Short summary of the previous chapters

In the previous six chapters I have discussed all independent variables that might possibly influence the hereby-motivational study.

The first chapter is dedicated to three issues: the gender issue of learning mathematics in the Israeli junior high school, facts about educational achievements of the various sub-populations in Israel, and a survey of the theoretical part of the work.

In the second chapter I have introduced the reader to the Israeli education system regarding the achievement gaps among different sectors included in it. These gaps can be divided to four main groups:

1. Between children of well off families, learning in good schools, and children learning in peripheral schools, whose families belong to a lower SES (e.g.

Assenheim, 31.8.2000; Ayalon, 1994, 1995; Ayalon & Yogev, 1997;

Birenbaum & Kraemer, 1995; Kashti, 1998; Suessapel, 1997);

2. Between Jews and Arabs;

3. Between Jews belonging to different ethnic groups (e.g. Ayalon, 1994, 1995;

Ayalon & Yogev, 1997; Sa’ar, 10.7.2002; Shachar, Ilil, 16.6.2002a;

Shachar & Saban, 9.5.2002; Statistics, Israel, 1999a, table 22.22);

4. Between boys and girls;

5. Between religious and non-religious schools 6. Between single-sex and mixed-sex classes;

I also described the demands expected from a high school graduate that influence the teaching, examining, tracking (Barak and Waks, 1997; Sa’ar, 10.7.2002), and dropout resulting from it.

The third chapter has dealt with the different aspects of mathematics and gender.

Starting with the description of gender math differences in participation and achievements in a variety of countries and cultures, it proceeds to the Israeli situation.

The second part of this chapter describes the connections between different

independent variables, such as age, and dependent ones, such as attributions to success and failure or aspirations level, and math gender differences.

The fourth chapter deals specifically with Israeli minority girls and their achievements in mathematics and science. There is a description of the main minority groups:

Arabic girls, with a special focus on Muslim, Christian, and Druses, and religious Jewish girls, including Orthodox and Ultra-Orthodox girls. A more detailed summary is given of Muslim girls, who belong to the largest minority non-Jewish Israeli group (about 90% of the Israeli Arabs are Muslim), and Orthodox girls who, unlike Ultra-Orthodox ones learn the same subjects in math and science as pupils of the general education system, and take the same matriculation examinations as well.

Chapter 5 discusses the single-sex class in general and in Israel in particular. It summarizes research findings about the advantages of single- versus mixed-sex classes in different places, subject matters, under different circumstances, and along different historical times.

Chapter 6 concentrates on the variety of motivational components that play a substantial role both in the learning process and in students’ achievements. It examines the different definitions of motivation, the diversity of motivation categories, potential correlations between personality characteristics and the different kinds of motivation, and the influence of many variables – such as the level of intelligence, culture, gender, age – on the 4 main different kinds of motivation:

extrinsic- versus intrinsic- and approach- versus avoidance motivation. In addition, the concepts of values, interest, effort, and competence regarding mathematical learning have been widely examined. Chapter 6 also introduces the reader with the dependent variables: the motivational components that influence educational results regarding mathematics among 12-16-year-old Israeli students. It describes the motivational orientations known from the literature, with special focus on learning-, achievement-, and avoidance motivation; theories of achievement and expectancies in general and in mathematics in particular; and attributions to success and failure regarding mathematics. The main part of this chapter is dedicated to the study of the following psychological and educational components that influence the learning of mathematics: valuing the subject of mathematics and school mathematics; belief in

own mathematical abilities; helplessness regarding mathematics; belief in flexible versus rigid abilities of mathematical intelligence; stability of mathematical abilities;

mathematical anxiety; and preference of extra mathematics afternoon class.

Unlike in many other countries, gender differences regarding mathematics achievement have not been a problem in the Israeli education system for over a decade. In fact – girls surpass boys in all classroom measures, and in all matriculation examinations grades (Eshet, 13.12.2002). While only 36.7% of 18-year-old boys were entitled to the matriculation certificate in the year 2001, the percentage of girls was much higher: 51.3% (Freilich, 21.5.2002). However, as explained in chapter 2, there are still gender problems regarding mathematical instructions, as well as many other problems regarding participation and achievement in this subject. The Israeli Ministry of Education has been involved in planning new, more effective teaching methods in order to improve the situation because of two main reasons:

1. The high level of inequality in the Israeli education system as was described in chapter 2,

2. Due to a constant deterioration in the level of mathematics achievements of Israeli school students that have resulted in decreasing from the first place in the world in 1963/4 in an international study (Husen, 1967), to the 28^th out of 38 countries examined in 1999 (e.g. Mullis et al, December 2000).

In spite of these two major problems, all programs and studies have been done lately stemming from a different point of view: rather than try to improve the achievements in general, focus on high achievement and high participation rate of some sub-populations, and then try to isolate the components that have led to these achievements. For example: in the Jewish sector the percentage of girls examined in the highest level mathematics matriculation exam has been 50% lower than that of boys; in the Arab sector it is higher (Statistics, Israel, 2002a). In fact, the number of Arab girls succeeding in this exam has been equal to that of boys in 2001 (ibid). In addition, while in the Jewish sector only 6% of the girls take the 5-point physics exam, in the Arab sector the percentage is 12. In the Jewish sector there are also differences regarding participation in mathematics and science: while in the general sector 54% of those examined in the 5-point chemistry matriculation examination are girls, in the religious sector the percentage is 73 (Statistics, Israel, 2000).

The major target of my study is to examine some of the educational, social, and psychological components that contribute to higher achievements and aspirations regarding mathematics.