# TEACHING AND LEARNING THROUGH PROBLEM SOLVING MIKE OLLERTON

He wondered if practicing in this way — he called it exploratory practice — would prove valuable. I am looking forward to hearing about it. Do you use exploratory practice in the classroom and have some resources to share? This helped them develop an understanding about proportions. However, an experienced mathematics teacher will organise this series of tasks hierarchically and provide scaffolding to illustrate and generalize… mathematical ideas.

Do you use exploratory practice in the classroom and have some resources to share? However, an experienced mathematics teacher will organise this series of tasks hierarchically and provide scaffolding to illustrate and generalize… mathematical ideas. He mentioned that he wants to work on conditional probability next. Recently I have been reading and learning about exploratory practice, thanks to a very interesting talk and a few articles. I am looking forward to hearing about it.

I wonder if this also extends to use of manipulatives? A good question, and one which I have not fully answered yet.

First, teaching through movement. The article includes an example about the teaching of division involving decimal numbers. He has done some work on proportional reasoning in which students raise their two arms to different heights above the desk while looking at a coloured screen.

# Mike Ollerton – In Pursuit of Great Mathematics Teaching

There are 9L of apple juice and every 1L is put in a jar. Yet some Western onlookers say that mathematics education in China is characterised by rote learning or passive transmission.

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. They recount that they were asked to read an article in advance: Recently I have been reading and learning about exploratory practice, problfm to a very interesting talk and a few articles.

She presents problem strings which are sets of questions that lead a learner to see patterns and make generalisations about number. He wondered if practicing in this way — he called it exploratory practice — would prove valuable. Skip to content Recently I have been reading and learning about exploratory practice, thanks to a very interesting talk and a few articles. Trninic linked this kind of exploratory practice to the way people learn dance or martial arts.

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Shanghai Maths and Procedural Variation This reminded me of some reading I have been doing about procedural learhing. 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. There are 9L of apple juice and every 3L is put in a jar.

In those disciplines, students learn through a collection of sequenced movements, making improvements as they go. 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. For example, when talking about transformations of shapes, we can use our hands to show reflection from palms up to palms down.

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This exercise might be considered rote drilling if computing for a correct answer is the focus. The article by Lai and Murray quotes international maths comparisons that show that Chinese learners ollegton a very secure understanding of the mathematics they have learned, and that they can apply it. This type of procedural variation involves varying the problem. There are 9L of apple juice and every 0. He mentioned that he wants to work on conditional probability next.

How many jars are needed? Dragan Trninic was talking about how maths can be learned through bodily movements. There are two other types of procedural variation: Do you use exploratory practice in solvinb classroom and have some resources to share? I am looking forward to hearing about it. This reminded me of some reading I have been doing about procedural variation.

Tweet me mathsfeedback or comment below. This helped them develop an understanding about proportions.