Abstract: Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic ‘‘seat time’’ in order to address standards. Mathematics research provides a solid basis for advocating for hands on resources to explore geometry and number concepts. Through the use of blocks in standards based mathematical tasks, students have the opportunity to develop important mathematical concepts and reasoning strategies. Kindergarten teachers’ instructional actions can be grounded in history, research, personal wisdom, and professional knowledge regarding what is appropriate and meaningful for their students in learning mathematics with thinking tools such as blocks.
Trang 1Building a Case for Blocks as Kindergarten Mathematics
Learning Tools
Cathy Kinzer1• Kacie Gerhardt2•Nicole Coca3
Published online: 4 July 2015
Springer Science+Business Media New York 2015
Abstract Kindergarteners need access to blocks as
think-ing tools to develop, model, test, and articulate their
math-ematical ideas In the current educational landscape,
resources such as blocks are being pushed to the side and
being replaced by procedural worksheets and academic ‘‘seat
time’’ in order to address standards Mathematics research
provides a solid basis for advocating for hands on resources
to explore geometry and number concepts Through the use
of blocks in standards based mathematical tasks, students
have the opportunity to develop important mathematical
concepts and reasoning strategies Kindergarten teachers’
instructional actions can be grounded in history, research,
personal wisdom, and professional knowledge regarding
what is appropriate and meaningful for their students in
learning mathematics with thinking tools such as blocks
Keywords Mathematics Standards History of blocks
Research informed instruction Practical Research and
practice
Visualize 5- and 6-year-olds in a kindergarten classroom
discussing ideas, solving problems, representing objects, and
observing the shapes, sizes, patterns, and qualities of a
complex block structure that they have constructed collec-tively Then, look to the majority of kindergarten classrooms
in the United States On a typical day, 5- and 6-year-old children spend less than 30 min—and often no time at all—
in child-initiated exploratory play or other learning activities with resources such as blocks (Miller and Almon2009) This article is the result of a university-school partner-ship in which university educators participate in early childhood classrooms, listening to teachers and learning with young children Through extensive interaction with educators, as well as visits to other kindergarten classrooms
in the area, a common concern emerged about the lack of opportunity for kindergartens to use physical blocks in their curriculum Historically, blocks have been an integral part of kindergarten classrooms as resources for play, instruction, and learning However, as academic seat-time
in kindergarten to address literacy and numeracy standards and carry out the required assessments has increased, the result has been fewer opportunities for children to develop visual, spatial, and fine motor skills by using blocks as mathematics thinking tools Many teachers in our part-nership expressed concern that, while their mandated cur-riculum includes pictures of blocks on worksheets, there are currently not many standards-based lessons that used real blocks—such as geoblocks, pattern blocks, unit blocks, tree blocks—for actively learning mathematics
In spite of the lack of support for utilizing physical blocks in contemporary standards-based curriculum, we observed how many teachers in our community continue to incorporate learning centers that include blocks whenever possible The learning centers are important because chil-dren can play, explore, and informally engage in mathe-matical ideas in ways that support their mathemathe-matical development; however, they are not enough Teachers in our partnership have advocated for ways to bring blocks
& Cathy Kinzer
cakinzer@nmsu.edu
Kacie Gerhardt
kk1338@nyu.edu
Nicole Coca
nicklecoca@yahoo.com
1 Mathematics Educator, New Mexico State University,
MSC 3CUR, Las Cruces, NM 88003-8001, USA
2 New York University, New York, NY, USA
3 Las Cruces Public Schools, Las Cruces, NM, USA
DOI 10.1007/s10643-015-0717-2
Trang 2back from the margins of the classroom One teacher
asked, ‘‘The opportunities to learn through using blocks are
disappearing from our kindergarten school day, except
occasionally in our centers! What can we do?’’
