Haneet Gandhi: Issues in Mathematics Teacher Education
-
Upload
amber-habib -
Category
Documents
-
view
224 -
download
0
Transcript of Haneet Gandhi: Issues in Mathematics Teacher Education
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 1/23
Issues in Mathematics
Teacher Education
Haneet GandhiDepartment of EducationUniversity of Delhi
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 2/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 3/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 4/23
! Understanding the subject
! Understanding the content
! Understanding the understanding of the
learner
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 5/23
! 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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 6/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 7/23
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?
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 8/23
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 9/23
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 10/23
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?
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 11/23
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.
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 12/23
! 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
!"#$%&'$()*+$+%,"%-".%
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 13/23
! If represents one unit then
represent 2/3 of this unit
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 14/23
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 15/23
To the following figure, four students’ responses are as
stated below. Analyze each response to explicate the
reasoning behind their responses.
!"#$%&"'()' *+,'-.'"/%'0/-1%'23'3/4$%$'
!"#$%&"'5)'' 6'7''23'3/4$%$'
!"#$%&"'8)'' *)'9':4;"3'4;%'3/4$%$'
!"#$%&"'<)' 9)*':4;"3'4;%'#&=3/4$%$'
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 16/23
!"#$%#&'()&#$(*$+"%##$&+,-#)+&$()$.$/,#&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%;''
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 17/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 18/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 19/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 20/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 21/23
While teaching triangles, a teacher noticed that students
had difficulty understanding “altitudes of a triangle”.
What pedagogic strategies would you suggest to theteacher?
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 22/23
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
8/3/2019 Haneet Gandhi: Issues in Mathematics Teacher Education
http://slidepdf.com/reader/full/haneet-gandhi-issues-in-mathematics-teacher-education 23/23
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