Progressions – preparing year 9 and 10 students for success in NCEA L1, 2 and 3 in statistics/probability National Workshop 1 Getting connected: engaging students in learning

What are the key concepts needed to be ready to succeed in statistics and probability at NCEA level 1? At which curriculum level do you start to teach each idea? NZC level

Know your students What curriculum level are they at? What level of literacy do they have? Your planning needs to start where the students are at and have a strategy for progression. Many statistical and probability investigations are rich tasks appropriate for students at a range of curriculum levels.

Getting started: make data cards as aclass On left, write the number of your birth month. On right, write your height (guess if you don’t know). At bottom, write the first letter of your favourite colour. At top number of people who live in your house.

What do you notice? Write 3 “I notice…” statements. Write 3 “I notice…” statements. Write 3 “I wonder…” questions. Write 3 “I wonder…” questions.

Important learning activities for year 9/10 statistics Developing the concept of a variable. Can do it with a question like “how can you describe a car?” Census at school units of work for curriculum level the students are at. PPDAC cycle including their expectation at the beginning of each investigation. What do I think will happen? Developing concepts of inference. Physically sampling from a box. Don’t teach skills until you need it to answer a problem.

Probability key ideas Randomness (mathstatsfacilitators website) variation PPDAC cycle including recording your hunch at the beginning Experiencing probability (play games and investigate the probability of winning) Numerical understanding of probability Numerical understanding of probability Probability language (eg fair, equally likely, possible) Probability language (eg fair, equally likely, possible)

NZC level 3 “Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.”

An investigation I wonder, if I roll a hexagonal pencil, what is the probability it stops with the writing on top? I wonder, if I roll a hexagonal pencil, what is the probability it stops with the writing on top? Record your hunch Record your hunch Roll the pencil Roll the pencil Gather results Gather results “I notice…. “ “I notice…. “ What is the answer to my question? Was my hunch correct? What is the answer to my question? Was my hunch correct?

Ideas for investigations What has worked for you? What has worked for you? Note that probability trees with fractions on the branches are now at level 7 of the curriculum. At level 2/3/4/5 of NZC we are dealing with equally likely outcomes or observations of situations with unknown probability. There may be some students in year 9/10 who are working at level 7 NZC.

“…the dogged pursuit of the nuts and bolts of statistical methods and data analysis takes valuable time and energy away from important skills and tools that students actually need for evaluating the many statistical arguments they encounter in their adult lives.” Daniel Schafer