Learning via Problem Solving by Terry Ng

Mathematical Problem Solving is the centre of MOE’s Primary Mathematics Framework and it is interesting to watch the teacher go through the Polya’s 4 stages of problem solving. The teacher constantly gets the students to understand the problem. She would tell them to devise a plan to tackle the problem and carry it out. Finally, she would ask them to check or reflect on their answers. As part of professional development for teachers, it would be interesting to model and represent what Polya’s 4 stages of problem solving entails. It would be in line with the concept of learning via problem solving – which appears to best embody the framework.

A study similar to Kai Fai Ho (2005), but with some modifications could be carried to test the effectiveness of learning via problem solving. The first stage similar to Kai’s study would be observations and interviews cum pretest to gather data on the teachers’ pedagogical approaches as well as the extent to which they apply Polya’s 4 stages of problem solving. Then the teachers are categorized according to the amount of time in which they use Polya’s 4 stages of problem solving during their lesson. Coding methods similar to that used in Kai (2005) study. The classes of students will be categorized based on their mathematical abilities. Stage 2 will cover the training of randomized selection of teachers and classes so that there will be a control and experimental group in each category. The selected teachers forming the experimental group will be trained to conduct math lessons based on the idea of learning via problem solving. A post test is conducted and students and teachers interviewed to gather information about the lessons, their learning and attitudes towards the lessons – both controlled and experimental groups. Issues that threaten the validity and reliability of the study should be looked into and eliminated or at least minimized or controlled.

The teacher has a key role in the learning of a child. The McKinsey Report, (2007) mentions that a good teacher teaching a full size class is as effective as an average teacher teaching a half sized class. The training of our teachers is crucial to the successful implementation of our national curriculum.

Blogging is a tool which allows many to share their ideas and experiences. This sharing is important to the development and improvement in educational pedagogies and knowledge. It creates a community of teachers and learners across the globe - all sharing the same passion - for the improvement of mankind through education.

References
Kai Fai H., John G. H. (2005). Teachers’ Pedagogies and Their Impact on Students’ Mathematical Problem Solving. Journal of Mathematical Behavior; vol. 24, 238-252.
Michael, B., Mona, M.(2007). McKinsey Report. McKinsey & Company.

Research on Verbal Questions asked by the teacher by Ria Arespacochaga

Watching the classroom observation video made me more aware of the different interactions that occur in a problem-solving classroom. The teacher designed the activity to encourage students to explain the “trick” behind the Ghost Whisperer Crystal Ball Activity. He asked questions that encouraged students to think about the situation critically (eg. “What did you find?”; “Why always a multiple of 9?”; “How do we use symbols?”; “Do you agree?”; “Why do you think always a star?”, etc.) I think it would be interesting to do a study on teacher-student dialogue/interactions in the classroom.

One possible study can focus on the types of verbal questions a
teacher asks in order to promote critical thinking in a problem-solving classroom. The website http://www.criticalthinking.org/resources/k12/socratic-teaching.cfm discusses the importance of Socratic Teaching where teachers challenge students to think critically by asking specific types of questions. The site http://www.engin.umich.edu/~problemsolving/strategy/cthinking.htm lists the six types of questions namely:
a. clarification questions
b. questions that probe assumptions
c. questions that probe reasons and evidence
d. questions that probe viewpoints and perspectives
e. questions that probe implications and consequences
f. questions about the question
This study may be done by conducting classroom observations wherein the researcher will take note of all the questions the teacher asks during the period. These questions will then be coded and classified according to the type of questions asked. A possible way of classifying is through the six types of questions already mentioned earlier. The researcher may also interview the teacher in order to find out his reasons for asking specific questions.

Another way to go about studying the effects of the types of questions a teacher asks in a mathematics classroom, the researcher may conduct a study between an experimental and control classroom settings. Once it has been determined that the classes are comparable in terms of mathematical ability, the researcher may begin the study. In the experimental classroom, the researcher specifies the types of questions a teacher should ask in order to promote critical thinking while the teacher in the control class goes about conducting the class in the normal way. Comparisons between the effects of the treatment may then be studied through the use of an achievement test given to both classes. A survey about the thoughts and feelings of the students (as well as the teacher) as they experienced the ‘treatment’ may also be done.

I believe researching about questions that effectively promote critical thinking will help mathematics teachers choose appropriate questions to ask in class. Based on the result of this research, teachers will be more purposeful in their questioning techniques. Rather than concentrating on questions that have only one correct answer, the teacher may be able to encourage students to think critically so that they can come up with solid justifications for their arguments rather than coming up with poorly-reasoned answers.

Using a blog such as this one can be an effective tool in conducting research since it has the capability of reaching a vast number of people. Surveys can be uploaded and answers from the survey are received instantaneously. Educators, as well as students from all over the world, may share different opinions, ideas and experiences through this medium. However, it is difficult to verify information (about respondents, about the data, etc.) received through the internet or blogs.

e-Learning

After you have viewed either the primary or secondary lesson on BlackBoard, please post an entry to propose a possible research on mathematical problem solving that can be conducted. Make specific reference to instances in the lesson that lead to your suggestions. For example, you may select two or three interesting observations and propose further research that can be done to illuminate the phenomena in those observations. Please complete this task by the time you submit your term paper.

Yeap Ban Har