Strengthening Mathematical Thinking: Program-Wide Efforts

This month’s newsletter explores many different ways that educators can incorporate math language and exploration into their learning environment.  At the program level, there are things the staff can do to ensure that everyone in the program is working toward the same math-rich environment.  Below is a list of recommendations put forth by NAEYC and the National Council of Teachers of Mathematics (NCTM) to help programs determine strengths and areas of need related to math instruction. 

Work with your staff and coworkers to rate your program on each of the following recommendations.  Once you have identified opportunities for growth, create an action plan and get to work!

In high-quality mathematics education for 3- to 6-year-old children, teachers and other key professionals should:

1. enhance children’s natural interest in mathematics and their disposition to use it to make sense of their physical and social worlds

2. build on children’s experience and knowledge, including their family, linguistic, cultural, and community backgrounds; their individual approaches to learning; and their informal knowledge

3. base mathematics curriculum and teaching practices on knowledge of young children’s cognitive, linguistic, physical, and social/emotional development

4. use curriculum and teaching practices that strengthen children’s problem-solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas

5. ensure that the curriculum is coherent and compatible with known relationships and sequences of important mathematical ideas

6. provide for children’s deep and sustained interaction with key mathematical ideas

7. integrate mathematics with other activities and other activities with mathematics

8. provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest

9. actively introduce mathematical concepts, methods, and language through a range of appropriate experiences and teaching strategies

10. support children’s learning by thoughtfully and continually assessing all children’s mathematical knowledge, skills, and strategies.

Details regarding each of these recommendations can be found in the joint position statement of the NEAYC and NCTM.

November 2019 Newsletter – Promoting Mathematical Thinking: Families

Because math is everywhere, families have an opportunity to reinforce math learning at home. Create resources for families that communicate the importance of early math skills. Give a list of math language that families should incorporate into their conversations with children. Be sure to explain the nature of early math and developmentally appropriate practices.  We don’t want families to feel like they have to use flashcards or worksheets to teach their children math.  There are plenty of fun ways to play with math throughout the day. You can also:

  • Establish a lending library of books that contain opportunities to discuss math at home.  Attach an index card with guidelines for parents to follow before, during, and after reading the book.
  • Create math backpacks that focus on a particular math skill. Allow families to sign out a back pack for the evening or the weekend.  Provide detailed instructions for the playful nature of the activity and describe the importance of the skill.  Help families decide which back pack to take home based on what you know about the child’s skills and abilities. 
  • Give math homework. Again, this should not be anything paper and pencil related. Ask families and children to count how many turns it takes to get from the school to home.  How many stop signs or traffic lights are between the school and home?
  • Help families see how they can incorporate math language and skills into running errands.  Create a fact sheet that explains the math language the can be used at the grocery store, for instance.  You can also include ideas for how families can keep children engaged during trips to the grocery store by incorporating a few math activities. 
  • Host a family math night.  Prepare a number of different activities and games that incorporate math skills and language.  Be a role model for families so they can hear the math language you use and take those ideas home with them.
  • Be sure to document children’s learning and display evidence of learning in a place families will see when they visit the program.  You may be able to use social media, bulletin boards, daily sheets, conferences, or newsletters to highlight math learning. 

How do you encourage families to engage in math language and exploration with their children? Tell us on Facebook.

For the main article Promoting Mathematical Thinking, CLICK HERE

For the article Infants & Toddlers, CLICK HERE

For the article Preschoolers, CLICK HERE

For the article Kindergarten & School-Agers, CLICK HERE

November 2019 Newsletter – Promoting Mathematical Thinking: Kindergarten & School-Agers

School-Agers are already receiving math instruction during their school hours.  They don’t necessarily need additional direct instruction while they are in their before/afterschool program.  However, you can incorporate mathematical thinking into fun activities that engage children’s creativity and personal interests.  Take a look at the K-12 learning standards in your state to remind yourself of the math skills children are expected to know at different grade levels, and then try to find fun ways to incorporate some of those skills into your routine.

  • Estimation/prediction stations – each week, set up a station where children can estimate or make predictions. 
    • Number of items in a jar
    • Time it will take for snow to melt
    • How tall the sunflowers will grow
  • Conduct a variety of science experiments.  Ask children to make predictions, observations, and collect their data.  Then help them create visual representations of their data.
  • There are so many opportunities to use math in cooking with children.  Be sure to include cooking in your program. You could also incorporate other activities such as sewing, knitting, or crocheting.
  • Create weekly survey questions that children can ask other students in the program, teachers, or their family members.  Again, help children determine the best way to gather the data and represent in a visual way.
  • Encourage children to create their own board games. They can create the materials for the game and teach their peers how to play.
  • Plan a fund-raiser.  Include the children in planning from start to finish, including budgeting, purchasing and making materials, promoting the fundraiser, etc.

