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Preparing students for a mathematics exam takes time, patience and careful planning. In this blog, I will share my ideas for teaching students how to prepare for their final exams. These strategies have worked well for me, and I have seen them work well for others.
Students need space and time to formulate their approach to solving complicated questions. Working in their book, on a mini whiteboard or in an exam booklet does not always provide enough space. Therefore, I let students write on their desks with dry wipe markers. They like doing this and often find it very helpful. It is very effective at helping students learn how to work together and promoting discussion.
As students enter the classroom, I give them two past exam questions that recap the previous lesson. The first is a more traditional style question, and the second has a greater problem-solving element. Shown below is an example of two questions on recapping simultaneous equations.
Question 1 Traditional Style
Solve the simultaneous equations.
2x + y = 18
x – y = 6
Question 2 Problem Solving
Joe travels for x hours at an average speed of 12 km/h.
He then travels y hours at an average speed of 4 km/h.
In total he travels 48 km at an average speed of 6 km/h.
Work out x and y.
The last 12 to 15 minutes involve completing a challenging exam question where the skill taught in the lesson forms a small part of a much bigger question. All the UK examination boards have released several problem-solving papers which provide many examples to choose from at varying levels of challenge.
Whenever possible, I show the class the examiner’s report on a question they are attempting. This helps the students to compare their performance against those who have been through the real thing.
I like it when the examiner’s report explains most candidates found the question challenging as this is an opportunity for the students to impress. Students who want a challenge have something to aim for, and those who struggle like knowing others have encountered the same problems.
In June of Year 11, students will be assessed on their performance to answer complicated questions. They will not be allowed to ask for help and will likely never know whether their answer to a question is correct. They will have to trust their interpretation of what they think the question is asking and their method in attempting to solve it. This is a scary experience which students must be prepared for.
When preparing students for a mathematics exam, they must learn how to overcome difficult questions in a maths lesson. If they do not know how to do this under the supervision and care of their maths teacher, they will not be able to do it in the final exam in June. Therefore, to help prepare students for the final exams, I rarely give them the help they want, and they are often too quick to ask for in lessons. For instance, I am frequently asked to check their answer, help them get started or check part of their method. My response is: “Read it out loud to me”, ˜Does it make sense to you?” or “What do you think?” then I walk away.
This can be frustrating for the students, but they understand I am giving them the help they need not the help they want. They need time and the trust of their teacher that they can overcome the struggle on their own.
Should a student ask for help, I will monitor them. If they continue to make no progress after a while, I will provide prompts and clues to keep them motivated. I always go through the questions in depth at the front of the classroom, but only after they have had enough time to attempt it the best they can.
Every week my exam classes must complete a past exam paper for homework. The lesson it is due in is always given to working through the paper as a class.
On Friday, when we review the exam paper, the class are asked to mark each other’s work by working in pairs or small groups. They do this without a mark scheme. I provide no answers or modelling for the first two-thirds of the lesson. I intend for students to discuss their answers and have the confidence to know their solution is correct by checking their reasoning against their peers. Where their answers differ, there is an opportunity to discuss and share methods. Students must agree on the correct answer before marking the next question.
If I were to provide the mark scheme early in the lesson, the students would have no reason to explain their reasoning to each other. This way, they learn how to validate their work by developing their sense with a peer.
In the final third of the lesson, we go through the mark scheme and quickly go through the questions that need resolving. Should students remain unclear about how to answer the question, I take the time to model the solution in-depth on the board.
In the final exam, all students are judged on their ability to answer the same questions. They can not choose which questions, or they will lose marks. Therefore, I have the same expectation for every student to attempt every question regardless of their self-perceived ability. Maybe they cannot achieve all 5 marks on a 5-mark question, but they could achieve 2 or 3 marks if given enough time.
When students apply such effort to attempting challenging questions, they mustn’t judge themselves by their final answer. Therefore, when feeding back the solutions, I work through the entire problem slowly and carefully, addressing all the misconceptions. This way, students can track their progress through the question and see what they need to have done next.
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