Kinder-garten teachers hope to make a case for using blocks as
learning tools to address mathematics standards and to be
an integral part of the curriculum One kindergarten teacher
in our district said,
If we can articulate both the research and the
con-nections to our standards, we will have a solid
foundation for advocacy… We are teaching lessons
aligned to the mathematics standards, but how that is
done—how students experience and contribute to the
learning—makes all the difference in the world
Ini-tially, children need concrete, hands-on tools for
thinking about and representing mathematical ideas
They have transitioned from their homes and
pre-schools where they were interested in using different
types of blocks in activities that stimulated language,
creativity, math knowledge, and enjoyment
Kindergarten educators recognize the need for relevant
interactive learning activities that connect physical objects
with abstract concepts, and they seek methods to use
learning tools in ways that promote conceptual
understand-ing of the standards that they are required to teach Another
teacher noted,
Blocks support my students’ learning and interest in
doing math It is more tangible and real for children as
they relate to blocks Children use 3-D blocks to
compare sizes and shapes and see relationships
between blocks They explore the features of shapes in
developing spatial sense and connecting to number
concepts like counting the number of sides or edges of a
block Children value using blocks as learning tools
The purpose of this article is to consider mathematics
learning opportunities with blocks through research and the
wisdom of teachers in kindergarten classrooms The hope is
that kindergarten teachers will gain historical, research, and
practice-oriented perspectives as well as instructional
resources that will enable them to advocate for incorporation
of blocks as learning tools in mathematics lessons while
addressing required state or district mathematics standards
The Context for Considering Blocks
as Mathematics Learning Tools
Blocks have been an integral part of many young children’s
lives, whether through child-initiated block play,
con-structions, or guided block-learning experiences Research
shows that children have powerful intuitive mathematical
competence (Ginsberg1983) They do not see mathematics
as a separate subject of study until they enter formal schooling Children naturally think mathematically as they compare, quantify, and explore space and shapes in the world around them The most powerful opportunities for learning mathematics in primary grades are those that seek
to build from children’s cultures, languages, and pre-ex-isting informal mathematical experiences Many kinder-garten students can connect with blocks as tools for exploration and learning because blocks are often part of their background experiences at home or in preschool These prior ways of knowing are powerful resources for developing learning activities in the kindergarten class-room (Moll et al 1992) Young children’s early experi-ences in mathematizing through familiar objects such as blocks can contribute to collective negotiation not simply
of mathematical knowledge but also social interactions and communication in the formal setting of kindergarten In the following section we discuss the historical landscapes of blocks as manipulatives that connect to students’ curiosi-ties, ways of knowing, and developing mathematical ideas
Historical Foundations for Blocks as Mathematics Learning Resources
Throughout history, humans have utilized natural materials
in the environment such as soap, wood pieces, rocks, and boxes to build and test their ideas and inventions (Hewitt
2001) The way that blocks became integrated into more formal educational environments is fundamental to under-standing why they are important resources for kindergarten classrooms today Many prominent early childhood edu-cators incorporated blocks into the curriculum because the structure and nature of blocks provide important opportu-nities for young learners to connect to, and further refine, their mathematical schemas That is, blocks and other manipulatives became foundational in educational contexts because they are a way of exploring and articulating the mathematical ideas that children are already beginning to develop In the following sections, we will highlight the history of block use within the educational practices of several seminal early childhood educators
Fredrick Froebel (1772–1852), the originator of kindergarten (‘‘children’s garden’’), utilized blocks in school as learning objects based on mathematical rela-tionships of size, shape, and geometric structures (Zuck-erman 2006) Froebel focused on children’s learning from the natural environment through structured activities and wooden materials to develop geometric concepts and spa-tial reasoning skills in young children through hands-on design and construction Following Froebel, Maria Montessori, a physician in Italy (1870–1952) dedicated her
Trang 3life to supporting students with special needs through
sensory training and stimulation for deliberate use of
‘‘di-dactic materials’’ that taught abstract concepts For
exam-ple, children constructed individual pieces of a ‘‘pink
tower’’—a graduated building made of blocks The wooden
blocks in the tower had specific qualities such as
dimen-sions, surface, temperature, and sounds (Montessori1916/
1964) Froebel and Montessori shared numerous principles
in designing sensory and concept-based modular learning