What fun and engaging ways do you reinforce math language and learning with school-agers? Tell us on our Facebook page now!

For the main article Promoting Mathematical Thinking, CLICK HERE

For the article Infants & Toddlers, CLICK HERE

For the article Prechoolers, CLICK HERE

For the article Families, CLICK HERE

November 2019 Newsletter – Promoting Mathematical Thinking: Preschoolers

Preschoolers continue to act like scientists as they explore the environment and materials available for learning. Continue to use a plethora (a math term meaning a large or excessive amount) of math language in your day to day conversations with children.  There are other ways you can boost the opportunity to use and think about mathematical concepts throughout the daily routine. 

  • Clean up is a sorting and classifying activity. Talk with children about the attributes of the items they are cleaning up. Discuss why some blocks go in one spot while others are located in a different container.  Place outlines of the shapes of blocks on shelves so children can practice matching blocks to their outlines.
  • Encourage children to add complexity to their building projects- younger children typically build tall straight towers.  Introduce children to images of sprawling and intricate castles and famous architecture.
  • Measure the weather. Move beyond dressing the weather bear.  Track temperatures over a week, month, and year.  Measure rainfall or snowfall, determine the direction of the wind, and explore shadows. Find ways to visually represent your data.  Ask children what they notice about the data they are collecting.
  • Measure everything.  You don’t have to assign this as a task, simply provide rulers, measuring tapes, spoons, cups, scales, a balance, etc. in different learning centers and encourage children to explore attributes of the object they encounter.
  • Use a variety of shapes to build new shapes.  A simple example is the way that two squares placed side-by-side create a rectangle.  What happens when you combine triangles? Or hexagons?
  • Explore characteristics of shapes.  Introduce more advanced shapes such as arches, cones, crescents, octagons, semi-circles, trapezoids, cubes, cylinders, and pyramids (3-D), etc.  Have manipulatives available for this exploration; stay away from worksheets at this time.
  • Introduce and use more-advanced directional language such as horizontal, vertical, diagonal, etc.
  • Play with symmetry and asymmetry. Use paint, loose parts, mirrors, etc. to create different forms.
  • Time is a pretty abstract concept for children of this age.  Rather than focusing on teaching how to tell time, focus on helping children learn the sequence of the routine.  Use language such as before, after, first, next, later, etc. 
  • Play active games incorporate mathematical concepts such as sorting materials, scavenger hunts (find shapes,  things that are 2 inches long, etc.), or obstacle courses using directional language. Also think about creating math games based on children’s favorite books and stories.

This list just scrapes the surface of all of the possibilities for exploring math with preschoolers.  Add your favorite ideas on our Facebook page.

For the main article Promoting Mathematical Thinking, CLICK HERE

For the article Infants & Toddlers, CLICK HERE

For the article Kindergarten & School-Agers, CLICK HERE

For the article Families, CLICK HERE

November 2019 Newsletter – Promoting Mathematical Thinking: Infants & Toddlers

Young children are natural explorers and observers.  During the first 3 years of life, children need the adults around them to help them make connections between what they observe and the language used to describe those experiences.  As with most development skills, early mathematical thinking is integrated into lots of other areas of development, for example – language skills. 

Use rich math language when talking to children.  They will not understand every word you use, but in order to learn the words, they have to hear them over and over again.  Try to use math language to create context or explain something about the child’s experience. Here are a few examples:

  • After feeding an infant, say “You must have been hungry, you drank your whole bottle,” or “You must not be very hungry right now, you only drank half of your bottle.”
  • When dressing a child say, “Your socks have a pattern – they are red/blue/red/blue,” or “Let’s put one leg inside the right pant leg, and the other leg in the left pant leg.”
  • While children are playing say, “You are sitting next to, or beside, Jamel,” or “You just placed the green block on top of the yellow one and the blue block is on the bottom.”
  • During circle time say, “Our group has 8 children in it today,” or “Usually, we have 8 children in our group, but David is sick today, so there are only 7 children here.” 
  • Before an art activity say, “Julianna, if you would like to paint, come sit at the blue square table,” or “Today we will be using wide and thin brushes to paint different kinds of lines.”  
  • When a child arrives say, “Your book bag is heavy today, there are many items inside it,” or “Good morning Theo, you are the first child to arrive today. I am glad you are here.”  
  • On a walk say, “Look at these two trees, one is very tall and the other one is short,” or “Can you put your hand around this small tree trunk? How many children would it take to give the big tree a hug?”
  • While children are exploring the sensory table say, “How many cups of sand fit into the red bowl?” or “Who has the biggest pile of sand in front of them?”
  • During clean-up time say, “Zoe, please pick up the circles and Max is going to pick up the squares,” or “Let’s see how fast you can put all of the blocks into the basket.”  

