Appendix H: ECIPs – Math (Cognitive)
Early Childhood Indicators of Progress: Minnesota’s Early Learning Standards
Introduction to Mathematics Domain
“We do math all day long in my PreK classroom at Lakeview Elementary School. As we arrive, we move a photo of ourselves from the Home column to the At School column. Then, at circle time, we count how many children are in each row. I like to count! Both at circle time and investigation stations, we sing counting songs and read counting books. One time, I counted all the connecting cubes it took to go from one end of the table to the other. My teacher, Kevin, helped me when I got to nineteen. I couldn’t remember what came next. It’s fun to build things with the different shapes in the block area. I tried to build a rainbow with only the rounded ones but they kept falling down. I figured out that I needed to stack some rectangles
on the bottom to make it stand. At the manipulatives table, we have baskets to sort different things into and pattern cards to help us create colorful, geometric patterns. I like when we have measuring cups and pitchers at the water and sand table. Kevin gives me a challenge: How many little cups of water will fill the pitcher? He writes it down on a clipboard so we won’t forget!”
Children’s development of mathematical understanding begins in the very first months of life and continues to grow and expand as they interact with others and with the world around them. Babies begin to see patterns in the world in familiar caregiving routines and attend to objects and sounds relative to themselves. Toddlers begin to understand the words “one” and “more” and maneuver through their world with growing spatial understanding. Preschoolers begin to make sense of numbers as they play with counting. Their math understanding is directly related to their playful explorations of blocks, water, sand, puzzles, and games.
The expectations that are set out in the Minnesota Early Indicators of Child Progress (ECIPs) recognize that young children are developing the foundational knowledge and skills that will lead to more rigorous academic study in the Mathematics domain in the elementary school years. The alignment of the ECIPs with the Minnesota Academic Standards for Kindergarten is included and, as the kindergarten standards are revised, this alignment will be updated.
The Mathematics domain includes five components:
- Component M1-6 Number Knowledge
- Component M7 Measurement
- Component M8 Patterns
- Component M9-11 Geometry and Spatial Thinking
- Component M12-13 Data Analysis
The subcomponents and indicators identified for the ages of birth through kindergarten entry address the specific expectations across the developmental spectrum.
For infants, indicators focus on the children’s beginning understanding of patterns and predictability as they anticipate familiar routines, spatial awareness as they respond to objects and sounds relative to themselves, and recognition of similarities and differences among people and objects.
Toddlers are growing in their mobility and independence in exploring the environment. Therefore, the indicators focus on the imitation of counting and early understanding of one-to-one correspondence, awareness of full and empty, following simple patterns, beginning awareness of shape and place in space, and matching and sorting.
The growing language capabilities of preschoolers include their use of an ever-increasing vocabulary of mathematical terms to describe and make sense of their world. They recite numbers and count objects with one-to-one correspondence to higher quantities. Preschoolers identify geometric shapes and use the comparative language of measurement. Developing sorting strategies that grow in complexity and duplicating and creating patterns using various rules are skills best developed within the context of preschooler’s play.
While the terminology and concepts in the domain of mathematics are unique and explicit, they are interrelated with children’s development in other domains as well. Mathematics is highly correlated with the domain of Language, Literacy, and Communications.
…research suggests there are rich connections between early literacy and early numeracy skill development that may help us think more broadly about children’s early academic learning. Ultimately, we can use this information to create rich environments that support both early literacy and numeracy skill development.” (Hojnoski 2014)
As children investigate mathematical concepts in hands-on experiences, they grow in their approaches to learning. They solve problems, think creatively, and apply concepts. Their social-emotional skills are enhanced as they develop greater confidence as learners and work collaboratively with others. Mathematics and science are linked easily in a rich, engaging early childhood environment where children experiment with water, sand, construction materials, and living things.
The indicators in the ECIPs are designed to work toward mathematics knowledge and skills; these goals are met most successfully as teachers and providers interact with children throughout each and every day. Children’s interest and understanding of mathematics is best supported by showing the importance of mathematics in daily life.
