Small group and Discussion based learning have their differences and similarities. Small group teaching methods relates mainly to cooperative learning, which is, when small groups of students collaborate together to reach a common goal, though the students are working together, each individual student is responsible for knowing the material being discussed (Nattiv, 1994). Discussion based methods do not always include small groups, the “Whole-group classroom discussions about solutions allow teachers to promote reasoning that moves students beyond merely noticing mathematical ideas toward developing a well-connected knowledge of concepts” (Cengiz, 2013, p. 450). Discussion based methods require participation from an entire classroom. Small group and discussion based learning is important to incorporate into teaching styles because it promotes reasoning and requires students to interact with other students, better improving social skills along with investigating solutions and strategies to provide deeper and critical understanding of the material at hand (Cengiz, 2013). It has been stated that students maintain a better understanding of the information and that the students hold and retain the information longer (Martine, 2003).
A method of discussion-based learning is called whole-group classroom discussion. This method requires students to analyze and describe their very own strategies they use. It also allows a student to understand whether a solution suits the problem and is logical. Whole-group discussions allow teachers to point out alternative solution methods for one problem and that allows the student to analyze and understand more than one mathematical solution. It also allows a student to identify and understand differences and similarities in solutions (Cengiz, 2013). An example of whole-group classroom discussion from Nesrin Cengiz (2013) article is as follows:
Yesterday at the park, I counted sixty-nine pigeons. When a big dog walked by, forty- seven of them flew away. How many were still there?
69–47 =? 60–40 = 20, 9–7=2, 20+2 = 22
The teacher then asked, “Can you explain your strategy?” and the following discussion ensued. Ian: I first subtracted forty from sixty, and then seven from nine. Then I added twenty and two and got twenty-two. T: Does this strategy make sense? Multiple students: Yes. No. T: What questions do you have for Ian? The teacher realized that Ian had only described his strategy, so in pursuit of the reasoning behind Ian’s solution, she asked his classmates to pose questions. Some of them asked Ian questions that suggested they were actively listening to his explanation: “Why did you take forty away from sixty?” “Where did the nine and seven come from?” “I thought this was a subtraction problem; why are you adding at the end?” Knowing how common it is for students to erroneously subtract two from twenty at the end of this strategy, the teacher decided to pursue this issue by asking students to provide...