Year 11 Statistical InvestigationsAMA Statistics Day 2013

jsaunders@cognition.co.nz

Pedagogy for improving learning

Year 11 Success for all in NCEA Level 1 Statistical InvestigationsSuccess for all in statistics may require re-thinking of teacher actions (aka pedagogy). Students need to think flexibly in context and apply both statistical and context knowledge. This workshop will explore teacher pedagogical knowledge for Year 11 students and how it can be adapted to students in other year levels.

Effective Pedagogy in Mathematics Glenda Anthony and Margaret Walshaw

Around the room, I have placed the pedagogies recommended by the Best Evidence Synthesis (NZ Ministry of Education).

Please choose one pedagogy and write down the evidence you would expect to see or to hear if that pedagogy was being enacted in the classroom.

Ten Principles1. An ethic of care2. Arranging for learning3. Building on students’ thinking4. Worthwhile mathematical tasks5. Making connections6. Assessment for learning7. Mathematical communication8. Mathematical language9. Tools and representations10. Teacher knowledge

Mrs Saunders, you are teaching us not telling usWhat is good? The attention you give us is great. This is a better

environment for me to be in rather than a class that’s better at maths than me.

Numbering everyone so that we get a chance to work on the questions.

Making sure everyone is using their initiative. Teaching methods are engaging and help me

understand more. You care about helping us. Freedom in doing work. Being able to help each other.

Pedagogies to improve learning

Students need to trust their teacher to know them as individuals

As the teacher, I am the authority in the room; from day 1 I begin the journey to convincing them they can learn

Teacher as authority

The teacher is the expert in the room: I take the students with me, by articulating a

pedagogy and asking them why I use it I claim my authority in all I say and doI am in charge, so I arrange the seating: in alphabetical order seldom changed, and only by me cycle rows forward from time to time

Pause

I wait at least 10 seconds after posing a question before accepting an answer

Why do you think I do this? Discuss briefly with the person next to you Tell me what the other person said

Re-frame the language

“Miss, is it . . .?” is banned And give students new language to use (and

reiterate it):I think it could be . . .It might be . . .I wonder if it could be . . .

We’re all allowed to make mistakes

Ask deeper questions

And give the students opportunities to think before answering

Give out scrap paper to use for working Encourage each student to think (and write

something down) before sharing in a pair

My favourite questions:

What can you see? What is the same and what is different? How do you know that? Blog with 26 questions you can ask instead

http://mathforum.org/blogs/max/26-questions-you-can-ask-instead/

Ask deeper questions

Try to minimise “What is the (one-step) answer” Aim up the SOLO taxonomy Ask multi-step questions Ask for reasons, meaning, applications

Every student has to be ready to answerDylan Wiliam’s method:http://www.dylanwiliam.org/Dylan_Wiliams_website/Welcome.html

Write each student’s name on an ice block stick Put sticks in a container, randomly pull out a

stick to select a student

Random numbers

Each student has a number on the roll and they write it down inside exercise book cover

Alphabetical order means . . . Use this when I want to choose a student to

answer – after pausing I teach one (volunteer) student how to use their

calculator to generate a random number from the class

That student always generates random numbers when I want them

Do now!

Every lesson starts Do Now Activity hand-written on board

Put up graph, ask for description, possible sources of variation in context, reason for shape in context…

Put up 2 graphs, ask for call and reason for making it, in context

Write a poor paragraph, ask for it to be improved

Homework These students need to learn that doing

homework matters I set a little almost every day I hold students accountable for doing HW Students mark their own HW Open books at start of lesson to show me HW

while they complete the Do Now Students highlight questions they need help

with I record in my mark book whether reasonable

attempt or not

Feedback Not just ticks and crosses or N, A, M, E Always a sentence about what understanding

student has shown, and what they need to do to progress

Talk about A and M: What level have we been working on?

Dan Meyer suggests

We need to be encouraging patient problem solving and being less helpful. Search for his TED talk: Math Class Needs a Makeover

http://blog.mrmeyer.com/ How can you resist the urge to be helpful?

What about NZC Level 6 Statistics?

Start from the beginning of L5, telling a story about the wider universe with supporting evidence.

Big Ideas

Data from a sample can be used to answer a question about a population

Data may need to be cleaned – need to know survey questions, who collected from, how collected…

I Census at School!

Big Ideas Continued

Inferences should be justified and in context There are rules we can apply to comparing

populations – aka making a call Reasoning based on shift, overlap, sampling

variability and sample size

Data Cards Rule

Students physically work with data cards for concept learning

Arrange cards on desks to find median and quartiles, then draw dot plots on provided axes, and draw box plots from the dot plots

Put graphs on wall and use them to develop rules for making calls

Getting to Merit and Excellence

Context requires students to Name the variables Give values and units

Build up a model for each part of PPDAQ cycle in turn by asking students to just have a go at, say, writing descriptions of graphs

Observe as they write, choose two or three who have good points and work with class to shape them

Practice the whole PPDAC cycle

As soon as possible, students should be working on the whole cycle

Plus? Minus? Interesting?

Feedback – one facet of an ethic of care

Students should understand where they are aiming

Personal feedback helps them improve How do you know that? What is the evidence for your statement?

Where is the evidence?

Some practice tasks

Practice tasks Generic questions