pd: planning to shift responsibility

2 Teaching and Learning Mathematics through Inquiry

OBJECTIVES OF PROFESSIONAL DEVELOPMENT

Ø To explore opportunities where the teacher may shift more instructional

responsibilities to the students

Ø To reflect upon concerns in giving students more responsibilities over their

learning

Ø To understand the responsibilities and the roles of students and the teacher

within a collaborative classroom community

Ø To create an effective classroom culture based on habits, rules, expectations,

behaviours, actions, interactions, beliefs and values which the teacher and the

students establish, understand and share

Teaching and Learning Mathematics through Inquiry 3

LOOKING AT YOUR CLASSROOM CULTURE

Mike Ollerton and Anne Watson (2001, p. 14) describe a list incorporating three elements for the culture of a classroom. This includes: (1) student actions and behaviour; (2) teacher actions and behaviour; (3) classroom environment.

Ollerton and Watson (2001, p. 15) continue:

For students to take personal responsibility, opportunities and encouragement must exist for them to make decisions about the direction, amount, pace and depth of work they do.

One very important question arises…

How is the teacher to exercise responsibility for ‘covering’ the syllabus?

1. Students need to be made fully aware of what they need to do for examinations and other assessments, if they are expected to make responsible decisions. Syllabus and assessment criteria need to be shared with the students so that they are not fully dependent on the teacher for monitoring progress.

2. The teacher must provide opportunities and access for all students to work on the syllabus topics.

3. Students need to be given the knowledge, structures and tools of how to behave responsibly. More importantly, students should be expected and trusted with being able to utilize those tools for their own benefits.

Reference: Ollerton, M. & Watson, A. (2001). Inclusive Mathematics 11-‐18. London: Continuum.

ü Student actions and behaviour Engage purposefully in their mathematical work; ask and answer questions of each other; ask and answer questions of the teacher; ask for and offer help; take independent responsibility for their work; respect each others’ right to work and participate

ü Teacher actions and behaviour Have a working relationship with students; respond seriously to, as well as initiate, interactions; prepare interesting approaches to mathematics; ensure students have access to the material presented; use a range of resources, teaching styles and strategies

ü The classroom environment Be sometimes calm and at others vibrant, but always, purposeful; be used flexibly with people, desks and chairs rearranged to suit the mathematical activities; contain a variety of easily accessible resources; have displays produced by students and teachers


SHIFTING MORE RESPONSIBILITY TO STUDENTS

In most classrooms, it seems that the teacher carries much of the responsibilities for

student learning. And rightly so, some might claim. However, teachers seem to

undertake full responsibility for what goes on in the classroom, with students

‘passively’ waiting for things to be done – by the teacher, for the students – because

that’s the way it is and that’s the way it should be!

In considering some of the key decisions, actions and expectations traditionally

undertaken by teachers, one might have a closer look at the following six aspects.

Teachers, and especially those of mathematics, are usually expected to:

⇒ Take absolute control on and of the mathematical problems, questions and exercises that students should do;

⇒ Ensure that students do all the work assigned to them, and will get some form of ‘punishment’ if students either refuse, refrain or forget to do it;

⇒ Collect and mark all the work assigned, providing students with corrections to any incorrect methods and/or answers;

⇒ Resolve the difficulties, struggles and challenges that students encounter during a particular lesson;

⇒ Help students study and do well in tests, assessments and examinations;

⇒ Provide students with detailed notes and worked examples about all the topics covered during the scholastic year.

Teachers may feel puzzled about implementing inquiry-‐based learning pedagogies

because they have so many responsibilities to shoulder. Moreover, these

responsibilities do not seem to resonate well with IBL. Indeed, they don’t! Teachers

feel increasing pressures with ‘delivering’ mathematical content to students, with

taking action and finding support when students do not do their work, collecting

and correcting all the work students do in class and at home, resolving the

difficulties that students may encounter in their work, and providing students with

notes about the topics covered. Especially in today’s world, these aspects have

become much more challenging to implement, realize and achieve.

