‘Not Normal’
Classroom Norms
Minnie Liu and Peter Liljedahl
Simon Fraser University
Numeracy
“Unlike mathematics, numeracy does not
so much lead toward in an ascending
pursuit of abstraction as it moves outward
toward an ever richer engagement with
life’s diverse contexts and situations.”
(Orrill, 2001, p. xviii)
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
The Nature of Numeracy Tasks
“…the questions [are] more challenging,
[and] require critical thinking. It gives you
an opportunity to solve problems as a team
and learn how to cooperate with each
other. You will find yourself discovering
new things while doing this task. [They]
will help your group work skill, critical
thinking skills and problem solving skills.”
Methodology
•
•
•
•
Grade 8 mathematics students (n = 30)
Mini School Program at a secondary
school in Vancouver
In class observation, field notes,
impromptu interviews, and survey
Grounded Theory Methods
Classroom Norms
(Yackel and Cobb)
“The problems are meant to help develop
the thinking involved. And to showcase
that there are different ways and thinking
to find an answer.”
“We have to finish the questions by the
end of the week and get a new one every
week.”
Classroom Norms
(Yackel and Cobb)
“The problems are meant to help develop
the thinking involved. And to showcase
that there are different ways and thinking
to find an answer.”
“We have to finish the questions by the
end of the week and get a new one every
week.”
Classroom Norms
(Yackel and Cobb)
“The problems are meant to help develop
the thinking involved. And to showcase
that there are different ways and thinking
to find an answer.”
“We have to finish the questions by the
end of the week and get a new one every
week.”
Classroom Norms
(Yackel and Cobb)
“The problems are meant to help develop
the thinking involved. And to showcase
that there are different ways and thinking
to find an answer.”
“We have to finish the questions by the
end of the week and get a new one every
week.”
Abnormal Norms
“[These are] odd questions that’s not often
seen [in other math classes].”
“… [Numeracy tasks] are often complicated
and allow you to use your brain. Many
other projects in class are basically revisits
from what we’ve done … [The numeracy
tasks and the projects] are on a complete
different level.”
Abnormal Norms
“[These are] odd questions that’s not often
seen [in other math classes].”
“… [Numeracy tasks] are often complicated
and allow you to use your brain. Many
other projects in class are basically revisits
from what we’ve done … [The numeracy
tasks and the projects] are on a complete
different level.”
Abnormal Norms
“[These are] odd questions that’s not often
seen [in other math classes].”
“… [Numeracy tasks] are often complicated
and allow you to use your brain. Many
other projects in class are basically revisits
from what we’ve done … [The numeracy
tasks and the projects] are on a complete
different level.”
Institutional Norms
Institutional norms “take the form of
cultural theories, ideologies, and
prescriptions about how society works or
should work… institutionalized cultural
rules define the meaning and identity of
the individual and the patterns of
appropriate economic, political, and
cultural activity.” (Meyer et al., 1987, p. 9)
Institutional Norms
Students’ experiences are
• Temporary
• Unique
•
•
Limit students’ mathematics experiences
Regression to past experiences
Ongoing Research Questions
1) What are some of the institutional norms in a
secondary school setting (specifically in a
mathematics classroom)?
2) How do institutional norms influence
students and teachers in a secondary school
setting?
3) Is it possible to normalize these ‘abnormal’
norms? How can this be done?
Thank you!
Contact Us
Minnie Liu
minniel@sfu.ca
Peter Liljedahl
liljedahl@sfu.ca
peterliljedahl.com
Sociomathematical Norms
• “Normative aspects of mathematical
discussions that are specific to students’
mathematical activity.” (Yackel and Cobb,
1996)
• Teachers’ endorsed norms, teachers’ and
students’ enacted norms, students’
perceived norms (Levenson et al., 2009)