Starter of the Day
• Name a number that has exactly 10 factors.
• What number can not be written as
consecutive sum?
[eg 26 = 12 + 13, 15 = 1+2+3+4+5, most can]
Work and Study Skills
Numeracy Unit Standards
Ngatea Teacher Day, June 15th
Hauraki Plains College
Jim Hogan, Sandra Cathcart, Brenda McNaughton
Faculty of Education
Team Solutions, Auckland University
Burning Questions
What is burning in
your head that
needs to be
answered this
session?
Objectives de jour
• To enhance teacher knowledge and
understanding of numeracy unit standards
• To experience a selection of problems
• To develop teacher capability for using
these standards effectively
War Plan
• Most minutes on the general nature of
• 10 minutes on Number and recording
• 10 minutes on Measure and recording
• 10 minutes on Statistics and recording
• 10 minute wrap up
NZQA Website
Contains everything being used in this .ppt.
Google “numeracy standards nzqa”
There may well be more efficient ways!
What is a problem?
In the context of numeracy of course and
mathematics in general.
Have a chat about this.
Definition of a Problem from clarifications
A problem is a question where the
pathway to the solution is not given.
The learner works out for themselves
how to solve the problem and selects
the strategies to use in order to do so.
Problems have a purpose and are
relevant to the learner.
Hogan’s Interpretation
• A problem is a question where the student:– Selects the method of solution
– Uses the result in some way
The purpose is the use.
A Useless Problem
Add the prices of these items to find the total
amount of money Fred needed at the shop.
Pie $3.50, Chips $3.00, Drink $2.50
Why is this not a problem?
A Useful Problem
Fred had $10 and wondered if he had enough to
buy these items for lunch.
Pie $3.50, Chips $3.00, Drink $2.50
Why does this now work as a problem?
Six Squared Resource
I do not have a copy (yet) but just run the
SELECT and USE
lense over every problem before
using it as assessment evidence.
Adult Learning Progressions
Remember these are Work and Study Skills
standards. They are designed for use by
adults in all sorts of occupations.
Hence the relevance statements and
“naturally occurring evidence comments.
An apprentice chef would use food
contexts.
X One-off Assessments X
Sorry, no use.
Hence, while the o/d Unit
Standards might be “practice” or
“in class work” they (generally)
can not be used for valid
evidence.
Classroom Work
• Real contexts may include “classroom”.
• A classroom is not just a mathematics
classroom.
• Hence this is a SCHOOL WIDE learning
consideration. (Signed and verified)
OVER TIME
This does not mean more pay!
This means the student has learned and
remembered how to use the mathematics involved
in solving this sort of problem.
So over a 2 or 3 month period evidence is collected.
This demonstrates learned skills and knowledge.
Calculators
Use them and always ask “Is my answer
reasonable?”
Preferable the Casio 82au Plus because 25% of 60
looks just like that and a fraction looks like a
fraction and it has an S<=>D button.
thinking
It is the
by selection and use that is
important here not the calculation.
One Step Solution
Does not mean a whole lot of single step trivia. Give students
appropriate and relevant problems.
Eg Fred wants to paint the fence outside the classroom and
needs to cost the job for the caretaker.
This is a many step problem. Each step is evidence for the
numeracy standards.
In this case, NUMBER and MEASUREMENT
and probably WRITING as well.
Orally, Visually or Written
The evidence can be spoken, noticed or written.
It could be a video.
It could be a computer .ppt
Encourage imagination….
Authenticity
Of course an assessor must be certain the
work is by that particular student (and
verified).
How can this be assured if a student does
number or measurement in an out of school
context?
With care, planning and the knowledge of
parents or associates. We have to accept
and trust but where there is doubt say “No”.
Verification
Evidence is to be verified. This is a two step
check system designed for industry buy we have
to use it in school.
Record oral evidence by notes and signing.
Record visual evidence by notes and signing.
You are a registered teacher!
Portfolio of Evidence
A moderator is only going to check your
decisions concerning the evidence.
Please carefully indicate which evidence is being
used and why.
A moderator is moderating your decisions.
Only give them the evidence you used.
Recording Sheets
Get the latest downloads from NZQA.
Which brings us to evidence requirements.
Evidence
See Number US 26623 Standards, Outcome 1.
All clearly stated.
Measurement US 26627
A measurement is not a measurement unless it
has units.
