national workshop 1 getting connected: engaging students in learning

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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?. - PowerPoint PPT Presentation

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Progressions preparing year 9 and 10 students for success in NCEA L1, 2 and 3 in statistics/probability

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 1 2 3 4 5 6 7 8Think, pair share get people to note down key concepts for statistics and probability, share their ideas with their neighbour, then gather on whiteboard by curriculum level statistics and probability separately. Note that the mean is not required until level 7, though it may taught earlier as it comes up in an investigation.

Discuss what this means for teaching at years 9 and 10.EgEssential learning for statistics years 7 to 10Statistical literacy and statistical investigationsPPDAC cycleasking a statistical question in students own language: summary, relationship, comparison.The eyes have it: reading information from graphs and tablesSampling: What you can find out about a population by looking at a sample (centre, spread, distribution proportion) and what you cant (eg max, min).Developing understanding of sampling variation.describing a distribution in students own language:Centre (median)Spread (working towards IQR)Unusual features Comparing two distributions in students own language:ShiftOverlapEssential learning for probability year 7 to 10Randomness, variationTrue probabilityModels of probability based on:Theoretical probabilityExperimental probability Expectation Independence Numerical understanding of probability (fractions, %, ratio)

2Know your studentsWhat 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 aclassOn left, write the number of your birth month.On right, write your height (guess if you dont know).At bottom, write the first letter of your favourite colour.At top number of people who live in your house.

This is one way to introduce statistics at year 9/10 (need pink and blue stickies)

Do this activity with the group, talking them through how to do it with the class.Girls get pink stickies, boys get blue.Students would actually do one or two measurements (eg wrist circumference and foot length with string and a ruler)Ask who is the shortest, get them to put their sticky on the board, then the tallestDraw a scale on the board from shortest to tallest.Get everyone else to put their sticky on the board, rearrange if necessary to make a dot plot.

See next slide.

4What do you notice?Write 3 I notice statements.

Write 3 I wonder questions.

You might give them a page with I notice.. and I wonder prompts.

Get someone to come to the board and draw the shape of the graph.

Talk about how you can ask students to draw it more and more simply until they get the idea of what the overall shape of a graph means.These data cards can be the basis of a few lessons, leading students through the PPDAC cycle, using students own questions to rearrange the cards, draw the shape, start to describe centre and shape in students own language and answer the question.

Develop students language for describing what they see: centre, spread, original shape

5Important 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.Dont teach skills until you need it to answer a problem.

Should have some data tiles in a box to demonstrate sampling eg Jims trout.6Probability key ideas Randomness (mathstatsfacilitators website)variation PPDAC cycle including recording your hunch at the beginningExperiencing probability (play games and investigate the probability of winning)Numerical understanding of probabilityProbability language (eg fair, equally likely, possible)If time do an activity on randomness like Fooling the teacher or show the misconceptions powerpoint if students havent seen it.

Eg Do an investigation: Is it harder to roll a 6 than another number when rolling a die?7NZC level 3Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary. Discuss the complex understanding required even at level 3 of the curriculum, where we are starting to develop the concepts of modeling the real world and sampling variation.Teaching should start to develop the concept of a model to represent the unknown true probability, using what we know about the world, experimental observations and theoretical probability.

May give the handout on true probability and probability models.8

Go over the PPDAC cycle for probability, may give handout.

Explain that recording the hunch is important because:It engages the emotional quick-thinking part of the brain which is often not used in maths/statsIt encourages more engagement with the problem -was I right?It encourages students to be aware that they have learned something newIt encourages students to relax about being wrong in a low-stakes situation.9An investigationI wonder, if I roll a hexagonal pencil, what is the probability it stops with the writing on top?Record your hunchRoll the pencilGather resultsI notice. What is the answer to my question? Was my hunch correct?Need a box of hexagonal pencils

Follow the PPDAC cycleStudents should have the opportunity to do investigations both into situations which can be modelled using theoretical probability and ones where there is no theoretical probability.

10Ideas for investigationsWhat 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.

Gather ideas on investigations.Discourage coin tossing just on its own. Coin tossing could be done as part of an activity such as Fooling the teacher, then combined into an investigation of long run probability.Good investigations of experimental probability include bottle top drop (nzmaths), dropping the long drawing pins.There are many good games which work for probability investigations including marble snap (nzmaths), probability bingo

11the 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

Nuts and bolts = statistical calculations and rules

Skills and tools = statistical reasoning, critical thinking, informed judgement the eyes have it12

ProblemI wonderMy hunch is?Conclusion Plan !?

Data Analysis I notice