National Workshop Mathematics and Statistics

National WorkshopMathematics and Statistics BACKMAPPING A LEARNING PROGRAMME Jim Hogan, Sandra Cathcart and Robyn HeAdifEn Team SoluTions Hamilton May 13, Rotorua May 14 and EIT Taradale May 15

Entree • This session is about designinga way to assure success for students at NCEA L2. • Hogan’s Plan is to have each standard at L2 backmapped to Year 7/8. • Firstly an example, then you will do one standard each in groups. Ham, Rot and EIT all collated and sent back to you.

Focus Ideas • Backward design means starting with the end in mind and planning for it, step by step. • Deep Knowledge focuses on the concepts and their relationships • Deep Understanding is about demonstrating profound meaning

Outcome I will collect all your work and put it in a spreadsheet for you to use. Each row will describe a YEAR of building blocks for learning, to meet goal. Resources, key ideas, skills.

Key Question • To achieve NCEA L2 what is it a student has to learn in previous years? • I want a description of what must be learned in Year 7/8, Year 9, Year 10 so that a particular topic can be accessed by students in Year 11 and 12. • NCEA L2 is the 85% PS Goal

The Learning Programme We should be able to inform/check a learning programme for a year level as a result. • Other factors like building problem solving ability, literacy and need to be considered

What do we need? • NZC – these are the AO’s. • National Standard Descriptions, Exemplars • Internet • – to see supporting SSTLG • – to access C@S • – to access nzmaths.co.nz • – to access math dictionary • – your knowledge • – two heads are better than one!

Learn by Doing • I have selected AS 91264 as a starter because it is probably familiar to us and it is a popular choice.

AS91264…methods • Using the statistical enquiry cycle to make an inference involves: • posing an appropriate investigative comparison question from a given set of population data • selecting random samples • selecting and using appropriate displays and measures • discussing sample distributions • discussing sampling variability, including the variability of estimates • making an inference • communicating findings in a conclusion.

1st Task - 3 minits • posing an appropriate investigative comparison question from a given set of population data • Just focusing on thismethod fill in • => for Year 11 • => for Year 10 • => for Year 9 • => for Year 7/8

My Attempt… • => for Year 11 • That AS 91035 has been attempted. Students can write conclusions to investigative questions. • => for Year 10 • That comparison questions have been practiced as part of PPDAC. The C@S analyser has been used to answer a question.

and… • => for Year 9 • That comparison questions have been practiced as part of PPDAC and the data cards have been used. See Stats nzmaths • => for Year 7/8. Students have asked investigative questions from familiar data sets. This means they have taken part in the C@S survey. They own the data.

2nd Task- 3 minits • selecting random samples • Just focusing on this method fill in • => for Year 11 • => for Year 10 • => for Year 9 • => for Year 7/8

My Attempt … • => for Year 11 • Students use random ideas to select a sample. The idea of sample to population is understood for making an inference. Non random ideas can be identified. • Chance language including bias, likely, outcome are used.

…and • => for Year 10 • Students use random sampler on C@S to find a sample. Biased samples, cleaning data, non-representative samples are identified. • => for Year 9 • Use a spreadsheet to generate random numbers • => for Year 7/8 • Sampling by hand, using dice and knowing what random means. Using random in language correctly.

3rd Task – 3 minit • selecting and using appropriate displays and measures • discussing sample distributions • Just focusing on this method fill in • => for Year 11 • => for Year 10 • => for Year 9 • => for Year 7/8

My Attempt … • selecting and using appropriate displays and measures • discussing sample distributions • => for Year 11 • Uses dot plots and box and whisker to show the information comparatively . Finds measures of middle and spread, IQR, shift and OVS. Clear diagrams. Labels. Writes correct statements about shape of distribution.

…and • => for Year 10 • Becomes fluent in interpreting box and whisker, making and describing dot plots. Use this information to help describe distribution of the data. • => for Year 9 and Year 7/8 • Draws dot plots and describes the data. Finds middle measures. Notices spread. Writes and speaks about the shape. Notices unusual data points.

4th Task – 3 minit • discussing sampling variability, including the variability of estimates

My Attempt … • discussing sampling variability, including the variability of estimates • => for Year 11 • This means noticing different samples usually give a different result but most samples will show the same trend. Knowing a sample of around 20 to 30 is not a bad choice for size.

…and… • => for Year 10 • Noticing different samples will look different as well. Explores visual spread and sample size relationship. Notices middle 50% is a good indicator of being typical. Can explain why some data supports a different conclusion.

…and • => for Year 9 and => for Year 7/8 • Noticing different samples look different and can explain why. States that this is usual and can be expected. Is not phased by having a different answer to the same question.

5th and Final Task – 3 minit • making an inference • communicating findings in a conclusion. • Just focusing on this method fill in • => for Year 11 • => for Year 10 • => for Year 9 • => for Year 7/8

My attempt cf • making an inference • communicating findings in a conclusion. • => for Year 11 • Uses middle 50%, OVS, Shift and other supporting evidence in making an inference. Can write clear correct statements using statistical language. Does not contradict findings with waffle or wobble.

…and • => for Year 10 • Uses ½ to ¾ rule for establishing validity of inference. Uses shape of distribution when appropriate. Makes and communicates clearly an inference. • => for Year 9 and Year 7/8 • Answers the question posed with supporting evidence based on shape and position.

Now… • Collect each Year level • Decide if “inference” is part of the learning programme for that year. • Compare with exisiting learning plans • Allocate time, resources, order of learning, pre and post test tasks. • Organise resources!

Organising • So I decide that inference is indeed going to be taught in Year 10. I will call the unit “Making an Inference” and allocate 3 weeks of time in Term 1. • Broad Content • That comparison questions have been practiced as part of PPDAC. The C@S analyser has been used to answer a question.

Content cont… • Students use random sampler on C@S to find a sample. Cleaning data. • Becomes fluent in interpreting box and whisker, making and describing dot plots. • Noticing different samples will look different as well. Explores visual spread and sample size relationship. • Can explain why some data supports a different conclusion.

Content more!!! • Uses ½ to ¾ rule for establishing validity of inference. Uses shape of distribution when appropriate. • Makes and communicates clearly an inference.

Key Learning • Key Learning • ½ to ¾ inference idea • Box and whisker plots • Measures of centre • Measures of spread

Resources • Census @ School data viewer • Using Census at School data from surveys • Writing frames for conclusions • …For Imagination • http://www.bigkidsmagazine.com/ • http://www.mathscentre.co.nz • http://www.youcubed.org

Your Turn… • Select a standard • List methods one at a time • Break down Learning at Y 11 to 7 • Make sure I have a copy • AS and method • Who? • Each Level – Key ideas

Hope that was useful • Thank you • Morning Tea • or • Coffee • and • Talk… • Back at 11am

National Workshop Mathematics and Statistics