MATH
Effective teaching
Which instructional methods
are most effective for math?
James Hiebert and Douglas Grouws reveal which elements
Work and talk
of math instruction have been shown to help students’
Teachers and students should intentionally
and explicitly talk about, and work on,
conceptual understanding and their skill effi ciency important mathematical relationships.
At least some time during each lesson
DECIDING WHICH INSTRUCTIONAL methods are most effective: conceptual should be spent on the following activities:
METHODS are most effective for increasing understanding – the construction
●
Examining relationships among facts,
students’ learning continues to be one of meaningful relationships among procedures, and ideas within a lesson and
of the great challenges for educational mathematical facts, procedures, and ideas; across lessons. Is one problem a special
research. Should teachers use Method A and skill effi ciency – the rapid, smooth, case of the preceding problem? How the
or Method B? Which one will show the best and accurate execution of mathematical problems solved today are similar to and
results? procedures. These two learning goals are different from the problems considered
An important truth about the effectiveness central to mathematics learning and have yesterday? How do linear graphs, tables
of instructional methods is that particular often competed for attention. of ordered pairs, and linear equations all
methods are not, in general, effective or represent the same linear function?
ineffective. Instructional methods are Conceptual understanding
●
Exploring the reasons why procedures
effective for something. Educators always Research conducted over the past 75 years work as they do. In addition to practicing
need to be clear about what this something has spanned a wide range of mathematics procedures, students should examine
is when they talk about the effectiveness of topics, age groups, and class settings. The and discuss why the procedures work,
instructional methods. results point to two important features of especially when new procedures are being
Focusing on the following two learning teaching that can help the development of introduced. Why do we usually add from
goals, we ask which instructional students’ mathematical understanding. right to left? When we solve an equation,
10 Better: Evidence-based Education fall 2009
Better(US) Fall09.indb 10 14/10/09 13:04:59
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