C l u s t e r I n n o v a t i o n C e n t r e , D e l h i U n i v e r s i t y

2013

DIFFERENTIATED INSTRUCTIONAL MODULE FOR POTENTIALLY GIFTED GIRLS: A CASE STUDY FOR MINORITY MUSLIM SCHOOL

Masters in Mathematics education, Meta University

Acknowledgement The successful completion of a project work requires efforts of several

intellectual minds. It has been a great learning experience for which I would like

to thank everybody who has been instrumental in the completion of my project

work. I take this opportunity to thank all of those individuals who have shared

their experience and have knowingly or unconsciously given their contribution to

my project work. I would like to acknowledge them sincerely for parting with

their valuable time.

I would like to articulate my profound gratitude and indebtedness to my project

guide Dr. Jyoti Sharma, Cluster Innovation Centre who has always been a

constant motivation and guiding factor throughout the project time in and out as

well. It has been a great pleasure for me to get an opportunity to work under her

and complete the project successfully. She taught us so much about research and

prepared us so well for the journey. We want you to know how thankful we are

for your advice, contacts, and expertise.

Also, I would like to thank the Khatiza tul kubra girls public school principal Ms.

Saba Farooqu, for sharing their insights and experiences during the interviews. I

would like to thank Ms. Wafa Rahmani, Ms. Midhat Shafi , Admission and

Examination Incharge, who assisted in the development of the Identification

surveys and in the initial planning stages of the project.

Ms. Roohi Amir & Ms. Faiza Burhan

Masters in Mathematics Education, Meta University

Cluster Innovation Centre, Delhi University

Certification

It is certified that the project work reported was carried out under my guidance towards partial fulfillment of the requirements for the award of Masters in Mathematics Education. The work was carried out by the following students.

Roohi Amir

Faiza Burhan

Dr. Jyoti Sharma

Cluster Innovation Centre

University of Delhi

List of contents

s.no Topic Page no.

1. Acknowledgement 2. Certification 3. Introduction 3.1. Purpose of the project 3.2. Research questions 3.3. Defining Mathematical promising 3.4. Characteristics to look for when identifying mathematically promising students 3.5. How to identify mathematically promising students 3.6. Myths about highly abled students 3.7. Contexts for discovering Giftedness in the classroom 4. Methodology 4.1. Population 4.2. Instrumentation 4.3. Fennema-Sherman Mathematical scales (FSMAS) 4.4. The domains of FSMAS 5. Analysis 5.1. Why these cases are exclusive? 5.2. Samples of instrumentation 5.3. Sample used for the item selection 5.4. Identifying the school 5.5. Special needs of highly abled Muslim girls 5.6. Barriers faced by Potentially abled Muslim Girls 5.7. Strategies for teaching abled girls in Inclusive classroom 5.8. Learning environment 5.9. Supporting potentially abled Muslim girls in mathematics 5.10. Differentiating content 5.11. Enrichment content of mathematics 5.12. Key components of mathematics curriculum for abled girls 5.13. Teaching approaches for mathematically abled Muslim girls 6. Conclusion 7. References

Introduction

Purpose of the project We are preparing differentiated instructions and teaching modules for mathematically abled Muslim girls by first identifying them in local government school then by making these Specialized instructions (after their keen assessment) are carefully planned, coordinated, individualized with their learning experiences that extend beyond the core curriculum to meet the specific learning needs evidenced by the individual girl child.

These Modules are for mathematically advanced and high ability learners. And this is providing abled girls with different options than those offered to their classroom peers in the general classroom for acquiring content, processing ideas, and developing products.

Research Questions 1. What are the math attitudes of 7th and 9th grade students on eight

domain of Fennema-Sherman Math Attitude Scales?

2. What are the special needs of mathematically abled Muslim girls? How can

we meet their needs?

3. What are the external barriers faced by Muslim abled girls?

4. What are the methods for identifying girls? Who demonstrate special

aptitude in mathematics?

5. What are the strategies for teaching math abled girls in the inclusive

classroom?

6. How we can improve learning environment to enhance mathematical

attitude in girls?

7. What are the differentiated instructions for potentially abled girls in

Mathematics?

Defining Mathematical Promising In order to discuss ways to identify and program for gifted and promising mathematics students, mathematical promise must be defined. The National Council of Teachers of Mathematics (NCTM) Task Force on the Mathematically Promising defined mathematical promise as a function of--

* motivation,

* belief, and

* experience or opportunity.

These variables are not fixed and need to be developed so that success for these promising students can be maximized. This definition includes the students who have been traditionally identified as gifted, talented, precocious, and so on, and it adds students who have been traditionally excluded from previous definitions of gifted and talented and therefore excluded from rich mathematical opportunities. This definition acknowledges that

"Students, who are mathematically promising, have a large range of abilities and a continuum of needs that should be met." (Richard Wertheimer)

Characteristics to Look for When Identifying Mathematically Promising Students There are many characteristics to consider when identifying which students are mathematically gifted. The following descriptors of characteristics of highly able mathematics students should be viewed as examples of indicators of potential. Few students will exhibit all characteristics and these characteristics can emerge at different times as the child develops cognitively, socio-emotionally, and physically.

The highly able mathematics student should independently demonstrate the ability to:

• Display mathematical thinking and have a keen awareness for quantitative information in the world around them.

• Think logically and symbolically about quantitative, spatial, and abstract relationships.

1

• Perceive, visualize, and generalize numeric and non-numeric patterns and relationships.

• Reason analytically, deductively, and inductively.

• Reverse reasoning processes and switch methods in a flexible yet systematic manner.

• Work, communicate, and justify mathematical concepts in creative and intuitive ways, both verbally and in writing.

• Transfer learning to novel situations.

• Formulate probing mathematical questions that extend or apply concepts.

• Persist in their search for solutions to complex, "messy," or "ill-defined" tasks.

• Organize information and data in a variety of ways and to disregard irrelevant data.

• Grasp mathematical concepts and strategies quickly, with good retention, and to relate mathematical concepts within and across content areas and real-life situations.

• Solve problems with multiple and/or alternative solutions.

• Use mathematics with self-assurance.

• Take risks with mathematical concepts and strategies.

• Apply a more extensive and in-depth knowledge of a variety of major mathematical topics.

• Apply estimation and mental computation strategies.

It is important to realize that these variables are not fixed and need to be continually developed.

2

How to Identify Mathematically promising Students Unfortunately, there is no single method for identifying gifted and talented students nor for assessing their performance. Ways of identifying mathematically promising students include:

Observation—while the students are working, particularly in problem solving situations of increasing difficulty or those designed to elicit the characteristics listed above.

Portfolios—students need access to exemplars from other students and the scoring rubric should include:

• patterns noted and generalized

• predictions made and verified

• interesting related problems posed and investigated

• measures of creativity—

• fluency (number of different solutions)

• flexibility (variety of solutions)

• originality (uniqueness of solutions)

• elegance (clarity of expression)

Questioning—individually, in small group, or whole class:

• Student interview

• Parent information

• Student interest/peer survey

• On-going assessment

• Rating Student Potential Teacher Checklist

• Diagnostic Thinking Tasks

• Math logs or journals

3

Myths about Highly abled Students There are many misconceptions about gifted students that may prevent schools from providing for their needs. The following are some of the most common myths that are cited as rationale for not providing differentiated opportunities for high-ability students.

Gifted children are smart, so they can get by on their own. When students are not presented with learning experiences that are appropriate for their abilities, they lose motivation and some- times even their interest in learning and school. Brain research suggests that the brain will not maintain its level of development if students are not challenged (Clark, 1997).

Gifted students excel in all school subjects. While there are students who are high achievers in all areas, many others have subject-specific strengths. Gifted students may struggle in some subjects or activities, while they soar in others. Some gifted stu- dents even have learning disabilities (Winner, 1996).

Gifted students are a homogeneous group. Just like any other group, gifted students have different interests, areas of strength, ability levels, and temperaments. There is not a definitive list of gifted characteristics, nor will all students’ needs be met with the same strategies. Providing differentiated instruction is a necessity, even in advanced classes (Parke, 1989).

All children are gifted. This is a well-intentioned belief, and it is true that all children can learn and all children have areas of strength. Nevertheless, it is a fact that some students learn more quickly and are capable of a higher level of work than their age peers. Gifted students need different content and instruction in order to meet their needs (Winner, 1996).

4

Methodology

Population

CLASS-VII

5

CLASS-IX

6

Instrumentation

Fennema-Sherman Mathematical Scales In an effort to study students' attitudes towards math, Elizabeth Fennema and Julia A. Sherman constructed the following attitude scale in the early 1970's. The scale consists of four subscales: a confidence scale, a usefulness scale, a scale that measures mathematics as a male domain and a teacher perception scale. Each of these scales consists of 12 items. Six of them measure a positive attitude and six measure a negative attitude.

This scale could give a teacher and an individual student useful information about that particular student's attitude(s) towards math. Because this scale was originally written twenty years ago and the subtle meanings and connotations of words have changed in that time period, it is important that this scale not be used for research.

Subjective

Nomination Forms

Teacher

peer

self

Objective

FSMAS

8-Domains of FSMAS

Mathematical Behavorial checklist

7

The domains of the Fennema-Sherman Mathematics Attitudes Scales Domains of the Fennema-Sherman Mathematics Attitudes Scales

Domain Description Attitude toward success This domain measures the degree to which students

anticipate positive or negative consequences as a result of success in mathematics

Mother’s math attitude This domain measures the support from the mother. Father’s math attitude The parent domain measures the support from the

father. Mathematics anxiety This domain measures the feelings of anxiety, dread,

nervousness, and other physical symptoms related to doing mathematics.

Effective motivation This domain measures perseverance when faced with challenging problems. It is not intended to measure interest or enjoyment of mathematics

Usefulness in math This domain measures beliefs about the usefulness of mathematics and in relationship to their future education.

Teacher attitude This domain measures students’ perceptions of their teachers’ attitudes toward them as learners.

Confidence in learning This domain measures confidence to learn and perform well on mathematical tasks.

8

Analysis

Why these cases are exclusive? This is crucial in striving not only to meet the particular strengths and needs of a Muslim girl identified as abled but also to prepare her for the ever changing conditions of the 21st century.

Adolescent mathematically abled girls

• Potentially abled Muslim girls’ math and IQ’s scores drop in adolescence, perhaps as girls begin to perceive the giftedness is undesirable.

• Highly abled girls are likely to continue to have higher academic achievement as measured by grade point average.

• Abled girls take less rigorous math courses than gifted boys after class-X. • Potentially abled Muslim girls maintain a high involvement in extracurricular and

religious social activities then in academics. • Highly abled Muslim girls often do not receive recognition for their achievements. • Highly abled Muslim girls do very well academically in high school but only few are

motivated further. • Highly abled Muslim girls attend less prestigious colleges than highly abled boys, a

choice that leads to lower status careers. • The age from twelve to fourteen years, when a strong shift if values occurs, is a critical

time for abled Muslim girls. • The change in values at this point is related to strong needs for love and belonging. • Adolescence may also bring a steep decline in self-esteem and confidence in opinions. • Abled Muslim girls fear having to choose between career and marriage.

9

Samples of Instrumentations

10

11

12

13

14

15

16

17

18

Sample used for item selection cases Class Strength Areas Needs

Case-1 VII Strong mental ability Problem Solving

Case-2 VII Unusual curiosity about numbers and mathematical information

Reasoning

Case-3 VII Ability to understand and apply mathematical concepts quickly

Unusual curiosity about quantitative relationships

Case-4 IX High ability to identify patterns and shapes Flexible and creative in problem solving

Case-5 IX Curiosity in objects and occurrences Face problem to transfer mathematical concepts to an unfamiliar situation

Case-6 IX Persistent in solving challenging problems Mathematical Intuition

Case-7 IX High concentration levels and self-sufficiency towards geometry

Reasoning

Case-8 IX Flexible and creative in their strategies to problems

Confusion in mathematical symbols

Identifying the school

About the school KHADIJATUL KUBRA GIRLS PUBLIC SCHOOL recognized by the Directorate of Education, Delhi, is functioning under the aegis of “ABUL KALAM AZAD ISLAMIC AWAKENING CENTRE, 4, JOGA BAI, JAMIA NAGAR, NEW DELHI-25”, a registered educational society established with the sole objective of providing modern education coupled with Islamic and religious teaching for the mental growth and development of children.

Location The school is situated at Joga Bai, near Jamia Millia Islamia (Central University) Jamia Nagar, New Delhi-110025. It is housed in a multistory modern building with well-equipped laboratories for Physics, Chemistry, Biology, Math's, SST and Home Science, a Computer Unit and a Library with books on all subjects. The school has a freshening atmosphere due to plants and greenery.

19

Syllabus CBSE Course along with Urdu, Deeniat and Holy Qur'an from Nursery class, Arabic language from class VI, and Computer Education from class III onwards are special features of school curriculum.

Why we choose this school?

We needed to accomplish our project on mathematically abled Muslim girls so that’s why we choose this school because this is a Muslim minority girls school.

Special needs of highly abled Muslim girls Like every highly abled child, abled Muslim girls too and often need more support than others at home and in the classroom, but this does not necessarily mean that they need more structured activities. Sometimes it means they need more freedom and a little more guidance instead. For abled girls, the discrepancy between ability and self-image may assume different forms, depending on their unique characteristics and background. Abled girls may be those who: achieve well but remain blind to their accomplishments; perform poorly despite their high ability and attribute their poor performance to low intelligence; are disinterested in school or achievement and excel socially, sometimes assuming popular leadership in negative ways.

These behaviors are signals that Muslim girls need help--signals that will become increasingly faint as they grow older.

So, the question may arise: What do abled Muslim girls need that all girls do not? The answer is that while all girls need an ongoing support system for their development and freedom, abled Muslim girls require support that is particularly sensitive to the dilemma that talent brings to the position of Muslim females in our society. Potentially abled girls face a quandary. They have abilities urging them forward, prompting them to explore all that education has to offer, yet education does not run to meet them. When boys ask questions, call out their answers (sometimes without raising their hands) or engage in debate, adults tend to see the signs of eager minds at work. Girls receive reprimands or disapproval for behavior deemed aggressive, pushy, unfeminine or impolite. This message is not lost on abled girls.

20

Muslim abled girls assume all sorts of extra burdens that educators need to understand. Often they don't know about their own gifts and talents. They only know they're different and, for many, they perceive that this difference is somehow strange or wrong.

In addition to their acute sensitivity and stereotype image in society, Muslim abled girls play mental games with themselves--learned games they do unconsciously--in response to the conflicting expectations they experience both as girls and as talented people. Two examples frequently explored in the research are:

"The Horner Effect" or fear of success, in which girls purposely hold back because of a need to please others (rather than compete with them), a need that is more intense with gifted than average girls (Kerr, 1994)

"The Impostor Phenomenon," in which girls feel pressured to explain away their success since it goes contrary to social expectations and their own self-image. They maintain that they performed well due to luck or because people did not evaluate them properly (Kerr, 1994). Adults need to develop strategies for helping gifted girls negotiate around this emotional mine field.

Adults who are not aware of the unique sensitivities of high potential girls may inadvertently encourage destructive behaviors. Alas, sometimes, too much praise and confidence in a girl's ability may make it difficult for her to admit she needs help or result in dismissing her requests altogether.

Abled girls can progress beyond self-defeating assessments of themselves when supportive adults listen to their concerns, questions and comments, and then go on to offer validation and reassuring responses that provide direction for their work.

Barriers faced by Muslim potentially abled girls Gifted and talented females face conflicts between their own abilities and the social structure of their world. They confront both external barriers (lack of support from families, stereotyping, and acculturation in home, school, and the rest of society) and internal barriers (self-doubt, self-criticism, lowered expectations, and the attribution of success to effort rather than ability). Partial responsibility for the conflicts and barriers faced by talented

21

women rests with the role confusion and ambivalence our society displays toward talented females and the barrage of conflicting messages which influence females throughout their lives. Examples of this ambivalence are plentiful currently as well as in the past.

The importance of environmental variables on the development of gifted and talented females cannot be overstated. Almost from birth, females find themselves in a world of limiting stereotypes and other barriers to achievement. Research has identified external barriers, which seem to negatively influence the development of talents

External Barriers

Parental Influences

• The first set of external barriers gifted women face deals with childhood family issues and statistics, such as number and sex of siblings, birth order of siblings, and presence or absence of one or both parents. Other childhood issues include the parental attitudes toward having and raising girls as opposed to boys. Children usually learn the stereotypical behaviors of their sex at an early age and display particular behavior patterns and play preferences even during preschool years.

• Parental influences have also been shown to have an impact on the lives of talented females, including the educational levels and occupations of father and mother, as well as the type and level of parental aspirations for children's educational and occupational goals.

• Stereotypical feminine behaviors often conflict with the personal attributes gifted female needs to succeed. Some parents require, or at a minimum, expect their daughters to be polite, well mannered, and consistently congenial. According to the stereotype, girls are not supposed to be too independent.

• Mothers seem to have a particular influence on their gifted daughters. Recent research has found that talented girls with career-oriented mothers tended to develop a variety of talents and interests early in life and feel less conflict about growing up and becoming independent, autonomous women.

External Events Influencing Creative Development

• The availability (or absence) of role models who can help gifted girls realize their potential has been a key issue with gifted females. If women have knowledge of or personal contact with someone who acts as a positive role model, especially in their area of career interest, attaining that career can seem like a much more reasonable

22

goal. Financial resources may also be a contributing factor in a woman's ability to realize her educational dreams.

Click, Click, Click: The Formation of Attitudes and Opinions

• Like a camera in the brain, each time a child has an experience, a snapshot is embedded in her experiential base. Millions of snapshots produce attitudes, which, in turn, affect actions.

• Stereotypes abound in our society, from shampoo commercials and newspaper ads to the teen magazines our daughters read.

• Newspapers and news shows on television regularly feature photographs and feature stories about men in positions of authority.

• Children's books, television shows, and textbooks all present more men than women and when women are presented, their appearances are usually stressed, rather than their talents, character, or value systems.

Stereotyping in School

• Gender equity has still not been achieved in school textbooks and classroom experiences. In the past ten years, a number of national reports and books have examined the impact of stereotyping on girls.

• Some research indicates that a few male students receive more attention than all other students in math classes. Some evidence exists that the amount of teacher attention given to girls is lowest in Math classes.

• Having mixed gender groups usually resulted in the boys dominating and conducting the hands-on math experiments.

• Qualitative data collected in the same study indicated that the talented girls who scored highest in math enjoyed competing with boys and liked trying to be the best.

• The mathematically talented girls studied were sometimes frustrated by the lack of challenge in some of the mixed gender and single sex cooperative learning groups.

Work in the Home

• Another external barrier many women and girls experience as they attempt to realize their potential is the burden of responsibilities females often shoulder at home.

• Daughters learn and watch as their mothers work out of the home, and come home to do the majority of work in the home, too.

23

Strategies for teaching abled girls in the Inclusive Classroom Muslim abled girls in the regular classroom describe five overall areas for differentiation:

1. modifying current mathematical content, 2. allowing for girls preferences, 3. altering the pace of instruction, 4. creating a flexible classroom environment, and 5. using specific instructional strategies.

Instructional strategies that have been linked to improved Muslim girls achievement in math and have been shown to increase critical thinking, problem-solving abilities, and creativity.

The following have been established as effective strategies

■ Posing open-ended math questions that require higher-level thinking

■ Modeling thinking strategies, such as decision making and evaluation

■ Accepting ideas and suggestions from students and expanding on them

■ Facilitating original and independent problems and solutions

■ Helping students identify rules, principles, and relationships

■ Taking time to explain the nature of errors

One of the most extensive studies that we have come to know on teaching highly abled girls in inclusive settings is a survey of classroom practices in schools that have a well- established reputation for meeting the needs of abled students.

The following strategies occurred most frequently while teaching highly abled girls in regular classroom settings

■ Establishing high standards

■ Making curriculum modifications

■ Finding mentors for students

■ Encouraging independent investigations and projects

24

■ Creating flexible instructional groups

“ACKNOWLEDGING THAT STUDENTS LEARN AT DIFFERENT SPEEDS AND THAT THEY DIFFER WIDELY IN THEIR ABILITY TO THINK ABSTRACTLY OR UNDERSTAND COMPLEX IDEAS IS LIKE ACKNOWLEDGING THAT STUDENTS AT ANY GIVEN AGE AREN’T ALL THE SAME HEIGHT: IT IS NOT A STATEMENT OF WORTH, BUT OF REALITY.”

Learning Environment THE PROCESS OF DIFFERENTIATING INSTRUCTION IS MOST effective in a flexible and supportive learning environment, which encompasses both the physical setting of the classroom and its climate. The teacher sustains a relaxed yet challenging environment by encouraging responsibility and autonomy, supporting students’ different needs, and emphasizing students’ strengths. In addition, sharing responsibility for the classroom climate with students helps to ensure that it is productive and comfortable for everyone.

Classroom Organization and Management During our project in Khatijatul kubra girls public school, we observed that the classroom were not organized which is important for flexibility and openness. There was also no space available for Muslim girls to engage in a variety of activities, both independently and in small groups. It is important that students are free to move as they need to, as long as they remain on task. We also observed that they were not able to leave the classroom in order to go activity room or computer lab except their respective periods. We were expected to see when students work on different content, use different learning strategies, and create different products, the teacher takes on an altered role in the classroom but due to shortage of time we couldn’t observe more. It is important to let the teacher knows that presenting the curriculum to students is no longer the teacher’s primary focus. Instead, she concentrates on creating and selecting learning opportunities for students, guiding them, and working with them to assess their progress.

Giving students choices and allowing them to schedule their activities encourages independence and keeps students engaged. It is recommended that students be allowed to choose what they want to work on at least part of the time. Students are still accountable for completing specific activities or demonstrating what they have learned within a certain period of time, but they choose when or how they will work.

25

The following strategies are helpful in organizing and managing the classroom for differentiated instruction:

■ Using “anchor activities” that students can complete with little supervision—tasks such as writing journal entries or working on a portfolio—provides time for the teacher to work directly with other students.

■ When students are working on different activities, it will be helpful to have instructions available for easy access. The teacher may want to create assignment cards rather than giving directions orally or writing multiple sets of directions on an overhead.

■ Teachers will also need to be sure that all students know how to get help when they need it, either by asking another student, going back to the directions, or working on another task until an appropriate moment for asking the teacher. A student might serve as “Expert of the Day” when she has shown a deep understanding of the concept or task.

■ Involving the students in creating classroom procedures and rules and in organizing their time helps them to build important skills in decision making, negotiating, and planning. It also ensures that students feel at home and involved in the classroom

Supporting potentially abled Muslim girls in mathematics Mathematically abled Muslim female students face many unique challenges and problems that tend to undermine their abilities and potential. There are about 90% of school have no knowledge about identifying mathematically abled female students from cultural minority

groups, there is not yet comparable attention to the challenge of providing support for highly abled Muslim female students. All Muslim girls may experience isolation and pressure to hide their abilities, and as minority students tend to feel the weight of these forces to an even greater degree. Highly abled minority female students report feelings of inferiority, as well as the need to constantly choose between using their talents and fitting in with their peers. Mathematically abled girls do not achieve at expected levels, especially in middle school and high school, and they often do not pursue careers appropriate to their abilities. Researchers have identified a number of reasons for female students’ underachievement: gender stereotypes pervasive in society, lack of role models, declining confidence in their

26

abilities, mixed messages and conflicting expectations from teachers and parents, and peer pressure to hide their abilities and intelligence.

More specifically, teachers often have less tolerance for girls who call out answers in class, ask numerous questions, and are confident in their opinions and willing to argue—behaviors that are likely to be accepted as evidence of giftedness in boys. Often girls are socialized in school and at home to be attractive, obedient, caring, agreeable, and submissive. As a result, girls have a tendency to hide their intelligence and downplay their abilities in order to conform to the socially accepted stereotypes of femininity Providing them with extra support is especially important in mathematics. In math fields, cultural stereotypes have contributed to the underrepresentation of minorities. It is also important to strike a balance between encouraging girls to pursue nontraditional fields while not devaluing traditional female strengths and interests. Although there is not yet a substantial body of published research, there are many suggestions and strategies developed by educators for meeting the needs of gifted minority female students:

■ Communicate high expectations.

■ Be sensitive to the experiences and beliefs of people from different cultural groups. Get to know all students and their cultures. Consider the challenges that students may face in school.

■ Continuously and firmly encourage students to go to college. Dis- cuss the necessary coursework, tests, and other preparations with students and parents.

■ Create a multicultural learning environment and make sure the curriculum reflects a variety of cultures.

■ Help students connect with role models and mentors. Organize peer support groups for students with similar interests and abilities.

■ Reach out to parents and family members. Enlist their support in providing encouragement and high expectations.

■ Provide students with a variety of learning options. Create or select activities that are engaging, active, and grounded in reality.

■ Listen to students’ concerns, fears, and beliefs about their experiences and their education.

27

■ Communicate with parents about their daughter’s abilities and the importance of mathematics for higher education and careers. Encourage them to identify and address sources of gender bias

■ Organize peer support groups for girls. Mathematics clubs encourage girls to develop their skills and abilities and help connect them to other girls who share their interests.

■ Avoid praising girls for their neatness or behavior. Point out specific examples of their excellent work and achievements. Actively correct them if they attribute their accomplishments exclusively to luck or hard work.

■ Provide opportunities for girls to use their leadership abilities.

■ Expose students to women in nontraditional careers. Help them to identify and connect with role models and mentors.

■ Openly discuss gender stereotypes and the mixed messages that society broadcasts about femininity, intelligence, and achievement.

■ Provide a safe environment for Muslim girls to share their confusion and fears.

■ Actively recruit girls to participate in advanced courses and extracurricular activities related to mathematics and technology.

■ Encourage students to research and report on female contributions to mathematics.

Differentiating content: Making modification to mathematics content is one aspect of in providing challenging learning opportunities. Abled educators recommend that in mathematics, students should study advanced content in earlier grade levels.

Organizing the curriculum around major themes and ideas is one of the first steps in differentiating content. Using broad concepts helps to create opportunities for learners to learn and apply integrated and complex ideas. Some key themes in mathematics include functions, patterns, scale, rates, and change.

It is important that mathematics content focus on more than computation, formulas, and vocabulary. All students benefit from a curriculum that does not focus exclusively on basic skills. A broader focus allows students who may not have strong computation or

28

memorization skills to demonstrate their abilities in abstract reasoning, creativity, and conceptual understanding. There are different methods for encouraging students to move beyond the basic concepts of the mathematics curriculum.

One recommendation for differentiating content for abled female students is increasing the level of abstractness and complexity (Maker & Nielson, 1996). For example, students might study a concept at the theory level: identifying and testing mathematical or scientific laws or connecting seemingly disparate ideas. Students might learn about or develop complex systems that have many sections and processes.

Adding variety to the content that students work with is another important strategy. Students are exposed to new materials, books, tools, and people, which helps to stimulate curiosity and creativity. Gifted students might work on projects in which they investigate the history of an idea or generate formulas or laws from their own observations. Adding topics that are not part of the regular curriculum can also be effective. For example, in mathematics, students might learn about transformational geometry, topology, number theory, and logic.

Bloom’s Taxonomy of Educational Objectives can be helpful in designing content for gifted students (Bloom,

1956). Bloom’s six levels of knowledge are knowledge:

1. comprehension, 2. application, 3. analysis, 4. synthesis, and 5. evaluation

The final three levels are most appropriate for potentially abled students and may help teachers to identify ways for students to work with content in more advanced and more challenging ways.

Analysis involves using content to classify, compare, contrast, investigate, and deduce information and ideas.

Synthesis will require students to use ideas and knowledge to create original work, using it to invent, design, and plan—for example, developing a theory or hypothesis.

Evaluation requires students to interpret, verify, criticize, defend, and judge ideas and information.

29

The upper pyramid shows Bloom’s taxonomy for mainstream students, where the emphasis

is on remembering, understanding and applying. For gifted students, the lower pyramid highlights

creating, evaluating and analysing as areas of focus (Adapted from Ministry of Education, 2000).

One of the simplest ways to present more challenging content is to pro- vide advanced materials for gifted students. Textbooks, and other resources from higher grade levels or even written for adults will help provide more complexity and will often be more appropriate. Teachers might want to provide library books on the subjects the class is working on or on related topics. Students might also use a list of suggested resources to find and select their own materials. It will also be helpful to provide mathematics or science texts from higher grade levels or even from the college level.

Creating

Evaluating

Analysis

Applying

Understanding

Remembering

Creating

Evaluating

Analysis

Applying

Understanding

Remembering

30

Enrichment content module Our enrichment content module for class VII and IX is based on five mathematical aptitudes:

1. Problem solving 2. Reasoning 3. Mathematical intuition 4. Creativity 5. Quantitative

Samples of Enrichment content module for class VII TOPIC: ALGEBRIC EXPRESSION

Aptitudes Question-1 Question-2 Problem solving Q. Shayam has 6 times as many

dimes as quarters in her piggy bank. she has 21 coins in her piggy bank totalling Rs100

Q. You have 6 litres of water that have 20% strawberry juice. How many litres of a 80% strawberry juice should be added to the mixture to make 75% strawberry juice

Reasoning Q. Solve 5x- 18 = 3x + 2 and write a reason for each step

Q. In the diagram, AB = CD. The argument below shows that AC=BD. A B C D

Mathematical Intuition

Q. Starting with some number, if I multiply by 6 and then add 66, I get 81.9.What number did I start with?

Q. When ted got home from his waiter job, he took the 81.90 that he earned that day and subtracted the 66 that he received in tips. Then he divided the remaining money by the 6 hours that he worked and found his hourly wage. How much does ted make per hour?

Creativity Q. Choose two expressions below, draw cartoons for: (a) x – 1 (b) y + 10

Q. Grid Trick: Create a number grid problem of your own. You can use any type of grid you would like, be it a 100s

31

(c) x – y (d) 2x + 1 You can be as creative as possible. The most creative cartoon will win you a surprising prize!

charts, or a calendar etc. Provide the reader with the grid and the instructions to the 'trick'. Either on the back, or hidden somewhere on the page, provides the algebra to solve the problem.

Quantitative Q. A room is 16 feet, 8 inches long, and the ratio of the length to the width is 4 to 5. What is the width of the room?

Q. In a bag of blue and yellow candies, the ratio of blue candies to yellow candies is 3:5. If the bag contains 60 yellow candies, how many blue candies are there?

Samples of Enrichment content module for class IX TOPIC: Circle

Aptitudes Question-1 Question-2 Problem solving Q. Let K be a point on a circle

sitting inside and touching a stationary circle of twice its diameter. Describe the path of K as the smaller circle rolls round the larger one without sliding

Q. The tires on a compact car are 18 inches in diameter. How far does the car travel after the tires turn once to the nearest inch? How far does the car travel after 2500 rotations of the tires?

Reasoning Q. The area of the bigger circle

minus the area of the smaller circle should be your answer, unless the circles intersect in some different way.

Mathematical Intuition

Q. In the figure above, the diameters of the 5 dotted semicircles are equal and lie on line segment AB. If the length of line segment AB is 20, what is the length of the dotted curve from A to B?

32

Creativity Quantitative Q. Circles A and B have radii of 2

and 3 , respectively. How much greater is the circumference of circle B than the circumference of circle A?

Key Components of Mathematics Curriculum for the abled

• _ Content with greater depth and higher levels of complexity • _ A discovery approach that encourages students to explore concepts • _ Focus on solving complex, open-ended problems • _ Opportunities for interdisciplinary connections

Teaching approaches for mathematically abled Muslim girls ■ Present students with paradoxes to analyze and test

■ Use analogies to introduce new concepts; ask students to create their own

■ Allow students to think about discrepancies in what is known

■ Ask provocative questions and provide time for inquiry

■ Examine examples of change and the process of change

■ Use examples of habit and the results of habit-bound thinking

■ Encourage tolerance for ambiguity with open-ended problems

■ Encourage students to use their intuition and follow their hunches

33

■ Study creative people and their thinking processes

■ Evaluate situations by analyzing possible consequences and implications

■ Help students practice creative reading, listening

Conclusion IT IS WORTH TELLING THAT MOST OF THE STRATEGIES presented in this project report will be effective for all students in the class- room including highly abled Muslim girls. This idea is essential in providing opportunities for all students to learn challenging mathematics and to demonstrate their strengths and talents. Differentiating instruction is a challenging process. Teachers will need both time and support as they adapt the strategies ac- cording to their students and their own teaching styles.

References http://www.irfi.org/articles/articles_501_550/educating_muslim_girls.htm

http://www.unicef.org/india/education_2891.htm

http://articles.timesofindia.indiatimes.com/2012-08-20/india/33286862_1_muslim-enrolment-muslim-girls-muslim-community

http://www.jeywin.com/wp-content/uploads/2009/12/An-Analytical-Study-of-Education-of-Muslim-Women-and-Girls-in-India.pdf

http://twocircles.net/2013may19/seminar_education_muslim_girls_held_imphal.html

http://www.academia.edu/1055155/Gender_gaps_in_mathematics_science_and_reading_achievements_in_Muslim_countries_a_quantile_regression_approach

http://www.aiel.it/bacheca/milano/papers/Murat.pdf

http://www.davidsongifted.org/db/Articles_id_10514.aspx

http://www.curriculumsupport.education.nsw.gov.au/policies/gats/assets/pdf/csmth23accsi.pdf

http://ssa.nic.in/news/girls-education-in-india-achievements-since-independence-press-release-wednesday-january-23-2008

http://www.guardian.co.uk/education/2013/mar/11/indian-children-education-opportunities

34

http://depssa.ignou.ac.in/wiki/images/3/39/Girls_Education.pdf

Benbow, C. & Stanley, J. C. (1980). Sex differences in mathematical ability: Fact or artifact?

Betz, N. E., & Hackett, G. (1983). The relationship of mathematics self-efficacy expectations to the selection of science-based college majors. Journal of Vocational Behavior, 23, 329

Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook 1: Cognitive domain. New York: Longmans, Green & Co.

Broadbooks, W., Elmore, P., Pedersen, K., & Bleyer, D. (1981). A construct validation study of the Fennema- Sherman Mathematics Attitudes Scales. Educational and Psychological Measurement, 41, 551-557.

Bruner, J. S. (1960). The process of education. Cambridge, MA. Harvard University Press. Brush, L. R. (1985). Cognitive and affective determinants of course preferences and plans,

Women and mathematics: Balancing the equation. 123-150. Hillsdale, NJ: Lawrence Erlbaum.

Callahan, C. M. (1979). The gifted and talented women. In NSSE yearbook on the gifted and talented. Chicago: University of Chicago Press.

Callahan, C. M., & Reis, S. M. (1996). Gifted girls, remarkable women. In K. Arnold, K. D.

Noble, & R. F. Subotnik (Eds.), Remarkable women: Perspectives on female talent development. (pp. 171-192). Cresskill, NJ: Hampton Press.

Carey, G. L. (1958). Sex differences in problem-solving performance as a function of attitude differences. Journal of Abnormal and Social Psychology, 56, (256-260).

Chipman, S.F., & Thomas, V. G. (1985). Women’s participation in mathematics: Outlining the problem. In S.F. Chipman, L.R. Brush, equation (pp. 1-24). Hillsdale, NJ: Erlbaum.

Cramer, J., & Oshima, T. C. (1992). Do gifted females attribute their math performance differently than other students? Journal for the Education of the Gifted, 17, (1), 53-73.

Dickens, M. N., & Cornell, D.G. (1990). Parental influences on the mathematics self-concept of high achieving adolescent girls.

Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman Mathematics Attitudes Scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. JSAS Catalog of Selected Documents in Psychology, 6, (31) (Ms. No. 1225).

35