difference between routine and non routine problem solving

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Introduction to Non-Routine Mathematics / Non-Routine Problem Solving

Creative problem solving or Non-Routine Mathematics involves finding solutions for unseen problems or situations that are different from structured Maths problems. There are no set formulae or strategies to solve them , and it takes creativity, flexibility  and originality to do so. This can be done by creating our own ways to assess the problem at hand and reach a solution. We need to find our own solutions and sometimes derive our own formulae too.

A non-routine problem can have multiple solutions at times, the way each one of us  has different approach and different solutions for our real-life problems.

Why non-routine Mathematics

• It’s an engaging and interesting way to introduce problem solving to kids and grown-ups.
• Its helps boost the brain power.
• It encourages us to think beyond obvious and analyse a situation with more clarity.
• Encourages us to be more flexible and creative in our approach and to think and analyse from an extremely basic level, rather than just learning Mathematical formulae and trying to fit them in all situations.
• Brings out originality, independent thought process and analytical skills as one must investigate a problem, reach a solution, and explain it too.

How to Analyse a Non-Routine Problem :

• Read the problem well and make note of the data given to you.
• Figure out clearly what is asked or what is expected from you.
• Take note of all the conditions and restrictions . This will help you get more clarity.
• Break up the problem into smaller parts , try to solve these smaller problems first.
• Make a note of data and properties or any similar situations ( faced earlier)
• Look for a pattern or think about a logical way of reaching a solution. Make a model or devise a strategy .
• Use this strategy and your knowledge to reach a solution.

Let’s try a few examples!

There are 50 chairs and stools altogether in a restaurant. Find the number of chairs and the number of stools, if each chair has 4 legs and each stool has 3 legs and there are 180 wooden legs in the restaurant?

First thing that comes to our mind is that we have two algebraic equations here and solving simultaneous equations is the only way to get a solution.

Not really! A small child and a Non-Math student can solve it too.

Logic: Each piece of furniture has at least 3 legs (stools-3 legs, chairs -4 legs).

So, minimum number of legs (for 50 pcs of furniture) in the restaurant = 3 X 50  = 150 legs  if there are only stools in the restaurant.                                                                       

Chairs have 4 legs i.e., each extra leg belongs to a chair.

(we have already taken 3 legs of each chair and stool into account)

Number of extra wooden legs in the restaurant

 =  total number – minimum possible number of legs for 50 pcs of furniture                  

 = 180 -150  = 30 legs

Each extra leg (4 th leg) belongs to a chair.

Therefore, the number of chairs in the restaurant = 30

So, number of stools = 50-30=20

For more on this topic: Solving without Simultaneous Equations

A cube is painted from all sides. It is then cut into 27 equal small cubes. How many cubes

• Have 1 side painted?
• Have 3 sides painted?

The cube is cut into 27 equal cubes of equal size that means it’s a 3x3x3 cube. Visualise the cube (have included 3x3x3 Rubix cube pic for reference)

a) Only the cubes at the centre of each face (that are located neither at corners nor along the edges) will have just one side painted.

In a 3 x 3 cube there is only one cube on each face which is located neither at corners nor along the edges.

There are 6 faces in any cube.

Therefore, 6 cubes have only one side painted.

b)The small cubes at the corners of the big cube have 3 sides painted.

There are 8 small corner cubes in the big cube.

Therefore, 8 cubes have 3 sides painted.

• Worksheet 1 - Rabbit and Chicken
• Introduction - Regions made by intersecting lines
• Intro Number of trees planted along a road

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Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics

• Original Article
• Published: 19 May 2009
• Volume 41 , pages 605–618, ( 2009 )

Cite this article

• Iliada Elia 1 , 2 ,
• Marja van den Heuvel-Panhuizen 2 , 3 &
• Angeliki Kolovou 2  

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Many researchers have investigated flexibility of strategies in various mathematical domains. This study investigates strategy use and strategy flexibility, as well as their relations with performance in non-routine problem solving. In this context, we propose and investigate two types of strategy flexibility, namely inter-task flexibility (changing strategies across problems) and intra-task flexibility (changing strategies within problems). Data were collected on three non-routine problems from 152 Dutch students in grade 4 (age 9–10) with high mathematics scores. Findings showed that students rarely applied heuristic strategies in solving the problems. Among these strategies, the trial-and-error strategy was found to have a general potential to lead to success. The two types of flexibility were not displayed to a large extent in students’ strategic behavior. However, on the one hand, students who showed inter-task strategy flexibility were more successful than students who persevered with the same strategy. On the other hand, contrary to our expectations, intra-task strategy flexibility did not support the students in reaching the correct answer. This stemmed from the construction of an incomplete mental representation of the problems by the students. Findings are discussed and suggestions for further research are made.

