Measure Up is an elementary mathematics research
and development
project of the Mathematics Section of the Curriculum Research &
Development Group (CRDG) at the University of Hawai‘i at Manoa, College
of Education. The project includes curriculum development, research on
student learning, and professional development. |
Project
Overview
Four characteristics guide the work in Measure Up to
help young children become
mathematical thinkers:
1 Students’ experiences with continuous quantities of volume, mass, length, and
area
introduce them to mathematical ideas, laying the foundation for algebraic
thinking.
2 An emphasis on communication engages students in talking about, listening to,
and
writing about mathematical ideas.
3 Students represent the mathematics with continuous quantities pictorially and
symbolically . These representations are used interchangeably rather than
sequentially.
4 Physical actions with continuous quantities al low students to make links to
mathematical concepts being investigated.
| Measure continuous quantities
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Communicate ideas about math
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Measure Up |
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Convey quantities using
pictures and symbols |
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Connect actions with concepts |
Project
Overview
The University Laboratory School, also known as The
Education Laboratory, a Hawai‘i New
Century Charter School, is operated by the CRDG under the College of Education.
The
school enrolls approximately 420 students in grades K–12 who are selected by
lottery to
create a student body that reflects the ethnic distribution of Hawai‘i, includes
a broad
range of student academic achievement and family socioeconomic levels, and is
evenly
distributed by gender.
The elementary division comprises three classes: grades K–1, 2–3 and 4–5. Each
combination class consists of 20 students, 10 at each grade level. Because of
the research
nature of Measure Up, students are separated by grade level for their
mathematics
instruction.
Students use a spring scale to measure units of mass of an
object (left). A student carefully measures volume using units
marked on the side of a container (right).
First Grade
• Generalized ideas rather than specific cases
are the focus.
Students model relationships with quantities, build
the notion of unit, and demonstrate actions of
computational concepts before they are formally
introduced to number.
• Numbers are used to describe specific quantities,
and the concept of unit is introduced.
Students use numbers to describe how much a
particular quantity is and to accurately describe how
much should be added or removed from that quantity.
|
Comparison of length on a worksheet. |
• Mathematical language is emphasized.
The use of appropriate and accurate vocabulary is introduced to students
from the very
start. This provides them with the means to communicate their thoughts
when
describing or explaining processes and/or concepts. |
Second
Grade
• Different number systems are used in the development
of the concept of place value.
Students learn that each digit in a multi-digit number represents how many of
that
place value unit there are. The size of the place value unit depends on the
number
system and its place in the multi-digit number. Instruction begins with smaller
bases so
that the decimal (base ten) system becomes just another case in the general
notion of
place value to the students.
A student uses counters to model counting in the base
three system.
• Addition and subtraction of multi-digit whole numbers
are based on place value ideas.
Students apply computational ideas from first grade to place value notions
in second
grade in order to perform addition and subtraction with regrouping. Quantities
continue
to be used as the context for these ideas.
• Writing prompts are introduced to elicit
student thinking on paper and encourage
extended responses in problem solving.
In first grade students describe their
reasoning orally. In second grade they
begin to communicate their thoughts
in writing. |
Sample of a Grade 2 writing prompt. |
Third Grade
Students develop agility solving numerical problems using
strategies that build from
their understanding of measurement relationships. Common strategies for
multiplication, such as repeated addition and skip counting, are presented in a
measurement context.
Fourth
Grade
• Rigid motions from transformational geometry
enhance spatial-visualization skills.
Students use translation, reflection, and rotation
to explore geometric concepts such as
congruence and symmetry.
• Numbers less than 1 are introduced through place
value notions and the use of a radix point.
Students first learn about rational numbers in |
Sample from a Grade 4 student page |
“decimal” form, extending experiences with bases and place value from
second grade.
The concept of unit is extended to partial units. Addition and
subtraction of rational
numbers in this form are also studied.•
Common fractions are introduced , and benchmark fractions are considered.
Common fractions are introduced as an alternate form of representing
rational
numbers. |
Fifth Grade
• Combinations and probability are explored through
continuous and discrete models.
Students apply their knowledge of quantities and
rational numbers in investigations related to
probability.
• The concept of angle is developed from a
transformational geometry perspective.
Students use rotation (introduced in grade 4) to
investigate notions of angle. Graphing calculators
enhance students’ experiences and understandings.
• Relationships between percents, fractions, and
decimals are investigated .
Quantity models help students relate different forms
of rational number representations. |
Exploration of shape combinations |
Students use cards to match diagrams with equivalent
fractions and percentages.
