Marcy is in the kitchen making lunch with her energetic three-year-old son, Julio. She counts out the grapes for her plate, “One . . . two . . . three . . . four . . . . How many grapes does Mommy have, Julio?”
“Four!” Julio yells gleefully.
“That’s right,” Marcy smiles at him. “And how many grapes do you want? Can you count them?”
“I want two!” Julio says and then grabs a small handful of grapes and sets them on his plate.
Marcy notices this and says, “Let’s count them together, one . . . two . . . three . . . How many grapes do you have?”
“Three!” Julio says. Impatient, he pops a grape into his mouth.
Marcy smiles and says, “Now you have two grapes.”
This interaction between Marcy and Julio may seem simple and natural. But for many parents, such interactions can be unfamiliar. Parents who feel comfortable engaging in regular story times with their children may feel anxious when it comes to conversations with their children involving mathematics. Yet, such parent–child mathematics talks are crucial for building strong foundations in mathematics.
As teachers, we work hard to ensure that our students’ days are filled with substantial mathematics talk. However, school experiences alone are not enough to overcome the wide disparities in students’ mathematics achievement. That is why it is critical to help parents understand the importance of mathematics talk and shared mathematics activity in the home. In this article, we discuss the importance of parent–child mathematics talk and share the Four Cs strategy that teachers can use to help parents increase the frequency and quality of mathematics-related interactions with their children. The Four Cs strategy (Converse, Count, Compare, and Categorize) is a memory aid that can help parents move their shared mathematics interactions beyond simple counting activities (e.g., count sequence and numeral recognition 1–10, etc.) toward a wider array of mathematical experiences such as more advanced counting (e.g., counting forward and backward within 10 and counting beyond 10–20), comparing quantities and attributes, and categorizing according to attributes. But perhaps most importantly, the Four Cs strategy can improve the variety and quality of parent–child mathematics talk, providing children with the oral language development needed to build a solid mathematics foundation.
WHY IS EARLY MATHEMATICS IMPORTANT?
Research has shown that early development of mathematics skills and knowledge is a strong predictor of later mathematics achievement. For example, Nguyen and colleagues (2016) found that certain advanced counting skills, such as counting on or counting forward from any number, are better predictors of later mathematics achievement than are the basic counting skills (e.g., counting to 10, etc.). Furthermore, students who leave kindergarten with these more advanced mathematics competencies, regardless of their school-entry knowledge, are more likely to maintain a higher level of achievement in mathematics later on. However, many children do not enter school nor do they leave kindergarten having mastered these more advanced counting competencies, which may contribute to ongoing mathematics difficulties as children move forward in their schooling. With this in mind, it is important that teachers look for ways to help students develop key mathematical competencies while they are still young.
HOW DO YOUNG CHILDREN DEVELOP UNDERSTANDING OF NUMBER?
Counting is sometimes viewed as a simple skill, but it is actually a complex, interconnected process (Carpenter et al. 2017). Children progress through different stages when developing their concept of number, including the stages of global quantification, one-to-one correspondence, and counting (see figure 1). These stages often overlap, depending on the number of objects to be counted. A child who can count to five might use counting when there are only a few objects, one-to-one correspondence when there are more than a few, and global quantification when there are many objects. It can take about a year or more for most young children to move from being able to produce a set of one to being able to produce a set of four or more (Wynn 1992). This process occurs differently for different children. At any given time, there may be a one- to two-year difference in the mathematics knowledge of students entering school (Gunderson and Levine 2011). This presents a monumental challenge for early elementary school teachers who must overcome this gap. To help address this, it is beneficial for teachers to look for opportunities to develop mathematics understanding that may exist outside of school. One such way is to leverage parent–child interactions to support mathematics learning.
Young children move through different stages as they develop their understanding of quantification (Moomaw and Hieronymus 2011).
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
WHY ARE PARENT–CHILD SHARED MATHEMATICS ACTIVITIES SO IMPORTANT?