Resource:
Hojnoski, Robin. August 11, 2014. What do the connections between early literacy and numeracy mean in preschool? http://www.schoolreadinessblog.com/author/robin_hojnoski/
Domain: Mathematics
Component M1-6: Number Knowledge
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M1 Rote counting: The child attends to sequences and use of number words, with or without items, sets, or numerals and without recognizing the link to quantity
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M1.1 Releases one item to reach for anotherM1.2 Uses body language to indicate a desire for more
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M1.3 Imitates use of at least one number wordM1.4 Imitates counting
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M1.5 Recites number words but not necessarily in the correct orderM1.6 Recites number words correctly, up to 3M1.7 Names familiar numerals
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M1.8 Shows interest in counting or number oriented play, and notices numbers in the environment during free playM1.9 Orders a few objects by size with assistanceM1.10 Recites number words in the correct sequence up to 10M1.11 Recognizes when others make errors in the number word sequence M1.12 Points to M1.13 Begins to |
M1.14 Recites number word aloud, forward, up to at least 29 (allow for some mistakes), without objectsM1.15 Recites number words aloud, backward, down from at least 10 without objectsM1.16 Is able to name the next number word for numbers up to 9M1.17 Reads and writes numerals from 0 to 10, with some reversals possible
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K.1.1.3 Count, with and without objects, forward and backward to at least 20K.1.1.2 Read, write, and represent whole numbers from 0 to at least 31
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| M2 Meaningful Counting: The child uses counting to identify how many items are in a set, using one to one correspondence; uses number words to identify “how many” |
M2.1 Imitates one to one correspondence
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M2.2 Correctly uses 1:1 correspondence up to 4 items
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M2.3 Demonstrates and uses 1:1 correspondence with sets larger than four |
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| M3 Cardinality: The child associates each of one or more number words to a unique and exact quantity, and knows that the final number word used when counting out an item set represents the exact number of items in the set |
M3.1 Responds to request to give a small quantity items (one, two)
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M3.2 Gives 1 item correctly, upon request
M3.3 Gives 2
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M3.4 Gives exactly 4 consistently when asked
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M3.5 Gives 5 or more items correctly and consistently when asked
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K.1.2.1 Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.K.1.2.2 Compose and decompose numbers up to 10 with objects and pictures |
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| M4 Ordinality: The child matches symbols (digits or numerals) to a position in a sequence |
M4.1 Identifies first or second item in a sequence, upon request |
M4.2 Uses terms like first; most; last; before, to refer to ordinal position |
M4.3 Recognizes that a number can be used to represent a position in a sequence |
K1.1.1 Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence |
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| M5 Comparing numbers and quantities: The child uses organizing strategies to know how many objects they have
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M5.1 Grasps one object and reaches for another
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M5.2 Demonstrates understanding of some descriptive words, such as responding to questionsM5.3 Separates a few items into groups using own method such as color, size, etc.M5.4 Nests smaller objects inside larger objects |
M5.5 Compares two sets of up to 4 objects accurately using terms like more/less; a little/a lot
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M5.6 Uses terms like more/less; bigger/smaller; a little bit/a lot; to refer to approximate quantities
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M5.7 Verbally estimates quantities without counting, although inconsistently and allowing for mistakes
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| M6 Relation and operations: The child can create a set or subset based on a rule, can combine or separate sets, and recognize the amount of items in a set does not change when the set arrangement changes
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M6.1 Notices when the quantity of a set of up to 4 objects has increased or decreased
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M6.2 States the number that comes next or before up to 5M6.3 Understands that a quantity changes (increases or decreases) when a set of objects is added to/subtracted from (respectively)
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M6.4 States the number that comes next or before up to 10M6.5 Understands that the quantity of a set of (more than 4) objects has been changedM6.6 Without recounting, can add one more to a set, even when the set isn’t visible after counting M6.7 M6.8 Uses simple physical strategies to |
K.1.1.4 Find a number that is 1 more or 1 less than a given number.K1.1.1 Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence.K1.2.2 Compose and decompose numbers up to 10 with objects and pictures. K.1.2.1 Use objects and draw
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Component M7: Measurement
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M7 Measurement: Child recognizes and makes comparisons of measurable attributes (length, height, width, area, volume, physical distance, time duration.)
