International Conference on Mathematics Textbook Research and Development 2014

PROBLEM SOLVING HEURISTICS IN MIDDLE SCHOOL MATHEMATICS TEXTBOOKS IN SAUDI ARABIA

Alafaleq and Lianghuo Fan

27 April 2020

Presentation Overview

• • • • • • •

Educational system in Saudi Arabia Mathematics textbooks in Saudi Arabia The study aims Problem solving heuristics Methodology The results Summary and conclusion

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Saudi Arabia

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Mathematics textbooks in Saudi Arabia

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



In Saudi Arabia, there is a considerable attention toward improving Mathematics and science textbooks after the Saudi Arabia first participation in the third Trends in International Mathematics and Science Study (TIMSS).



The disappointed test results of students' performance in (TIMSS) were a high alert to rise the quality of education particularly in mathematics.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



policy makers in the Ministry of Education have emphasized reforming textbooks alongside many improvements in Mathematics education since textbooks content mostly reflect what happened in the classrooms.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



After many stages of reform and improvement, the first edition of the new mathematics textbooks series was released in 2007 for primary schools and middle schools , and in 2008 for secondary schools.



In 2010 the new series has been adopted in mathematics classrooms by all Saudi schools



The whole series was developed and revised by the Ministry of Education.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

The study aims

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

As all teachers in Saudi Arabia are required to adhere to the textbook as a main resource for teaching this study aims to: 1) Examine to what extent the new textbook in Saudi Arabia reflect the mathematics curriculum goals in problem solving. 2) Address the following question: how the new national middle school mathematics textbooks in Saudi Arabia represent problem solving heuristics?

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

problem solving heuristics

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

•

A heuristic is “a general suggestion or strategy, independent of any particular topic or subject matter, that helps problem solvers approach and understand a problem and efficiently marshall their resources to solve it” (p. 23). Schoenfeld (1979

) Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Martinez (1998) stated heuristics "is a strategy that is powerful and general, but not absolutely guaranteed to work.

Heuristics are crucial because they are the tools by which problems are solved" Heuristics are tools that may make solving problems easer

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

The following table describes heuristics that are represented in Saudi national textbooks.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Guess and check Look for patterns Work backwards Draw a diagram Make a list Simplify the problem Act in out Restate the problem Use equations Use a model Use Venn diagram Logical reasoning Draw a picture Think of a related problem Make a reasonable guess of the answer, and check the result against the conditions of the problem to see if it is the answer.

Observe common characteristics, variations, or differences about numbers, shapes, etc in the problems to find a solution.

Attack the problem from the outcomes or conclusions backwards to find what conditions the problem solver eventually need.

Draw a graph based on the information to visualize the problem.

Construct on organized list containing all the possibilities for a given situation and find the answer.

Change the complex numbers or situations in the problems into simpler ones without altering the problem mathematically.

Use people, objects to physically show what is exactly described in the problem.

Approach the problem from a different angle.

Use the letters as variables to represent unknown quantities.

Translate the problem in different way by Using lines, points.

Represent the problem by using Venn diagram.

Reasoning from one or more true statements.

Drawing figures or graphs.

Recall related problem solved before to solve the recent problem.

mathematics textbooks in Saudi Arabia 27 April 2020

METHODOLOGY

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Textbook analysis :



In this study, we analysed the student books as each textbook consists of student book and work book.



Analysis procedure was based on problem solving heuristics introduced in the main text, e.g., in examples, due to teachers using them in class discourses or groups work.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Coding procedure



: We assigned the units that contain mathematical problems.



We categorised the heuristics we had found.



We measured the reliability of coding, by inviting external coder. The Inter-rater Agreement according to the Intra-class Correlation Coefficient (ICC) was 0.98 on heuristics in general and 0.97 on heuristics existence in each book thus, this result indicates a high agreement in coding

.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

THE STUDY RESULTS

The results from the coding revealed that the Saudi middle school textbooks represented a variety of problem solving heuristics and the results can be seen in Figure 1.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



Fourteen different heuristics are introduced in the three books.



The majority of problems in the three textbooks were solved based on Polya's four stages.



The data revealed that grade 8 textbook represents the highest number (12) of the (14) heuristics, followed by grade7 (11) heuristics and the lowest number was coded in grade 9 (9) heuristics.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



"guess and check" and "look for a pattern" are nearly the most frequently used heuristics represented in the 7 th and 8 th grade textbooks, whereas these heuristics seem to be less present in grade 9 textbook.

The result is interesting in comparison with what Fan and Zhu found in their study, namely, "guess and check" and "look for a pattern" were the least frequently used heuristics in mathematics textbooks in China, Singapore and USA at the lower secondary grade level (Fan & Zhu, 2007)

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



In the grade 7 textbook, we can find that the most frequent heuristic is "think of a related problem", whereas in the grade 9 textbook, there is no "think of a related problem" heuristic at all.



The numbers of "logical reasoning" and "use equations" heuristics in the three books are increased gradually from the grade 7 to 9 textbooks.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



"use equations" is the major problem solving heuristic represented in the grade 9 textbook.

Polya (1973) once explained that using equations is like “translation from one language into another and the difficulties which we may have in setting up equations are difficulties of translation”

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



There are 11 and 9 examples using the "work back word" heuristic in the grade 7 and 9 textbooks respectively.

Charles and Lester (1984)’s study found that using a verity of heuristics like logical reasoning, work back word and make a list for teaching Grade 5 and 7 students improved students' ability to understand the problem and choose the right solution to

solve the problem.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



"use a model", " use Venn diagram" and "make a systemic list" are the least frequently heuristics used in both grade 7 and 9 textbooks, whereas these heuristics are represented frequently in the grade 8 textbook.

Fan and Zhu (2007)’s study reported that "act it out" and "use a model" were among the four least heuristics presented in China, Singapore and USA textbooks. It seems worth further investigation on whether using "act it out" and "use a model" are more appropriate for students at certain levels with certain backgrounds

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Most heuristics in the three textbooks are introduced and labelled as special topics, which reflects the textbooks authors' vision of focusing on heuristics as a tool to solve problems.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Summary and conclusion

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



The results to a large degree indicate how problems solving is being taught in Saudi classrooms and it is clear that problem solving heuristics get a very high attention in middle schools textbooks



As the majority of examples were solved by one heuristic, we suggest it will be helpful when such problems are solved by two or more heuristics, when it is appropriate, so the students can learn from different solutions for the same problem.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



The frequency of using some types of heuristics was low in some textbooks whereas, the frequency of these types was high in other textbooks.



It is necessary for textbooks developers and mathematics educators to consider heuristics' distribution to the students at this level.

in the three textbooks and reconstruct these heuristic regarding the usefulness of these heuristics

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020



The three textbooks represent and label problem solving heuristics as specific topics and that might lead teachers and students to treat these heuristics separately.



It would be beneficial to consolidate the heuristics with other topics to help students to tackle the problem better.

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020

Problem solving heuristics in middle school mathematics textbooks in Saudi Arabia 27 April 2020