Download Northcote College course outline - Auckland Mathematical Association

Yes
No
DOES THE DAMN THING WORK?
Yes
LIAR
DID YOU DESIGN IT?
No
YOU
IDIOT
DOES ANYONE
KNOW?
Yes
Yes
OH NO
No
No
ARE YOU
GOING TO
BE IN
TROUBLE?
CAN YOU BLAME
SOMEONE ELSE?
NO PROBLEMS
Yes
No
What are the
fundamental themes
in the AO’s that our
students need to
learn?
How can the
themes be linked
from course to
course and year to
year?
Pathways
Engagement,
relevance and
usefulness of units
of work
Workload for
teachers and
teacher “buy in”
Assessment
Endorsements
91026: Apply
numeric
reasoning in
solving
problems
•
•
•
•
•
•
Linear
proportions
Primes,
multiples,
factors, powers
Fractions,
decimals,
percentages,
integers and
conversions
Standard form,
sig figs,
rounding,
decimal place
value
Integer and
fractional
powers
Rates
91027: Apply
algebraic
procedures in
solving
problems
•
•
•
91028: Investigate
relationships
between tables,
equations and
graphs
91031: Apply
geometric
reasoning in
solving
problems
Generalise
• Optimal solutions
• Angles
•
operations
using numerical
intersecting
with fraction
approaches
lines, parallel
sand integers
• Solve linear
lines, polygons
Generalise
equations ,
• Similar shapes,
operations
inequations,
proportional
•
with rational
quadratic, simple
reasoning
numbers and
exponential
• Trigonometric
•
exponents
equations and
ratios and
Form and solve
simultaneous
Pythagorus’
linear
equations with two
theorem in
•
equations ,
unknowns
two
inequations,
• Relate graphs,
dimensions
quadratic,
tables, equations to • Angle
simple
relationship
properties
exponential
• Relate rate of
related to
equations and
change to gradient
circles
simultaneous Actively look to reduce assessment
equations with If standards unsuitable/unworkable do not assess
two unknowns Student performance National/Decile 9
91037:
Demonstrate
understanding
of chance and
data
Evaluate
statistical
investigations or
probability
activities
Calculate
probabilities
Evaluate
statistical
reports
Investigate
situations
involving
elements of
chance
20
91026: Apply
numeric
reasoning in
solving
problems
•
•
•
•
•
•
Linear
proportions
Primes,
multiples,
factors, powers
Fractions,
decimals,
percentages,
integers and
conversions
Standard form,
sig figs,
rounding,
decimal place
value
Integer and
fractional
powers
Rates
91029: Apply
linear algebra
in solving
problems
•
•
•
•
Form and solve
linear
equations
•
Solve linear
equations and
•
inequations
and
simultaneous
equations
Relate graphs,
•
tables and
equations to
linear
relationships
Relate rate of
change to the
gradient
20
•
91032: Apply
right-angled
triangles in
solving
measurement
problems
91033: Apply
knowledge of
geometric
representations
in solving
problems:
Construct and
describe loci
Points and lines
on coordinate
planes, scale
and bearings on
maps
Nets for
polyhedra,
connecting
three
dimensional
solids with
different
representations
Coordinate
plane or map to
show points in
common or loci
•
•
•
•
Use
trigonometric
ratios and
Pythagorus’
theorem
Similar shapes
and
proportional
reasoning
Select and use
appropriate
metric units
for length and
area
Measure at an
appropriate
level of
precision
91038: Investigate
a situation
involving elements
of chance
•
•
Compare and
describe variation
between
theoretical and
experimental
distributions in
situations involving
chance
Investigate
situations that
involve elements of
chance
91031: Apply
geometric
reasoning in
solving
problems
91257: Apply graphical methods in solving
problems
91257: Apply graphical methods in solving
problems
91261: Apply algebraic methods in solving
problems
91256: Apply co-ordinate geometry methods
in solving problems
91262: Apply calculus methods in solving
problems
91258: Apply sequences and series in solving
problems
91261: Apply probability methods in solving
problems
91259: Apply trigonometric relationships in
solving problems
91260: Apply network methods in solving
problems
17
17 - 19
91268: Investigate a situation involving
elements of chance using a simulation
91260: Apply network methods in solving
problems
91261: Apply probability methods in solving
PLD through first term on new approach to graphs
problems
12MTA course just finished single internal, remainder
of year to focus on teaching and learning in depth not rushing
for assessments
13STA
11MTA
12MTA
13CAL
11MTN
12MTN
?
Problem – whilst standards we chose
matched, assessment tasks provided on
TKI did not. So we have had to look at
developing our own tasks and there has
been a lot of debate around this.
Our tasks needed to reflect the
teaching and learning that had
occurred in the units, students
should be given the best possible
opportunity to showcase their
learning of the AO’s the course had
emphasized.
Andy Begg on rich
learning activities
ASSESSMENT
• Sound assessment tasks are vitally important and whilst there is a huge body of research
around principles underpinning design of tasks, there is no one ‘style’ of task that is more
valid than others across all situations.
• Teachers/MU holders who feel confident in interpreting the standards should feel
empowered to try to write tasks and get constructive feedback about the tasks from as many
sources as possible (colleagues, moderators, Team Solutions etc)
• Moderators do not hold a monopoly on the style of assessment in regard to the SOLO
framework. Whilst their judgements about style are valid in contexts specific for themselves,
they cannot make ‘value’ judgements about the style of tasks others have written. Their
feedback should only be in regard to the standard itself not the style of presentation of the
problem.
There are many similarities between the Bloom and SOLO taxonomies. It
is necessary when using both taxonomies to know the context of
learning, and it is expected that the questions asked follow from some
form of instruction or prior exposure to the information required. There
is also the premise that the concepts in the instruction are hierarchical.
There are also fundamental differences between the Bloom and SOLO
taxonomies. The Bloom taxonomy presupposes that there is a necessary
relationship between the questions asked and the responses to be
elicited(see Schrag, 1989), whereas in the SOLO taxonomy both the
questions and the answers can be at differing levels. Whereas Bloom
separates 'knowledge' from the intellectual abilities or process that
operate on this 'knowledge' (Furst, 1981), the SOLO taxonomy is
primarily based on the processes of understanding used by the students
when answering the prompts. Knowledge, therefore, permeates across
all levels of the SOLO taxonomy.
Hattie, J. & Purdie, N. (1998) The Solo model: Addressing fundamental measurement issues. In Dart, B. & Boulton-Lewis, G. M. (Eds.) Teaching
and learning in higher education. Camberwell, Vic, Australian Council of Educational Research.
Hattie, J.A.C. & Brown, G. T. L. (2004). Cognitive processes in assessment items: SOLO taxonomy (Tech. Rep. No. 43). Auckland, NZ: University of
Auckland, Project asTTle.