polya problem solving seminar

Polya Problem Solving Seminar

Course description, grading basis, course repeatable for degree credit, total units allowed for degree credit, course component, enrollment optional, does this course satisfy the university language requirement.

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Problem solving - what have we learned since Polya's introspection

Due to the current global situation regarding the Covid-19 pandemic this event is not going ahead in its original form of face-to-face seminar. However, Alan Schoenfeld, who has cancelled his planned trip to the UK has agreed to give his presentation as the first ever CRME webinar. This will be streamed live 4:30 - 6:00 pm (GMT) on Thursday 26th March. Please join us.

To join this webinar please use the following link:

https://zoom.us/j/751235269

You will be asked to provide a name and email address to take part. 

The webinar will be made available for viewing later and the link will be posted on our recorded seminars webpage .

Centre for Research in Mathematics Education Seminar Series 2019/20

Presented by  professor alan schoenfeld , university of california, berkeley.

75 years have passed since George Pólya introduced the idea of heuristic strategies, rules of thumb for effective problem solving, in his classic book How to Solve It. What do we know now that we didn’t know then?

Pólya was right – the strategies work – if you know how to use them. They are more complex than we thought and there are more of them to consider. Issues of self-regulation and students’ beliefs can cause problems.

The bigger question is: How do we create learning environments in which students learn to be effective problem solvers? This involves a shift of frame, moving our focus from what the teacher does (which is still vitally important) to how the student experiences the classroom environment. I will discuss the Teaching for Robust Understanding (TRU) framework and what it means for our teaching.

Biography: Alan Schoenfeld is a leading figure in mathematics education research, receiving the ICMI Felix Klein Medal for lifetime achievement in 2011. A professor at the University of California, Berkeley, he has worked on a series of collaborative projects with the Shell Centre team at Nottingham, where he is an Honorary Professor. His work ranges widely across thinking, teaching, and learning in mathematics but he has focused successively on three major areas: problem solving, models of teaching, and impact-focused work to improve classrooms.

On problem solving, he made the first empirical study of how far mathematics undergraduates tackling non-routine problems can use the strategies set out in George Polya's reflections on how he solved problems. Schoenfeld's study found that the strategies alone are weak, and need to be strengthened by complementary domain-specific tactics. He has worked with the Shell Centre team on projects to develop tools for teaching and assessment, culminating in the Mathematics Assessment Project. Complementing this he developed a theoretical framework, Teaching for Robust Understanding (TRU) – a model of classrooms in which productive learning is likely to occur.

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10.1: George Polya's Four Step Problem Solving Process

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Step 1: Understand the Problem

• Do you understand all the words?
• Can you restate the problem in your own words?
• Do you know what is given?
• Do you know what the goal is?
• Is there enough information?
• Is there extraneous information?
• Is this problem similar to another problem you have solved?

Step 2: Devise a Plan: Below are some strategies one might use to solve a problem. Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.)

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Polya theory to improve problem-solving skills

K R Daulay 1 and I Ruhaimah 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1188 , The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018 3 November 2018, Yogyakarta, Indonesia Citation K R Daulay and I Ruhaimah 2019 J. Phys.: Conf. Ser. 1188 012070 DOI 10.1088/1742-6596/1188/1/012070

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Author affiliations

1 Universitas Negeri Medan, Jalan Willem Iskandar Pasar V, Medan Estate, Sumatera Utara, Indonesia

2 SMP Muhammadiyah 8 Medan, Jl. Utama No.170 Kota Matsum II, Medan Area, Kota Medan, Sumatera Utara 20215 Indonesia

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This research is to improve problem-solving skills in SMP Muhammadiyah 8 Medan students through Polya learning theory in the material of linear equation systems in two-variable. This research method is Classroom Action Research. The research subjects were class VIII SMP Muhammadiyah 8 Medan totalling 29 students. The object of research is the ability to solve mathematical problems — data from research results obtained from observation and test results. The results showed that the use of Polya learning theory could improve students' mathematical problem-solving abilities. In the pre-cycle, there was 10.34% (3 students) of the 29 students who achieved the passing grade. The test results in cycle 1 showed there was 51.72% (15 students) of the number of students who reached passing grade, whereas in cycle 2 there was 75.86% (22 students) of the number of students who reached passing grade. The average value before the cycle is 54.50, while at the end of cycle 1 the average value of the test is 64.60, and at the end of the second cycle is 85.72. Then it can be concluded that the objectives of the research carried out have experienced success. In other words, the application of Polya learning theory can improve students' mathematical problem-solving abilities.

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The William Lowell Putnam Mathematical Competition and the Polya Problem-Solving Seminars 2007