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5.7: Standards

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    Course Competency 5. Examine strategies that teach early math skills.

    CRITERIA 5.7. examine the National Council of Teachers of Mathematics standards.


    Standards describe what students are expected to learn in each grade and each subject. Each state Department of Education creates standards for schools within the state. These standards become the basis for the way teachers are trained, what they teach and what is on state standardized tests that students take. Without standards, districts and schools don’t have goals. By matching what is taught in the classroom to the standards in each subject area, students will know what teachers should be teaching, what students should be learning, and what they will be tested on (GreatSchools Staff, 2012).

    As an early childhood teacher in Wisconsin, you need to be familiar with three sets of standards: the Wisconsin Model Early Learning Standards, the Wisconsin Standards for Mathematics, and the National Council of Teachers of Mathematics Standards.

    Young children playing

    Wisconsin Model Early Learning Standards

    The Wisconsin Model Early Learning Standards were first completed in 2003, with revisions in 2008, 2011, and 2013, and an update to the 2013 standards was completed in 2017. See the Wisconsin Early Childhood Collaborating Partners website to learn more about the purpose and the guiding principles of the standards.

    Research shows that young children can do mathematics and solve problems. Long before entering school, young children explore and use mathematics and do it naturally. Children at play begin to learn essential math skills such as counting, equality, addition, subtraction, estimation, planning, patterns, classification and measurement. They compare, notice similarities and differences, and group toys and materials. This ability to organize information into categories, quantify data and solve problems helps children learn about time, space and numbers. Over time, they develop the vocabulary and skills to:

    • Measure,
    • Describe patterns,
    • Express order and position, and
    • Describe relationships between objects in the

    Mathematics helps children make sense of the physical and social worlds around them and they naturally incorporate math as they make comments such as:

    • “He has more than I do!”
    • “That won’t fit in there, it’s too big.”
    • “I can’t move it, it’s too heavy.”

    Organization of the Wisconsin Model Early Learning Standards

    The Wisconsin Model Early Learning Standards for Mathematical Thinking have been divided into six broad areas or strands.

    • Number Sense -- B. EL. 1 Demonstrates an understanding of numbers and counting.
    • Number and Operations -- B. EL. 2 Understands number operations and relationships.
    • Geometry -- B. EL. 3 Explores, recognizes, and describes, shapes and spatial relationships. Algebra and Functions (Classification and Patterning)
    • Algebra -- B. EL. 4 Uses the attributes of objects for comparison and patterning.
    • Measurement -- B. EL. 5 Understands the concept of measurement.
    • Data Representation -- B. EL. 6 Collects, describes, and records information using all senses

    Wisconsin Standards for Mathematics

    These Standards define what K-12 students should understand and be able to do in mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it.

    Organization of the Wisconsin Standards for Mathematics

    There are two sets of standards; Content Standards and the Standards for Mathematical Practice.

    The standards for mathematical content are focused on number and quantity, algebra, functions, geometry, modeling, and statistics and probability. For kindergarten through grade 8, the content standards are organized by grade levels. The 9-12 standards do not use grade bands, but instead have broad conceptual categories. All content standards are organized by Domain, Cluster, and then Standards.

    Domains are larger groups of related standards. The Domain is the big idea.

    Clusters are groups of related standards. At the beginning of each cluster, the bold label is referred to as the Cluster Heading

    Standards define what students should understand and be able to do.

    Young boy with thumbs up

    Standards for Mathematical Practice

    The Standards for Mathematical Practice (SMPs) describe varieties of expertise that mathematics teachers at all levels should seek to develop in their students. The SMPs represent the habits of mind that represent thinking and understanding.

    Standards for Mathematical Practice

    1. Make sense of problems and persevere in solving them.
    2. Reason abstractly and quantitatively.
    3. Construct viable arguments and critique the reasoning of others.
    4. Model with mathematics.
    5. Use appropriate tools strategically.
    6. Attend to precision.
    7. Look for and make use of structure.
    8. Look for and express regularity in repeated reasoning.

    Please see the Wisconsin Standards for Mathematics for more information on the Content Standards and the Standards for Mathematical Practices.

    © Copyright 2010. National Governors Association Center for Best Practices and the Council of Chief State School Officers. All rights reserved.

    National Council of Teachers of Mathematics (NCTM)

    To learn more about the NCTM guiding principles and the content and process standards see NCTM website.

    Supporting Mathematical Reasoning

    The Wisconsin Model Early Learning Standards do not have math process or reasoning standards.

    Mathematical reasoning is a key process in learning and developing mathematical knowledge in all areas of mathematics, including number and operations, classification, patterning, measurement, and geometry. It involves the ability to think and reason logically, to apply mathematical knowledge in different problem-solving situations, and to come up with different solutions. Mathematical reasoning is natural to most young children as they explore the environment and make sense of the world around them. View the California Learning Standards for mathematical reasoning below.