Even the smallest changes made by parents to foster more positive mathematics-related interactions with their children can lead to the increase in mathematics achievement (Levine et al. 2010). In one study, Levine and colleagues (2010) tracked the number-related words that occurred in the natural interactions between parents and their children (ages 14–30 months) and measured the differences in numerical understanding at age 4. The results showed that children in families with more frequent number talk significantly outperformed children in families with low number talk on measures of numerical understanding. Despite these encouraging findings, the study highlighted the unfortunate fact that most parents simply do not spend much time talking to their children about number. For many parents, however, it is simply a matter of not knowing how to engage their children in “number talk” in a natural way. Teachers can help parents by sharing the Four Cs strategy, a simple mnemonic that guides and reminds parents of the best ways to support the development of their children’s early mathematics foundation (see video 1, Using the 4Cs).
Using the 4Cs: Converse, Count, Compare, and Categorize—an Interview with Revital Heller High
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
HOW CAN THE FOUR Cs HELP?
As researchers studying the home numeracy environment, much of our present work involves talking with parents about their shared mathematics practices with their children. It has been through these conversations that we have come to realize that much of the shared mathematics activity between parents and their preschool age children consists primarily of learning the count sequence to 10, counting objects to 10, and recognizing and writing numerals 1 to 10, which is consistent with findings in the literature (Elliot and Bachman 2018). Parents of the youngest learners do not frequently describe engaging in activities that move beyond simple, rote counting activities to the more advanced counting activities that are better predictors of later mathematics success, nor do they describe engaging regularly (if at all) in comparing or categorizing activities, such as comparing quantities (e.g., Who has more?, How do you know?, etc.). These conversations combined with our review of the research literature indicate that parents seem to have a narrow view of what early childhood mathematics is, considering it to consist primarily of simple counting experiences. This may explain, at least in part, why so many children begin school with only modest mathematics skills and understanding—a knowledge deficit that can have lasting consequences for the learner.
Sometimes, providing parents with the support they need can seem like a challenge. In our work, we have found the Four Cs strategy to be a simple way to help parents be mindful of the importance of extending their shared mathematics activities beyond the basics of counting from 1 to 10. The strategy is easy to remember and employ, especially once parents become familiar with examples of how each “C” fits within their daily parent–child activities.
Converse
Parents who do not talk about mathematics-related topics with their children have limited opportunities to promote, prompt, and probe the child’s thinking. As teachers, we want to help parents increase the frequency and the quality of their parent–child mathematics talk and interactions. Shared mathematics activities and conversations should feel natural and be centered in everyday activities. Children are likely to be more engaged in activities that are related to their everyday experience and get more out of them than more formal mathematics experiences such as workbooks, handouts, or flashcards (Elliot and Bachman 2018). This is because an everyday activity is more relevant and meaningful to the child, helps the child understand the purpose of mathematics in context, and often provides the child with information they can readily use in their life. Consider when a child is able to count and label how many cookies she has, then she is better able to decide if she has enough to share one with each family member—an idea that most children find very useful indeed. Pretend play is another area where mathematics talk can be integrated in seamless ways. In video 2, Ruby Counts with Grandpa, we see Ruby and her grandfather having a pretend tea party. Ruby’s grandfather encourages her to use one-to-one correspondence to count the spoonfuls of “sugar” she pretends to put into his tea. Notice that as she counts the number eight, she forgets to put in a spoonful, indicating that her one-to-one correspondence is still developing. Ruby’s grandfather uses warm encouragement to prompt Ruby to put in another spoonful of sugar to represent the number eight in the count sequence. This encouragement is critical; parents and caregivers should strive to keep conversations warm and nurturing because doing so will help children build positive associations around mathematics.
