The first goal in the Mathematics section is

“Goal 6 – Demonstrate and apply a knowledge and sense of  numbers, including numeration and operations”

 

The associated learning standard is

“Learning Standard A – Demonstrate beginning understanding of number, number names and numerals”

and the benchmarks are

6.A.ECa – Count with understanding and recognize “how many” in small sets

6.A.ECb – Use subitizing (the rapid and accurate judgment of how many items there are without counting) to identify the number of objects without counting in sets of four or less

6.A.ECc – Recognize and describe the concept of zero

6.A.ECd – Connect numbers to quantities they represent using physical models and representations.

6.A.ECe – Differentiate numerals from letters and recognize some written numerals

6.A.ECf – Verbally recite numbers from 0 – 10

 

Without looking at the example performance descriptors, I think we could come up with a thousand and one ways to look for examples of the children meeting these benchmarks.  Using a variety of math manipulatives, regularly as a part of your everyday program, children will begin to know how many pips are on a die without counting them (6.A.ECb), count the number of Unifix cubes there are in a set, (6.A.ECa, 6.A.ECf) identify numbers in a matching game and name them (6.A.ECe), and so on.

It is important to note that although the authors of this document provide performance descriptors, that we as practitioners, do not get caught up in “teaching to the test.”  It would be easy to use these examples as specific ways that we look for successful achievement for children, but it is much more developmentally appropriate to expect that there are a variety of ways that children can show us what they know.

This goal is about number- recognizing a written numeral saying its name and differentiating those symbols from letter symbols. It is about understanding the concept of “nothingness” and that “nothing” can be represented by the symbol “0”.  It says that, just by looking, children should be able to tell how many of something are in a set of 4 or less and that they should be able to count individual items in a set accurately.  Children should be able to answer the question, “how many?” and make representations of that number by creating a set using physical numbers and representations of that number.

In April, I plan on exploring perhaps the most important book ever to be written about young children and number….it is aptly entitled “Number” and hopefully, this discussion will continue to shed let on how children achieve these goals and meet these benchmarks.

Over the next several weeks, we are going to look at the Standards and Benchmarks for each of the areas in mathematics.  This week, simply because we have spent so much time on “Attributes” I am going to review the exact Standards and Benchmarks for this one mathematical concept.

Goal 8 states that children will “Identify and describe common attributes, patterns and relationships in objects.” Learning Standard A under Goal 8 says that children will, “Explore Objects and Patterns.”

The benchmarks for this Goal and Standard are:

8.A.ECa – Sort, order, compare and describe objects according to characteristics or attributes.

8.A.ECb. – Recognize, duplicate, extend, and create simple patterns in various formats.

So, how do we know that children are meeting their benchmarks?  We look at the next section called “Example Performance Descriptors.”

Compare and describe various objects (e.g., describe different rocks by referring to their size, shape, weight, etc.).

 

Create a simple repeating pattern using classroom objects (e.g., build a tower of alternating blue and red cubes).

 

Replicate patterns in music (e.g., repeat a sound pattern by clapping or tapping foot lightly; sing a repetitive song such as B-I-N-G-O; play finger game such as Open, Shut Them).

 

Sort objects according to different characteristics (e.g., sort crayons by color and size; sort small blocks by shape and color).

 

Order objects in a series by a single attribute (e.g., order fire trucks from shortest to longest; order rocks from smooth to rough).

 

Is your head spinning?  Mine sure is.

For me, the most helpful way to sift through this information is to consider the smallest and most specific details and begin there.  You will see that until a child can recognize a simple attribute (one characteristic) they will not be able to do the rest or meet these benchmarks via these example descriptors.  Begin with what children know- and work up.  Don’t start at the highest or widest point and work down.  Children don’t learn that way.