' Would a sketch help? ' - the golden question to survive the new spec
Sketching can give students anxiety
Having taught the A Level specifications for all exams boards over the last ten years, I saw how the act of needing to sketch a curve to answer a question gave students anxiety. Even though these were familiar sketches from their GCSEs, there was always a sense of sketches feeling like a task rather than an indispensable tool for mathematical deduction and problem solving.
The need for a shift
Some old spec exam questions explicitly instructed students to sketch a curve. Sure there were very often transformations involved and sometimes they used sketches to demonstrate a point but students were often explicitly instructed to provide a sketch.
To a large extent this explicit instruction removed the opportunity for us to sell sketching to students. Sketches help bring a problem to life, you can visualise and bring clarity to how curves are interacting and bring validation to algebraically produced answers. This benefit is only believed by students if they have witnessed it themselves.
Being TOLD to sketch a curve in a question takes away from the enlightening process of considering if one would be helpful, then doing one anyway and realising just how much it unloads the burden of solving a difficult problem. This is where we truly sell it to students - they need to own the idea of sketching without any instruction to do so.
The new specification and sketching
With an increased emphasis on Problem Solving and Mathematical Argument, the new specification focuses on teaching students to strategise. Given a lot of information, an end goal, and little breakdown into simpler parts, they will need to unpack problems on their own. Crucially, it will be entirely on them to ask themselves : would a sketch help me here?
Where getting by without a sketch was possible before, it will become much harder to justify not doing one for questions in the new specification
How we have adapted
We have thousands of students using MarkIt to practice their Problem Solving and Thinking skills by doing our step by step exam questions online. The questions give feedback, without giving answers away - they have to think about each thought process and self correct.
We have been thoroughly researching the new specification to help students make the transition smoothly by tailor making new exam style questions mapped to the new curriculum. These questions will have far more Proof, Modelling and Problem Solving to truly prepare students for the new expectations and provide resources on top of the specimen papers. Try these for free here.
Here's an example:
Try this question on MarkIt - direct demo here!
Same Maths, New Expectations
Will students think to sketch the curve on their own? Will they use coherent mathematical argument to connect their sketch with a circle theorem? Will they see that they will need to find p in order to solve the rest of the problem?
"Would a sketch help?" - creating the mindset
While attending a CPD session for the new A Level, I was given some very good advice when it comes to embedding a culture of sketching throughout the year. When faced with any question, before jumping into it straight away, students should ask - ‘ Would a sketch help? ’.
Making this part of the narrative in the classroom will establish a culture that makes sketching an invaluable starting point and a tool that demystifies many exam questions, instead of a task the question demands. By doing this, students will get hooked to the clarity sketches bring and we will see them take to sketching the way they take to calculators!