    At around 48 months of age

    At around 60 months of age

    1.0 Children use mathematical thinking to solve problems that arise in their everyday environment.

    1.0 Children expand the use of mathematical thinking to solve problems that arise in their everyday environment.

    1.1 Begin to apply simple mathematical strategies to solve problems in their environment.

    1.1 Identify and apply a variety of mathematical strategies to solve problems in their environment.

    Figure 5.4: This boy uses mathematical reasoning when he constructs his train tracks.[17]

    Teachers can support children’s development of the mathematical reasoning foundations with the following:

    • Identify and create opportunities for mathematical reasoning through both spontaneous interactions and planned experiences
    • Pose meaningful questions that promote investigation and inquiry and challenge children to think through a problem and come up with a solution
    • Support preschool children in reasoning mathematically by providing clues, encouragement, and modeling, as needed[18]

    Guiding Principles for Supporting Mathematics

    The following principles will guide teachers’ classroom practices in establishing a high-quality, challenging, and sensitive early mathematics preschool program. These principles are partially based on the ten recommendations in Early Childhood Mathematics: Promoting Good Beginnings set forth by the National Association for the Education of Young Children and NCTM in 2002.

    • · Build on preschool children’s natural interest in mathematics and their intuitive and informal mathematical knowledge
    • · Encourage inquiry and exploration to foster problem-solving and mathematical reasoning
    • · Use everyday activities as natural vehicles for developing preschool children’s mathematical knowledge
    • · Introduce mathematical concepts through intentionally planned experiences (in addition to what they spontaneously engage in)
    • · Provide a mathematically rich environment
    • · Provide an environment rich in language, and introduce preschool children to the language of mathematics
    • · Support English learners in developing mathematical knowledge as they concurrently acquire English
    • · Observe children to discover opportunities to clarify, extend, and reinforce their existing mathematical concepts and to help them discover new mathematical concepts
    • · Provide an environment in which all children can learn mathematics, set appropriately high expectations for all children, and support individual growth
    • · Establish a partnership with parents and other caregivers in supporting children’s learning of mathematics[1]

    Engaging Families

    Teachers can use the following strategies to help families to develop their children’s mathematical understanding:

    • Communicate to families
      • the broader aspects of developing number sense; for example, using counting in real-life situations, comparing numbers and discussing which is more or less, making estimations (e.g., How many grapes are in this bowl?), and solving simple addition and subtraction problems.
      • what classification and patterning are about and how they contribute to children’s understanding of mathematics.
      • the importance of early measuring experiences and types of measurement experiences they can do with children.
      • that mathematical reasoning is being able to think mathematically and explore different ways of solving problems
    • Remind parents that daily use of numbers (which are everywhere!) can become learning experiences for children.
    • Provide number-related games and books that children can take home or that families can make or purchase.
    • Encourage parents to
      • involve children in everyday measurement experiences
      • refer to shapes in the environment when talking with children
      • use spatial words in everyday interactions with children
      • recognize math in everyday events and interactions and turn them into learning experiences[1]
    Figure 5.6: Cooking and baking are excellent opportunities to explore math with children.[2]

    Things to Remember

    Young children have a natural interest, curiosity, and competence to explore and construct mathematical concepts. Mathematics is a way of thinking and organizing the world around us. It is a natural part of day-to-day activities and events. Mathematics in preschool is learned through children’s play and exploration as in the blocks area or the sand­box, through everyday routines such as setting the table and cleaning up, and through participation in teacher-initiated activities. Some teacher-initiated activities are designed with a focus on math, and others may focus on art, movement, literacy, or science but present opportunities for math learning.

    When teachers recognize the potential for exposure to math in different situations, they can turn everyday occurrences into exciting and effective mathematics-learning experiences. Children are excited to explore the size or volume of objects, to discover and create patterns, to manipulate and build with shapes, to sort and classify objects, and to try to figure out “how many.” Teachers get to experience with children the day-to-day excitement of learning and discovering math. This process is joyful for the children and for the teacher, who guides and challenges them in building mathematical concepts, skills, and language [1]

    Pause to Reflect

    Many adults (including parents and teachers) shy away from math because they “aren’t good at it.” How do you feel about math? How comfortable are you “teaching” math? Has the way this chapter presented math affected that at all? If so, how?


    [17] Image by Nicholas Wang is licensed by CC-BY-2.0

    [18] The California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission

    5.7: Standards is shared under a CC BY license and was authored, remixed, and/or curated by Janet Stramel & Vicki Tanck (Northeast Wisconsin Technical College).