Teaching Mathematics at Secondary Level

  

A STRATERGY FOR 

TEACHING secondary MATHEMATICS

Different stages of teaching and learning of mathematics, different stages of intelligence, fundamentals of teaching mathematics, present senario of teaching mathematics.

Hand Out - 1 

Why students face problems in Learning Mathematic

Given below are some reasons due to which students face problems in Mathematics. Rank these as per your observation 1 to 10

Sr. No.	Problems in Mathematics	Rating (1-10)
1	The way in which the topics are introduced is inappropriate.
2	There is a lack of understanding of concepts.
3	There is a lack of practice.
4	There is more focus on formulae and calculations.
5	The importance of learning about a particular concepts is not explained to the learners.
6	Mathematics requires a lot of memorisation.
7	Students are often distracted.
8	The time spent on interacting with students is less
9	There is more focus on finishing the syllabus rather than effective learning of concepts.
10	There is a difficulty in comprehension.

Hand Out - 02

Common Errors in Secondary Mathematics

Activity Tamplet

Area of Mathematics : ......................................

Figure out some of the errors committed by students in learning Mathematics. What could be the reason for it ? Suggest a suitable remedy for removing the error.

S. No.	Common errors	Reasons	Remedial Measures
1
2
3

Hand Out - 03

Types of Technologies

There are various types of technologies currently used in traditional classrooms. Among these are: Radio, television, audio tape, video tape, allied projector, overhead projector are of passive learning when interaction of the learner is less.

Computer in the classroom: 

Having a computer in the classroom is an asset to any teacher. With a computer in the classroom, teachers are able to demonstrate a new lesson, present new material, illustrate how to use new programs, and show new websites.

Class blogs and wikis: 

There are a variety of Web 2.0 tools that are currently being implemented in the classroom. Blogs allow for students to maintain a running dialogue, such as a journal, thoughts, ideas, and assignments that also provide for student comment and reflection. Wikis are more group focused to allow multiple members of the group to edit a single document and create a truly collaborative and carefully edited finished product. 

Wireless classroom microphones: 

Noisy classrooms are a daily occurrence, and with the help of microphones, students are able to hear their teachers more clearly. Children learn better when they hear the teacher clearly.

Mobile devices: 

Mobile devices such as clickers or smart phone can be used to enhance the experience in the classroom by providing the possibility for professors to get feedback.

Interactive Whiteboards: 

An interactive whiteboard that provides touch control of computer applications. These enhance the experience in the classroom by showing anything that can be on a computer screen. This not only aids in visual learning, but it is interactive so the students can draw, write, or manipulate images on the interactive whiteboard.

Digital video-on-demand: 

Digital video eliminates the need for in-classroom hardware (players) and allows teachers and students to access video clips immediately by not utilizing the public Internet. Online media: Streamed video websites can be utilized to enhance a classroom lesson. Online study tools: Tools that motivate studying by making studying more fun or individualized for the student.

Digital Games: 

The field of educational games and serious games has been growing significantly over the last few years. The digital games are being provided as tools for the classroom and have a lot of positive feedback including higher motivation for students. There are many other tools being utilized depending on the local school board and funds available. These may include: digital cameras, video cameras, interactive whiteboard tools, document cameras, or LCD projectors.

Software used for teaching learning Mathematics

• Graphic Calculators
• Dynamic graphing tools (Geo Gebra )
• Dynamic geometry tools
• Microsoft Excel/ spreadsheet
• Microsoft Mathematics
• Geo Gebra
• Auto shape
• Mat lab

Learning resource centre (Indian system of Education)/Websites 

National Policy of Education (NEP-2020)

This page completely explain the new policy of educatio and National curriculam framwork

Learning Objectives and Outcomes 

This page is an e-resource of class-wise learning objectives and outcomes of mathematics.

Thousands websites provide e-resource for both offline and online teaching -learning. 

