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Making connections : Post 16 Level 2 : Mathematics-specific Pedagogy


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Post 16 Level 2
Making connections
Question 2 of 3

2. How confident are you that you can support learners in making connections between solving problems in a different way?

a. Activity One


Activity

Have a go at these problems. As you do each one think about:

  • whether it matters which methods you use;
  • how you would encourage your learners to try different methods, and
  • how you might help your learners devise efficient ways of solving problems that do not just rely on a set technique.

1. Find at least two different methods for making g the subject of the formula 5g + h = 23

Prompt 1.

 

Here are two ways - did you find others?
Prompt:

Problem 2

 

2. Work out the answer to 34 x 246 as many ways as you can.

Prompt 1.

Which of these methods do you prefer?

Problem 2

3. Now solve this NRich problem:

“If today is Monday, it will be Monday again in 7 days, 770 days, and in 140 days. It will be Wednesday in 2 days, 72 days, 702 days and in 772 days. What day of the week will it be in 1000 days' time?” (Work this out initially without a calculator and then with a calculator.)

Prompt 1.

Have a look at the various solutions suggested by learners at Nrich.

Commentary

“In many mathematics sessions, learners apply a single taught method to a variety of questions. It is comparatively rare to find sessions that aim to compare a range of methods for tackling a few problems. Many learners are left feeling that if they do not know ‘the right method’ then they cannot even begin to attempt a problem. Others are stuck with methods that, while generating correct answers, are inefficient and inflexible. These activities (in Improving learning in mathematics) are designed to allow learners to compare and discuss alternative solution strategies to problems, thus increasing their confidence and flexibility in using mathematics. When ‘stuck’, they become more inclined to ‘have a go’ and try something. They thus become more powerful problem solvers.” Improving Learning in Mathematics: Challenges and Strategies M Swan

There are many strategies that you can encourage your learners to use when they start to solve a problem and we should make sure that all our learners are aware of all of them:

  • Drawing a picture (or a table)
  • Looking for a pattern
  • Estimating and checking
  • Making a systematic list
  • Using logical reasoning
  • Working backwards from the answer

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