objects for young learners to engage in three-dimensional
exploration to develop mathematical and science concepts
such as identifying attributes, materials, structures, and
relationships including shape, size, and symmetry that are
present in our geometric world
Swiss psychologist Jean Piaget formalized many
educa-tional theories and built on the ideas of Froebel and
Montessori Piaget developed the learning schema for
chil-dren’s logico-mathematical knowledge that includes
important ideas in both arithmetic and spatial knowledge
Piaget supported learning through active experiences,
uti-lizing concrete materials, interconnecting subject areas, and
peer interactions According to Piaget, the principle goal of
education is to develop people who are capable of doing new
things, not simply repeating what other generations have
done—people who are creative and inventive discoverers
(Piaget 1976) Many early childhood educators have
con-tended that children should be actively engaged in learning
processes for constructing knowledge, social skills, and
dispositions that engender curiosity and contribute to
col-lective knowledge building Children’s spatial and
geomet-ric learning trajectory is dependent on their opportunities to
develop relevant language while exploring concepts through
spatial activities such as planning and building block cities,
designing homes for animals, studying towers around the
world, and building ramps to study movement of objects
[National Research Council (NRC)2009]
Pratt (1948/1990) designed unit blocks with
mathemat-ical proportions of 1:2:4 These wooden unit blocks
pro-vide foundations in geometric properties and empower
students as structural designers as they build, compare,
describe, and analyze block construction Pratt’s unit
blocks are utilized in home and school settings today (City
and Country and School2015) These blocks are powerful
tools for creating a mathematical unit, or unitizing, which
occurs in geometry, number, and measurement contexts in
early childhood settings Children might combine three
blue triangular pattern blocks to make a unit of one yellow
hexagon or make a repeating pattern with wooden blocks
that includes a cube, then a triangular prism, then another
cube and triangular prism, as the unit of the ab pattern The
activity of combining blocks to make a composite shape or
knowing that ten ones is a unit of ten are very important
math concepts and reasoning processes for young learners
in developing an understanding of the base ten number system (NRC 2009)
Blocks are typically an integral part of the constructivist curriculum in Reggio Emilia schools that originated after World War II (North American Reggio Emilio Alliance
2014) This curriculum emanates from students’ interests, curiosity, and relationships with peers and materials in their learning environment Reggio-inspired schools typically view children as having impressive potential and curiosity Children are seen as capable of constructing their own learning and negotiating a sustained process of shared learning in their environment Media and materials such as blocks are utilized to promote play, discovery, and cogni-tive and social connections in the processes of learning (Gandini 2008) Children explore sizes and shapes of blocks to engage in visualization, problem solving, and development of collaborative social skills in an environ-ment that connects their creations to reading, science, mathematics, storytelling, and art Children in Reggio-in-spired settings often view learning as engaging, connected, and interdisciplinary This is a way for educators to utilize blocks in instructional activities or sequences of related activities that integrate content domains such as numeracy, literacy, art, history, and science
Blocks as Mathematical Reasoning Tools
While the preceding examples provide a historical per-spective for blocks as resources for mathematics learning, blocks should continue to serve as powerful objects to externalize and advance children’s mathematical thinking
in today’s classrooms Their attributes are particularly important for uniting concepts that are foundational for learning Mathematics Learning in Early Childhood (NRC 2009) research synthesis recommends two foci in mathe-matics for young children: (a) number, and (b) geometry/ measurement Individually, these domains are important for young learners, but the connections between number and geometry are equally significant, for example, dividing
a rectangle into two equal parts or quantifying categories or attributes of 3–D shapes Through the use of blocks, these mathematical connections between numbers and geometry become tangible and observable
In the area of geometry, children can move through succeeding levels of thought as they learn about geometric shapes in two and three dimensions (Clements and Battista
1992; van Hiele 1986) Initially, children recognize geo-metric shapes and form visual schemes for 2-D and 3-D shapes and spaces As they develop spatial capacity through experiences with tools such as blocks, they match 3-D shapes, name common geometric shapes, use rela-tional language, categorize shapes based on properties, and
Trang 4represent 2-D and 3-D relationships with objects Children
use spatial structuring as they build in space with blocks
They fill rectangular containers with layers of cube blocks
They begin to understand the concepts of perspective,
symmetry, and size through building block configurations
