Principled Teaching for Deep Progress - Improving mathematical learning beyond methods and materials

An NCETM research study module

This module is based on

Watson, A., & De Geest, E. (2005). Principled Teaching for Deep Progress - Improving mathematical learning beyond methods and materials

This is an academic paper about the project that was also reported in ‘Watson, A., De Geest, E., & Prestage, S. (2003). Deep Progress in Mathematics: The Improving Attainment in Mathematics Project. Oxford: University of Oxford, Department of Educational Studies.’

What teaching practices support lower attaining secondary to students to make deep progress in mathematics?

This study module focuses on a piece of action research, conducted by Anne Watson and Els De Geest in the early 2000s that aimed to improve attainment in mathematics among low attaining secondary students. In this module, you will explore: • different views of lower attaining students’ mathematical experiences;• strategies used by the teachers involved in the project to enrich their students’ experiences;

And by engaging with the study and its findings, begin to consider the impact for your own teaching.

Who are the researchers?

Anne Watson is a Professor of Mathematics Education at the Department of Education, University of Oxford.

Els de Geest Els is a Research Fellow in the Department of Education, University of Oxford and also Lecturer in Mathematics Education at the Centre for Mathematics Education at the Open University.

Begin by writing down all the different factors that you think prevent the lowest attaining secondary students’ from achieving well in mathematics.

If you are working with colleagues, compare what you have written with others and discuss the similarities and differences. Did any common themes emerge?

If you were going to work in a sustained way to improve your lower ability students’ experiences such that they would ‘do better’ in mathematics, what would you do? Write them down.

Task 1: What influences lower attaining students’ experiences of learning mathematics

Make a list of the improvements you would hope to see in the classroom and, if you are working with others, discuss your lists.

Compare your list with the list that the teachers involved in the research project agreed upon (after much discussion).

Task 1: What influences lower attaining students’ experiences of learning mathematics

Task 2: How do you currently organise the mathematics provision for lower attaining students?

How does your school organise the mathematics provision for the lowest attaining students?

Do you use any prescribed materials or teaching approaches?

Write a short paragraph in response to these questions and/or share this with other colleagues.

Read Section 1 and Section 2 of the research paper, which describes the context for the research.

Task 3 (optional): How was the research project organised?

if you are interested in reading about how the research project was organised…

Anne Watson and Els De Geest designed a two-year research project to create ‘a team of teachers who wanted to work on students’ mathematical thinking as a way to develop their achievement and interest in mathematics within the current curriculum and assessment regimes’.

Read Section 6 of the research article to find out how they carried out the project and analysed the research data in order to come to some conclusions about the project teachers’ practices.

Task 4 So what is ‘Deep progress' in mathematics?

The research concluded that the researchers and teachers involved in the project shared a goal that they described as ‘deep progress’ with respect to their low attaining students experiences of learning mathematics.

What do you think that ‘deep progress’ might mean?

Note down some thoughts and, if you are working with colleagues, share your responses.

Task 5: What did the research find out?

The students:

•were more willing to work and more engaged mathematically;

•showed significant improvement in the use of thinking skills to tackle unfamiliar tasks, or tasks involving some complex organization and adapted knowledge;

•Were more enthusiastic.

Read section 8.1 of the paper to find out about the shared teaching strategies developed by the teachers that achieved these outcomes.

Which of these strategies can you identify in your own practice?

Task 5: What did the research find out? (contd)

The common principles that underpinned the teachers’ practices were: • all have a right of access to a broad mathematics curriculum;• all students should develop their reasoning and thinking in and through

mathematics;• mathematics can be a source of self-esteem;• students have to become mathematical learners;• adolescents have to develop the ability to exercise rights and

responsibilities of citizenship through mathematics;• teachers have to take account of reality.

Read Section 8.3 to find out about each of these principles in more detail.

Which of these principles underpin your practice? Give some examples.

Task 6

Read the full version of Watson and De Geest’s research article.

As you are reading, engage actively with the text by highlighting or noting:•any salient points, which your own experiences and practice lead you to agree with;•other points with which you disagree or would question;•terminology within the article that is unfamiliar to you.

You will probably want to read the article a couple of times, the first time to gain a sense of Watson and De Geest’s research study, and a second time to engage more fully with its content.

Task 7: So what?

If you were to focus on improving the mathematics provision of the lower attaining students in your school, which of the themes from the research would you start with?

Choose one or two of the common principles described in Section 8.3 and discuss with colleagues how you might work together to embed them into your classroom practices.

Definitions of improvement

• being more active in lessons, for example by participating in discussion, asking and answering questions, volunteering for tasks, offering their own methods

• being more willing to share ideas with others: teachers, peers, whole class

• showing more interest in mathematics, for example by doing more homework, working on extended tasks, commenting positively in evaluation tasks

• being more willing and able to tackle routine, non-routine and unfamiliar tasks

• looking for and expecting to find coherence in tasks; expecting mathematics to make sense

• doing better than expected, or than comparison groups, on certain types of question in national and in-house tests

• showing improvements in behaviour and attendance

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