By B. Yushau, M. R. Alaimia & M. H. Omar Mathematical Sciences Department

1. The problems of “Word Problems” in Mathematics Classroom for Students acquiring English as Second Language By B. Yushau, M. R. Alaimia & M. H. Omar Mathematical Sciences Department KFUPM, Dhahran, Saudi Arabia

2. Contents • Background • Why word problems • Literature review • Aim of the study • Methodology • The Questions of the study • Results and Discussion • Conclusion and Recommendation

3. Introduction and Background In many classrooms around the world, in both developed and developing countries, many students are learning mathematics in their second or third language (Austin & Howson 1979; Ellerton & Clarkson 1996). • Communicating mathematically in these classes is by • means of managing the interaction between the following: • Ordinary English (OE) and mathematical English (ME). • Formal and informal mathematics language. • Procedural and conceptual discourses. • Learners’ main language and the LoLT. (Setati, 2003)

4. Introduction and Background • Most of the empirical studies on bilingual attempted to find the relationship and interaction between L1 (first language) and L2 (second language) from both social and cognitive domain. • Studies have shown that the task of acquiring language of instruction, and at the same time struggling to learn mathematics in the new language is not an easy task. • Most of the findings indicated that students achievement in mathematics are higher if taught in their native language. • Similarly, Conceptual understand of mathematics seems higher in students that learn in their native language

5. In terms of Classroom Discourse, both students and teachers discuss more freely in their native language than in a different Language of instruction • L2 students are not facing much difficulty in general English. However, they face greater difficulties with technical mathematical Discourse (Barton & Barton, 2003) • Compared to natives, L2 students experience a 10% disadvantage in overall performance through lack of understanding mathematical text (Barton & Barton, 2003) • L2 students unjustifiably rely on symbolic modes to make • up for textual disadvantages (Barton & Barton, 2003)

6. Why Study Word Problems? Word Problems is language laden most of the students are bilingual having minimal English proficiency. . Now that English is gradually becoming the language of instruction at university level in Middle East Then it became imperative to investigate how these student are coping with the language issue particularly in Word Problems

7. Why Study Word Problems? Word Problems are commonly used by teacher for one of the following reason: • Application of mathematics in common real world settings. • Sharpening of students problem solving skills to new • situations. . • Bridging the gap between mathematics in the classroom • and mathematics for the real world. Word Problems are known for their difficulty. Students generally find them difficult regardless of their language proficiency.

8. Literature Review “Word Problems” have different meaning to different people. For a review of different definition and framework of Word Problems, see Craig (2001) . In this study, we define word problem in contrast to other algebra problems That is: a problem presented fully or partially in English language, and some command of English language is required for understand the problem.

9. Literature Review A review of literature revealed that intensive studies have been done on Word Problems This include issues related to the: • Complexity of Word Problems . • Classification of Word Problems • Strategies students used in solving Word Problems • Difficulties students face in solving Word Problems. etc

10. Literature Review However, 1) All these studies were largely carried out in primary and secondary schools level. . 2) Not much is known with regards to the university students 3) In particular, not much is documented with regards to the bilingual Arab university students.

11. Aims of the Study The study aims at investigating the difficulty bilingual Arab students, who are acquiring English as a second language at the same time learning mathematics in English, faced while solving Word Problems. Specifically, we intend to know: What are the problem solving strategies of bilingual Arab students in solving Word Problems? What language related problems bilingual Arab students face in solving Word Problems?

12. Aims of the Study How are these problems if any hindering them in understanding mathematics? How do these affect their achievement on assessments in mathematics? How are the performance of the student in comparison to other symbolic problems? Are the findings different from what is available in the literature?

13. Methodology Two set of Exams were used for data collection, and Two set of students were involved in this study • Math 001, consisting of 48/251 students (20%) • First Preparatory Year Mathematics 2. Math 002, consisting of 251/828 students (30%) • Second Preparatory Year Mathematics. • Four questions were selected from each exam • The questions were not premeditated • The Exams are all multiple choice

14. Methodology 1) The dichotomous (right vs wrong) grading were done by computer 2) While a hand grading was done to the sample polychotomously (wrong, partially correct to fully correct). The grading was done carefully with the aim of answering the research question stated earlier. Our areas of concentration include: • Students attempt of the question • Putting the appropriate graph or equation • The algebraic processes followed, and • Interpretation of the obtained results.

15. Methodology How many students attempted the questions? How many students did not? How many students among those attempted got them right? How many among these did not? What are the strategies of the students who got it right? What are the mistakes of students who got it wrong? Compared to the other symbolic questions, what are the students performance?

16. The Questions –Math 001 1. The coefficient of in the product is equal to 2. The sum of all solutions of the equation is equal to 3. If the expression is written in the form then ab is equal to 4. Three students decided to share the cost of a car. By bringing in an additional student, they can reduce the cost of each students by 400 Saudi Riyals. The total cost of the car is

17. The Questions –Math 002 1. The length of an arc that subtends a central angle of in a circle of radius 40 ft is 2. If the hypotenuse of a triangle is 10cm, then the perimeter of the triangle is equal to 3. If a car with a wheel of radius 40cm is moving with a speed of 120 kilometers per hour, then the angular speed of the wheel of the car in radian per minutes is 4. Two buildings are 240 meters apart. The angle of elevation from the top of the shorter building to the top of the taller building is . If the shorter building is 8 meters high, then the taller building is

18. ResultsTable 1.Number Of Students Attempting Question or Showed Work

19. ResultsTable 2. Percent of Students with different levels of Correct Solutions to problems

20. Results The following are the preliminary findings in this study: 1. Bilingual Arabs students do not seem to have much difficulty with mathematics problems that involves mathematical English such coefficient and sum This is unlike monolingual, they also do not have much problem with “Words which occur in both OE and ME, but which have a different meaning in ME from that of their meaning in OE, e.g. the words “Revolution” and “Product”. This is likely because they are not aware of the other meaning. Therefore, the mastery is on the ME.

21. Results 2. The performance of the students in Word Problems is Below average compared to the clear algebraic problems. 3. The Word Problems that students have difficulty is indeed difficult either due to linguistic or cognitive demands in the question. 4. The inclusion of a single unfamiliar word can destabilize the meaning of the question. Example “Reciprocal”, etc. 5. The variation between the dichotomous grading and the polychotomous grading is wider with pure Word Problems.

22. Results 6. The tendency of guessing is more in word problems compared to pure algebraic problems. 7. The number of students who did not attempt question are more in worded problem compared to pure algebraic problems especially for MATH 001 8. Although students have problems with Word Problems, their Algebraic skills also need to be sharpen.

23. Concluding Remarks: • Findings are pointing to the fact that language factors have serious ramification for mathematics education • There are language factors that affect students understanding and achievement in mathematics. • There is a need to pay special attention to these language constraints of our students while teaching mathematics especially to bilingual students. • Although students have problems with word problems, their algebraic skills also need to be sharpened.

24. Concluding Remarks: • Deeper studies are required to investigate the language issues among bilingual Arab university students. • In particular, the problem of “Word Problems” need further investigation. • A premeditated investigation should be carried out with well prepared questions that will target specific research questions.

25. Many Thanks for Listening