They can describe why some blocks stack easily (or why
they do not), according to their attributes These block
activities bolster students’ understanding of geometric
shapes and mathematical reasoning
According to the Mathematics Learning in Early Childhood
recommendations (NRC 2009), children use four major ideas,
or reasoning processes, in their study of mathematics content
Blocks are explicitly named as tools for developing
mathe-matical reasoning within these four ideas Children in
kinder-garten often compose and decompose numbers and geometric
shapes For example, several smaller rectangular prisms are
combined to make one large rectangular prism This idea of
composing and decomposing is very important in learning
about number or quantities and their relationships (e.g.,
knowing that the quantity or total of 9 can be taken apart into the
addends or parts of 7 and 2 or 8 and 1) The second major idea is
unitizing, or creating or discovering, a mathematical unit To
create a repeating pattern, children have to know the parts that
make up the unit (square rectangle square, repeated) and see it
as a composite whole or unit Relating and ordering are major
mathematics ideas that are developed with blocks This is
investigated when children compare two stacks of blocks that
have the same number of blocks but are different in height, or
one stack has more than another stack Through this process
they observe, compare, and describe differences in measureable
attributes such as length The fourth major idea in mathematical
reasoning for young learners is looking for patterns and
struc-tures and organizing or classifying information Blocks are
resources for building, describing, and extending unit patterns
For example, a unit of hexagon and a rhombus can be taken as
the basis for understanding patterns when children are asked,
‘‘What would the pattern look like if we repeated this unit four
times?’’ Or, kindergarten children can be asked to determine
how groups or categories of blocks are similar or different
These four main ideas in developing mathematical reasoning
guide mathematics learning in kindergarten and build a strong
foundation for mathematics studies in later grades Children’s
geometric thinking is strengthened through well-designed
activities, use of appropriate physical manipulatives (e.g.,
blocks, computer), and resource-rich learning opportunities that
support their growing geometric and spatial skills
The historical and research review presented above
leads to the question, How might blocks be a typical
resource to support mathematics learning in kindergarten
classrooms today? In response to current accountability
and high-stakes testing practices, many kindergarten
edu-cators have pushed blocks and other useful instructional
resources to the side to meet curriculum requirements
Kindergarten teachers are often part of the substantive educational accountability systems and focus on testing that is occurring in many schools In this realm, classroom activities and learning experiences are often narrowed to procedurally ‘‘cover’’ academic standards The standards are not always the prominent issue The high-stakes testing that is driving educational ‘‘reform’’ has an impact on the quality of learning experiences in early childhood class-rooms The emphasis on developing academic skills quickly limits opportunities for creativity, negotiation, communication, and relational problem solving with mathematical tools
Contemporary Perspectives on Blocks as Learning Tools
There are contemporary examples of schools that integrate blocks in the kindergarten curriculum The City and Country School in New York City develops a range of intellectual, social, mathematics, problem solving, and research skills through creative block projects (City and Country School
2015) However, a growing number of kindergarten teachers have determined that their current Common Core State Standards (CCSS) ‘‘aligned’’ curriculum resources include more skills-based worksheets that do not involve using manipulatives or, worse, that students do not engage in rich problem solving or activities that promote mathematical reasoning, as they are often told step-by-step how to ‘‘solve the problem.’’ While the current curriculum presents a scarcity of mathematics tasks that are interesting on an individual basis, children are further alienated from oppor-tunities for deep mathematical learning through limited peer interactions, including sharing individual or collective mathematics thinking strategies Children begin to believe that mathematics is about doing worksheets rather than engaging in rich activities that include resources for learning and require students’ mathematical reasoning and commu-nication of important mathematical ideas
Currently, there is a crisis in kindergarten as teachers report major factors that inhibit children’s opportunities to learn through block play or block activities (Miller and Almon2009) Early childhood educators are often required
to teach prescribed standards, evaluate student progress, and utilize most of the day’s schedule to focus on literacy and numeracy, the two content areas that are assessed by CCSS standardized tests in later grades This leaves little or
no time for exploring, creating, or utilizing geometric objects as thinking tools to promote deeper understanding
of number and geometry concepts Meeting academic standards should not come at the price of denying young children access to engaging and robust mathematics learning experiences