Sing songs about itsy-bitsy spiders and great big bears.  Include clapping to the rhythm of the song or poems. Songs like the Hokey Pokey can be modified to be easier for young children to understand.  You can switch out left and right for one arm and the other arm, for example.

Be sure to provide a routine that allows children time to explore the environment, experiment, and make observations.  More importantly, provide a wide variety of safe and interesting materials for children to explore. 

Go to our Facebook page to tell us how you incorporate math language into your conversations with infants and toddlers.

For the main article Promoting Mathematical Thinking, CLICK HERE

For the article Preschoolers, CLICK HERE

For the article Kindergarten and School-Agers, CLICK HERE

For the article For Families, CLICK HERE

ChildCare Education Institute Offers No-Cost Online Course on Mathematical Talk and Play

ChildCare Education Institute® (CCEI), an online child care training provider dedicated exclusively to the early care and education workforce, offers CUR115: Mathematical Talk and Play as a no-cost trial course to new CCEI users November 1-30, 2019.

By engaging in math at an early age, children develop critical thinking and problem solving skills which are used in all academic areas. In spite of the fact that research shows a correlation between mathematical competence and academic success, early care and education (ECE) professionals in North America spend more time building literacy skills than math skills. In the United States, children are estimated to receive up to 1,000 hours of literacy education in childcare environments before they start school, whereas, mathematical learning is limited to simple sorting, rote counting, and patterning.

Given that millions of children spend a considerable amount of time in early learning settings, ECE professionals have a tremendous opportunity to support and advance young children’s mathematical development before they start school. Unfortunately, many teachers lack the training and confidence needed to provide high-quality math instruction, so they downplay mathematics. As a result, children receive little or no high-quality math education and, as a result, they begin school catching up on math skills they should already know. For children from disadvantaged backgrounds, playing catch-up when they start school is even more profound, putting these children at risk of persistent low performance throughout their schooling.

This course presents practices and strategies for promoting mathematical talk and play in the early learning environment. Course participants will learn how to expand the early math curriculum beyond rote counting, sorting, and patterning activities by incorporating more advanced concepts such as stable order, one-to-one correspondence, order irrelevance, cardinality, and abstraction into children’s play and routines.

“Early childhood teachers can build basic math skills through mathematical talk, purposeful mathematical play, and by setting up the classroom environment to promote mathematical learning,” says Maria C. Taylor, President and CEO of CCEI.  “Course participants will learn why math is so important in early childhood and a number of strategies for incorporating more math learning throughout the early childhood curriculum, particularly through informal talk and play.”

CUR115: Mathematical Talk and Play is a two-hour, beginner-level course and grants 0.2 IACET CEU upon successful completion. Current CCEI users with active, unlimited annual subscriptions can register for professional development courses at no additional cost when logged in to their CCEI account. Users without subscriptions can purchase child care training courses as block hours through CCEI online enrollment.

For more information, visit or call 1.800.499.9907, prompt 3, Monday – Friday, 8 a.m. – 5 p.m. EST

ChildCare Education Institute, LLC

ChildCare Education Institute®, a division of Excelligence Learning Corporation, provides high-quality, distance education certificates and child care training programs in an array of child care settings, including preschool centers, family child care, prekindergarten classrooms, nanny care, online daycare training and more. Over 150 English and Spanish child care training courses are available online to meet licensing, recognition program, and Head Start Requirements. CCEI also has online certification programs that provide the coursework requirement for national credentials including the CDA, Director and Early Childhood Credentials.  CCEI, a Council for Professional Recognition CDA Gold Standard™ training provider, is accredited by the Distance Education Accrediting Commission (DEAC), is recognized by the Council for Higher Education Accreditation (CHEA) and is accredited as an Authorized Provider by the International Association for Continuing Education and Training (IACET).