Unit 3: Discussions in Math Class
Benefits of Using Discussions in Mathematics Classrooms
Discussing the answer
The atmosphere that your classroom has is very important in how discussions will occur. The atmosphere needs to be a conjecturing atmosphere. A big part is the way a teacher phrases their questions as well as their responses to their students. By stating something is wrong you are completely knocking down the idea and not allowing students to build upon the idea or modify it. Students respond and give thoughts based on the idea that they are trying out a theory and modifying or changing it if a problem occurs with it. This type of atmosphere also gets those who are unsure of themselves to answer or or express their ideas as well as have the students who are sure to help the ones who are shy out. The students will be discussing and questioning mathematical theories and ideas. In a conjecturing atmosphere students will develop a deeper understanding of the Mathematical world. To help promote this conjecturing atmosphere students need to be thinking about three tasks: convince myself, convince my neighbor, and convince a skeptic. Keeping these three tasks in mind will make students to organize their thoughts so they can make a clear argument and try to convince the people around them.
Types of Discussions
Small Group Discussions
The best way to get students expressing their ideas and theories on Mathematical topics is to have them discuss them with a small amount of people listening. A common fear among students is public speaking as well as being put down in front of their peers. That is why students need to feel safe in the classroom about contributing. In smaller groups they can test their conjectures and see what other might think. Also in smaller groups students are able to work through problems helping each other through difficult parts. In smaller groups you are limited to the number of students in each group and their thinking. It is very difficult to share distribute information learned or discovered to everyone.
Whole Class Discussions
During Whole class discussions you have everyone in the class giving out their beliefs or knowledge on a subject. With all these opinions being given it is very easy for someone to get hurt. It is essential that students express their opinions toward other comments rather than other students. That is why it is essential for you to have a completely safe environment for students to express themselves. Fear of negative feedback might make a shy student to continue being quiet because they do not want to be embarrass in front of their peers Through questions you pose to your students you are able to assess your students on their knowledge on the subject. At the same time you are able to make sure you get as many people involved as possible. Depending on the amount of time you give towards the discussion will depend on how many students you are able to get involved with that particular discussion. Whole group discussions will have your students staying more focus because they know there is a chance that they might be called upon.
Important Factors for Discussions
Teacher's Responsibility
The teacher has many responsibility to have good discussions occur into their classroom.
- The teacher needs to establish and maintain a respectful and supportive environment. This will help the shy students to share their thoughts on the topic.
- Keep the discussions focus on Mathematics.
- Allow enough time for everyone to participate in large or small discussions.
- Ask questions to prompt deep thinking rather than tell them large hints or answers. This will have students learn the information and be able to retain if much better than being told what it is.
- In smaller groups go around to each group and see where they are at instead of sitting back at your desk doing nothing.
- If you have smaller groups talking about their findings for a particular problem, have them explain it in order from least information to most about the problem. This way the students can see the evolution of the problem and see where it starts to where the farthest group gets.
- In larger groups give time for every student to think about the problem before getting answers. It can very distracting to some students if they see people raising their hands and causing commotion.
Wrong Answer
Discussion is a place where students are able to express their thoughts on a topic freely. It is also a valuable place to check and see if they have understood a lecture or reading materials. Therefore it is crucial to not criticize a wrong answer. Ask other students what they think of the answer, this way the right answer comes out (if there is a right answer) and no one gets hurt. Also ask students about their procedure for coming up with their answer. This will force them to go over each step individually and it might make them see their mistake. Wrong answers can spark critical thinking and that is why you never just throw them away.
Thought Questions
The NCETM is a math organization station in England. Review these web pages. From these web pages and the earlier information answer a few questions.
- Develop discussion in Mathematics. [1]
- Mathematical Discussion. [2]
- Creating an Atmosphere for Useful Conjecture. [3]
- Open and Closed Questions. [4]
- Talking in Pairs. [5]
- Explain in your own words why it is important to have discussions in a math classroom.
- Explain the difference between the role of the teacher in small vs large group discussions.
- What is the difference between open and closed math questions and which one is more valuable?
- Why is it important to have a conjecturing atmosphere?
Resources
MATHEMATICAL DISCUSSION IN THE CLASSROOM. PHILOSOPHY OF MATHEMATICS EDUCATION JOURNAL , 16.
National Centre for Excellence in the teaching of mathematics. (2009, 10 14). Mathematics Knowledge Networks. Retrieved 10 15, 2009, from National Centre for Excellence in the teaching of mathematics: https://www.ncetm.org.uk/enquiry/16952