MATHEMATICSKLA Years 1 to 10

Thinking, reasoning and working mathematically

MATHEMATICSYears 1 to 10

Purpose of presentation

to define thinking, reasoning and working mathematically (t, r, w m)

to describe how t, r, w m enhances mathematical learning

to promote and support t, r, w m through investigations.

Thinking, reasoning and working mathematically

involves making decisions about what mathematical knowledge, procedures and strategies are to be used in particular situations

incorporates communication skills and ways of thinking that are mathematical in nature

is promoted through engagement in challenging mathematical investigations.

Thinking, reasoning and working mathematically

also

promotes higher-order thinking develops deep knowledge and

understanding develops students’ confidence in their

ability ‘to do’ mathematics connects learning to the students’ real

world.

What is thinking mathematically?

making meaningful connections with prior mathematical experiences and knowledge including strategies and procedures

creating logical pathways to solutions

identifying what mathematics needs to be known and what needs to be done to proceed with an investigation

explaining mathematical ideas and workings.

What is reasoning mathematically?

deciding on the mathematical knowledge, procedures and strategies to use in a situation

developing logical pathways to solutions reflecting on decisions and making

appropriate changes to thinking making sense of the mathematics

encountered engaging in mathematical conversations.

What is working mathematically?

sharing mathematical ideas challenging and defending

mathematical thinking and reasoning solving problems using technologies appropriately to

support mathematical working representing mathematical problems

and solutions in different ways.

How can t, r, w m be promoted?

By providing learning opportunities that are: relevant to the needs, interests and abilities

of the students strongly connected to real-world situations based on an investigative approach — a

problem to be solved, a question to be answered, a significant task to be completed or an issue to be explored.

Planning for investigations

Identify how and when reporting of student progress will occur

Identify how and when judgments will be made about students’ demonstrations of

learning

Identify how evidence of demonstrations of learning will be

gathered and recorded

Select and sequence learning

activities and teaching strategies

Identify or design assessment

opportunities

Select learning outcomes on which

to focus

Select strategies to promote consistency of teacher

judgments

Choose the context(s) for learning

Make explicit what students need to know and do to

demonstrate their learning

How do investigations promote t, r, w m?

Sample investigations present the learning sequence in three phases: identifying and describing understanding and applying communicating and justifying.

Each phase promotes the development of thinking, reasoning and working mathematically.

Identifying and describing

Students: identify the mathematics in the investigation describe the investigation in their own words describe the mathematics that may assist

them in finding solutions identify and negotiate possible pathways

through the investigation identify what they need to learn to progress.

Phase 1

Sample questions to encourage t, r, w m in

phase 1

What mathematics can you see in this situation?

Have you encountered a similar problem before?

What mathematics do you already know that will help you?

What procedures or strategies could you use to find a solution?

What do you need to know more about to do this investigation?

Understanding and applying

Students: acquire new understandings and knowledge select strategies and procedures to apply to the

investigation represent problems using objects, pictures,

symbols or mathematical models apply mathematical knowledge to proceed through

the investigation generate possible solutions validate findings by observation, trial or

experimentation.

Phase 2

Sample questions to encourage t, r, w m

in phase 2

What types of experiments could you do to test your ideas?

Can you see a pattern in the mathematics? How can you use the pattern to help you?

What other procedures and strategies could you use?

What else do you need to know to resolve the investigation?

Is your solution close to your prediction? If not, why is it different?

Communicating and justifying

Students: communicate their solutions or

conclusions reflect on, and generalise about, their

learning justify or debate conclusions referring to

procedures and strategies used listen to the perceptions of others and

challenge or support those ideas pose similar investigations or problems.

Phase 3

Sample questions to encourage t, r, w m in

phase 3

What is the same and what is different about other students’ ideas?

Will the knowledge, procedures and strategies that you used work in similar situations?

What mathematics do you know now that you didn’t know before?

Teachers can support t, r, w m by:

guiding mathematical discussions providing opportunities for students to develop

the knowledge, procedures and strategies required for mathematical investigations

presenting challenges that require students to pose problems

providing opportunities to reflect on new learning.

The syllabus promotes

t, r, w m by:

describing the valued attributes of a lifelong learner in terms of thinking, reasoning and working mathematically

encouraging students to work through problems to be solved, questions to be answered, significant tasks to be completed or issues to be explored

advocating the use of a learner-centred, investigative approach in a range of contexts

emphasising the connections between topics and strands that are often required in dealing with mathematics in ‘real-life’ situations.

Materials to support thinking, reasoning and working mathematically

How to think, reason and work mathematically (poster)

About thinking, reasoning and working mathematically (information paper)

Prompting students to think, reason and work mathematically (paper)

Thinking, reasoning and working mathematically in the classroom (paper)

Papers described in the annotated bibliography in the ‘Additional information’ section of the support materials

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Visit the QSA website at www.qsa.qld.edu.au

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