IGNOU (http://www.ignou.ac.in):  The Indira Gandhi National Open University (1GNOU),

http://www.ncert.nicinNCERTS/textbook/textbook.htm : The website is a e-resource for syllabus, online text books, other publications such as sample question papers and multimedia packages which helps both the students and teachers in teaching learning Mathematics.

https://www.cbsemathematics.com

This site is a e-resource for mathematics formulas, worksheets, assignments and sample papers for practice and lesson plan in mathematics for 8th, 10th and 12th standard.

https://lessonplan51.blogspot.com/

This site is an e-resource for mathematics lab mannual, lesson plans for 9th and 11th standard and mathematics modelling.

https://mathsmcq51.blogspot.com/

This site is an e-resource for mathematics MCQ, Case study based questions and assertion and reason based questions.

http://www.ciet.nic.in : Central Institute Of Educational Technology(CIET provides information of educational technologies viz. radio, TV, films, Satellite communications and cyber media either separately or in combinations.

www.cbse.nic.in &http//www.icbse.coml : It provides information regarding online application for different examinations such as Mathematics Olympiad.

http://www.mathplayground.com/ASB_MeteorMultiplication.html : It is a very good website which allows the learner to motivate learning Mathematics through different game.

http://cbse.meritnation.com/cbsesignup2?mncid=Adwords_ Banner Test&gclid=CJnSm9yj2LMCFQV66wodpnQAgg 

http://www.ixl.com/math/algebra-1/absolute-value-and-opposites

http://mathforum.org/ibrary/ Lesson Plan http://Alluminations.nctm.org 

http://www.discoverveducation.com/searchlite/pageMathematics/Geometry/Worksheets. It is a very interactive website for Geometry.

There are some other useful sites provide wonderful mathematical investigations for our students and answers to the many perplexing questions that invariably arise in the classroom, for general teaching- learning mathematics.

http:/www.montgomeryschoolsmd.org'departments/hiat/websites/math. shtm helps teacher for lesson plan.

NRICH(www.nrich. maths.org.ukl) 

MATH CENTRAL(mathcentral. uregina.ca) 

MATH FORUM(www.mathforum.com) 

PBS(www.pbs.org/teachersource/math) 

DR.MATH(www.mathforum.com/dr. math)  Here the teacher as well as student will find answers to the many questions that teachers and others have posed.

http://www.ex.ac. uk/cimt&www.mathsplayground.com This site presents a wonderful rationale for using math games in your classroom and a significant collection of easy- to-use and friendly math games. www.discoveryleducation.org

Suggested Videos- sites such as

www.mathplayground.com, 

www.mathtu.com,

www.brightstorm.com, 

etc. may be used to access videos on Mathematical topics.

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Hand Oout-04

Suggestions for Hands on Activities for different toples

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Rangometry

Design a Rangoli pattern using coloured cut-outs of different kinds of triangles, circles, sectors and segments on A-3 size cardboard.
The students will be asked to:

• Count the number of different kind of shapes used & present the data in a tabular form.
• Find the area of the largest triangle, largest circle, largest segment & largest sector used.
• Find the 'mode' of the shape used.

Monument Visit

• Students can be taken out for a field trip to a heritage site.
• They will explore and identify various 3-dimensional shapes in the structure (for example, dome, pillar, etc.)
• A small worksheet can be designed to test their knowledge of application of mensuration to the structure. 

It can comprise of questions like

• Number of pillars of cylindrical shape
• Number of domes in the shape of hemisphere
• Dimension of any one pillar
• Volume of a pillar

Collage/PPT on Number System
Make a collage or PPT on- The Journey From Counting Numbers to Real Numbers.

Statistics
To find the mean height and weight of the students of their class.

• Students will be asked to measure the height and weight of all the students of their class in the Mathematics laboratory.
• These observations will be recorded on the board.
• The students will then find the mean height and mean weight of all the students of their class.
• Prepare a grouped frequency distribution table.

Layout Plan for a 3 Bedroom House

Design a layout plan for a 3 bedroom house on an A3 size sheet. Use the measurements in cms and find the space enclosed by each room in the layout.

Map Activity on Coordinate Geometry

The location of any place ona map is identified using longitudes and latitudes. Take the latitude as x-axis and longitude as y-axis, On the map of India, locate the four metropolitan cities and find their coordinates. Also find the distance between any 2 of the cities using distance formula.

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Hand Out-05

Theory of Multiple Intelligences

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The theory of multiple intelligences is a theory of intelligence that differentiates it into specific (primarily sensory) "modalities", rather than seeing intelligence as dominated by a single general ability. This model was proposed by Dr. Howard Gardner in his 1983 book

 Frames of mind'', 

'Theory of Multiple Intelligences'. 

Instead of considering intelligence a single entity described psychometrically with an IQ score, Gardner understands of intelligence views it as many different things. Gardner says that oyr schools and culture focus most of their attention on linguistic and logical-mathematical intelligence. He further says that we should also place equal attention on individuals who show gifts in the other intelligences: the artists, architects, musicians, naturalists, designers, dancers, therapists, entrepreneurs, and others who enrich the world in which we live. Unfortunately, many children who have these gifts do not receive much reinforcement for them in school. Gardner has identified different types of intelligences that each individual has the capacity to possess. The idea of multiple intelligences is important because it allows for educators to identify different strengths and weaknesses in students 

Summaries of Nine Intelligences:

Linguistic intelligence involves sensitivity to spoken and written language, the ability to learn languages, and the capacity to use language to accomplish certain goals. This intelligence includes the ability to effectively use language to express oneself rhetorically or poetically; and language as a means to remember information. Writers, poets, lawyers and speakers are among those that Dr. Howard Gardner sees as having high linguistic intelligence.

Logical-mathematical intelligence consists of the capacity to analyze problems logically, carry out mathematical operations, and investigate issues scientifically. In Dr. Howard Gardner's words, it entails the ability to detect patterns, reason deductively and think logically. This intelligence is most often associated with scientific and mathematical thinking.

Musical intelligence involves skill in the performance, composition, and appreciation of musical patterns. It encompasses the capacity to recognize and compose musical pitches, tones, and rhythms. According to Dr. Howard Gardner musical intelligence runs in an almost structural parallel to linguistic intelligence.

Bodily-kinaesthetic intelligence entails the potential of using one's whole body or parts of the body to solve problems. It is the ability to use mental abilities to coordinate bodily movements. Dr. Howard Gardner sees mental and physical activity as related

Spatial intelligence involves the potential to recognize and use the patterns of wide space and more confined areas. This area deals with spatial judgment and the ability to visualize with the mind's eye.

Interpersonal intelligence is concerned with the capacity to understand the intentions, motivations and desires of other people. It allows people to work effectively with others. Educators, salespeople, religious and political leaders and counsellors all need a well-developed interpersonal intelligence.

Intrapersonal intelligence entails the capacity to understand oneself, to appreciate one's feelings, fears and motivations. In Dr. Howard Gardner's view it involves having an effective working model of ourselves, and to be able to use such information to regulate our lives.

Naturalist intelligence involves understanding the natural world of plants and animals, noticing their characteristics, and categorizing them; it generally involves keen observation and the ability to classify other things as well.

Existential intelligence entails an ability to contemplate phenomena or questions beyond sensory data, such as the infinite and infinitesimal.

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Hand Out-06

Gender Sensitization

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We often do not realize that our actions in the classroom are sometimes discriminatory in nature. Gender bias creeps in our teaching-learning processes without us even being aware of it. Thus, the first step in providing a gender equitable environment is to be aware of gender issues. A teacher's role is central in the teaching learning process and the actions, language and behaviour of teachers convey meaning to the learners. That is why whether we realize or not, teachers' perceptions on gender issues influence students' understanding of gender roles. The terms and expressions used by the teachers, the tone of their voice or inadvertently reinforce gender stereotypes. There is a need to act gestures may responsibly towards gender issues and take appropriate actions to correct any conscious or unconscious gender biases. 

A common misconception is that boys are inherently better at learning Mathematics than girls. Such preconceived notions are to be debunked if gender equity has to be endorsed. Promoting gender equity in the classroom involves not only providing equal resources to both girls and boys but also providing equal opportunities to learn.

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Promoting Gender Equitable Environment

Encourage equal participation of girls and boys in various learning activities. Ensure that gender stereotypes are not promoted in any of the learning materials. Ascertain that the learning material is equally accessible to both girls and boys. Build up the confidence of girls and make them realize that they are equally adept at learning Mathematics.

Provide for adequate time to students, especially girls, who may be shy or afraid to speak up. Always try to incorporate both female and male names in the examples or questions that you frame. For group activities, always make groups consisting of both boys and girls and encourage everybody in the group to participate equally.

Discuss the contribution of female mathematicians in the classroom.

Activity:- Work in your respective groups. Go through the sample lesson plan given below. One group will present a role play based on step 5 of lesson steps. The other groups will observe the role play from a gender perspective. After the role play, the observations may be discussed.

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Hand Out-07

Child Abuse

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Child Abuse is the Physical, Sexual or Emotional maltreatment or neglect of a child. Child neglect is the failure of a parent or other person with responsibility for the child to provide food, clothing, shelter, medical care etc, Even lack in attention and love is considered as neglect. Child abuse can occur in child's house or in the organization, School or communities the child interact with.

There are 4 major categories of child abuse:

a) Neglect
b) Physical abuse
c) Psychological or emotional abuse
d) Sexual abuse

A) Neglect: 

Neglected kids experience delay in physical, psychosocial development, resulting into psychosocial and impaired neuropsychological functions effecting their language, memory, attention and social skills. There is increase in aggressive & hyperactive behaviour. They find difficulty in forming and maintaining relationships.

B) Physical Abuse: 

Involves physical aggression directed at a child by an adult. E.g. Physical corporal punishment, Humiliation, Spanking, Slapping, Beating, are the forms of physical abuse.

C) Psychological or emotional abuse: 

Loud yelling, coarse and rude attitudes, harsh criticism, are kind of emotional abuse. Victims tend to use abusive language and tend to have insulting behaviour. This kind of abuse leads to a tendency of blame learned helplessness & overly passive behaviour.

D) Sexual Abuse: 

Child sexual abuse is a form of child abuse in which an adult or older adolescent abuses a child for sexual stimulation. It includes asking a child to engage in sexual activities & exposure of sexual organs to a child, displaying pornography, Sexual Contact etc. The Victim gets nightmares, insomnia, low self-esteem, depression, & finds himself/herself guilty.

Indicators: 

Thumb Sucking, sleep disturbances, bed wetting, trouble walking or sitting, displays knowledge or interest in sexual act inappropriate to his/her age, avoids specific person.

Say 'No' When someone touches inappropriately
Say a firm NO
To get away fast,
To call for help,

Online Safety: 

Al information should not be revealed on any site. Everyone online is not a friend, do not meet any online friend alone. The abuses results into different forms of violence against children like child labour, Child Trafficking, Child Marriage, Child Prostitution etc.

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Hand Out-08
Handout on Revised Bloom's Taxonomy

Understanding Blooms Taxonomy (Revised)

Before moving on to classroom teaching or testing, instructional objectives must be properly understood because they play a key role in the instructional process. When properly stated, they serve as guidelines for both teaching and evaluation. A clear description of the intended outcomes of instruction helps in selecting relevant materials and methods of instruction, in monitoring pupil learning progress, in selecting and constructing appropriate evaluation procedures.

An objective is 

• an intent communicated by a statement describing a proposed change in a learner 
• a statement of what the learner is to be like, when he/she has successfully completed a learning experience

Taxonomy of Educational Objectives:

Taxonomy is a classification system that is arranged in a hierarchy. Dr. Benjamin S. Bloom and his associates have classified instructional objectives into three major domains: cognitive, affective and psychomotor. The cognitive domain includes those objectives that deal with recall or recognition of learned material and the development of intellectual abilities and skills. The largest proportion of educational or instructional or teaching learning objectives falls into cognitive

domain. 

The affective domain includes objectives that emphasize interests, attitudes and values and the development of appreciation and adequate adjustment. The psychomotor domain is concerned with physical, motor or manipulation skills. Handwriting, map drawing, preparation of graphs ete. are examples of psychomotor domain. The cognitive domain as described by Bloom et al. (1956) is focused on the feature of complexity. They are ordered from simple to complex. The cognitive domain consists of the following six major levels: Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation.

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Bloom's Revised Taxonomy of Instructional Objectives

Lorin Anderson, a former student of Bloom, revisited the cognitive domain in the learning taxonomy in the mid-nineties and made some changes, with perhaps the two most prominent ones being, changing the names in the six categories from noun to verb forms, and slightly rearranging them (Anderson et al., 2000; Pohl, 2000). This new taxonomy reflects a more active form of thinking and is perhaps more accurate.

REVISED BLOOM'S TAXONOMY ACTION VERBS

These are the different stages of learning and understyanding the concepts

Remembring

This is the first stage of introducing any technique to the students. At this stage some basics, guidelines or some formulas are given to the students to learn.

Understand

After understand students tri to understand all these formulas or key points properly.

Applying

Here students will be given some simple problems, so that students can apply the formulas or the algorithms to reach the target.

Analysing: 

At this stage students will be given some more complex problems to understand the topic properly.

Evaluating

At this stage students starts relating the concepts with other problems or with other situations. Here students can find the result with one algorithm and then verify it with another alorithm and formulas.

Creating

At this stage students start creating and solving other stuations with the same technique as their own.