Ruby (age 2.5 years) Counts with Grandpa
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
Count
Number words are tricky because they are used not only in the count sequence or to label the quantity of a set but also as the labels for numerals and as labels for order or position (e.g., “Let’s get in line. Daddy will be number 1, I will be number 2, and you will be number 3.”). Other important counting ideas include what gets counted; making, comparing, and ordering counting collections; and subitization (Carpenter et al. 2017). Because of this, it is important to provide children with frequent and various exposure to the different uses of number words in different contexts. Doing so ensures that children are more likely to develop their understanding and be able to differentiate between uses of number words without becoming confused.
Developing basic counting knowledge, such as knowledge of the order of the count sequence (stable-order principle), counting (one-to-one correspondence) and labeling (cardinality) sets of objects, as well as counting out from a group (e.g., “Let’s count out four plates for dinner”) is important. However, it is equally important for parents to engage children in more advanced counting experiences, such as reciting the count sequence forward or backward from any number, counting beyond 10, or counting-on one group of objects to another (see figure 2). The demonstration of these advanced counting skills, especially by the time the student leaves kindergarten, is significantly correlated with higher mathematics achievement in fifth grade (Nguyen et al. 2016).
Counting skills can be classified by difficulty as either basic or advanced (adapted from Nguyen et al. 2016).
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
Frequent and varying counting experiences are vital to the development of children’s strong number sense. As teachers, we can help parents to develop their own awareness of the different types of counting experiences they can share with their children, from exploring the count sequence, to count all, to count out, and to count on. As parents become more knowledgeable about the differences between basic and advanced counting skills, they can better support the development of these skills through shared counting experiences.
Compare
The ability to notice that objects (or groups of objects) have characteristics that can be compared is an important foundational concept in many areas of mathematics, including spatial reasoning, geometry, measurement, data, and patterns. The understanding that quantity is also an attribute that can be compared is a critical milestone in number sense as well. Fostering children’s thinking about comparisons is easier than parents might think. Opportunities to compare quantities (e.g., “How many pennies do I have? How many pennies do you have? Who has more? How do you know?”) or to compare other attributes of objects or activities (e.g., “What shape is this? Is this round or square? Which one is bigger, taller, shorter, and smaller? Which takes longer? How can you tell?”) abound in everyday parent–child conversation.
Puzzles are another great way for parents to help children think critically about comparisons. When completing a puzzle, one must carefully regard each puzzle piece and its attributes (i.e., image, shape, size, etc.) and analyze it to determine how a specific piece fits together with other pieces as part of a whole. Comparisons of this nature provide children with a chance to develop and use their spatial reasoning and to become more familiar with spatial words such as above, below, over, under, in front of, and behind. Parents can easily include such language in natural ways while engaging in puzzle activities with their children (e.g., “This piece goes above that piece. This one goes next to that one). Comparisons also offer the chance to describe the location and position (e.g., “Your shoes are behind the door. Put your umbrella on top of the book shelf,” etc.). As a result, parents who engage their children in comparison activities are helping their children to develop critical thinking, spatial reasoning, and important mathematics vocabulary.
Categorize
Soon after young children start to notice that objects have attributes that can be compared, they can begin to sort items into groups with similar attributes. It is not uncommon for toddlers and preschoolers to want to make groups of similar things (e.g., “These are all my blue toys. I put all the circle stickers together,” etc.). Everyday activities present many opportunities for children to categorize and sort. Even the youngest children can decide how they will organize dishes in a dishwasher or on a drying rack or how they will group the dinnerware (e.g., plates, cups, forks, knives, spoons, etc.) for a family meal. Such tasks provide opportunities for parents and children to have informal discussions about how and why things might be sorted in a certain way and to think about the different characteristics that define categories of items (e.g., “I put all the forks together because the forks are prickly and spoons are round,” etc.).
