But this is not just because I feel younger students are not cognitively developed enough to cope with the demands of that content, it is also because I feel it is important to leave some surprises, some topics that have not yet been covered, for students' final years of high school mathematics.
All of this does not make differentiation any easier, but it does suggest to me that giving all students the opportunity to achieve is better than putting them into categories before the lesson. If misconceptions do become apparent in the course of teaching (exposed via the techniques of Formative Assessment), then of course differentiation will be needed. But the point here is that - perhaps unfortunately - we may only be able to deduce this within the lesson itself.
My favourite quote:
If a child, or even the whole class, does not understand something, you should not assume that the task you posed was not developmentally appropriate. Maybe the students are missing the necessary background knowledge. Or maybe a different presentation of the same material would make it easier to understand.

Research Paper Title: How Do Teachers' Expectations Affect Student Learning
Author(s): D. Stipek
My Takeaway:
One aspect of differentiation is planning different materials to give to students, and the potential problems with this have been outlined in the paper above. However, perhaps a more common form of differentiation is the help we give to different students during lessons. In particclar, I have been inclined to offer more help to students who I perceived as lower ability, or who I thought might struggle with a particular concept. This fascinating paper offers up a stark warning against that. It surveys research into the ways in which teachers' beliefs about students affect their behavior toward students. One thing that struck me more than anything way this: by simply offering up help, we may be communicating to the student in question that we have low expectations of them. That makes perfect sense. Many times I will set my class off on some work and immediately ask a student who is prone to struggling something like "do you need any help?", or "give us a shout if you get stuck on anything". I will do this quietly so other students do not hear, and I am genuinely doing it with the best of intentions, but what message is it sending to that student? As we have seen in the Praise and Motivation section, if students do not believe themselves that they can achieve, motivation and subsequent achievement will likely diminish, and we as teachers are key to helping them believe in themselves. My major takeaway from reading this is often the best intentions of teachers can lead to students believing we have low-exceptions of them. In future, I will think more carefully before I act and, as difficult as it may be for all parties involved, let all students struggle for a while.
My favourite quote:
Helping behavior can also give students a message that they are perceived as low in ability, and it can undermine the positive achievement-related emotions associated with success. Meyer (1982) describes a study by Conty in which the experimenter offered unrequested help either to the subject or to another individual in the room working on the same task. Subjects who were offered help claimed to feel negative emotions (incompetence, anger, worry, disappointment, distress, anxiety) more, and positive emotions (confidence, joy, pride, superiority, satisfaction) less than subjects who observed another person being helped. Graham and Barker (1990) report that children as young as six years rated a student they observed being offered help as lower in ability than another student who was not offered help.