# TEACHING AND LEARNING THROUGH PROBLEM SOLVING MIKE OLLERTON

He mentioned that he wants to work on conditional probability next. There are two other types of procedural variation: In this series of tasks, the total amount of apple juice was kept constant while the amount in a jar was varied from a whole litre to less than a litre. However, an experienced mathematics teacher will organise this series of tasks hierarchically and provide scaffolding to illustrate and generalize… mathematical ideas. Trninic linked this kind of exploratory practice to the way people learn dance or martial arts. How many jars are needed? For example, when talking about transformations of shapes, we can use our hands to show reflection from palms up to palms down.

In those disciplines, students learn through a collection of sequenced movements, making improvements as they go. This helped them develop an understanding about proportions. He mentioned that he wants to work on conditional probability next. In this series of tasks, the total amount of apple juice was kept constant while the amount in a jar was varied from a whole litre to less than a litre. I wonder if this also extends to use of manipulatives? I have been encouraged by a recent Jo Boaler article to use movement and gestures more. In the UK, there has recently been a two-year-long teacher exchange with Shanghai.

In those disciplines, students learn through a collection of sequenced movements, making improvements as they go.

Shanghai Maths and Procedural Variation This reminded me of some reading I have been doing about procedural variation. There are 9L of apple juice and every 3L is put in a jar. I wonder if this also extends to use of manipulatives? He has done some work on proportional reasoning in which students raise their two arms to teadhing heights above the desk while looking o,lerton a coloured screen. He mentioned that he wants to work on conditional probability next.

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In this series of tasks, the total amount of apple juice was kept constant while the amount in a jar was varied from a whole litre to less than a litre.

The article includes an example about taeching teaching of division involving decimal numbers.

# Mike Ollerton – In Pursuit of Great Mathematics Teaching

A good question, and one which I have not fully answered yet. I am looking forward to hearing about it. Do you use exploratory practice in the classroom and have some resources to share?

First, teaching through movement. Trninic linked this kind of exploratory practice to the way people learn dance or martial arts. There are 9L of apple juice and every 0. For example, when talking about transformations of shapes, we can use our hands to show reflection from palms up to palms down.

There are two other types of kike variation: This helped them develop an understanding about proportions. Yet some Western onlookers say that mathematics education in China is characterised by rote learning or passive transmission.

The article by Lai and Murray quotes international maths comparisons that show that Chinese learners have a very secure understanding of the mathematics they have learned, and that they can apply it. I have been encouraged by a recent Jo Boaler article to use movement and gestures more. Skip to content Recently I have been reading and learning about exploratory practice, thanks to a very interesting talk and a few articles.

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## Tag: Mike Ollerton

She presents problem strings which are sets of questions that lead a learner to see patterns and make generalisations about number.

This exercise might be considered rote drilling if computing for a correct answer is the focus. Dragan Trninic was talking about how maths can be learned through bodily movements. However, an experienced mathematics teacher will organise this series of tasks hierarchically and provide scaffolding to illustrate and generalize… mathematical ideas. This reminded me of some reading I have been doing about procedural variation. He wondered if practicing in this way — he called it exploratory practice — would prove valuable.

Recently I have been teachinh and learning about exploratory practice, thanks to a very interesting talk and mi,e few articles.

This type of procedural variation involves varying the problem. How many jars are needed? Tweet me mathsfeedback or comment below.

Exploratory practice, on the other hand, is set up by the teacher in a way that students are asked to learn as they go by trying to generalise. There are 9L of apple juice and every 1L is put in a jar. In the UK, there has recently been a two-year-long teacher exchange with Shanghai. They recount that they were asked to read an article in advance: