Teach a Same Lesson: Teach a Same Lesson: A Professional Development Strategy in China Jun Li Deakin...
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Teach a Same Lesson: Teach a Same Lesson: A Professional Development Strategy in China
Jun LiJun Li
Deakin UniversityDeakin University
[email protected]@deakin.edu.au
The amount and percentage of school teachers in 2010
1.52 million Senior high school teachers work in 28.6 thousand schools
5.62 million Primary school teachers work in 257.4 thousand schools
3.53 million Junior high school teachers work in 54.9 thousand schools
53%
14%
33%
In Guangzhou:413 schools355,300 students4480 math teachers
High School Young Mathematics Teachers’ Exemplary Lesson Demonstration Contests in Jiangsu Province, 2007
Figure 1: Temporal phases of curriculum use (Stein, Remillard and Smith, 2007)
“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)
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 •procedures without connections•procedures with connections tasks•doing mathematics
lower-level
higher-level
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
Sudden Temperature Increase Task
Can you describe the sudden temperature increase in the last two days by a mathematical model?
Average rates of change
Doing mathematicsTask features: •with real-life context;•multiple representations; •not open-ended; •single solution strategies
• 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
Can you describe the sudden temperature increase in the last two days by a mathematical model?
Average rates of change
Doing mathematics
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. ……
procedures with connections
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? ……
Task features: with real-life context; multiple representations; not open-ended; single
solution strategies
• Great expectations of students• Using realistic context problems• Discussing misconceptions with students• Connecting and making use of previous knowledge and multiple
representations
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)