My students don’t hate maths anymore
Ask your students where in their daily life they use such concepts
as percentage or pie and note how many respond. Yes, it is true that many of
the students here don’t really know the application of these fundamental
concepts in mathematics.
The application of mathematics in its true sense enables ordinary students to
do extraordinary work. The use of differential equation enabled scientists to
calculate the Voyager’s journey to the planets, category theory — a theory of
mathematical structures, to develop computer software, statistics — in ecology,
to provide the theory and methodology when studying the laws of population
change and also in medicine, for analysing data on the causes of illness and on
the utility of new drugs.
The question is how Pakistani math teachers would be able to move the
students from lower to higher order thinking skills in mathematics to enable
them to apply their learning for innovation and creation; how the students will
love mathematics instead of hating it.
First of all a maths teacher must foster a positive attitude in students
toward the subject matter. Judy Willis, a middle and elementary school teacher
and a former neurologist, in her latest book Learning to Love Math examines
strategies for building math “positivity” in students. She states, “Before
children can become interested in math, they have to be comfortable with
it. Students build resilience and coping strategies when they learn how
to use their academic strengths to build math skills and strategies. A
teacher’s intervention helps them strengthen the networks that carry
information through their brains’ emotional filters to the area where
higher-order thinking skills are concentrated, the prefrontal cortex (PFC).
With practice, they will be able to use the highest-level analytical
networks in the PFC to evaluate incoming information and discover creative
solutions to maths problems.”
Second, a maths teacher must find ways to strengthen the cognitive processes
required to compute maths problems because what looks like a struggle with
maths may actually be a deficiency in the underlying cognitive processes. Mel
Levine, author of A Mind at a Time and other books on learning differences,
identifies many of the brain’s processes that math requires (see Figure 1).
Broyles and Pittard, faculty of The Howard School, applied Mel Levine’s
model for the teaching of long division and verified the usability of the
model. They found that in order to solve a long division problem a student must
remember and complete more than 20 steps which require sustained attention to
the process — procedural recall, language processing, detailed paper
organisation, scattered visual tracking, and a strong working memory.
Together there were at least 13 of the above sub-processes at work in long
division. If teachers just teach the order and process of the algorithm,
instead of investigating at what point the process is breaking down, the
student will likely continue to struggle.
Third, while teaching a maths problem a maths teacher must keep the
following additional points in mind:
• Distinguish between skill in computation and skill in mathematical
thinking: Many students who struggle with pencil and paper computation are
strong spatial thinkers and mathematical problem solvers. If students are
verbally asked, “If you put nine balls evenly in three baskets, how many go in
each?” And a student can answer it, he understands division. If the same
student cannot do long division, then some process besides conceptual
understanding is breaking down. In this case, calculators may be allowed during
problem solving.
• Suggest ways that improve working memory: A weak working memory has
tremendous impact on maths performance. Even simple computation requires
working memory to complete, and as the complexity in maths increases, so does
the demand on working memory. One way to help students is to allow them to
write each step of the problem, jotting notes along the way and having the
steps of a procedure available as a checklist.
• Devise easier ways to explain complex concepts: All students move through
a developmental sequence from concrete to abstract, and many need the physical
representations for a longer period than is often provided in Pakistani
schools. Also, many students may need the concrete-to-abstract sequence
represented for each new concept. In Figure 2, I have shown one worksheet that
I developed to teach the concept of rounding-off the decimal fractions.
Students were asked to suggest (the bunny on the worksheet) the shortest way to
escape the rain.
• Develop students’ mathematical vocabulary: Many students with language
difficulties almost certainly have difficulties in receiving instruction
through language-heavy methods. Students with phonological processing issues
may make errors like writing 13 for 30. Language issue becomes worse in such
schools where textbooks and the medium of instruction are English but students’
processing of instruction is done in languages other than English.
Language also becomes a barrier when students attempt to solve word
problems. Word problems should be approached with many of the same strategies
used for reading comprehension, with special attention to the maths words that
cue the student to perform a particular operation.
• Relate mathematics with other subjects: Thirty to 60 minutes a day is not
enough for maths. If maths abilities are to develop in the sense of use and
application, then maths should be part of all subjects when appropriate. The
maths teacher should work in collaboration with other teachers. For example,
social studies teachers should ask students to compare elements such as land
area, GDP and population. Science teachers should have students collect and
process data. Language arts teachers should have the students work with numbers
that occur in literature for instance distances, dates and time, and so on.
Math is hard for many students. Left-brainers usually love maths and
right-brainers do not. Teaching for people who struggle with maths should be
done with appropriate examples, hands on activities, objects and online
tutorials which show various ways to teach any topic with the focus on tapping
into neuro-developmental processes hence developing students who are
mathematical thinkers, not algorithm solvers.
As teachers and schools become better educated about the cognitive processes
involved in maths, all students, including those with learning differences, can
become mathematical thinkers.
The writer is a lecturer at a private university in Karachi
zeeshan.paul@ndie.edu.pk