Society’s technological, economic, and cultural changes of the last 50 years
have made many important mathematical ideas more relevant and accessible
in work and in everyday life. As examples of mathematics proliferate, the
mathematics education community is provided with both a responsibility and an
opportunity. Educators have a responsibility to provide a high-quality mathematics
education for all of our students.
Nowadays, environmental issues including air and water pollution, climate
change, overexploitation of marine ecosystems, exhaustion of fossil resources,
conservation of biodiversity are receiving major attention from the public,
stakeholders and scholars from the local to the planetary scales. It is now
clearly recognized that human activities yield major ecological and environ-
mental stresses with irreversible loss of species, destruction of habitat or cli-
mate catastrophes as the most dramatic examples of their eﬀects.
Constructivism is the bedrock on which the whole reform movement,
especially the three NCTM volumes [N1]-[N3], rests. Roughly, this is the
education philosophy which holds that the acquisition of knowledge takes
place only when the external input has been internalized and integrated
into one’s own mind. Thus learning requires the construction of a mental
image in response to the external input.
While a little bit of group learning and guiding-on-the-side is good in
the classroom, too much poses an obstruction to eﬀective dialogue between
teacher and students as well as to the eﬃcient transfer of knowledge from
teacher to students. In such a climate, gone is the possibility that the teacher
can share with students his or her insights or warn them against pitfalls, or
that students can learn enthusiastically from their teacher in class and do
the mental construction at home — with or without a group of friends.
The PhD in Biostatistics provides training
in the theory of probability and statistics in
biostatistical methodology. The program is
unique in its emphasis on the foundations
of statistical reasoning and in requiring its
graduates to complete rigorous training in
real analysis-based probability and statistics,
equivalent to what is provided in most
departments of mathematical statistics.
PhD candidates are required to pass a
comprehensive written examination covering
coursework completed at the end of
their first year.
If the card is the 4♦, pull out the 8♦ for the suit, then the 4♠ for the
value. In this case, you don’t add the suit card to the other cards to make
Practise so you are confident with working out the set of cards you need
for each selection, and practise the patter or dialogue as that’s what sells
the trick. Remember, this is a great feat of mental powers, so make sure it
looks like it.
You could present this as a psychic experiment where you claim you can
read the printing on the cards with...