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The learning environment : Post 16 Level 2 : Mathematics-specific Pedagogy


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Post 16 Level 2
The learning environment
Question 1 of 4

1. How confident are you that you can create a learning community that allows learners to think, reason, communicate, reflect upon, and critique the mathematics they encounter?

a. Activity One


Activity

Two teachers describe the make-up of their respective GCSE mathematics resit classes.

Read their descriptions and think about the questions below.

A GCSE maths teacher working at a general FE college

This was the first time I have taught GCSE maths and at the start of the year I had 26 students on the register - the youngest was 16 and the oldest 38. Most of the students are 17 or 18 years old and most of them took functional skills at level 1 or 2 last year (with varying success). Of course the vast majority of the students are also doing other courses at the college – many of the older ones are also doing English GCSE, the younger ones are either doing A levels or a vocational course like business studies.

Some of the older students tell me they have not had a good experience of maths in the past and many of the younger ones tell me they don’t like maths! I’d estimate that about half of them don’t have English as their first language, but only 3 have real difficulties in reading and writing English. Many of my students had sat GCSE maths at school and got a D or E grade (a few had an F and one had a G). Some of them (mainly the older students) have never sat a GCSE maths exam before and one student tells me he has the equivalent of an A level in Maths from Nigeria but has to take GCSE maths because no-one will accept his qualification.

I also have one student who is the mother of two young children. She is often absent from the class because she is having problems with childcare… I only have 90 hours to cover everything so any absence at all can cause real difficulties.

Initially I thought that I wouldn’t be able to cope with a group of students from such a wide range of backgrounds but through talking with my more experienced colleagues I was able to try out strategies that had worked for them in the same situation and even develop some of my own.

A teacher in a Sixth Form College who mainly teaches A-level Maths but also teaches one GCSE resit class each year.

There are over thirty students in my class. There is meant to be an average of 25 students in each class but it depends on which other subjects they are doing. Some of the students in my class are high achieving students who had a series of supply teachers at their school – you can imagine what they feel about Maths! Others say that since they left Primary school, Maths has been ‘boring’.

Just before Christmas, a very bright student arrived from India too late to start an A-level course, so he was put into my class. He wants to achieve an A* and is very good at algebra and trigonometry but has never done any statistics, probability or money management! Then there’s a girl who wants to become a Primary teacher, hates maths and has already sat GCSE three times.

This year I also have a group of students who got Fs, Gs and Us. Previously students with those grades used to do a Numeracy course before doing GCSE but the teacher who ran that course left and we couldn’t get a replacement teacher.

How often do I see them? One double period a week and a single period. That’s all. And homework? Apart from Arpan (the boy from India), it’s like getting blood out of a stone!

This is the only GCSE maths class I teach – the rest of my work is A level. Over the past few years I have been making my A level classes more active through the use of discussion and group work. I am working on using these approaches with my GCSE class too but I have to think more carefully about how I arrange the students to make the best of their differing experiences and attainment.

  • Choose one of these teachers and describe the issues he/she might face in trying to create a supportive learning community that would allow the learners to think, reason, communicate, reflect upon, and critique the mathematics they encounter.

Prompt 1.

A mathematics learning community consists of a group of learners who engage in reflective dialogue and who are open about sharing the thinking behind their mathematical ideas. The community has a collective focus on student learning, collaboration, and shared norms and values.

  • If this was your group how might you deal with these issues?

Prompt 2.

For example, think about how you could arrange the learners in the classroom to take advantage of their wide range of experiences.

Commentary

Commentary

A mathematics learning community consists of a group of learners who engage in reflective dialogue and who are open about sharing the thinking behind their mathematical ideas. The community has a collective focus on student learning, collaboration, and shared norms and values.

In the scenarios described in the task, some of the issues faced by the teacher in creating this type of community could include all/some of the following:

  • A wide range of previous mathematical achievement
  • A big age difference between some learners
  • Very different past experiences in learning mathematics
  • Different emotional experiences when studying mathematics
  • Students’ different reasons for studying GCSE maths
  • Different expectations of what it means to study mathematics
  • Some students’ need to achieve a C or more; so that they can follow their chosen pathway.
  • Learners who learn best in different ways

The diverse nature and needs of the learners in this group coupled with the restricted teacher contact time allowed for the course, means that the teacher’s attitude and expectations at the outset will be crucial to helping develop a mathematics learning community.

One thing which unites all the learners in these classes is the goal of attaining a grade C or better in their GCSE. The teacher should make clear at the outset their own high, but realistic expectations of student achievement and create a strong mathematical focus right from the start of each lesson so that the learners become used to walking through the door and starting immediately on some mathematical task, perhaps by having a problem or past paper question on the tables ready for them when they come in.

Teachers can help create a harmonious environment by respecting and valuing the mathematics and cultures that the learners bring with them to the classroom. Some of the students’ previous experience of studying mathematics may mean they are not confident about participating in class discussion. The teacher’s role here is to help the class to “expect” and “accept” i.e. expect learners to answer questions and accept all responses as worthy of consideration. By showing interest in the ideas they construct and express (no matter how unexpected!) the teacher can encourage all learners to make thoughtful judgements about the soundness of the mathematics behind the expressions. For diffident learners, this may be easier to do (at least at the start) in small groups. Learners can become more open about sharing thinking behind their mathematical ideas in collaborative small group work and the teacher could ask the whole class to generate an agreed set of ground rules for discussion during this sort of work.

The teacher could use the life experience of the older students to create a context for learning various mathematical topics. For example they may already have taken out or considered taking out a loan, may have had to manage their money effectively, used mathematics in a workplace or done some DIY. The teacher could also use examples of mathematics from the vocational areas in which some of her learners are studying. Alternatively, they could consider incorporating the Maths in Work videos or one of the It’s In the News! PowerPoints from Issue 88 or earlier of the Secondary Magazine into their course.

Because the teachers have limited class contact time, one way in which they could foster a sense of community is by encouraging the learners to form study groups outside the classroom possibly through providing homework tasks that require a collaborative approach.

Attending to and respecting the different needs of the group will allow the learners to develop a positive attitude to mathematics, which, in turn, could lead to a greater confidence in their capacity to learn mathematics.

Although this example is looking at the make-up of a GCSE class, you could create a similar scenario for any group you work with - perhaps you are working with learners in a vocational setting. You may like to create a scenario reflecting your group and discuss it with your colleagues in a professional development session.

The strategies outlined above are looked at in more depth in other questions in this SET. For example strategies for organising and managing groups are discussed in the third activity of this section and more information can be found in the Next Step. You may want to revisit this question at the end of the SET after you have had a chance to reflect on the rest of the questions.

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