Effects of Differentiation Strategies and Student’s Ability to Choose on Learning Jo Walker, Mathematics Teacher I have observed that younger students often lack the mature learning skills required to tackle multi-stage contextual problems efficiently or have the study skills to push themselves to the limit of their abilities. Some students seem afraid to make choices and sometimes lack the self-belief in their own understanding, preventing themselves from following their own correct plan to a solution. From my observations of the first time Year 9 GCSE students were offered a simple choice, they looked afraid and uncertain. We had reviewed some areas of maths that they had covered before, spending time on those they had forgotten or where they still had misconceptions. They then had a range of questions covering these areas and of differing complexity. The instruction was to decide what they needed to practise and ensure they challenged themselves, only do questions which made them think and skip some if they decided it was too easy after all. Gradually they made their choices, in some cases just working through questions and finding it easy, I suggested that they try a hard one then move on. At the end of the lesson they wrote a sentence outlining areas to work on and set their own homework. The feedback was positive in terms of students valuing the time to work on their own weaknesses. When I used this again they were much more comfortable making their choices, some students preferred to decide which questions to do in pairs so they could work together rather than what they individually required.
There are several different ways to differentiate tasks, but the articles I read examining younger students show that a student’s ability to make the correct choices independently is essential. I decided not look at differentiation via questioning as this is imbedded in my natural teaching style and design of resources. To be able to look at the effects of age on making choices I looked at year 9 to 11 students, all of whom are studying the same syllabus and were taught by me so the effects of age on responses can be examined without differing teaching styles playing a part. When actually applying differentiation in lessons I feel it is important not to pigeon hole students into an always support / always main / always extend group as I have found that students can be more able in one area compared to another, or can suddenly be inspired when several areas click together so jump from main to extend for instance. Therefore I will always try to set up tasks so that pupils can choose where to start but understand that they can change their mind if their initial choice is too easy or too challenging. My classroom set up and my ethos is to promote discussion and my classes make the choice of how to work, either alone, in pairs or small groups. I looked at the following styles of task: Differentiation by outcome – investigational / problem solving tasks where students make decisions about how to tackle a given problem, how to write up their findings and how far to generalise results using algebra. Differentiation by outcome – through trial and improvement, learn about a previously unknown area of mathematics.
Differentiation by question – from an exercise students choose where to start, how many to do and where to jump to. They then move on to a further extension task which is harder but in the same area of maths. Differentiation by task – within a given strain of mathematics which has briefly been reviewed at the beginning of the lesson or in the previous lesson, students choose which they are to spend time on and which grade to target ensuring they meet their target grade and, if time permits, exceed it.
Findings All age groups found differentiation by question and task easier to access and learn from than either of the differentiation by outcome options. They also found them slightly more interesting and easier to make decisions about where to start. For all types of differentiation they found it easier to decide what to do in terms of start point and how to tackle problems when they had been doing so for a year. They generally thought differentiation in lessons was important but not as highly as I would have expected. Overall the ratings for differentiation by question were highest for all groups but this could be due to the fact that they are easy to access, requiring only a finite number of steps to solve. When choosing questions or tasks students generally commented that, with time, it became simpler to skip easy questions or tasks and find the correct place to start, showing an increase in confidence and a growing ability to challenge themselves. They also appreciated the freedom to learn at their own pace and focus on individual areas of weakness. When making their choices, being able to work with someone and having a simple start
point were the reasons given for choosing the wrong task by 50% of students. About 25% to 30% did not want to stand out as being able in front of their peers, wanted a ‘can do’ feeling or thought they lacked the maturity and experience to make the correct decisions. The feedback shows that students in all the groups find the breaking down of complex tasks / investigations one of the hardest skills to master. Their responses show that it is essential to make good use of peer support and class discussion and questioning to help develop their ability to identify a start position, to allow the required information to be found and hence the problem solved. Learning by outcome or experimentation was another area which was challenging for many students, but I feel it is a valuable life skill to be able to learn by looking at the world around you. The students had mixed opinions on this, from knowing what they needed to take away from the lesson and being able to remember it, to finding it confusing and in one case a knock to their confidence.
Recommendations
We fully imbed all types of differentiation in mathematics lessons, beginning the process in KS3. Develop the students’ ability to break down problems and a focus on using patterns to discover facts for themselves. We need to build students’ selfconfidence and independence, and encourage students to push themselves. Learning through investigation tasks for each unit, planned centrally and shared across the department. A brief idea of levels / grades for each year group would be essential.