Fiona Allan

Adults Don’t Count

Adults Don’t Count

Aims

To think about the effective teaching and learning Maths

To explore questioning further To revisit the principles for effective

teaching To network and learn from each other To enjoy doing some Maths!

Principles for effective teaching

• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,

individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned

Using only 1, 2 and 3, how many numbers between 0 and 10 can you make using addition, subtraction, multiplication and division?

For example: 1 + 2 – 3 = 0

Starting with Starters

Using 2,4 and 6, can you make an odd number?

Using 3, 5 and 7, can you make an even number?

Starting with Starters

Using 2, 3, 4What is the biggest number you can make?What is the lowest number you can make?Make an even numberMake an odd numberMake a square numberMake a multiple of 2Make a multiple of 4

Starting with Starters

Results from North Hertfordshire College project

Attendance in the classes taking part is at 90% - for those not taking part the attendance rate was 78%.

The pass rate for GCSE Mock has increased to 77% in the classes taking part, compared to a College pass rate of 52% in 2009/2010.

In an AS Level mock exam learners achieved an average of 1.57 grades higher than the grades predicted by their GCSE scores.

Developing effective questioning

Why do teachers ask learners questions?

Write one reason on a post-it.

On another post-it write an example of this type of question.

Focusing on Questioning

In your group, compare your answers and group them.

Can you think of any other reasons and types of questions?

Focusing on Questioning

Handout after task: Resource Sheet 1 from NCETM Departmental Workshop Questioning

Focusing on Questioning

‘Twas brillig, and the slithy tovesDid gyre and gimbal in the wabe;All mimsy were the borogoves,And the mome raths outgabe.”

(from Jabberwocky by Lewis Carroll)

1. What were the slithy toves doing in the wabe?2. How would you describe the state of the borogroves?3. What can you say about the mome raths?4. Did you need to understand the text in order to answer questions 1 to 3?5. Why were the borogroves mimsy?6. How effective was the mome raths’ strategy?

Focusing on Questioning

Questions 1, 2 and 3 ask “What?” and seek facts.Question 4 is a follow up to questions 1, 2 and 3.Question 5 asks “Why?”Question 6 seeks an opinion.Questions 5 and 6 cannot be answered by extracting information from the text. They require thought and understanding as well.

Focusing on Questioning

The answer is 7

What is the question?

Write your answer on a Post-It and then compare your answers with the others on your table.

Focusing on Questioning

Writing open questions usingResource Sheet 2 andResource Sheet 3 fromthe NCETM Departmental Workshop onQuestioning

Writing open questions

Writing open questions using a Mathematical Moment:Money (Using higher order questions)

Writing open questions

Write down 3 closed questions which you might ask your students.

Writing open questions

Now change the questions you have written into open questions.

Writing open questions

When is it appropriate to use closed questions?

Writing open questions

Write down all the words that are used in exam questions on a piece of poster paper (spread them out with a space around each)

Pass your poster to the next group

Rewrite the words in language your learners will understand

Developing language

Think before you ask!

If you don’t ask the right questions, you won’t get the right answers!

Asking the right questions!

Review of last term’s session

One step at a time …….

Principles for effective teaching

• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,

individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned

Range of Activity TypesSee Improving learning in mathematics

Multiple representations Evaluating statements Creating problems Analysing Solutions Classifying Questioning Use of IT Card activities Ideas for open questions Encouragement to develop and extend ideas

Building on the knowledge that learners already have

‘If I know this I also know that ..’

Write a multiplication sum in the centre of an A4 sheet of paper

Pass it to the person on your left. They should write down

Encouraging reasoning

Do the task from Air Miles produced by the More Maths Grads project

Describe ….. using as many mathematical words as you can.

Developing language

Creating connections with the real world

Do the estimation task from Channel Tunnel

Choose one of the Durham Maths Mysteries and work on it with the others on your table.

Using rich collaborative tasks

Play the Biggest take away game and then think about how and why you would ask your learners to play it.

Confronting difficulties

Always, Sometimes, Never True

Exposing misconceptions

Write down all the words that are used in exam questions on a piece of poster paper (spread them out with a space around each)

Pass your poster to the next group

Rewrite the words in language your learners will understand

Developing language

And now ….

What will you do next week?

What will you do for the rest of the term?

Fiona Allan

Adults Don’t Count