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Social Learning Theory—Albert Bandura

The use of cronbach’s alpha when developing and reporting research instruments in science education.

Keith S. Taber

Multiple Intelligences Theory—Howard Gardner

CITO (Central Institute for the Development of Tests) provides Dutch schools with standardized tests for different subjects and grade levels. One of the CITO Tests is the Student Monitoring Tests for Mathematics. The DLE Test (Didactic Age Equivalent Test) is a different instrument published by Eduforce that teachers can use to measure their students’ development in a particular subject.

The original versions of these problems have been developed for the World Class Tests. In 2004, Peter Pool and John Trelfall from the Assessment and Evaluation Unit, School of Education, University of Leeds who were involved in the development of these problems asked us to pilot them in the Netherlands.

The coding scheme was developed by two of the authors, Marja van den Heuvel-Panhuizen and Angeliki Kolovou, and our Freudenthal Institute colleague Arthur Bakker.

This control coding was done by Conny Bodin-Baarends who was involved in the data collection, but did not participate in the development of the coding scheme.

Altun, M., & Sezgin-Memnun, D. (2008). Mathematics teacher trainees’ skills and opinions on solving non-routine mathematical problems. Journal of Theory and Practice in Education, 4 (2), 213–238.

Google Scholar  

Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1–34). Mahwah, NJ: Lawrence Erlbaum Associates.

Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7 (1), 87–106. doi: 10.1016/S0959-4752(96)00012-6 .

Article   Google Scholar  

Bodin, A., Coutourier, R., & Gras, R. (2000). CHIC: Classification Hiérarchique Implicative et Cohésive-Version sous Windows—CHIC 1.2 . Rennes: Association pour la Recherche en Didactique des Mathématiques.

Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34 , 719–737. doi: 10.1080/00207390310001595401 .

Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58 , 45–75. doi: 10.1007/s10649-005-0808-x .

Charles, R., Lester, F., & O’Daffer, P. (1992). How to evaluate progress in problem solving . Reston, VA: NCTM.

De Bock, D., Verschaffel, L., & Janssens, D. (1998). The predominance of the linear model in secondary school students’ solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathematics, 35 , 65–83. doi: 10.1023/A:1003151011999 .

De Corte, E. (2007). Learning from instruction: The case of mathematics. Learning Inquiry, 1 , 19–30. doi: 10.1007/s11519-007-0002-4 .

Demetriou, A. (2004). Mind intelligence and development: A cognitive, differential, and developmental theory of intelligence. In A. Demetriou & A. Raftopoulos (Eds.), Developmental change: Theories, models and measurement (pp. 21–73). Cambridge, UK: Cambridge University Press.

Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in the Netherlands. ZDM-The International Journal on Mathematics Education, 39 , 405–418. doi: 10.1007/s11858-007-0043-2 .

Elia, I., Panaoura, A., Gagatsis, A., Gravvani, K., & Spyrou, P. (2008). Exploring different aspects of the understanding of function: Toward a four-facet model. Canadian Journal of Science, Mathematics and Technology Education , 8 (1), 49–69.

Follmer, R. (2000). Reading, mathematics and problem solving: The effects of direct instruction in the development of fourth grade students’ strategic reading and problem solving approaches to textbased, nonroutine mathematical problems . Unpublished doctoral thesis, University of Widener, Chester, PA.

Freudenthal, H. (1991). Revisiting mathematics education . Dordrecht: Reidel.

Gras, R., Suzuki, E., Guillet, F., & Spagnolo, F. (Eds.). (2008). Statistical implicative analysis: Theory and applications . Heidelberg: Springer-Verlag.

Jonassen, J. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48 (4), 63–85. doi: 10.1007/BF02300500 .

Kaizer, C., & Shore, B. (1995). Strategy flexibility in more and less competent students on mathematical word problems. Creativity Research Journal, 8 (1), 77–82. doi: 10.1207/s15326934crj0801_6 .

Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8 , 163–180. doi: 10.2307/748518 .

Kolovou, A., Van den Heuvel-Panhuizen, M., & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks-A needle in a haystack. Mediterranean Journal for Research in Mathematics Education, 8 (2), 31–67.

Krems, J. F. (1995). Cognitive flexibility and complex problem solving. In P. A. Frensch & J. Funke (Eds.), Complex problem solving: The European perspective (pp. 201–218). Hillsdale, NJ: Lawrence Erlbaum Associates.

Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children . Chicago: University of Chicago Press.

Martinsen, O., & Kaufmann, G. (1991). Effect of imagery, strategy and individual differences in solving insight problems. Scandinavian Journal of Educational Research, 35 (1), 69–76. doi: 10.1080/0031383910350105 .

Mayer, R. E. (1985). Implications of cognitive psychology for instruction in mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving (pp. 123–145). Hillsdale, NJ: Lawrence Erlbaum.

Muir, T., & Beswick, K. (2005). Where did I go wrong? Students’ success at various stages of the problem-solving process. Accessed August 13, 2008 from http://www.merga.net.au/publications/counter.php?pub=pub_conf&id=143 .

Pantziara, M., Gagatsis, A., & Elia, I. (in press). Using diagrams as tools for the solution of non-routine mathematical problems. Educational Studies in Mathematics .

Pape, S. J., & Wang, C. (2003). Middle school children’s strategic behavior: Classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31 , 419–449. doi: 10.1023/A:1025710707285 .

Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Garden City: Doubleday.

Schoenfeld, A. (1985). Mathematical problem solving . San Diego, CA: Academic Press.

Schoenfeld, A. H. (1983). The wild, wild, wild, wild, wild world of problem solving: A review of sorts. For the Learning of Mathematics, 3 , 40–47.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: MacMillan.

Shore, B. M., & Kanevsky, L. S. (1993). Thinking processes: Being and becoming gifted. In K. A. Heller, F. J. Monks, & A. H. Passow (Eds.), International handbook of research on giftedness and talent (pp. 131–145). Oxford, England: Pergamon.

Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM. Zentralblatt für Didaktik der Mathematik, 29 (3), 75–80. doi: 10.1007/s11858-997-0003-x .

Stacey, K. (1991). The effects on student’s problem solving behaviour of long-term teaching through a problem solving approach. In F. Furinghetti (Ed.), Proceedings of the 15th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 278–285). Assisi: PME.

Stanic, G., & Kilpatrick, J. (1988). Historical perspectives on problem solving in the mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). Reston, VA: NCTM.

Torbeyns, J., Desmedt, B., Ghesquière, P., & Verschaffel, L. (2009). Solving subtractions adaptively by means of indirect addition: Influence of task, subject, and instructional factors. Mediterranean Journal for Research in Mathematics Education , 8 (2), 1–29.

Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1 (3), 195–229. doi: 10.1207/s15327833mtl0103_2 .

Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (in press). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education .

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Iliada Elia

Freudenthal Institute for Science and Mathematics Education, Utrecht University, Aïdadreef 12, 3561 GE, Utrecht, The Netherlands

Iliada Elia, Marja van den Heuvel-Panhuizen & Angeliki Kolovou

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Elia, I., van den Heuvel-Panhuizen, M. & Kolovou, A. Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education 41 , 605–618 (2009). https://doi.org/10.1007/s11858-009-0184-6

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Accepted : 23 April 2009

Published : 19 May 2009

Issue Date : October 2009

DOI : https://doi.org/10.1007/s11858-009-0184-6

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KS1 and KS2 Maths – Problem solving

• Author: Mike Askew
• Main Subject: CPD
• Subject: Maths
• Date Posted: 20 June 2012

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If children use well worn techniques to solve problems without understanding or modelling the context, their maths skills won't fully evolve

Children, from birth, are proficient problem solvers. By the age of two or three they have solved what are probably life’s two biggest problems - how to walk and how to talk. As they get older they solve practical problems, such as sharing a bag of sweets fairly with others, long before they’ve heard of division. In this article, I look at how we can build on this natural propensity to solve problems in teaching mathematics.

Routine and non-routine problems

Routine problems are problems children know how to solve based on their previous experiences. The sort of thinking required by routine problems can be described as reproductive: the child only needs to recall or reproduce a procedure or method they have previously learnt. A problem like ‘Apples’, for example (see below), is likely to be a routine problem for most children at the upper end of primary school; they know to multiply the two numbers together without having to think deeply about what operation to use.

• Apples on a supermarket shelf are in bags of eight. • If Jane buys six bags, how many apples is that?

In contrast, non-routine problems are where the learner does not immediately have a solution tucked under his belt. The problem solver has to put some effort into understanding the problem and creating, rather than recalling, a solution strategy. Non-routine problems engage learners in productive thinking.

We often think of non-routine problems as needing to be unusual or not having, to us as adults, an immediately obvious method of solution. ‘Stamps’ is typical of this type of non-routine problem.

• Clearing out a desk draw I found a collection of 5p and 6p stamps. • I have a parcel to post that needs 58p worth of stamps on it. • Can I create this exactly using the stamps I found? • If so, is there more than one way of doing this?

In choosing problems to work with, we need to decide whether or not we think a problem will be routine or non-routine for the particular children working on it. In the rest of this article, the problems chosen are being treated as though they are non-routine problems for the children working on them. That’s not to say that I don’t think routine problems have a place in the curriculum - they do. Here, however, I want to deal with some of the issues around teaching and learning non-routine problems.

The importance of context

• Four hungry girls share three pizzas equally. • Eight hungry boys share six pizzas equally. • Does each girl get more pizza than each boy, less or the same?

As a routine problem, the ‘story’ of pizzas and hungry children doesn’t serve any real purpose: children quickly learn to disregard the context, to strip out the mathematics and to work some procedure. The problem could just as easily have been put in the context of builders sharing bricks and many learners would happily say each builder would get 3/4 of a brick, without stopping to question the near impossibility of sharing out bricks.

We can, however, treat ‘Pizzas’ as a non-routine problem and use it to introduce children to thinking about fractions and equivalences. The context of hungry children and pizzas then becomes important. It is not chosen simply to be window-dressing for a fraction calculation. Nor are pizzas chosen because children are intrinsically motivated by food, making the unpalatable topic of fractions digestible. No, the context s chosen because children know about fair shares and slicing up pizzas - they can solve this problem without any formal knowledge of fractions. As the researcher Terezhina Nunes once pointed out, young children would not be able to solve the ‘bald’ calculation 3 divided by 4 but, “show me four young children who, given three bars of chocolate to share out fairly, hand the bars back saying ‘it can’t be done.”

Children have ‘action schemas’ for solving problem like ‘Pizzas’ - they can find ways to solve this with objects, pictures, diagrams and, eventually, symbols. Teaching can then build on the children’s informal solutions to draw out the formal mathematics of fractions. From being one of 20 ‘problems’ on a worksheet to complete in a lesson, ‘Pizzas’ can become a ‘rich task’ taking up the best part of a lesson, if children work on it in pairs and carefully selected solutions are then shared with the class.

Creating mathematical models

Part of the productive thinking in working on rich, non-routine problems requires children to create mathematical models, and we can teach to support this.

• At the supermarket Myprice, milk costs £1.08 per litre. • This is 7 pence less per litre than milk costs at Locost. • How much does 5 litres of milk cost at Locost?

What is missing from this approach is attention to setting up an appropriate model of the problem. Ultimately this could be a mental model of the problem context, but it helps initially to encourage children to put something on paper that can be shared and discussed. In problems involving quantities, like ‘Milk’, simple bar diagrams can help children create the appropriate model. These help children examine the relationships between the quantities (as opposed to simply fixing on specific numbers and keywords).

Setting up a diagrammatic model begins with creating a representation of what is known in the situation. In this example, we know milk at Myprice costs £1.08, so a diagram for this would look like:

MYPRICE £1.08

This provides the basis for talking about what the picture for the price of milk at Locost is going to be. Will the bar be longer or shorter? Where is the bar for the 7 pence to be drawn?

Two different models can be set up and children asked to describe the relationship between the prices at the two supermarkets, to see which diagram fits with the information in the problem. If the diagram for the price at Locost is shorter by 7, then two statements can be made:

MYPRICE £1.08p LOCOST     7p

• Myprice milk costs 7 pence more than milk at Locost.