The idea is to shift some of these responsibilities onto the students and achieve some

balance in responsibility between teacher and students. In classrooms where

students carry more responsibilities for their learning, students carry out different

Teaching and Learning Mathematics through Inquiry 5

duties and play more active roles: authority, responsibility and agency are seen to be

constantly shifting between the teacher and the students.

Another very important question arises…

But how can such a balance be attained, structured and negotiated?

The table below identifies potential classroom demands and teacher dilemmas that you may want to address differently in order to occasionally shift more responsibility to your students.

SOME CLASSROOM DILEMMAS AND DEMANDS

TEACHER RESPONSIBILITY

SHIFTING MORE RESPONSIBILITY

What and how much work do you assign?

I select the same type and amount of classwork and homework exercises that all

students should do

Students select the amount and type of problems and questions to do based upon an assessment of what each individual student feels s/he

should focus on

What if students do not do their work?

I make sure that students do all the work assigned, and

they know that they will get a report for not doing it

Students have some degree of freedom with the amount of work they do, but need to justify their decisions

What about correcting students’ work?

I collect and mark all the work assigned, providing students with the necessary

corrections

Students get to mark and correct their own work, and the teacher gets to provide

ideas when students get stuck

What do you do when your students struggle with mathematical ideas and

concepts?

If students do not manage to work things out I usually tend

to tell them how to do

Students appreciate that, for learning to occur, they need to struggle and solve their own mathematical issues

How do you get your students to study and do well in mathematics?

I usually plan to give surprise tests on a regular basis, thus I keep my students on edge

and prepared for their exams

Students are aware when and why assessments are carried out, have time to prepare for them and are expected to be

well-‐prepared

What do you do to facilitate studying for your students?

I ask students to copy notes from the board, otherwise I provide a structured set of notes that include definitions and worked examples for

every topic

Students are encouraged to write and create their own notes; copying whatever they feel is helpful from the board

How do you group students when you need them to work collaboratively?

I always choose and decide with whom they will work

More often than not, students are free to decide with whom

they will work


ESTABLISHING A DIDACTICAL CONTRACT WITH STUDENTS Teachers might argue that secondary school students may not be ready to take

responsibility for their learning – either because they are not used to undertaking

such a proactive role or because they are still not mature enough for it. However, it is

assumed that students may learn to become more responsible if they are

encouraged, allowed and supported to do this.

The culture of the classroom, thus, becomes crucial. It requires teachers, together

with their students, to create, cultivate and inhabit a classroom that encourages

autonomy, creativity, communication, trust and respect for one another. When

students are trusted as active and autonomous learners, they are more likely to

make and take decisions responsibly, creating more meaningful mathematical

learning for themselves. Indeed, Ollerton (2006, p. 51) claims that ‘if I am to educate

my students to take responsibility, then I must also learn when to take a step back,

when to loosen my grip’, and to trust that eventually students will be in a better

position to take more control of and over their learning.

Active learning pedagogies, like inquiry-‐based learning, call for a modified didactical

contract – one that enhances students’ acquisition of a much greater sense of

ownership, agency and responsibility over their learning. For a start, if students are

to develop into active constructors of mathematical meanings and knowledge, the

responsibility for teaching and learning has to pass from the sole domain of the

teacher to become one that is shared within the classroom community.

This relates to the realization that when students are trusted with ‘deciding how

much they need to do to understand the mathematics involved, an important shift

takes place: away from doing something because they have been told to do so,

and towards doing something because they recognize the value of making

progress’ (Ollerton, 2006, p. 198). When students are handed some degree of

control over what and how they learn mathematics (Ollerton, 2006), they get a sense

of ownership of their learning which helps them, in turn, to progressively develop a

positive sense of self and the subject (O’Neill & Barton, 2005).

References:

Ollerton, M. (2006). Getting the Buggers to Add Up (2nd Edition). London: Continuum.

O'Neill, T., & Barton, A.C. (2005) Uncovering student ownership in science learning: The making of a student created mini-‐documentary. School Science and Mathematics, 105(6), 292-‐301.

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