Trang 5Advocacy Research
Blocks provide opportunities for many forms of play and
can support development of mathematics concepts and
processes Through engaging with blocks, children
clas-sify, measure, count, and explore symmetry, shape, and
space (Piaget and Inhelder 1967; Kamii et al 2004)
Research conducted by Wolfgang et al (2001) determined
that children who engaged in sophisticated block play
during preschool years were more successful in junior high
and high school and achieved higher mathematics grades
and overall achievement scores
Exploratory play by young children often reflects the
logic of, and causal structure of, scientific inquiry (Cook
et al 2011; Schulz and Bonawitz 2007) The inherent
mathematical qualities of blocks support geometric
rea-soning and mathematical thinking as children explore their
shape and combinatorial aspects (Ginsburg, Inoue, and Seo
1999) Young children use blocks to reason spatially in
three dimensions—a skill that is necessary for future
engagement in mathematics, science, and engineering
disciplines Spatial thinking is important in many areas,
such as measurement and geometry, and is predictive of
achievement in mathematics and science (Clements and
Sarama2007; Shea et al.2001) Using blocks can develop
mathematical and scientific thinking; young children who
engaged in block learning experiences also scored
signifi-cantly higher than peers without these experiences on
language acquisition assessments (Christakis et al.2007)
Based on this review, it is clear that blocks can support
academic learning, innovative play, and achievement
across subject domains In addition to cognitive
develop-ment, blocks as learning tools promote a range of
socioe-motional skills and competencies and provide children with
opportunities to interact, design, plan shared goals,
nego-tiate, and develop persistence in solving problems together
(Cartwright1995)
Professional Wisdom: A Vignette
of a Kindergarten Classroom
In light of current trends that eliminate such valuable
hands-on learning materials, it is imperative that teachers and
administrators understand and articulate the research and the
implications of including thinking tools such as blocks in a
child’s learning day Through professional knowledge,
educators are empowered to make informed decisions in
planning learning activities for young children They can
take action based on historical perspectives, research, and
professional wisdom regarding what is appropriate for their
kindergarten students Young children need access to blocks
as thinking tools, particularly in mathematics, to develop, construct, test, and reflect on their learning One of the teachers in our partnership, who has a range of learners in her inclusion classroom, described this imperative:
As a kindergarten teacher, it is important to provide young students with many opportunities to explore and manipulate blocks to deepen their geometry understanding By allowing students time to build with blocks while using guiding questions, they begin
to make important connections between various shapes that can be composed and decomposed
This teacher described how her use of blocks in the classroom arises out of the children’s own understandings and experiences of shape in the everyday world as this abstract understanding is concretized through block activ-ities that are integrated across the academic year:
At the beginning of kindergarten, students enter with their own conceptions about shapes, and through guided explorations they begin to develop a more concrete understanding of geometry Students have a general idea of shapes in the environment and some students with preschool experience know the correct names of shapes Through songs, literature, class-room discussions, activities, and videos, all students are exposed to shapes and their attributes By pro-viding time for them to use blocks they begin to make
a tangible connection to these attributes and are then able to gain a conceptual understanding of geometry rather than just an abstract understanding
This teacher highlighted how pattern blocks and other 2-D resources not only provide an essential connection to mathematical ideas, but enable students to develop essen-tial vocabulary and social competencies in the classroom: Throughout the first semester of kindergarten, 2-D shapes are the focus Students learn the proper names
of these shapes, how they can be composed and decomposed, as well as how to describe their attri-butes, and how to sort and classify these shapes by their attributes While students are engaged in various tasks with blocks, they are able to verbalize their geometry connections while using correct vocabulary and mathematical reasoning When students are allowed to use blocks they are excited to share their creations with each other and their teacher This excitement provides a wonderful avenue to develop their vocabulary and geometry concepts as students describe, and draw or represent, what they have built
By the second semester, this teacher’s class has made substantial progress in naming and recognizing shapes through their work with 3-D shapes, block activities, and
Trang 6the use of supporting video and literature The teacher
described how the second semester’s activities build from,
and promote, further study of shapes and their properties:
During the second semester of kindergarten, when 3-D
shapes are introduced in our class, block activities help
reinforce children’s knowledge of shape and the
proper-ties and relationships of shapes They begin to point out
