Teaching Tip: Developing Classroom Discourse in Mathematical Teachers

Name:

Sun Jui-Po

Economy:

Chinese Taipei

School:

Elementary School, National Hsinchu University of

Subject:

Elementary Mathematics

Tip:

Mrs. Dai who is a professional teacher in Elementary School, National Hsinchu University of Education in Taiwan cooperated with our teachers to develop classroom discourse communities in which the students learn to construct and evaluate mathematical arguments collectively. This professional community contains one researcher- Mr. Tsai who is an associate professor in National Hsinchu University of Education in Taiwan, elementary school principle, four elementary teachers of same grade, and several graduate students of mathematics education participated this project. To create the opportunities of learning from others’ concerns, routine meetings were scheduled once every other week. The teachers were invited to report their concerns relevant with the critical teaching issues in the routine meetings after they observed one teacher’s teaching. The lessons of the four teachers were scheduled in turn to be observed his or her teaching on Friday morning and were immediately followed by a routine meeting in the afternoon to address what they concerned with the teaching and learning issues. After the meeting, the teacher who conducted the teaching lesson was asked to watch her own teaching video tap, to identify the teaching learning issues addressed in the meeting, and be encouraged to write the reflection journal.
This project was conducted with six years long from first grade to sixth grade. The main purpose of this project was to develop social norms and sociomathematical norms to improve students’ social autonomy and intellectual autonomy in classroom discourse. Especially we identified many normative aspects of what counts as acceptable reasoning processes in classroom communities.

All students got amazing improving on their mathematical learning. We shared some parts of teaching tips in this program as following (You can look this paper first then see the video clip description attached):

1. Regular teaching process as fallows: first, teacher pose the problem to whole class, second, students solve the problem individually and were forbidden to look each other, third, each student explains his/her solution to their group in turn, and finally each group chose one better solution to explain to whole class.
2. When students solve the problem individually students need to write their solution on the 40cm×55cm white paper that were bigger than regular B4 size paper and especially ordered from paper company. This is a very good tip to let students record their solutions publicly. It is easy for students to explain their solutions to other students in group discussion or whole class discussion and also easy for listeners to evaluate the solution process reasonable or unreasonable.
3. Researcher and teachers cooperated with each other try to develop the sociomathematical norms in their classroom communities. This is one of nice tips to develop their students’intellectual autonomy. For the limitation of this paper we just share one reasoning norm of what counts as an acceptable reasoning process in explaining their solutions. The first explaining norm was when students explained their solutions of number sentence to their group or whole class they needed to explain the solution based on what the knowledge they have learned before. This tip is very powerful way to improve students’ mathematical learning because students always need to think about what the knowledge they have learned before and how this knowledge related to their solution. Gradually, knowledge that students have learned before will connect each other and form a net. This process not only improves classroom discourse and also improves students’ mathematical understanding. Finally, they develop the deductive mathematical thinking. Therefore, if students just read the number sentence was not acceptable in their class.
4. The following process was one of sixth grade teaching lesson. We attached the video clip description. Students just learned the unknown variable to set an equation to solve the mathematical problem. All students needed to solve the problem individually and explained their solutions to their group or whole class. We described the teaching sequence as follows for some one who can follow the video tap easily:

(1) Teacher posed the problem: “There are 10 chickens and goats totally. There are 32 legs of chickens and goats totally. How many chickens and how many goats are there?”
(2) Students solved the problem individually. There are 4 Group6’s solutions as follows:
S1: chickens+goats=10
4+6=10
4×2=8
6×4=24
24+8=32 A:4 chickens,6 goats
S2: 4-2=2
10×2=20
32-20=12
12÷2=6
10-6=4 A:4 chickens,6 goats

S3: 10÷2=5
5×2=10
5×4=20
32-30=2
4×2=8
6×4=24
8+24=32 A:4 chickens,6 goats
S4: chickens+goats=10
32÷4=8
32÷2=16

(3) Each student presented his or her solution to his or her group and listener asked the questions.
(4) Each group attached his or her group’s better solution on the black board then teacher chosen one group to present its’ solution based on the sequence from simple to complexity.
(5) Different Groups presented their group’s solutions to whole class. We just chose Group 5 Presenter to explain their group’s solution as follows:
Group 5 solution: I assume there are x goats in there.
X+ chickens =10

When she explained relation between the equation 4x+(10-x)×2=32 and the equation 4x+10×2- x×2=32. She explained she used the distribution law she has learned before. When she explained the relation between 2x+20=32 and 2x+20-20=32-20. She explained she used the equal substation law she has learned before… Teacher also checked with other students whether they understood what the speaker told about. This explained process become the normative aspect of what count as the acceptable explained process in this classroom community.

Note: If you want to know about our professional community in our elementary school you can get into our school web side as follow: http://www.wretch.cc/blog/mathtalk

Video: