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