Unformatted text preview: Mathematics Education
Mathematics
at Second Level
A Teacher’s Views
Teacher’s
E. E. Oldham
E.
with Neil Hallinan
Members of the Irish Mathematics Teachers’
Members
Association
Association
Symposium on “The Place of Mathematics
Symposium
Education in Ireland’s Future”
Education
2nd February 2010 Why me
(a third level lecturer in
mathematics education)? It’s a school day…
… difficulties with regard
to substitution and
supervision!
Lecture prepared with IMTA
colleague, Neil Hallinan Neil’s background
Neil’s Experienced secondary teacher … with a track record of reflective and
innovative approaches
innovative Longstanding member of the IMTA Dublin Branch Committee
Editor of and contributor to the IMTA
Editor
Newsletter [mathematics education journal for
IMTA members]
IMTA
Ex officio on IMTA national Council My background Former second level teacher In my fortieth year of membership of the IMTA Time in many different schools / classrooms Role as H. Dip. Ed. / Postgraduate Diploma in
Role
Education supervisor etc.
Education Former Education Officer (NCCA) Experience of crossnational studies of
Experience mathematics curriculum and achievement
mathematics SIMS, TIMSS, PISA Context
Context Ireland was deeply involved in the
Ireland curricular changes in mathematics in the
1960s…
1960s…
Not my IMTA colleagues! … but was slow as a general concern and at
general system level to focus on issues of the 1980s
system
1980s
and onwards with regard to teaching and
learning rather than curriculum content
learning Problem solving, modelling, applications
Teaching for / learning with understanding
“Realistic Mathematics Education” “Voices crying in the
wilderness” … … “Sowing the wind and reaping the whirlwind” Project Maths! So consider “a teacher’s views…”
So Mathematics education has a central role in
Mathematics
central Ireland’s future
Ireland’s Essential for recovery from recessionary present Mathematics teachers act as guardians of a
Mathematics mathematical culture that they have
mathematical
received
received To be maintained and transmitted to the next
To
generation of practitioners
generation Questions on teachers’ practice
Questions
1.
2.
3.
4.
5. Who do we teach?
What is mathematics education for?
for
What do we teach?
How do we teach?
Where has mathematics teaching been and
where is it going?
going 1. Who do we teach?
1. Almost everyone!
Almost everyone More students sit Leaving Certificate
More
Mathematics than sit any other subject
Mathematics
• 2009: Maths. 51 905; English 51 033; Irish 45 643…
2009: Implications for performance / achievement Students have priorities reflecting the current
Students
reflecting
current culture
culture Passing examinations rather than learning
Social networking, social skills, etc. 2. What is mathematics
2.
education for? In our teaching we are conscious (not always
In explicitly) of the role and purpose of
education in mathematics
education Transmitting culture
Transmitting culture
Developing skills for employment
Developing skills
Assessing intelligence
Assessing intelligence
Assessing character (diligence, perseverance…)
Assessing character
Developing intelligence, logical skills and
Developing intelligence logical
visualisation skills
visualisation
./.
./. And also Developing appreciation of methods of proof
Developing appreciation methods
as well as beauty of structure
beauty
Developing models of reality for better
Developing models
understanding and use
understanding
Preparing for further mathematical
Preparing
achievement (developing fluency as well as
achievement developing fluency
understanding)
understanding
develop recreational options, selffulfilment
develop
and satisfaction of insight
and … all in a crowded
curriculum… …with less time than formerly
given to Mathematics
at 1st & 2nd level 3. What do we teach?
3. This includes Numerical skills
Geometricspatial skills
Symbolic representation skills
Visual representation skills
Practical instrumental skills
Logical skills
Procedural skills
Problemsolving skills There is limited time for skill development!
There limited For a future intending to place more emphasis
For on timedependent skills than in the past, it is
necessary to consider the implications of this
for the whole set of skills involved
whole Achieving deeper understanding, more fluent
Achieving skills and better problem solving will require More time…
… or acceptance of content reduction
content
• … unaccompanied by shouts of “dumbing down”
unaccompanied
• …or by further reduction of time given to mathematics! 4. How do we teach?
4. Under pressure!
Under pressure “Covering” the syllabus
Having very limited resources (room space,
Having
laboratories, technology…)
laboratories, Methods used Often those designed to increase the “delivery”
Often
of concepts per unit of time ratio
of
Insufficient opportunity for “up close work”
with students
with Note There are, and always have been, many good
There
teachers in our schools
teachers
• Dedicated to and knowledgeable about the subject
knowledgeable
• Vibrant and gifted in developing knowledge and love of
gifted
the subject in (many of!) their students
the They may be “traditional” in using wholeclass
They
teacherled approaches, but teaching actively
actively
• Emphasising (relational) understanding, encouraging
Emphasising
questions from students, identifying and addressing
misconceptions, describing applications, etc.
misconceptions, They may be “progressive” in using discovery
They
learning and handson (and “minds on”) methods
learning Project Maths is emphasising the latter way Yes, we can do with more of it…
… but there may be those (teachers and students)
whom it does not suit
whom
• Variety to suit different needs can be good And yes, there are other teachers as well as
And yes there those described on the last slide
those For example, some teachers of other subjects who
For
are asked to teach mathematics…
are
… and may not have the vision / content knowledge
/ specialised knowledge of teaching mathematics
specialised
… so teach rules without reasons
rules Examples Take it over and change the sign… Why?
Take
That’s the rule!
That’s
Why are we doing this? It will be examined in
Why
Paper 2, question 6, part b (ii)
Paper
• [and if they put it in part b (i), that’s a dirty trick
[and
and how could you possibly be expected to answer
the question?]
the A parody, but … … and students tend to
reinforce this “didactical
contract” 5. Where was / is mathematics
teaching going?
teaching Teachers have been (and are, and are willing to
Teachers be) to the forefront in developing new
syllabuses and teaching approaches
syllabuses One of the most appropriate developments is
One the LC Certificate Foundation level course
LC … which was not given adequate recognition for
recognition
what it contains…
… so students take Ordinary level and the culture
of rote learning / teaching is reinforced
rote For strong students, teachers support Young
For strong
teachers Scientists and Mathematics Olympiad entrants
Scientists … though the PISA study indicates we have
comparatively few highflying students…
comparatively
… but also comparatively few low achievers (hence,
but
“average” [mean] performance)
“average” A thought on the gatekeeping role of the LC
thought
gatekeeping Getting through the gate is often seen as much more
Getting
much
important than what you bring with you…
important
Incentivising through rewarding Mathematics is not
Incentivising
not
the answer?
the
Give a 10% bonus in every other subject done by a
Give
every
student of Higher Mathematics?!
student Hard problem!
Hard The syllabuses have LONG advocated learn ing with understanding rather than by rote
ing
understanding For decades we have tried to increase uptake
For of Higher levels, but the “baseline” pattern
of
but
was established in the 1960s and before…
1960s …so issues arise in aiming for greater
so uptake / depth / understanding vs. “dumbing
down”
down” If it were easy, we’d have solved it long since ...
View
Full Document
 Winter '08
 Staff
 Math, IMTA

Click to edit the document details