• Locost milk costs 7 pence less than milk at Myprice.

In comparison, making the bar for milk at Locost longer by 7 gives different comparative statements:

MYPRICE £1.08p 7p LOCOST    

• Myprice milk costs 7 pence less than milk at Locost.

• Locost milk costs 7 pence more than milk at Myprice.

Children can then talk about which of these situations fits with the wording in the problem.

Having established that Locost milk must be £1.15 a litre, children can go on to produce the bar diagram model for this.

Supporting non-routine problem solving

Where the problems were played out as non-routine, three factors identified are worth noting. First, in choosing the tasks, the teachers made sure they would build on learners’ prior knowledge - as I suggest a problem like ‘Pizzas’ can. Second, in contrast to focusing on getting the answer, the researchers observed what they called ‘sustained pressure for explanation and meaning’. In other words, the teachers pressed for children to explain what and why they were doing what they were doing rather than simply focusing on whether or not they had got the correct answer. Third, the amount of time children were allowed to work on the problem was neither too long or too short: children need enough time to ‘get into’ a problem, but too much time can lead to a loss of engagement.

Share good practice

Gather together a collection of problems covering all the years of education in your school (or ask teachers to each contribute two or three problems).

Working together in small groups, teachers sort the problems into three groups:

1. Problems they think would be routine for the children they teach 2. Problems they think would be non-routine for their children 3. Problems they think would be much too difficult for their age group

Everyone agrees to try out a problem from group 2 with their class. Discuss how too much focus on getting the answer can reduce the challenge and stress the importance of pressing children to explain their working. At a subsequent meeting, people report back, focusing in particular on strategies they used to keep the problem solving non-routine.

About the author

Mike Askew is Professor of Primary Education at Monash University, Melbourne. Until recently, he was Professor of Mathematics Education at King’s College, University and Director of BEAM.

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Grade 5 Mathematics Module: Solving Routine and Non-routine Problems Involving the Circumference of a Circle

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

Hi, Mathletes! In this module, you will learn how to solve routine and nonroutine problems involving the circumference of a circle. Routine problems use clear procedures. You may follow a step-by-step process to solve them. In contrast, non-routine problems use procedures that are not immediately clear. Such problems challenge our thinking skills. They may be solved using different strategies.

After going through this module, you are expected to:

• solve routine and non-routine problems involving the circumference of circle.

Grade 5 Mathematics Quarter 3 Self-Learning Module: Solving Routine and Non-routine Problems Involving the Circumference of a Circle

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Classification of Students' Non-Routine Problem Solving Skills

A A A Sita Pramayudi 1 , IGP Sudiarta 1 and IWP Astawa 1

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1503 , International Conference on Mathematics and Natural Sciences 2019 (IConMNS 2019) 30-31 August 2019, Bali, Indonesia Citation A A A Sita Pramayudi et al 2020 J. Phys.: Conf. Ser. 1503 012016 DOI 10.1088/1742-6596/1503/1/012016

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1 Mathematics Department, Faculty of Mathematics Natural Science Universitas Pendidikan Ganesha, Bali-Indonesia, 81116

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Non-routine mathematical problems are complex problems that require a level of creativity and uniqueness in solving them. Classification students' characteristics of solving non-routine problems have not been many researchers who provide an overview. This study aims to classify the characteristics of students' problem solving skills. This type of research is a qualitative study involving five students of class VIII at SMP Negeri 1 Kintamani. Five students were selected through a purposive sampling technique on the condition that students of class VIII have high, medium and low mathematical skills. Data regarding non-routine mathematical problem solving students are collected through problem solving tests and supported by interview tests to obtain a picture of students' ability to understand the questions along with an understanding of the answers that have been done. Data were analyzed with data reduction, data presentation, and data verification steps. Data that has been verified are analyzed using the constant comparison method. Characteristics of non-routine mathematical problem solving students can be classified into 4 levels, namely Level 1 (students' understanding of problems along with mathematical problem solving is very lacking), Level 2 (Students' understanding of problems less and students' problem solving is lacking but able to plan problem solving), Level 3 (students 'understanding of problems takes a long time and students' problem solving is good), and Level 4 (students 'understanding of problems is good and students' problem solving is very good). Classification is obtained based on reference to problem solving according to Polya.

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