DMG Blog

Developmentally Appropriate Practices for the Young Child

07 May, 2009

The authors of this book believe that it is especially important for all teachers of preschool and young children to use Developmentally Appropriate Practices (DAP*). The activities in our upcoming activity book presented at the Preschool level (PK) are meant to provide teachers with ideas about math concepts, about which young children can develop, familiarity. Teachers must however be constantly aware of each child’s maturation level. Concepts and activities should be carefully matched with each child’s cognitive, emotional, and social levels of readiness.

Mathematics should be an enjoyable endeavor for the child. Activities can be presented in different ways. The activities could be set up in a center for children to explore. They can be presented one-on–one or in a small group. We would prefer most learning occur in natural settings by adapting concepts to real-life experiences in which the child is engaged. No matter how the children are investigating the concepts, it is up to the teacher to ask thought provoking questions so the child will make connections between the manipulative and the math being learned.

A strict didactic approach is not necessary for the young child to learn these math concepts. Providing fun, hands-on activities and connecting the conceptual learning to real-life situations will be the most appropriate for this age child.

  • For more information about DAP, visit the National Association for the Education of the Young Child (

Inservice in Lubbock

21 February, 2009

Debra and I had the opportunity to travel to Lubbock, Texas and talk to preschool teachers about the essential pre-number and number concepts. There were great questions and Debra and I although tired were very excited that we had made an impact. We think that these teachers will focus on these important concepts and change their daily routines. We hope to hear from them and listen to how it goes in their classrooms. A big thank you to Yolanda in Lubbock.

What Do You Remember?

02 February, 2009

Mark and I were talking about what we did at a young age to help us develop number sense. We were talking about natural activities that promoted the essential pre-number concepts of matching, sorting, comparing and ordering. I remember playing store with my grandma where she would put money amounts on different knick-knacks and I would have a change purse with different coins. I thought it was so fun to pick out different objects and add up the total and pay with the change. I was probably between 4 and 5 when I did this. Mark remembers taking a bag of M&Ms and sorting the candy by color then eating one piece at a time until the different piles had the same amount. Email us and let us know what you did to help you learn these important pre-number concepts in the early years of your life.

District Administration Magazine recognition

20 January, 2009

Our assessment was featured as a top 100 products for 2008. Please visit the website to give a comment:


08 November, 2008

If you did not receive a copy of the power point presentation that we used in Dallas, please download a copy. Thank you to everyone and let’s keep spreading the message about how to better help the young child develop a firm foundation in the essential number concepts.

*Conducting the DMA*

22 February, 2008

In this podcast you will view a teacher conducting a one-on-one, shoulder-to-shoulder interview. You will see how the teacher sets out the material and gets ready to conduct the Developmental Math Assessment.

Number Concepts

10 September, 2007

Students in Kindergarten, Grade One, and Grade Two must develop a sound understanding of number concepts to be successful mathematicians. Number Concepts are divided into four categories: word, quantity, symbol, and relationships.
Word – Students need to know the number words appropriate for their age level. They need to use the words in the appropriate sequence, both counting forward and counting back.
Quantity – Students should learn to demonstrate an understanding of quantity through appropriate object counting.
Symbol – All school-aged students need to know how to identify and write age level appropriate numeral symbols.
Relationships – At the heart of the number concepts are the relationships:
1 or 2 more
1 or 2 less
visual patterns
part/part/ whole and place and value
These concepts are critical for students to develop in the primary years. Many math educators believe that the number concepts and in particular part/part/whole relationships are the foundation for number sense.
DMG believes that Operations are best presented to young students after the student has demonstrated a grade-level appropriate understanding of the number concepts beginning at kindergarten. DMG provides resources, information, and an assessment (DMA) to support student development in the following areas:

• Addition/Joining
• Subtraction/Separating
• Multiplication/Grouping
• Division/Partitioning

Preschool: Matching

21 August, 2007

Matching leads to understanding the concept of one-to-one correspondence. When a child passes out cookies, each child in the room gets one cookie. Maybe there are just the right amount of cookies or maybe there are extra cookies. When counting blocks, each block is counted once and only once. Matching forms the basis for our number system. When a child can create “the same”, it then becomes possible to match two sets. This becomes a prerequisite skill for the more difficult tasks of conservation.

Matching occurs in many everyday activities:
  • Getting dressed, eating, school, playing, and other activities: setting the table, folding the laundry (match socks and clothes to child, mom, dad), sharing birthday treats.

The following are different ways that children can practice matching skills. Number Concept Dot Match and Sort Sets are available to support conceptual development.

(Use the Match and Sort Number Concept Dots or other like materials)

1. Matching items that are different
(Visually easier to match items that are different).

• Use the Number Concept Dot Match and Sort Set or similar items. Place 4 paper plates in front of the child. Give the child 4 circles. Have the child use the circles and match a circle to each of the plates.
Extend: Give the child more plates and/or different shapes.

2. Matching items that are the same
(More difficult to determine if each item has a mate)

• Use the Number Concept Dot Match and Sort Set or similar items. Use 2 red circles, 2 red squares, 2 red triangles, and 2 red rectangles. Lay out one of each. Give the child the remaining red shapes. Ask the child to match each shape with one that is the same. This has the child looking for “sameness” of shape.
Extend: Give the child all of the squares and ask them to make color matches.

3. Match a few items (1 – 5) Match many items
(easier to match in the 1-5 range)

• Use the Number Concept Dot Match and Sort Set or similar items. Begin with 1 to 5 shapes in two colors. Place all of the shapes in one pile. Ask the child to find two shapes that are the same. Continue until all shapes are matched.
Extend: Increase the number of shapes and/or the colors that are given to the child.

• Place 3 shapes in one row. Place 5 shapes in a second row (3 of the same shapes). Ask the child to match. Watch to see what the child does with the extras.
Extend: Increase the number of shapes in rows one and two.

4. Match items that have the same number in each set

• Use the Number Concept Dot Match and Sort Set or similar items. Make a set that has three different shapes. Make a second set that has the three shapes and three other shapes. Ask the child to build a matching set. In this task, the child is matching sameness of number.
Extend: You can increase the number of shapes in both sets.

• Place 4 different colored circles on a paper plate, Give the child a paper plate and one colored circle. Ask the child to make a match on his/her plate.
Extend: Change the shapes that you place on the plate. It becomes more difficult when you ask the child to look for color and shape matches.

5. Match items that do not have the same number in each set/row

• Use the Number Concept Match and Sort Set. Lay out any color circle, triangle, square, and rectangle in a line. Give the child three of the four shapes and ask them to match each. Watch to see what the child does when he/she cannot find a match for one of the shapes. Ask questions to help the child see that sometimes all items do not match.