|
|
Year 4 – 6 Numeracy Exploratory Study
Executive Summary
In 2000, the Ministry of Education offered New Zealand schools
a pilot professional development programme, the Year 4–6
Numeracy Exploratory Study, to improve the teaching and learning
of number concepts and skills.
The Numeracy Exploratory Study presented teachers with a
framework of broad stages in students' mathematical thinking
in which the different stages are characterised by the range
of strategies that students use to solve problems. A key part
of the Study involved the teachers in using a diagnostic interview
to assess the stages of their students' thinking. On the basis
of this interview, their students were then grouped for instructional
purposes. The Study also introduced the teachers to problem-solving
strategies and the activities to develop them. The overall
aim of the Numeracy Exploratory Study was to develop the teachers'
knowledge of number concepts, student strategies, and instructional
practice in order to improve student achievement in years
4 to 6.
This report evaluates the impact of the Year 4–6 Numeracy
Exploratory Study on twelve teachers in six schools, three
in the Auckland area, two in the Waikato area, and one in
the Wellington area. The evaluation report identifies changes
in teacher knowledge and practice that can be attributed to
the professional development provided by the Numeracy Exploratory
Study.
The research addressed three main questions:
- Does the Year 4–6 Numeracy Exploratory Study have an
impact on the teachers' professional knowledge? If so, what
changes?
- What experiences and factors do the teachers report as
influencing these changes?
- Do the teachers perceive that changes in their professional
knowledge have an impact on their classroom practices? If
so, how?
Key Findings
- One of the key results of the Year 4–6 Numeracy Exploratory
Study was an increased emphasis on number over the other
strands of the mathematics curriculum. Each of the teachers
reported that they adjusted their long-term plans so that
number was at least half of their total mathematics programme.
The ways in which they did this varied. For example, some
of the teachers taught number specifically on one day of
every week, while others taught number in each alternate
week of their year's programme.
- There was a shift in emphasis on which aspects of number
were taught. Each of the teachers focused more on mental
strategies and de-emphasised and delayed the introduction
of the written algorithm.
- The emphasis on students' strategic thinking appeared
to engage both the teachers and the students in the mathematics
and to become a way into mathematics, enabling the students
and the teachers to work with numbers.
- Emphasising strategies allowed the teachers to think differently
about the ways in which they taught the times tables and
conducted maintenance of previous learning, often referred
to by teachers as the “Quick Ten”.
- The teachers saw mathematical knowledge as underpinning
their teaching of the strategies. This view of knowledge
was a shift from their previous view, in which knowledge
constituted the main content of their mathematics programmes.
- This shift in emphasis to mental strategies had an impact
on the ways in which teachers taught their students, as
evidenced by changes in the types of mathematics equipment
and the ways in which this equipment was used, by a greater
emphasis on questioning and students' explanations, and
by a change in the basis of instructional groups.
- The diagnostic interview appeared to be a trigger for
many of these changes as it provided teachers with more
detailed knowledge of student thinking.
- The teachers reported having a greater understanding of
number and how they might teach it more effectively.
- The facilitators' demonstrations of lessons and diagnostic
interviewing, backed up by in-class support, appeared to
enable the teachers to improve their knowledge and classroom
practice.
Recommendations
- The Year 4–6 Numeracy Exploratory Study enhanced the ways
in which the participating teachers implement the number
and mathematical processes strands of Mathematics in the
New Zealand Curriculum through improving their subject and
pedagogical content knowledge. The teachers hoped that the
project would continue in future and be made available to
all New Zealand schools.
Chapters 1 to 5
Chapter One: Introduction
(PDF, 15K)
Chapter Two: Methodology
(PDF, 11K)
Chapter Three: Concept-maps
(i) (PDF, 527K)
Chapter Three: Concept-maps
(ii) (PDF, 395K)
Chapter Four: Analysis
of the Teacher Interviews (i) (PDF, 25K)
Chapter Four: Analysis
of the Teacher Interviews (ii) (PDF, 26K)
Chapter Four: Analysis
of the Teacher Interviews (iii) (PDF, 20K)
Chapter
Five: Summary
|
|
|
