Teach a Same Lesson: Teach a Same Lesson: A Professional Development Strategy in China Jun Li Deakin University [email protected].

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

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

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

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?

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

Results: From written curriculum to intended curriculum

• 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

Lecture-oriented model ： 1 →2 →3

Practice-oriented model ： 2 →3 →1