Modelling
Tasks
Lessons
Assessment
Assessment
Reflecting
Modelling
Tasks
Lessons
Assessment
Assessment
Summative
Reflecting
Formative
Summative
Feedback
Objectives
To consider how:

learners progress in developing modelling competencies

to assess learners’ modelling
Assessment
3
Formative
Summative
Feedback
Outcomes
You will devise a set of criteria which you can use to
judge learners’ solutions to modelling tasks
Assessment
4
Formative
Summative
Feedback
Task
In the UK more than 1.8 million people signed an electronic petition
asking ministers to scrap plans for road charging. Would it have been
more news worthy to have delivered the signatures on paper?
In Spain a petition of 4 million signatures was delivered to the
government in 10 vans. All Spanish newspaper published pictures with
the big boxes and the vans needed to transport the sheets of paper to
the congress.
Assessment
5
Formative
Summative
Feedback
Activity 1
Individually:
Pairs:
Look at the solutions
of your students.
Rank the solutions
in order from not so
good to good.
What makes a good
solution?
What makes a
solution not so
good?
Assessment
In groups:
Draw up a list of
aspects of the
students’ work that
you would consider
important when
assessing it.
Can you organise
this into groups?
6
Formative
Assessment
Summative
Feedback
7
Formative
Assessment
Summative
Feedback
8
Formative
Summative
Feedback
Activity 2
 Identify which of your criteria are task specific (if any)
and which might apply to any task
Assessment
9
Formative
Summative
Feedback
Modelling cycle – assessing students’ work
Real-world
problem
1
2
3
5
Mathematical
5
Assessment
Problem
4
Real solution
“Real world”
Mathematical
solution
“Mathematical world”
10
Formative
Summative
Feedback
Reporting the
work
Real-world
problem
1 up
2 the
Setting
model
3
Mathematical
Problem
Validation &
5
reflection
Working
4
accurately
Real solution
Mathematical
Interpretation
5
“Real world”
Assessment
solution
“Mathematical world”
11
Formative
Setting up a
model
Summative
Working
accurately
Interpreting
Feedback
Validating &
reflecting
Reporting
1
2
3
4
Assessment
12
Formative
Summative
Feedback
Activity 3
In groups:
Use the key headings to devise criteria at 4 levels
increasing of sophistication.
Assessment
13
Formative
Summative
Feedback
Setting up a model
1
Students require support
to simplify the situation
2
3
Students make good decisions that allow
4 them to simplify a complex situation
Assessment
14
Formative
Summative
Feedback
Setting up a model
1
Students require support
to simplify the situation
2 Students can find and use some necessary information to
simplify parts of a complex situation.
Students can use a range of information to simplify a
3 situation.
Students make good decisions that allow
4 them to simplify a complex situation
Assessment
15
Formative
Summative
Feedback
Possible progression in assessment criteria
Setting up a
model
Working
accurately
1
Students require support to
simplify the situation
2
Students can find and use someStudents can identify the
necessary information to
mathematics to use and solve
simplify parts of a complex
parts of the problem but not
situation.
always accurately
3
4
Students can use a range of
information to simplify a
situation.
Students need help in deciding
on the mathematics & do not
always work accurately
Interpreting
Validating &
reflecting
Students have difficulty and
require a lot of support in
interpreting the situation
Students do not reflect on the
validity of their model
With support students (eg by
being asked appropriate
questions) are able to interpret
the situation
Students are aware of the
validity of some but not all
aspects of their model
Reporting
Students are not
independently able
to report their work
satisfactorily
With support and guidance
students are able to
produce a satisfactory
report of their work
Students are able to interpret the Students reflect critically about
Students are able to solve the
task independently using correct situation, but not in depth
many aspects of their model
Students can
mathematics but not all results
understanding its limitations
independently produce a
are correct
good account of their work
Students make good decisions Students use mathematical
that allow them to simplify a
language and symbols
complex situation
accurately
Assessment
Students interpret the situation Students have a good critical
thoroughly and in depth
understanding of the validity
and limitations of their model
Students produce a
comprehensive report of
their work
16
Formative
Summative
Feedback
Activity 4
Use your assessment grid to assess a student’s work.
Work in pairs with work that you have brought to the session.
Each marks one student’s work and then exchanges with the
other.
When you have each marked the two pieces of work discuss
your findings. Try to agree with each other.
Repeat the process
Assessment
17
Formative
Summative
Feedback
Discussion
What issues have emerged when assessing the modelling
work of students?
How will you assess students’ modelling in your classroom /
school?
How do we give a grade / mark?
Can we use our assessment grids to support both formative
and summative assessment?
Assessment
18
Formative
Summative
Feedback
Objectives
To consider how:

learners progress in developing modelling competencies

you to assess learners’ modelling
Assessment
19
Formative
Summative
Feedback
Outcomes
You will devise a set of criteria which you can use to
judge learners’ solutions to modelling tasks
Assessment
20
Formative
Summative
Feedback
Teacher diaries
Don’t forget to use your teacher diary to reflect on this
session.
Use this to consider issues relating to how you will assess
students’ work and how you will give feedback to students.
Assessment
21
Formative
Summative
Feedback
Before this module you will have…….. used one of these
tasks with a group of your students :
Task 2
How long does it take to wash
the windows of a tall building?
Assessment
22
Formative
Summative
Feedback
Task
In the UK more than 1.8 million people signed an electronic petition
asking ministers to scrap plans for road charging. Would it have been
more news worthy to have delivered the signatures on paper?
In Spain a petition of 4 million signatures was delivered to the
government in 10 vans. All Spanish newspaper published pictures with
the big boxes and the vans needed to transport the sheets of paper to
the congress.
Assessment
23
Formative
Summative
Feedback
Before this module you will have…….. used one of these
tasks with a group of your students :
Task 3
How long does it take to
evacuate a building?
Assessment
24