Charles Ungerleider, Professor Emeritus of Education, The University of British Columbia [permission granted to reproduce if authorship acknowledged]
Ontario Premier Doug Ford’s pledge to eliminate inquiry oriented math (sometimes referred to pejoratively as “discovery math”) is one of the
most recent volleys in the mathematics war. Ford’s pledge, made in the heat of
an election campaign, politicized a long-simmering argument about the teaching
and learning of mathematics.
In 1999 - many scientists,
mathematicians, and educators in the US signed an open letter published in the Washington
Post.
They called into question ten mathematics programs considered exemplary by the
U.S. Department of Education. The letter was written in part because parents
had beseeched its author, David Klein, to help them do something about the way
mathematics was being taught.
In
April of the following year Klein wrote an article in the April 2000 issue of the American School Board Journal, accusing
the U.S. Department of Education of promoting programs that de-emphasized
arithmetic and algebra. Klein compared mathematics to martial arts and music.
“A novice cannot hope to achieve mastery in the martial arts without first
learning basic katas or exercises in movement,” argued Klein. “A violinist who
has not mastered elementary bowing techniques and vibrato has no hope of
evoking the emotions of an audience through sonorous tones and elegant
phrasing. Arguably the most hierarchical of human endeavors, mathematics also
depends on sequential mastery of basic skills.”
Preferring evidence to emotion, my
colleagues and I recently reviewed a segment of the vast literature devoted to
mathematics that addressed the question “What are effective instructional
practices in K-12 mathematics education?” The research we examined* indicates
that direct or explicit instruction
has a positive impact on mathematics performance and achievement. When teachers
provide students with explicit step-by-step instructions about how to use
problem solving strategies, paired with extensive practice, learning outcomes
are positive across age groups and student populations.
The effectiveness of teacher-facilitated instruction and inquiry-based
mathematics is less conclusive. While the effects seem to be positive, they
also tend to be small. Some authors suggest that authentic problem solving and
facilitated learning may be effective after students have learned foundational
concepts and procedures.
David Robitaille, the Canadian study director for the
Third International Mathematics and Science Study, a collaborative effort of
forty-two nations, agrees with the critics who say students need to know the
basics. “You can’t be comfortable doing mathematics if you have to think about
what seven times eight is. And you shouldn’t need to use a calculator to
estimate the cost of several purchases at a store.” He argues that students
need to develop good “number sense” and a high level of comfort with numbers
and how they work. On the other hand, Robitaille says that students do not need
to do worksheets of long division with multi-digit dividends and divisors.
Other practices that affect achievement include peer-assisted learning,
the use of visuals and manipulatives, and the provision of feedback to teachers
and students about their progress. Peer-assisted learning has a consistent
positive effect on achievement and performance, but the magnitude of the impact
differs across studies. Providing feedback to students also tends to improve mathematics achievement, though the
magnitude of the effect also varies. Visuals and manipulatives can be
effective, but their effect seems to be limited to specific types of skills
(e.g., retention and problem solving) and requires carefully planned and executed
instruction.
There is a range of instructional programs for teaching mathematics. The
evidence seems to favour those that focus on one specific math content area rather
than those that focus on multiple content areas. The instructional techniques
found to be effective for students with special needs are much the same as the
techniques that have been found to be successful for students without special
needs. Direct instruction (explicit instruction) seems to be particularly
effective with this population.
I lament the politicization of mathematics instruction or
instruction in any subject because it encourages people to choose sides
depending upon the personalities involved and the emotions those personalities
evoke rather than considering the evidence. When the evidence is ignored it is to
the detriment of everyone, but especially students and teachers.
* A list of the references that informed our judgments about
effective instructional practices in mathematics is available upon request.
Please send an email to On.Education.Canada@gmail.com.