when they find cubes or cylinders in the environment In
fact, students are also able to identify rectangular and
triangular prisms and consider how to construct
equiva-lent shapes by making connections to geometry videos,
(like the Shape Name Game; Have Fun Teaching.org),
that they have previously viewed in the classroom
While this kindergarten teacher is addressing the
required state standards, the integration of blocks and other
manipulatives contributes significantly to student learning
and confidence in geometry For this teacher, a
resource-rich approach to geometry includes foundational
experi-ences that are needed to progress to higher levels of
geo-metric thinking:
All students are capable of learning the names of
shapes and can identify them in everyday situations
However, students that are allowed to explore with
various types of blocks have a deeper understanding
of geometry and are able to verbalize their
under-standing more articulately These students have a
greater understanding of spatial relationships and can
see how shapes can be composed and decomposed,
made into a unit or pattern that can repeat, or
clas-sified and ordered with more ease than students who
have not had the opportunity to learn geometry
through these interactions and experiences
While a significant body of literature substantiates this
teacher’s views, the practical implications of using blocks
in ways that align with Common Core State Standards is
worth further discussion
Block Activities
Many types of blocks can be used in block activities in
standards-based mathematics lessons When implementing
such activities, the role of the teacher is critical for
inte-grating learning with hands-on experience A kindergarten
teacher in our partnership remarked, ‘‘I have the essential
role of asking questions that connect the block activities,
math concepts, and children’s thinking.’’ Effective
ques-tioning and listening to children’s ideas as they engage in
thinking, reasoning, and making sense of mathematical
ideas are critical to supporting learning
Another instructional strategy is to integrate literacy activities that include writing, representing mathematical concepts, graphing, and so forth There is a wealth of children’s educational books that focus on blocks, block constructions, and geometry to support these activities Books recommended by kindergarten teachers include: Bear in a Square (Blackstone1998), The Shape of Things (Dodds1996), Mouse Shapes (Walsh 2007), When a Line Bends a Shape Begins (Gowler1997) and Shapes, Shapes Shapes (Hoban1996) These literacy resources connect to geometry activities Several examples linking literacy and numeracy are incorporated in the block learning opportu-nities that follow
Blocks provide many opportunities to integrate both the Common Core Content and Standards for Mathematical Practices (National Governors Association Center for Best Practices 2010) When children are solving problems, modeling, representing ideas, reasoning quantitatively, developing persistence, constructing, and using blocks as thinking tools in mathematics, they are experiencing the mathematics practice standards In addition to the mathe-matical concepts and big ideas, children need opportunities
to develop habits of mind or ways of engaging in mathe-matics as described in the Standards for Mathematical Practices These eight practices in the CCSS are mechanisms for children to develop, refine, and extend their mathematical thinking They are the ways in which mathematicians make sense of complex ideas; for young children, they are avenues
to reasoning and communication in problem solving Chil-dren engage in these mathematical practices when they solve mathematics problems using various types of blocks For example, using of mathematical tools such as blocks to think about mathematics concepts while solving problems could include Mathematical Practice Standards 1 and 5 Kinder-garten teachers often have these practices displayed as anchor charts in the classroom:
Eight Mathematical Practices
1 I can make sense of problems and solve them (persistent problem solver)
2 I can use numbers, words, and objects to understand problems
3 I can explain my mathematical thinking to someone else and I listen to understand others math ideas
4 I can show/model mathematical problems in different ways
5 I can use math tools to solve problems and know why I chose them
6 I can figure things out in math so I am accurate (Mistakes are opportunities to learn)
7 I can use what I know to solve new problems
8 I can look for patterns and organize information to help solve problems
Trang 7Child-friendly versions of the Mathematical Practices
are available online Standards-based lessons provide
important opportunities for children to develop these
practices and ways of learning mathematics while engaging
in rich tasks utilizing blocks
It is important for young students to have something
tangible when learning about shapes and their attributes
Tangible objects allow them to feel the sides and touch the
corners that they are expected to describe in CCSS
Through access to blocks, children begin to come to their
own conclusions about how shapes are related or different
To develop clear understanding of geometry, children need
to use these materials extensively with their hands A
kindergarten teacher noted,
They cannot learn that a building is made of cubes
from a picture of a building made of cubes unless
they have hands-on experience with a ‘‘real cube.’’
