Teach a Same Lesson: A Professional
Development Strategy in China
Jun Li
Deakin University
jun.l@deakin.edu.au
The amount and percentage of school
teachers in 2010
5.62 million Primary
school teachers work
in 257.4 thousand
schools
53%
In Guangzhou:
413 schools
355,300 students
4480 math teachers
1.52 million Senior high
school teachers work in
28.6 thousand schools
14%
33%
3.53 million Junior high
school teachers work in
54.9 thousand schools
Teach a same lesson is a popular
collaborative teaching research activity
High School Young Mathematics Teachers’ Exemplary Lesson
Demonstration Contests in Jiangsu Province, 2007
Winners of the teaching contest
“A mathematical task is defined as a classroom activity, the purpose of which is
to focus students’ attention on a particular mathematical idea. An activity is not
classified as a different or new task unless the underlying mathematical idea
toward which the activity is oriented changes” (Stein etc, 1996, p.460)
Figure 1: Temporal phases of curriculum use (Stein, Remillard and Smith, 2007)
Research Questions:
1. From written curriculum to intended curriculum, what and how tasks were
kept, adapted, replaced or ignored by the teachers?
2. From intended curriculum to enacted curriculum, to what extent do the
tasks as implemented remain consistent with the ways in which they were
set up?
Task features
• with/without real-life context
• single/multiple representations
• open-ended/not open-ended
• single/multiple solution strategies
Task cognitive demands
• memorization
lower-level
• procedures without connections
• procedures with connections tasks
higher-level
• doing mathematics
Lesson Topic: Average Rates of Change
Level: Grade 11
Data sources:
•3 first prize-winning videotaped lessons
•Written “lesson explaining”
•e-resources used in teaching
•Teaching plan
•Textbook & Teacher’s Manual
Textbook Pages (p.5,6,7)
Sudden Temperature Increase Task
Can you describe the sudden
temperature increase in the last two
days by a mathematical model?
Task features:
• with real-life context;
• multiple representations;
• not open-ended;
• single solution strategies
Doing mathematics
Average rates of change
• read the graph
• make the connections between "the
steepness of the graph" and "the speed
of change"
• as slope could be used to measure the
steepness of a straight line, it is
reasonable to use it as an approximate
measure of the steepness of a curve
Sudden Temperature Increase Task
Task features: with real-life context; multiple representations; not open-ended; single
solution strategies
Can you describe the sudden
temperature increase in the last two
days by a mathematical model?
procedures with connections
T: Please turn to page 4 and
read the question on your
textbook.
T: Finished? Okay. Look at the
big screen. The temperature
increased 15.1°C from March
18 to April 18, but increase
14.8°C suddenly from April 18
to April 20. ……
Doing mathematics
Average rates of change
S: The temperature rose rapidly in the second
time period. So…
T: (interrupt) You said that the temperature rose
rapidly, why? Shall we calculate the
temperature change from April 18 to April 20?
Come on, you tell me the answer together. How
many? ……
Results:
From written curriculum to intended curriculum
35
30
25
Teacher C
Teacher B
Teacher A
Textbook
20
15
10
5
real-life context
representations
answers
single
multiple
not open-ended
open-ended
single
multiple
without
with
0
solution strategies
•
•
•
•
Great expectations of students
Using realistic context problems
Discussing misconceptions with students
Connecting and making use of previous knowledge and multiple
representations
Results
From intended curriculum to enacted curriculum
Some topics could be used for elicit further reflection on
the three lessons
• To form the concept of average rates of change is the
important point of this lesson. Besides of the concept slope,
what other previous knowledge could be connected? What is
the big idea we should highlight in this lesson? What is your
way of deepening students’ thinking beyond calculation?
What we can learn from the three teachers?
• There are two difficulties in teaching of this lesson. One is
related to mathematics, i.e., how to help students find out
that we could use the slope of the secant line to measure the
steepness of a curve. The other is related to motivation, i.e.,
how to engage students and capture their interest in learning
the formula? What is your way to deal with them? What we
can learn from the three teachers?
Processes associated with the decline of
high-level cognitive demands
(Stein, Remillard and Smith, 2007)
Processes associated with the maintenance
of high-level cognitive demands
Discussion
• Direct instruction by teacher combined with
frequent teacher questioning --- a dominant
teaching strategy used in China
• “Teach a same lesson” is embedded in the
Chinese teaching culture
1.Changes in teacher
knowledge and
belief
Lecture-oriented model：1 →2 →3
Practice-oriented model：2 →3 →1
3.
2. Changes
Changes in
student
learning
in teachers’
behavioural
patterns in
classroom
outcomes
teaching