Correct units.
A student selects their own measuring device
for the purpose and reads it to appropriate
accuracy.
Range for Measurement
See standard, all clearly stated.
Conversions and estimation.
Location using direction and distance.
GPS, Navman, Google Maps, all good. How
about navigating in a flight simulator?
Capacity or Volume?
Capacity is a liquid measure or how much
a container will hold.
Volume is a spacial measure which could
be used for liquids but is generally
referring to the “amount of 3d space”.
Either is OK for this standard.
Interpreting Statistics
The range involves
- general features of data
- measures of centre
- extremes, shape, trends
Appropriate conclusions are
drawn from the evidence.
Conclusions… where from?
Lists, tables, graphs, diagrams, pictures,
text.
Which reminds me of the Hungry
Planet.
Google!
http://www.time.com/time/photogalle
ry/0,29307,1645016,00.html
Pathways from my Workshop 1
Low ability Y10
students, how do
they get numeracy? Students who have 10
Students who have 14
credits all at
Achievement level
and NCEA L1.
Now what?
numeracy credits
ONLY – now what?
Expectation and Relationship
I think that a course with Numeracy standards
should also offer some credits in Achievement
Standards.
91026
91030
91033
91034
91036
Aims from Jen Hudson (JH)
• To build student’s confidence in mathematical
abilities and skills
• Prepare them for real world by incorporating
life skills
• Use Brainstorming to get ‘by-in’ as they help
plan the unit
• Use of Projects to collect the evidence:
personal choice & the more they do the more
they get out of it (including evidence)
Year Plan JH
• Began with Themed Unit booklet & test –
Amusement Park (NZAMT)
– Use the Assessment as a tool to understanding
collecting evidence
• Themed projects – On Holiday & Going Flatting
• Achievement Standards :
–
–
–
–
–
1.1 Numeric Reasoning
1.10 Multi-Variate Data
1.5 Measurement?
Bi-Variate Data?
Geometric Transformations?
Themed Unit – Amusement Park JH
• NZAMT website(www.nzamt.org.nz) for
Amusement Park Unit booklet & Assessment
– Supplement with notes and practicing of skills from
Units In Maths textbook and Beta textbook
– Complete individual portions of the booklet after
completing practice
– Test at the end of topic
– Go through the assessment with students as they
record evidence they have shown in the test
– ALL students able to achieve some success and tick off
some boxes on the Number Unit Standard
Themed Unit – ON HOLIDAY JH
• Brainstorm group & class activity
• Use ‘On Holiday’ and ‘Earning Money’ books by Faye Cowin to
develop and practice skills
• Develop Project parameters as a class
• Computer room – to research & collect info
–
–
–
–
•
•
•
•
Travel
Accommodation
Holiday Activities
Food
Project Presentations – poster, brochure, PowerPoint
Oral Presentation
Recording of evidence
ALL students who submitted a project, collected some evidence
Themed Unit – GOING FLATTING JH
• Brainstorm group & class activity
• Explore career options – www.careers.govt.nz
–
–
–
–
Schooling needed
Income
Job prospect
How to get into the career
• Budget
– Find a job
– Find a flat
– Other expenses
• Sprucing up the flat (measurement)
– Carpeting
– Wallpapering
– Curtains
Quotes from Students –
End of Term 1 JH
• I really enjoy maths class this year, I don’t feel like
cabbage at maths anymore. I’m more confident
with maths. I LOVE doing projects to help with our
evidence to get our credits for Level 1.
• The assignments are fun because it is like real life.
AS 1.1 Numeric ReasoningJH
• About 75% of students achieved
• Worked to develop the Number skills all
year
• Only spent 4 concentrated weeks to
revise before testing
• Only focused on the Achieve
level..hmmmm?
Numeracy Resources
• www.TEC.govt.nz
• Adult numeracy progressions.
• This is where the standards come
from. Level 5 of the progressions
across the board.
• This correlates to NZC CL 4 or being
multiplicative, in broad terms.
Resources
• http://www.nzqa.govt.nz/qualificationsstandards/qualifications/ncea/subjects/literacy-andnumeracy-level-1/
• NZAMT
Thank you!
Kia kaha and try something new. Remember
that for low success students previous
mathematics pedogogy did not work.
Involve student!
See BES Mathematics for more ideas.