They begin to see that shapes can be composed of
other shapes and are enthusiastic in their discoveries
as they connect tangible objects with abstract
concepts
Through structured activities, blocks can be a vital part
of the primary mathematics curriculum The examples of
lessons that follow provide explicit connections to the
CCSS They are not entire lesson plans; rather, they present
key ideas for early childhood educators to consider in
providing opportunities for kindergarteners to learn
through using blocks as thinking tools to address CCSS for
mathematics Learning environments should provide
opportunities for children to experience instructional
activities that include blocks, as well as learning centers
that honor children’s ways of making sense of geometric
ideas This requires understanding the broader policy
landscape and advocating for teaching and learning
expe-riences that are informed through research and the wisdom
of practice to ensure a viable engaging mathematics
edu-cation that integrates blocks as learning resources for
young children in kindergarten
Connecting Blocks as Learning Tools to Common
Core State Standards for Mathematics
in Kindergarten: Lesson Learning Opportunities
How do Blocks Help me in Learning Geometry?
What are the Names, Shapes, and Attributes of 2-D
and 3-D Shapes?
Learning Opportunity: Pattern Block Sort
Learning Goals: I can analyze and compare shapes
(K.G.B.4.1) (Kindergarten Geometry Standards) This can
also address Counting and Cardinality Standards (K.CC.4.a.b.)
Selected Mathematical Practice Standards
MP 1: I can make sense of problems and solve them
MP 2: I can use numbers, words, and objects to under-stand problems
Students are provided a small bag with an assortment of 8–10 pattern blocks Students utilize work mats or yarn tied
to make a circle They study the shapes of the pattern blocks and organize or group them by attributes Attributes may be size, shape, color, and number of sides or corners They put their categories/groups on separate work mats or encircle them with yarn They then describe their categories and ways
of thinking about their shapes to another student or to the class Math conversations: ‘‘How did you group the blocks? What did you notice about the shapes? How are the shapes alike or different? How many groups did you make?’’ Were students thinking about the attributes of the 2-D shapes? How did students describe the groups? Did stu-dents utilize the vocabulary word wall? What did stustu-dents notice about the shapes? Take pictures or make a poster of several students’ representations for further study
Learning Opportunity: Pattern Block 2-D Design and Count
Learning Goals: I can make a design with 5 to 15 pattern blocks and count the colors and/or geometric shapes (K.CC.4.A.B.C) and (K.G.B.5)
MP 3: I can explain my mathematical thinking to someone else
MP 4: I can model mathematics problems in different ways
Trang 8Students select a specified number of pattern blocks from a
tub or bag They design a shape with that number of pattern
blocks They count and record on paper how many of each
color and shape they used They share their strategy and
thinking with a learning partner The teacher documents
several student responses and asks the class to analyze and
respectfully agree or disagree with the work Several of the
students’ representations can be used the next day during a
math talk for ten minute math activities
Learning Opportunity: Pattern Block Pictures
Learning Goals: I can correctly name shapes (regardless of
the orientations/positions or size) (K.G.A.2)
MP 3: I can explain my mathematical thinking to
someone else
MP 6: I can figure things out in math so I am accurate
Students use pattern blocks either to create their own
pic-tures or to complete pattern block picpic-tures that the teacher
has provided Once the pictures are completed, they
stu-dents describe the picture to a partner by sharing the shapes
that were used For example, ‘‘I used three squares and four
triangles to make my picture.’’ Once the designing partner
has shared the work, the listening partner asks a question,
such as, ‘‘Did you use any hexagons?’’ This could also be
done with wooden or foam blocks during a free-choice
center This would address (K.G.A.3): Identify shapes as
two-dimensional (lying in a plane, ‘‘flat’’) or
three-di-mensional (‘‘solid’’) as well
Learning Opportunity: Guess My Shape
Learning Goals: I can describe attributes of shapes by
analyzing and comparing them (K.G.B.4)
MP 1: I can make sense of problems and solve them
MP 6: I can figure things out in math so I am accurate Students are given a set of pattern and/or attribute blocks along with a folder or some sort of divider The divider will be used to shield blocks from the partner or small group in which the student is working One student asks the other student to cover his/her eyes and then selects a block and places it behind the divider The first student then gives the partner or group clues about the selected shape by giving statements about its attributes For example, if the student selected a triangle, the student could say, ‘‘This shape has three sides This shape has three corners This shape has straight edges This shape looks like a slice of pizza.’’
