A writing rubric for “describe” or “explain”
questions in Maths and Stats.
Presented by Jeremy Brocklehurst
*
Co-educational secondary school: Y913.
15 minutes out of Christchurch.
Roll: About 1600.
School-wide focus on developing thinking (SOLO Taxonomy) since 2007.
(Pam Hook: http://hooked-on-thinking.com )
Then in 2012, school wide focus on developing templates for writing.
Success criteria for this workshop!
Examples of describe/explain questions
Compare the performance of these 2 players over the seasons shown in the
graph.
2013 Level 2 Probability external
Compare and contrast the two distributions.
You should discuss shape, centre and spread in relation to the context.
2014 Level 2 Probability external
Discuss the distributions.
In your answer you should
include some relevant
calculations and some
comparisons.
You should also discuss
shape, centre and spread.
2014 Level 2 Probability external
Discuss the distributions.
In your answer you should
include some relevant
calculations and some
comparisons.
You should also discuss
shape, centre and spread.
2013 L3 Probability Distributions
2014 L3 Probability Distributions
Number of Latte’s out of 5 made with trim milk
Heights of male and female students from the South
African Census @ School Database
Describe features of the distributions comparatively.
And it’s not just a Stats thing…
In Scholarship Calculus:
From the 2012 exam:
Use calculus to explain why the simple equation
𝐴 𝑡 = 𝐴0 𝑒 𝑘𝑡 models such a wide range of real world situations.
Write at most half a page.
Have a go at one:
The following graphs are distributions of ages in two
populations. The United States of America (based on US
census data) and Facebook users:
Describe features of the distributions comparatively. Aim
to make at least three statements. Support your statements
with statistical evidence.
Have a go at one:
The following graphs are distributions of ages in two
populations. The United States of America (based on US
census data) and Facebook users:
Describe features of the distributions comparatively. Aim
to make at least three statements. Support your
statements with statistical evidence.
Context…
When given an “explain”, “describe” or “compare and
contrast” task:
What are common difficulties that
students have?
What people said in workshops…
When given an “explain”, “describe” or “compare and
contrast” task:
What are common difficulties that students
have?
-
Getting started.
Handling lack of information or information they don’t understand.
Confidence – fear of being wrong so I won’t try.
Not sure what statistical terms to use.
Stating what’s obvious and spelling it out.
How to back up my points using evidence from these graphs?
Comparitive language. If asked to compare the features of 2
distributions of data, students tend to describe them separately
rather than comparing them.
Talk about the graphs but no contextual links.
Write only about context – no links to statistical evidence (social
studies answer).
Having the right language/vocab – what does “compare” actually
mean I have to do? Likewise “discuss” vs “explain”.
Writing rubrics can be useful
What the OSEM writing frame means:
O stands for Obvious observations
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what? Write Write down what
each of your points tells you about the original problem/situation. What
else
could we find out?
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what? Write Write down what
each of your points tells you about the original problem/situation. What
else
could we find out?
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what? Write down what each of
your points tells you about the original problem/situation. What else
could we find out?
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what? Write down what each of
your points tells you about the original problem/situation. What else
could we find out?
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what?
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what?
Write down what each of your points tells you about the problem/situation.
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what?
Write down what each of your points tells you about the problem/situation.
This is all about the context.
The “Meaning” bit has 2 aspects:
M is for Meaning: Make sense of it.
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
Implications
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
1. Make sense of it.
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
1. Make sense of it.
Explanations.
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
1. Make sense of it. Explanations.
“This makes sense because...”
So what?
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…”
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…”
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
The “Meaning” bit has 2 aspects:
Implications
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
2. So what?
The “Meaning” bit has 2 aspects:
Implications
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
2. So what?
Implications.
The “Meaning” bit has 2 aspects:
Implications
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
2. So what?
Implications.
• How is this relevant to your original question?
• Research – what have other studies found out about this?
How can we show “Statistical Insight” here?
The “Meaning” bit has 2 aspects:
Implications
M is for Meaning: Make sense of it.
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
2. So what?
Implications.
• How is this relevant to your original question?
• Research – what have other studies found out about this?
