My First School
I began my career in teaching at a fantastic inner city school in Birmingham. The children were motivated to learn and the senior leaders were experienced and supportive of the teachers. We didn’t use books and instead had profiles that contained a few larger pieces of work for each subject. The planning had been refined over years and new teachers were encouraged to write their own activities and help develop existing ones. This was a blessing as it gave me a secure framework from which to explore activity design.
As many teachers do, I looked for worksheets online to help me plan sequences of learning. I am sure that I am not alone in expressing my disappointment with most of them. I felt that many had been produced very quickly with little regard for their intended use or for mathematics pedagogy. Questions of the same type, with randomly chosen numbers, did little to deepen my pupil’s understanding. A lack of scaffolded challenge meant that many pupils could complete worksheets with little cognitive effort. It was a far cry from my ideas about effect learning. What I needed was to do some research…
Further Research Required
In 2013 I began a two year maths specialist teacher course with the University of Northampton. This was a catalyst for me to dive into the research of Mathematics teaching. From this point I began to experiment with the ideas that I had read about, including them in my own resources. I found that my class could make more connections and understand concepts with greater depth. This spurred me on to read more and to refine my approach further.
I discovered that I particularly enjoy writing activities that involve ‘varied practice’. This part of the lesson comes after you have introduced a new concept and given the children an opportunity to get to grips with it by rehearsing and copying modelled examples. Then the varied practice phase enables children to deepen their understanding by tackling a task that includes carefully chosen and sequenced questions.
There are several elements that I consider when creating varied practice worksheets:
Variety of Questions– There needs to be enough variety of question type to ensure that pupils see multiple presentations of the same concept. I also like to consider how we move from one question type to another throughout the activity.
Variation Theory– Questions are ordered so that some elements are kept the same and others are varied. This illuminates the underlying structure of the concept and helps pupils make connections with other ideas.
A few examples of variation theory in action.
Range of examples: A range of examples can help to show a concept’s scope. I like to consider common examples, non-examples, boundary examples and unusual examples.
Mathematic Representations: Each concept needs to be encountered through an appropriate representation to aid understanding. Concrete resources and pictures allow pupils to develop conceptual understanding and support abstract notation.
Reasoning– Activities that give children the chance to consider specific examples and move from these to generalisations. Part of the reasoning process is also to make conjectures and refine or prove them.
Design- This is important so that activities are clear and do not contain any extra or distracting elements.
Many ideas lend themselves to visual representations such as Dienes blocks, number lines, tens frames etc. I am a big fan of using my interactive whiteboard to model examples using these types of representations. They are great to develop understanding and the visual matches the practical equipment children use at their tables. There are many online manipulatives out there, however I have often found them difficult to use in lessons. It is really tough to model a problem by asking my class questions, explaining, writing calculations and giving feedback, all whilst moving around objects on an interactive whiteboard!
This is why I started designing my own animations in which I can select specific examples to show my class. By pausing and replaying the animation at different points I can focus on the discussion rather than on clicking and moving images on the screen.
4 Colour Maths
I have found that many online worksheets and resources are difficult to use because they lack the quality that my students deserve. I want my activities to be carefully crafted and to contain important pedagogical ideas to deepen my pupil’s understanding. I love animations because they make it easy to maintain the flow of a lesson whilst modelling problems. 4 Colour Maths is a way for me to share these resources with other teachers. I hope you (and your pupils) enjoy them!