‘Engaging students in dynamic and
collaborative statistics’
Barb Wallis – for workshop resources
bwallis@masseyhigh.school.nz
• A workshop of activities and ideas, for a
differentiated teaching approach, that
develops the statistical confidence of Year 9
students in multi-level classrooms.
• A progression of understanding for students
that allows for a movement from ‘counting’
aspects of discrete data to full appreciation of
the inquiry cycle and the descriptive interpretative aspects within it.
WORKSHOP DO NOW:
• Fold the paper into eighths – 8 pieces, halves,
quarters then eighths. Write the number 1 to
8 in the top left corner going across 1 then 2
etc.
• Write answers to the survey questions
• [Done with students as the first Yr 9
introduction of the PPDAC cycle – whole class,
groups, individual assignment]
Survey questions
1. How did you travel here this morning
2. What colour eyes do you have - choose from blue,
brown, hazel, grey
3. How many motor vehicles do you have at your home –
include motorbikes
4. What ethnic group do you identify with most strongly
5. What is the length of your hand-span to the nearest
centimetre
6. What time did you get up this morning
7. In what area is your school located (what was your Year
8 school for students)
8. How many people slept at your house last night
INTRODUCTION:
• Background referring to the ideas
and thinking behind my Maths &
Stats teaching and where they have
arisen from.
• Pip Arnold
Multiple aspects of the PPDAC statistical
inquiry cycle
• Peter Hughes
Mathematics Pedagogical Content knowledge
• Caroline Yoon
Model Elicitating Activities
• Jo Boaler
How to learn Math
MAIN IDEAS
• Teaching as a wide NET of ideas and approaches
• Maths learnt as a whole process and emphasis on
relating/understanding
• Inquiry relationship with maths
• Statistics alive for them
• Communication and collaboration
• Yr 9 scheme progression/expectations
• Student engagement
• Low entry – high ceiling
• Jo Boaler believes by encouraging inquiry,
curiosity, confidence & intuition students will
develop an inquiry relationship with maths. I
think that in our statistics lessons we have an
opportunity to act towards this goal.
The world our students will work in relies on
teams of people developing ideas,
communication and collaboration. As a Maths
teacher we can offer them that experience.
Yr 9 MAIN ACTVITIES
• Class survey questions
• ‘Investigate the throwing of a paper
dart’
• ‘Ruler drop reactions’
• ‘Foot sole comparison’
• C@S Data cards investigations
• ‘Helicopter rotor blade length’
• ‘Big Foot’
• Getting started: Stats 1
• Data collection for a Year 9 class.
• 8 Survey questions
• PPDAC cycle ---whole class for one survey
question then groups for rest
---- draft, feedback, posters
--- individual assignments using new
data following marking schelude.
• Collect up data – redistribute and follow PPDAC cycle to make a
poster. MW & WL PPDAC cycle, posters.
Student engagement Stats 1
• ‘Investigate the throwing of a paper dart’
• PPDAC cycle process complete, relaxed
overview
• Use of a summative question.
Refer separate sheet. Based on ‘Harrier dart ‘ from
Peter Newell workshop AMA Sat morning
Low entry – high ceiling
Check out our mind-set about ourselves as teachers. We can ask
ourselves when looking at a problem, situation or an
investigation - ask ‘who is doing the maths’? Our classrooms
need to be places where people actually do Maths. Problem
solve, plan, find the question to ask, explore, give it a go, get it
wrong, alter, decide what knowledge is needed, what method
would be useful, discuss ideas with each other, explain their
methods, hear other ideas and methods. Just as in music if we
practice writing the notes and never play or hear an instrument,
where is the joy and wonder in that?
Stats 1:
‘Ruler drop reaction times’
Can take an activity and put the life back in.
Can choose parts to structure.
Some instructions for data collection are
given. Work is done in pairs.
Article as conclusion for extension
Refer separate sheet
Stats 3:
Comparing and Relationship questions
Comparing the foot-length of boys & girls
Worked through with the students providing a structured model over
5 to 8 periods. Diving off into particular areas such as ‘Question
types’, ‘sources of variation’, ‘data of interest’, ‘cleaning the data’ ,
dot plots to box & whisker graphs, ‘graph shape and descriptions’,
statistical measures, intervals for histograms etc.
Provision of a complete model of the investigation.
Census in schools data cards
Explore own question. Quick process teacher provided graphs for
question on relationship between popiteal length and height.
Students add own data.
‘Helicopter rotor blade length’
The structured worksheet is adapted to a PPDAC
investigation in a similar way to the ‘paper dart’ and
‘reaction time by ruler’ activities. It is a more advanced use
of the PPDAC cycle, sources of variation sorted in planning,
expanded to whole class data collection and leads to
source of ‘box & whisker’ plots -including graphics
calculators if available - use of statistical measures for ‘I
notice…’ and conclusions.
Also can be used as a basis of discussion of sample results;
– same scale boxes placed on the wall & then can look at
the median variation by forming lines as a border (also
upper and lower quartiles). Compare to combining the
samples for stats information.
‘Big Foot’
Is an example of a model elicitating activity; Involves a
warm-up activity, then a situation that teams work
together on to develop an appropriate model that can be
used beyond the current situation. In a class where this
was used, a girl organised the rest of her group to stand
against the wall apart, in proportion to their foot length.
A cut-out of the footprint was placed in the best fit place
of foot size. The top of the heads were marked as a line
and then measured to find height of the person for the
police. The model was then written up as a method and
developed with the help of the teacher into a scatter
graph form, using measurements rather than actual
people.
RESOURCES
Helicopter investigation
Alan Santos/Gillian Frankcom
Big Foot
Caroline Yoon
PPDAC power points and model of ‘foot length investigation’
Annie Matthews, Roopa Ashok, Barb Wallis & Nik Wallis
Peer assessment
Julie Stewart
Dirty data
Pip Arnold
Black sticks investigation
Jen Triggs
Dot plots and Box & Whisker graphs
St Marys Freemans Bay
Marking scheludes Stats 1 & 3
Julie Stewart, Barb Wallis, Robin Knox & Sowbhagya Gundugollu
EXIT CARD
• [CARD example such as ‘write on the axes
what these graphs could be showing’ collect in
to check understanding – individual/class]
• Workshop = write one workshop idea
you are going to enact.