Statistical Insight : Link Stats + Context and look deeper.
The “Meaning” bit has 2 aspects:
Explanations
M is for Meaning: Make sense of it.
Implications
So what?
1. Make sense of it. Explanations.
“This makes sense because...” “This could be because…” “This is surprising
because…” “Another factor that could be involved here is…”
2. So what?
Implications.
• How is this relevant to your original question?
• Research – what have other studies found out about this?
Statistical Insight : Link Stats + Context and look deeper.
What the OSEM writing frame means:
O stands for Obvious observations:
Write down one thing you notice, then leave a gap, and write down
something else you notice. Try to get 3 obvious things.
S is for Specific: Under each obvious observation, explain what you mean
so that another person would get it.
E is for Evidence: Support each observation with numbers or calculations.
M is for Meaning: Make sense of it. So what?
Write down what each of your points tells you about the problem/situation.
This is all about the context.
Examples of student work…
Observe (look for obvious)
Specific with
Evidence (numbers)
Meaning:
Meaning: So what?
Meaning: So what? What does this tell us
about the situation?
Year 9…
Year 10 chance investigation: Win at the Fair
Obvious
observations
Specific
Evidence
(numbers,
calculations)
Meaning
- Make sense of it.
- So what?
Year 10 chance investigation: Win at the Fair
In the Level 1 Multivariate Data standard (1.10),
my students found OSEM a useful guide when
writing their conclusions:
Height:
Min:
LQ:
Med:
UQ:
Max:
Girls
Boys
120
123
135
143.75
149.5
154
158
168.5
245*
193
3. a) Appropriate dot plot drawn
b) Appropriate box plot drawn
MF Heights
220
210
200
190
180
170
Male
160
150
140
130
120
Female
110
100
110
Female
Male
120
130
140
150
160
TallCentimetre
170
180
190
200
1.10 Multivariate – Conclusion
1.10 Multivariate – Conclusion
And even in Level 2 Coordinate Geometry
And even in Level 2 Coordinate Geometry
Obvious
observations
Specific (labelling)
Evidence (calculations)
Meaning (so what?)
(Relate back to
problem)
Reference for SOLO Taxonomy symbols: Pam Hook: http://hooked-on-thinking.com
Great resources to practice describing
displays using NZ data
Wiki New Zealand website:
http://wikinewzealand.org/?cat=280
Wiki New Zealand site:
Wiki New Zealand site:
Wiki New Zealand site:
School students are paid to deliver
weekly advertising leaflets to houses.
(a) Leaflets from us – pay a fixed amount per
leaflet
(b) Leaflets delivery co. pays them per
bundle of 50 leaflets.
If a student delivers more than 300 leaflets
they are paid more per bundle.
In groups:
1. Each person has a sheet.
2. Each person fills in one Obvious
observation.
3. Then fill in the “Specific” part for
your observation
3. Continue in this way, passing each
sheet around until OSEM are
completed for all 4 boxes.
4. Then have a go at the Extended
Abstract part.
Success Criteria: OSEM
Unistructural
Multistructural
Relational
Obvious
observations:
Specific with
Evidence:
Meaning:
I can identify
one relevant
feature.
My description
includes
specific details
(e.g. locations
on the scale)
AND
is supported by
evidence
(numbers and
units).
I can relate my
specific
observations
back to the
context the
graph
represents.
(link – sequence,
classify, compare and
contrast, explain
causes, explain
consequences,
analyse (part whole)).
Extended
Abstract
Go somewhere
with it…
I can make decisions
based on the
evidence
I can predict the
effects of changes to
the features.
I can adapt my
observations to other
situations (generalise)
(new way –
generalise, evaluate,
predict, and create).
Examples of describe/explain questions
School students are paid to deliver
weekly advertising leaflets to houses.
(a) Leaflets from us – pay a fixed amount per
leaflet
(b) Leaflets delivery co. pays them per
bundle of 50 leaflets.
If a student delivers more than 300 leaflets
they are paid more per bundle.
Explain how and why the graph in part (b) is different to the graph in part (a).
(b) Leaflets delivery co. pays
them per bundle of 50 leaflets.