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M7.1 Experiments with “full” and “empty”M7.2 Orders a few objects by size with assistance
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M7.3 Brings objects closer together to compare themM7.4 Imitates using an object to measure another object M7.5 Identifies M7.6 Uses |
M7.7 Shows understanding of measurement terms (longer/shorter, taller/shorter, fullest, farthest, closest)M7.8 Uses terms like more/less; a little bit; a lot; to refer to continuous properties like water, sand, height
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M7.9 Compares and orders more than two items in some wayM7.10 Uses comparison vocabulary (longer/shorter, taller/shorter, farthest/closest)
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K.3.2.1 Use words to compare objects according to length, size, weight and position.K.3.2.2 Order 2 or 3 objects using measurable attributes, such as length and weight
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Component M8: Patterns
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M8 Repeating patterns: The child can identify create and describe sequences in objects, colors or numbers with sequences that increase, decrease or grow in complexity
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M8.1 Anticipates familiar routines
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M8.2 Carries out familiar routinesM8.3 Follows a familiar simple pattern (sound, body movement sequence like Patty Cake)
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M8.4 Follows an unfamiliar simple pattern (sound, body, color, size, movement)
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M8.5 Recognizes repeating patternsM8.6 Copies existing pattern with same materials M8.7 Extends a
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M8.8 Uses words or pictures to describe a simple patternM8.9 Applies a simple pattern rule to different materials or mode (sound, body, color, size, movement) M8.10 Copies M8.11 Applies a |
K.2.1.1 Identify, create, complete, and extend simple patterns using shape, color, size, growing or shrinking such as ABB, ABB, ABB or number, sounds and movements
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Component M9-11: Geometry and Spatial Thinking
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M9 Knowledge and visualization of shapes: The child recognizes shapes, can describe 2 dimensional (2D) and 3 dimensional (3D) shapes and manipulate shapes with purpose.
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M9.1 Shows interest in shapes
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M9.2 Begins to recognize 2 dimensional (2D) and 3 dimensional (3D) shapes such as circles, spheres, squares, and cubes, such as by sorting or puzzle pieces
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M9.3 Points to familiar 2D and 3D shapes (circle, spheres, squares, cubes, triangles) when asked, thereby showing recognition of shape names M9.4 Recognizes
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M9.5 Begins to describe the features (attributes) that define 2D and 3D shapes, including sides and corners M9.6 Puts M9.7 Composes |
K.3.1.1 Recognize basic two- and spheres. and three dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and sphere
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| M10 Transformations and symmetry: The child can locate and manipulate shapes in space
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M10.1 Attends and responds to moving objects and sounds, relative to themselves
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M10.2 Develops increasing ability to change positions and move body from place to place M10.3
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M10.4 Adjusts position and movement of own body relative to objects M10.5 Explores M10.6 Rotates
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M10.7 Rotates, flips, or turns an object to fit once they realize object doesn’t fit a defined space
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M10.8 Puts together (composes) and takes apart (decomposes) shapes to create new shapes M10.9 M10.10 Shows |
K.3.1.3 Use basic shapes and spatial reasoning to model objects in the real world
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| M11 Location, spatial relationships and landmark use: The child recognizes where a person or object is in relation to other people of objects
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M11.1 Shows preference for familiar toys
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M11.2 Recognizes familiar objects from different vantage points
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M11.3 With verbal cues, uses simple maps to relate to real world
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M11.4 Uses terms like near/far; under; below; front; middle; end M11.5 Uses a
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M11.6 Recognizes and describes position of objects in space with greater accuracy M11.7 Draws a |
K.3.1.3 Use basic shapes and spatial reasoning to model objects in the real-world
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Component M-12: Data Analysis
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M12 Sorting: The child recognizes that objects can be sorted by attributes
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M12.1 Recognizes differences among people and among different objects
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M12.2 Matches items based on attributes meaningful to the child
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M12.3 Explores sorting M12.4 Imitates
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M12.5 Sorts objects based on an observable attribute M12.6 Demonstrates
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M12.7 Describes the attribute used for sorting or comparing M12.8 While |
K.3.1.2 Sort objects using characteristics such as shape, size, color and thickness
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Component M13-14: Data Analysis
| Subcomponent | 0-1 year | 1-2 years | 2-3 years | 3-4 years,
K-Readiness |
4-5 years,
K-Readiness |
K Alignment |
| M13 Collects, classifies, and organizes information: The child collects, classifies and organizes data based on distinguishing characteristics.
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M13.1 Participates in simple data collection discussed by an adult or other child M13.2 Collects
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M13.3 Participates as group member in the collection of data that is put on a chart or graph M13.4 Sorts M13.5 |
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| M14 Describes data: The child can describe data by using data sets to solve problems or asking questions |
M14.1 Identifies patterns, differences, or similarities of information collected M14.2 Uses |
M14.3 Uses language to compare data M14.4 Uses data M14.5 |
Source:
