Document Type : Research Article


Methods of Teaching Mathematics - College of Education for Pure Sciences Ibn Al Haytham - University of Baghdad - Iraq


The Research aim is to determine the essence of the relationship between students' mathematical representations in high school and their mathematical ability.
The following null hypotheses were established in order to achieve the research objectives:

There is no statistically significant difference at the level of (0.05) between the average true performance and the average hypothetical performance of third-grade intermediate students in the General Directorate of Education in Baghdad / Rusafa 1/, Al-Rashdiyah district, on the multiple mathematical representations test prepared for the aforementioned purpose and according to the gender variable.
There is no statistically significant difference at the level of (0.05) between the average true performance and the average hypothetical performance of third-grade intermediate students in the General Directorate of Education in Baghdad / Rusafa 1/, Al-Rashdiyah district, on the mathematical ability test prepared for the aforementioned purpose, according to the gender variable.
There is no correlation relationship at the level of significance (0.05) between Multiple mathematical representations and Mathematics ability among third-grade middle school students in the General Directorate of Education in Baghdad / Rusafa 1/ district AL-Rashidiya, according to the gender variable.

After identifying the research community, which represented high school students in the General Directorate of Education in Baghdad /Rusafa 1/, Al-Rashidiya district, third-grade intermediate students were determined  in order to conduct the field study.Thus, the size of the research sample reached (269) male and female students (134) male and (135) female students. For the purpose of collecting data for this research, two tests were constructed:

Test of multiple mathematical representations according to the Lesch model (Lesh):in its finalized form of (25 ) A test paragraph with (21) of the objective type and (4) of the Assay type.
Mathematical Ability Test: It consists of (28) test items of the objective type.

Then, appropriate statistical analyzes were conducted for the two test items, and to verify the psychometric properties of them. After adopting the statistical tools for analyzing the results of applying the two tests, the results reached showed that:

The third-grade intermediate students have the research sample of multiple mathematical representations.
The superiority of females over males in the multiple mathematical representations test.
Third-grade students possessing the average of the research sample, the mathematical ability.
Females surpass males in the mathematically ability test.
There is a positive and strong correlational relationship among students between multiple mathematical representations and ability They have a positive relationship.

In light of the research results, several recommendations were made, including:

Curriculum designers in the Ministry of Education must emphasize the multiple mathematical representations of students when building and developing mathematics curricula, as well as adding exercises and heritage activities that develop their  mathematical abilities.
Exposing students to various practical and life situations that require them to use mathematical representations  and  to employ their mathematical abilities.
Raising the awareness of mathematics teachers of the importance of multiple mathematical representations and the mathematical ability of students as one of the important goals of teaching mathematics advocated by the National Council of Mathematics Teachers( NCTM, 2000).

According to the results, several proposals were suggested, including:

Conduct  a similar study for the elementary and preparatory stages, to see if they possess  Multiple mathematical representations and types of Mathematical ability.
Conduct a similar analysis in other governorates for the same grade and compare the findings.
Conduct experimental studies to employ some software to employ various mathematical representations that will help students improve their mathematical abilities.


Main Subjects

  1. Ibrahim, Muhammad Mahmoud Muhammad, (2016): The effect of using mathematical representations on developing problem-solving skills of fourth-grade students and their motivation towards mathematics, (published master's thesis), Al-Quds University, Palestine.
  2. Badawi, Ramadan Massad, (2019): Strategies in Teaching and Evaluating Mathematics Learning, 2nd Edition, Dar Al-Fikr, Amman.
  3. Al-Toudari, Awad Hussein Muhammad, (1999): The effectiveness of private computer teaching in studying mathematics students in the College of Education and its impact on developing their mathematical ability, (unpublished master's thesis), College of Education, Assiut University, Egypt.
  4. Al-Harbi, Muhammad Swaid Ayed. (2014): The relationship between multiple mathematical representations and solving verbal problems for sixth grade students, (published master's thesis), Umm Al-Qura University, College of Education, Kingdom of Saudi Arabia.
  5. Al-Zuhairi, Haider Abdul-Karim Mohsen, and Al-Naeli, Muhammad Murid Arak. (2016): The Effect of Mathematical Representations on Fifth Grade Primary Pupils' Achievement in Mathematics and Their Visual Thinking, Journal of the College of Basic Education for Educational and Human Sciences, University of Babylon, No. 30, pp.
  6. Syed, Imam Mustafa, (1979): Mathematical Ability and its Relation to Achievement in Modern Mathematics, (Unpublished Master Thesis), Faculty of Education, Assiut University, Cairo.
  7. Shaheen, Murshed Yusef, (2011): The Impact of Using Multiple Representations in Teaching Algebra on Seventh Grade Students' Achievement, (published master's thesis), Birzeit University, Palestine.
  8. Al-Sheikh, Suleiman Al-Khudary, (1990): Individual Differences in Intelligence, Dar Al-Thaqafa for Printing and Publishing, Cairo.
  9. Abdullah, Hussam Obaid Abd Al-Abbas, (2018): The mathematical ability of middle school mathematics teachers and its relationship to the creative thinking of their students, (unpublished master's thesis), University of Baghdad, College of Education, Ibn Al-Haytham, Iraq.
  10. Al-Absi, Muhammad Mustafa, (2009): Games and Thinking in Mathematics, 1st Edition, Dar Al Masirah for Publishing, Distribution and Printing, Amman.
  11. Al-Otaibi, Khalid bin Nahis Muhammad, (2001): The effectiveness of a proposed program for developing inferential thinking among a sample of high school students in Riyadh, (published master's thesis), College of Education, King Saud University, Saudi Arabia.
  12. Afifi, Ahmed Mahmoud. (2008): The effect of using metacognition strategy on achievement and development of mathematical communication skills among first-grade middle school students, Journal of Studies in Curricula and Teaching Methods, Egypt, Issue (141), pp. 14-68.
  13. Freeh, Ghosoun Rasheed, (2011): The Mathematical Ability of the Students of Teacher Education Institutes, (Unpublished Master Thesis), University of Baghdad, College of Education, Ibn Al-Haytham, Iraq.
  14. Al-Qubati, Abdul Salam Muhammad Saeed, (1993): Mathematical ability and its relationship to logical thinking and achievement, (published master's thesis), Yarmouk University, Irbid.
  15. Mahmoud, Ibrahim Wajih, (1985): Mental Abilities, 3rd Edition, Dar Al Maaref, Cairo, Egypt.
  16. Al-Mutreb, Khaled Saad, Bayoumi, Yasser Abdel-Rahim (2012): The effect of teaching a unit developed in light of school mathematics standards on developing mathematical abilities among students of the Department of Special Education in the College of Education, King Faisal University, Journal of the College of Education - Kafr El Sheikh University, Issue 5).
  17. Moawad, Khalil Mikhail, (1983): The Abilities and Characteristics of the Talented, Alexandria, University of Thought House.
  18. Johnson, Elizabeth Lee. (2017): " A New Look at the Representations for Mathematical Concepts: Expanding on Lash's Model of Representations of Mathematical Concepts.
  19. Kattou, M. , Kontoyianni, K., Pitta-Pantazi, D. & Christou, C.(2012): Connecting  mathematical creativity to  mathematical ability, Department of Education, University of Cyprus, P.O. Box 20537, 1678.
  20. Lesh, R., (1987): The evolution of problem representation in the presence of powerful conceptual amplifiers. In C. Janvier (Ed), Problem of representation in teaching and learning mathematics pp.174- 196. Hilis-dale, NJ: Lawrence ErIbaum Associates
  21. Lesh, R., Post, T, & Behr M. (1987): Representations and translations among representation in mathematics learning and problem solving. Problems of representation in the teaching and learning of mathematics, 21, 33-40.
  22. National Council of Teachers of Mathematics (2000): Principles and standards for school mathematics. Reston, VA, NCTM.