Learning Opportunity: Pattern/Attribute Block Share and Ask
Learning Goals: I can describe attributes of 2D or 3D shapes (K.G.B.4)
MP 3: I can explain my mathematical thinking to someone else
MP 6: I can figure things out in math so I am accurate Students are given pattern and/or attribute blocks to work
in small groups They are also given the following sentence frames: ‘‘I have a shape with _sides Who has a shape with _ sides?’’ or ‘‘I have a shape with _ corners Who has a shape with cor-ners?’’ They fill in the blanks with their own number of sides or corners, depending on the selected shape When asking the ‘‘Who has’’ portion of the question, they do not have to use the same number of sides or corners as the selected shape Thus, they learn to identify and describe the attributes of shapes This can be done with other types of blocks, such as geoblocks and addresses (K.G.A.3)
Trang 9Learning Opportunity: Making Shapes
Learning Goals: I can use simple shapes to make a larger
shape (K.G.6)
MP 4: I can show/model mathematical problems in
different ways
MP 5: I can use math tools to solve problems
Students are given a variety of shapes of blocks and asked to
use two or more blocks to compose larger shapes or shapes
that have different faces and shapes (triangle, rectangle,
square, hexagon), for example, ‘‘Find other unit blocks that
can make a square prism.’’ Over time, students name the new
shapes that kindergatrteners have formed, as well as the
shapes that they used to compose the new shape
Students construct a block wall or building with equivalent
blocks (e.g., a rectangular prism that is equal to two triangular
prisms) They compose and decompose physical block shapes
to make sense of their attributes, shapes, and sizes in informal
ways They can make equivalent shape blocks over time
Kindergatrteners are asked to find all the possible ways to
make this rectangular prism using other blocks
How did students compose shapes? What did they
dis-cover? How did children approach this task? What did
students notice about equivalency?
Learning Opportunity: Building Block Houses for Animals
Learning Goals: I can model shapes in the world by building shapes from components (K.G.5) I can actively engage in groups with peers and in reading activities with purpose and understanding (RL.K.10) I can use a combi-nation of drawing, dictating, and writing to compose an informative text (W.K.2)
MP 1: I can make sense of problems and solve them
MP 4: I can show/model my work in many ways The teacher reads a book about animal houses, such as Too Tall Houses (Marino2012) Students select a stuffed animal and build a house for the animal, including a door that fits the animal Once the animal house is complete, the student draws a diagram of the house and writes a description Stu-dents are developing informal measuring skills, representing 3-D buildings in their 2-D drawings and expressing their mathematical ideas in response to literature
Trang 10Learning Opportunity: Building Towers
Learning Goals: I can model shapes in the world by
building shapes from components (K.G.5) I can participate
in shared research and writing projects (W.K.7) I can
participate in collaborative conversations with diverse
partners about kindergarten topics (SL.K.1) I can use a
combination of drawing, dictating, and writing to compose
an informative text (W.K.2)
MP 1: I can make sense of problems and solve them
MP 4: I can show/model my work in many ways Students use unit blocks to build towers or tall structures or buildings They research real-world towers and post pic-tures of these towers, such as the Empire State Building They engage in discussion about what defines a tower and the necessary components of towers, for example, ‘‘What is the best way to build a foundation that a tower could be built on?’’ Once the tower is built, each student draws a diagram of the tower and writes a description The block gallery includes students’ ‘‘towers’’ and diagrams and descriptions for discussion and inquiry
Learning Opportunity: Building Bridges
Learning Goals: I can model shapes in the world by building shapes from components (K.G.5) I can compare and contrast adventures and experiences of characters in familiar stories (RL.K.9) I can actively engage in group and reading activities with purpose and understanding (RL.K.10) I can participate in collaborative conversations with diverse partners about kindergarten topics (SL.K.1) I