Engaging Students with Mathematics

Te manu e kai i te miro, nōna te ngahere.Te manu e kai i te mātauranga, nōna te ao.The bird that partakes of the miro berry reigns in the forest.The bird that partakes of the power of knowledge has access to the world.

Overview•Shift in Thinking

•Warm Up - Michelle and Rachel

•Celebrating Success - Student Achievement

•Vedic Maths

•Engaging Students in Mathematics

•Learning Competencies in Mathematics - assessment/learning stories

•Organisation - Mathematics at Reremoana School 2011

Why Are We Teaching MathsWe now have a more mathematical world.

It is a more quantitative world than we have ever had...

We need to start focussing on not only computation but problem solving....

What it looks like in the real world

Dumbed down problems

Lots of calculating

NOT THE REAL WORLD

Celebrating SuccessStudent Achievement in Numeracy:

A shift in thinking: Students are no longer underachieving in Numeracy.

How are we providing opportunity to extend our children?

What changes to our programmes are we going to need to make to see increases in

Student Achievement in 2011?

Are we.......Confident that mathematics learning at Reremoana School is promoted through

problem solving and mathematical thinking?

Do you understand the opportunities that mathematical problems offer?

Are you selecting problems to promote connections between mathematical

concepts?

What does our Student Achievement Data Show...

What do we need to do in our

programmes to increase student achievement in mathematics...

Maths Make-Over•Dan Meyer: Math Class Needs a Makeover

•Looking at the maths stereotype

•Maths Education - computation/reasoning (problem solving)

•Importance in maths programme - lifelong learning. Math makes sense of the world.

•Amazing time to be a maths teacher - we have the tools to create this amazing curriculum - cameras, internet

Five Symptoms Lack of Problem Solving...

1. Lack of Initiative

2. Lack of perseverance

3. Lack of retention

4. Aversion to word problems

5. Eagerness for formula

No problem worth solving is simple

Patient Problem Solving•Text books - not set up to develop patient

problem solving. What problem have you ever had where you know all the information.....

•We don’t want it to just be about understanding the text book and being able to slot the numbers into the formula.

•Filling up the container.......visual - question, structure, steps - taking a compelling question, and a compelling answer and get those conversations going. Maths serving the conversation.

Patient Problem-Solving

The formulation of the a problem is often more essential than it’s solution, which may be merely a matter of mathematical or experimental skill.

-Albert Einstein

Are we involving the students in the problem....

Patient Problem-Solving•Use the text book and restructure the

question in the maintenance, question time, display......

•Eliminate sub-steps, students have to formulate the steps.....

•21st Century let’s talk about it in the real world? Maybe get the kids to use their ICT skills here.....

•Ideas to consider something around the playground/measuring something

•Conversations important

How do you know when this is successfully operating in the class...•Conversation...

•No longer intimidated by math

•No long averse to word problems because we have redefined what a word problem is.....

•Student achievement improvement

10 minutes per day1. Use multimedia - bring the real world in...

2. Encourage student intuition - level playing field

3. Ask the shortest question you can

4. Let students give it a go - talk

5. Be less helpful

Effectively Engaging Students with MathsProgramme Design: Planning

Strand Development and a Focus on Problem Solving

Teachers use problem solving in a variety of contexts to help students to explore mathematical and statistical ideas. The development of Strand in 2010 saw us integrating a more hands on/inquiry based approach to mathematics.....

How can we take this further.

The Numeracy Team is asking you to reflect on your maths programme to determine how you are going now/what can do in 2011:

Using the Reremoana School Inquiry model as a vehicle for investigations• apply skills and knowledge in solving problems and modelling situations• communicate to offer and justify ideas• investigate problems that have multiple lines of inquiry and solutions• use tools and representations to develop mathematical and statistical ideas.

After knowledge and during your maintenance time, planned time to complete a whole class problem. In your tumble, wall display.......

Delivering a single problem to teach mathematical understandings at many different year levels.

From problems A, B, and C below, choose the one that best suits the level you are teaching at or focusing on.

1 Consider the following questions:2 What mathematical learning does the problem offer?3 How might students respond to the problem? Is there a progression in students’

likely responses?4 What expectations from the standards does this problem relate to?5 How might we organise the responses of students to provide evidence of their

achievement?Problem AToby has 6 marbles. Rewa has 10 marbles. How many more marbles does Rewa have than Toby? How many marbles does Rewa need to give Toby so that they have the same number?

Problem B5 cows have 12 bales of hay to share equally. 3 horses have 8 bales of hay to share equally. Which animals get the biggest share each: the cows or the horses?

Problem C Starting from your home, how far could you travel over a period of 4 hours? How much would the journey cost?

Problem Solving

1 It must be accessible to everyone at the start2 It needs to allow further challenges and be

extendable3 It should invite learners to make decisions4 It should involve learners in speculating, hypothesis

making and testing, proving and explaining, reflecting, interpreting

5 It should not restrict learners from searching in other directions

6 It should promote discussion and communication7 It should encourage originality/invention8 It should encourage 'what if' and 'what if not'

questions9 It should have an element of surprise10 It should be enjoyable.

What Makes a Rich Mathematical Task?

. Are tasks interesting and engaging to students? How do we know?

1 . How do teachers determine which contexts will be familiar or interesting to students? Money, food, celebrities, landmarks - making connections.

2 .Do tasks provide appropriate challenge? How do we know?

Key QuestionTo what extent are you considering your students’ prior knowledge and experience when selecting tasks?

Share an example of a problem that you gave to your students and that you considered interesting and relevant to them. We are going to share and consider the following questions:

1 Why would your students have found this problem interesting?

2 How did the problem link to students’ prior knowledge and experiences?

3 What are the learning opportunities offered by the problem?

4 What curriculum objectives and expectations from the standards could the problem help students to meet?

Key QuestionTo what extent are you considering your students’ prior knowledge and experience when selecting tasks?

In a discussion with two or more classroom teachers, chart the tasks or activities they use for each class in a specified week. Identify the learning outcomes, the standard(s) to which the tasks relate, and the ways in which mathematical understanding is developed through each task.1 How 'open' are the learning outcomes in terms of the

ways in which they might be achieved? To carry out the tasks, what kind of thinking would students need to engage in?

2 How will we know when or if the students have reached each outcome? Can we use this as evidence towards making an overall teacher judgement?

3 How do we use the tasks and activities to help students to justify and explain their thinking?

1 What tools (e.g., diagrams, equipment) are most commonly used as learning supports?

2 How do you select and use these tools to support the diverse learners your class?

In what ways, and how effectively, are you supporting mathematics learning for diverse

learners?

1 Are some tools more useful than others for different groups of students? Why might this be?

2 What pre-conceived ideas might influence the use of some tools? For example, do we favour pencil and paper or mental calculation over the use of calculators? Is this always justifiable?

3 To what extent are students involved in choosing tools to use?

4 Which tools (or ways of using tools) do we want to learn more about? How can we do this?

5 What pedagogical content knowledge do we need to make better use of tools to support understanding?

Consider the following questions....