Early Math—Living in a Mathematical World

For the past couple of weeks, we’ve been talking about a newly-released guide from the US Department of Education Institute of Education Sciences entitled Teaching Math to Young Children.  They provide 5 recommendations for teaching math to young children.  The first recommendations are to “teach number and operations using a developmental progression”, “teach geometry, patterns, measurement, and data analysis using a developmental progression,” and to “use progress monitoring to ensure that math instruction builds on what each child knows.”  This week, we will talk about the fourth recommendation, to “teach children to view and describe their world mathematically.” 

Through the first recommendations, we understand the numbers, operations, and concepts children need to understand to help them explore and explain their world and how to make sure that each student is acquiring these concepts.  We then work on making sure that they can apply these concepts to real life…kind of like the geometry student who wants to know “when will I ever need this”. 

The recommended strategies for viewing and describing the world mathematically include:

• Teaching children to solve math problems informally.  We don’t start with an equation like 3+2=5, we start with “If you have 3 blocks and get 2 more, how many do you have all together now?”
• Teach children formal math vocabulary.  Now that they have the basic math concepts, we can start explaining that “subtract” means the same thing as “take away”, describing who is “first” in line, or which stack of blocks has “more” or “less” than another.
• Open-ended questions.  This is an area where early childhood teachers excel!  Questions with set answers can assess a child’s knowledge, but not encourage deeper thinking.  Use questions that start with “how could we find out”, “how else could we”, or something else along those lines.
• Talk about math in everyday situations.  Encourage children to help out with everyday tasks that involve math concepts.  “How many cups do we need for snack time for everybody to have a drink?”  “How did you know that?” 

For more information and suggestions on implementing these recommendations, check out the guide at: http://ies.ed.gov/ncee/wwc/pdf/practice_guides/early_math_pg_111313.pdf#page=18

Misty

Early Math—Progress Monitoring

For the past couple of weeks, we've been talking about a newly-released guide from the US Department of Education Institute of Education Sciences entitled Teaching Math to Young Children.  They provide 5 recommendations for teaching math to young children.  The first two recommendations are to “teach number and operations using a developmental progression” and to “teach geometry, patterns, measurement, and data analysis using a developmental progression.”  This week, we will talk about the third recommendation, to “use progress monitoring to ensure that math instruction builds on what each child knows.”

Through the first two recommendations, we understand the numbers, operations, and concepts children need to understand to help them explore and explain their world.  Like anything else that we do in teaching children, we need to identify which of these concepts each child has mastered and which ones need more practice.  We can then teach new concepts sequentially. 

The recommended strategies for progress monitoring include:

• Use introductory activities, observations, and assessments to determine each child’s existing math knowledge, or the level of understanding or skill he or she has reached on a developmental progression.  You are probably already doing this in compiling portfolios on each child and/or utilizing developmental checklists on a regular basis.
• Tailor instruction to each child’s needs, and relate new ideas to his or her existing knowledge.  What interests the child and how can you use that interest to further his or her understanding of the math concept you are teaching?  For example—count the musical instruments, arrange the dinosaurs by size, sort the blocks by shape.
• Assess, record, and monitor each child’s progress so that instructional goals and methods can be adjusted as needed.  Does the child need more practice in a particular skill or is he or she ready to move on to the next concept?

For more information and suggestions on implementing these recommendations, check out the guide at: http://ies.ed.gov/ncee/wwc/pdf/practice_guides/early_math_pg_111313.pdf#page=18

Misty

Early Math—Understanding Shapes, Patterns, and Measurement

Last week we started talking about a newly-released guide from the US Department of Education Institute of Education Sciences entitled Teaching Math to Young Children.  Their first recommendation is to “teach number and operations using a developmental progression.”  This week, we’ll talk about the second recommendation, to “teach geometry, patterns, measurement, and data analysis using a developmental progression.”  Again, there is a focus on developmental progression, but this recommendation is stretching last week’s skills a bit. 

While children must understand numbers and operations, they also have to see how mathematical concepts exist in the world around them and how they can use those concepts to explore and explain their world. 

Early concepts include:

• Shapes—Recognizing, naming, and comparing shapes, then combining and separating those shapes to create new shapes.
• Patterns—Finding, identifying, extending, correcting and creating patterns. 
• Measurement—Using both standard and nonstandard units and tools for measurement. 
• Graphing—Collecting and organizing information and representing the information graphically.

For more information and suggestions on activities to teach these concepts to children, check out the guide at: http://ies.ed.gov/ncee/wwc/pdf/practice_guides/early_math_pg_111313.pdf#page=18

Misty

Early Math—Understanding Numbers and Operations

The US Department of Education Institute of Education Sciences has recently released a guide entitled Teaching Math to Young Children.  The goal of the publication is to provide specific, evidence-based recommendations on teaching math to young children.  They provide 5 specific recommendations.  We will spend the next few weeks going through those recommendations. 

The first recommendation is to “teach number and operations using a developmental progression.”  Just like most things that we learn, there are foundational concepts and skills that must be gained before the higher-level skills can be learned.  Good teachers can determine which concepts and skills their students possess and, thereby, understand what they need to learn next. 

The first concepts of early number knowledge to be acquired are:

• Small-number recognition—to be able to recognize by sight how many items are in a collection without having to count them.  Initially, work on up to 3 items, then increase to up to 5 items.
• One-to-one correspondence—to be able to assigning a counting number to each item in a collection to determine how many total items are in the collection.  The child must understand that each item receives one, and only one, number.
• Compare quantities—to be able to use counting and number words to compare two collections and use words like “less” and “more” to describe the relationship between the collections. The child must understand that each number is exactly one more than the previous number.
• Solve basic problems—children can add or subtract items from the collection to determine “how many are there now” when items are added and “how many are left” when some are removed.

For more information and suggestions on activities to teach these concepts to children, check out the guide at: http://ies.ed.gov/ncee/wwc/pdf/practice_guides/early_math_pg_111313.pdf#page=18

Misty