Haneet Gandhi: Issues in Mathematics Teacher Education

8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education

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Issues in Mathematics

Teacher Education

Haneet GandhiDepartment of EducationUniversity of Delhi



Outline of the Presentation

! Part A: Issues of the Mathematics teacher

programmes

! Part B: Examples of teachers mathematical

Understanding! Part C: Structure of Teacher Education

Programmes in Delhi University



Mathematical knowledge for teaching?

! Mathematical Knowledge at college and

Mathematical Understanding for teaching.

! Mathematics of procedures versus

Mathematical thinking, central to conceptualunderstanding.

! Belief towards the subject: mathematics to be

taught/ mathematics to be evolved



! Understanding the subject

! Understanding the content

! Understanding the understanding of the

learner



! Issues of Elementary teachers: Understanding

elementary mathematics content, learners and their

socio-cultural background

! Issues of secondary school teachers: bridging the

content of primary with senior secondarymathematics, Understanding the mathematical

thinking processes

! Issues of senior secondary level: teaching abstract

concepts, bridging the content to real life application,

preparing students for a professional/ academic life





programmes






Examples

I own a Bakery shop and each day I make several

rectangular sheet cakes which needs to be cut into

eights.

To attract customers, I need to cut the cakes into eights

different ways for each day. Can you suggest some of the different ways to cut the cake?



Post Activity

! How can we verify that pieces that are not the

same shape contain the same amount of

cake?

! What factors should be considered whendeciding whether the two designs are

different?



Let’s Think

! Opportunity to represent parts of a whole by

using area model of fractions. Negating the

over-generalisation and believe that the

pieces have to be congruent rather than have

the same area.

! Value is not in determining the final “right”

answer but rather is in the process and

determining how different factors are relevant.



! Represent 7/2 pictorially

! Which fractional part is greater? Explain your

answer

! Which of the following figures represent 2/3 of

the whole. Explain your choices

!"#$%&'$()*+$+%,"%-".%



! If represents one unit then

represent 2/3 of this unit



To the following figure, four students’ responses are as

stated below. Analyze each response to explicate the

reasoning behind their responses.

!"#$%&"'()' *+,'-.'"/%'0/-1%'23'3/4$%$'

!"#$%&"'5)'' 6'7''23'3/4$%$'

!"#$%&"'8)'' *)'9':4;"3'4;%'3/4$%$'

!"#$%&"'<)' 9)*':4;"3'4;%'#&=3/4$%$'



!"#$%#&'()&#$(*$+"%##$&+,-#)+&$()$.$/,#&0()$1$2"34"$

3&$5%#.+#%$678$(%$879:$.%#$.&$&+.+#-$;#<(=>$

!"#$%&"'(')'' (3',=*>9'4&$'?=,>9'"/%;%.-;%'@-"/'"/%'.;4AB-&3'4;%'%C#41D'

!"#$%&"'5)' E/%'3/4$%$':-;B-&'2&'"/%'3%A-&$'FG#;%'23'G;%4"%;'"/4&'"/%'

' ' 3/4$%$':4;"'-.'F;3"H'"/%;%.-;%',+?'23'G;%4"%;'"/4&'*+,'

!"#$%&"'8)' I41.'-.','23'9'7'4&$'*'23'A1-3%;'"-'9'7'J'

' ' I41.'-.'?'23'*'7'4&$','23'K-;%'"/4&'$23"4&"'.;-K'*'7'J'

' ' L&',+?'H'"/%;%.-;%'K#A/'1%33':-;B-&'"/4&'/41.'0211'@%'

1%M'-N%;'' ' "/%;%.-;%',+?'23'@2GG%;''





programmes






Pre-service Teacher programmes of

Delhi University

! Bachelor of Elementary Education – B.El.Ed

! Bachelor of Education: B.Ed

! Math A : Secondary School

! Math B : Senior Secondary School! Math C : Primary Level



Bachelor Elementary Education

(B.El.Ed)

4 year Integrated course pursued after Class XII

Pedagogic Courses Liberal Options (Mathematics of tertiary level)

First year: Revisiting the mathematical content

Third Year: Understanding the subject, Theoriesrelated to mathematics learning, understanding thelearner and their (Mis)conceptions.

Practicum : Identifying and collecting resources

Fourth year: Focus is on understanding theconcepts and nature of the subject at middleschool.

Practicum Part: School Internship Programmeof 6 months divided across primary and middleschool teaching

Studied in Second andThird year

Course: Mathematics of

tertiary level



There is one symbol that we have in the base –ten system

that does not exist in the Egyptian system that is very

important.

What is the symbol?

Why is this symbol so important when writing numbers and

adding and subtracting in the base ten? Evolve a system of your own that has the following

attributes

a) Base 6

b) Positional value of symbols determine the numbers



While teaching triangles, a teacher noticed that students

had difficulty understanding “altitudes of a triangle”.

What pedagogic strategies would you suggest to theteacher?



B.Ed Maths A level

! Limitation of the course is its duration.

! Content understanding is ensured at the entrylevel

! Pedagogy course

! Nature of discipline

! Nature of learner

! Instead of content the focus is on the thinkingprocesses: Algebraic thinking, Proportional

Thinking and Geometrical Thinking! Critically analysing the issues in evaluation



B.Ed Maths B

! Content understanding is assured at entrylevel

! Challenge here is to help make studentsunderstand the exist level that is needed after

schooling and this ranges from higher mathematics, vocational mathematics,professional or functional mathematics

! Thinking processes: Teaching of Calculus,

Teaching of Stochastic, Teaching of Trigonometry

Haneet Gandhi: Issues in Mathematics Teacher Education

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