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

EntreeO This session is about designing a way

to assure success for students at NCEA L2.

O Hogan’s Plan is to have each standard at L2 backmapped to Year 7/8.

O Firstly an example, then you will do one standard each in groups. Ham, Rot and EIT all collated and sent back to you.

Focus IdeasO Backward design means starting

with the end in mind and planning for it, step by step.

O Deep Knowledge focuses on the concepts and their relationships

O Deep Understanding is about demonstrating profound meaning

OutcomeAS91256

AS91257 AS91258 …

Y12 Method•

•••••

Y11

Y10

Y9

Y7/8

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 QuestionO To achieve NCEA L2 what is it a

student has to learn in previous years?

O 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.

O NCEA L2 is the 85% PS Goal

The Learning ProgrammeWe should be able to inform/check a

learning programme for a year level as a result.

OOther factors like building problem solving ability, literacy and need to be considered

What do we need?O NZC – these are the AO’s.O National Standard Descriptions,

ExemplarsO Internet

O – to see supporting SSTLGO – to access C@SO – to access nzmaths.co.nz O – to access math dictionaryO – your knowledgeO – two heads are better than one!

Learn by DoingO I have selected AS 91264 as a

starter because it is probably familiar to us and it is a popular choice.

AS91264…methodsO Using the statistical enquiry cycle to make

an inference involves:O posing an appropriate investigative

comparison question from a given set of population data

O selecting random samplesO selecting and using appropriate displays

and measuresO discussing sample distributionsO discussing sampling variability, including

the variability of estimatesO making an inferenceO communicating findings in a conclusion.

1st Task - 3 minitsO posing an appropriate investigative

comparison question from a given set of population data

O Just focusing on this method fill in O => for Year 11O => for Year 10O => for Year 9O => for Year 7/8

My Attempt…O => for Year 11O That AS 91035 has been attempted.

Students can write conclusions to investigative questions.

O => for Year 10O That comparison questions have been

practiced as part of PPDAC. The C@S analyser has been used to answer a question.

and…O => for Year 9O That comparison questions have been

practiced as part of PPDAC and the data cards have been used. See Stats nzmaths

O => 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 O selecting random samples

O Just focusing on this method fill in O => for Year 11O => for Year 10O => for Year 9O => for Year 7/8

My Attempt …O => for Year 11O 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.

O Chance language including bias, likely, outcome are used.

…and O => for Year 10O Students use random sampler on C@S to find a

sample. Biased samples, cleaning data, non-representative samples are identified.

O => for Year 9O Use a spreadsheet to generate random numbers

O => for Year 7/8O Sampling by hand, using dice and knowing what

random means. Using random in language correctly.

3rd Task – 3 minitO selecting and using appropriate displays

and measuresO discussing sample distributions

O Just focusing on this method fill in O => for Year 11O => for Year 10O => for Year 9O => for Year 7/8

My Attempt …O selecting and using appropriate

displays and measuresO discussing sample distributions

O=> for Year 11OUses 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.

…andO => for Year 10O Becomes fluent in interpreting box and

whisker, making and describing dot plots. Use this information to help describe distribution of the data.

O => for Year 9 and Year 7/8O 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 minitO discussing sampling variability, including

the variability of estimates

My Attempt …O discussing sampling variability,

including the variability of estimates

O => for Year 11O 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…O => for Year 10O 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.

…andO => for Year 9 and => for Year 7/8

O 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

O making an inferenceO communicating findings in a

conclusion.

O Just focusing on this method fill in O => for Year 11O => for Year 10O => for Year 9O => for Year 7/8

My attempt cfO making an inferenceO communicating findings in a conclusion.

O => for Year 11O 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.

…andO => for Year 10O Uses ½ to ¾ rule for establishing validity

of inference. Uses shape of distribution when appropriate. Makes and communicates clearly an inference.

O => for Year 9 and Year 7/8O Answers the question posed with

supporting evidence based on shape and position.

Now… O Collect each Year levelO Decide if “inference” is part of the

learning programme for that year.O Compare with exisiting learning

plansO Allocate time, resources, order of

learning, pre and post test tasks. O Organise resources!

OrganisingO 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.

O Broad ContentO That comparison questions have been

practiced as part of PPDAC. The C@S analyser has been used to answer a question.

Content cont…O Students use random sampler on C@S to

find a sample. Cleaning data.O Becomes fluent in interpreting box and

whisker, making and describing dot plots. O Noticing different samples will look different

as well. Explores visual spread and sample size relationship.

O Can explain why some data supports a different conclusion.

Content more!!!O Uses ½ to ¾ rule for establishing validity of

inference. Uses shape of distribution when appropriate.

O Makes and communicates clearly an inference.

Key LearningO Key LearningO ½ to ¾ inference ideaO Box and whisker plotsO Measures of centreO Measures of spread

ResourcesO Census @ School data viewerO Using Census at School data from

surveysO Writing frames for conclusions

O …For ImaginationO http://www.bigkidsmagazine.com/O http://www.mathscentre.co.nz O http://www.youcubed.org

Your Turn…O Select a standardO List methods one at a timeO Break down Learning at Y 11 to 7O Make sure I have a copy

O AS and methodO Who?O Each Level – Key ideas

Hope that was usefulO Thank you

O Morning Tea O orO CoffeeO and O Talk…

O Back at 11am