Sorting and categorizing items on the basis of characteristics also provide children opportunities to practice quantifying and comparing. For example, when organizing the kitchen cupboard, a child might notice something like the following: “We have four cans of tomatoes and six cans of corn. We have more cans of corn than tomatoes!” As children begin to sort and classify, they are also doing the important work of recognizing and describing patterns. They are able to think critically about the similarities and differences in the attributes of objects, and they are better able to construct mental models of relationships—the foundation for algebraic thinking.
HOW CAN TEACHERS HELP PARENTS GET FAMILIAR WITH THE FOUR Cs?
One simple way to help parents become more familiar with the Four Cs is to use a homework menu. A homework menu is a tool that features a grid of various activities that parents can choose to do with their children (see figure 3). By giving parents the instruction to do at least one activity in each column and one activity in each row each week, teachers can ensure that parents and children are engaging in a variety of activities across all Four Cs. This tool further increases parents’ awareness of and attention on the importance of engaging in activities beyond simple rote counting and demonstrates how easy it can be to incorporate mathematics talk into their everyday living. As teachers, we can be strategic about the kinds of activities we place onto the grid, varying the types and complexity as we respond to the needs of our students.
This sample 4C mathematics menu for parents can be downloaded directly at https://www.facebook.com/parentchildmathtalk/menu/.
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
WHAT ARE SOME ADDITIONAL TIPS TEACHERS CAN PROVIDE TO PARENTS?
Many parents want to engage mathematically with their children, and they are just unsure of how to do so. Teachers can help parents by providing them with simple mathematics engagement strategies like the Four Cs that are easy to implement for anyone, regardless of their background (see figures 4 and 5 for more ideas). In addition, teachers can help parents understand these basic ideas:
Opportunities occur every day to talk to about numbers and mathematics and so use them! Encourage parents to have their children help out with daily tasks around the house, such as setting the table for dinner, loading the dishwasher, and helping out at the grocery store or in the garden. Consider using some of the questions in figure 4 to help parents get their mathematics conversations started.
Parents can use activities that work best for them. Parents are most likely to engage in everyday activities that feel easy and accessible. Provide parents with many different examples of parent–child mathematics interactions, and encourage them to find and use those interactions that work best within their family context—whether that means having their child help out in the kitchen or making up mathematics bedtime stories.
The “Four Cs” can help parents remember what to do. Parents need to understand that simply rehearsing the count sequence is not the most effective way to boost children’s mathematics understanding or help them be “school-ready.” Instead, they should converse with their children, and invite them to count, compare, and categorize objects in a variety of different ways.
Parent–child mathematics talk helps deepen the child’s understanding of mathematics. As parents increase the frequency and variety of their mathematics talk and interactions, they provide critical opportunities for their children to build their mathematics vocabulary and increase the depth of their mathematics understanding. Moreover, when parents talk to their children about mathematics, they show their children that mathematics matters. Ultimately, mathematics talk between parents and children has the potential to improve and strengthen the mathematics performance of their child.
Using conversation can promote and strengthen the other Cs.
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
The Four Cs in Action show tips and examples to share with parents.
Citation: Mathematics Teacher: Learning and Teaching PK-12 MTLT 113, 10; 10.5951/MTLT.2019.0161
CONCLUSION
The Four Cs strategy can help parents recognize and make the most of the many opportunities that exist to talk with their children about mathematics. Nothing formal is required—no notebooks, activity sheets, flashcards, special computer programs, or smartphone apps. Suggestions in this article are provided for teachers to better help parents understand the ways they can make a difference in the numerate lives of their children, but using the Four Cs strategy is beneficial for anyone who spends time with young children, including grandparents, caregivers, teachers, aides, childcare centers, and more. Why not try the Four Cs strategy with your students’ parents, and see what benefits emerge? After all, the research tells us there’s nothing to lose and so much to gain. _
REFERENCES
Carpenter, Thomas P., Megan L. Franke, Nicholas C. Johnson, Angela Chan Turrou, and Anita A. Wager. 2017. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Portsmouth, NH: Heinemann.
Elliot, Leanne, and Heather J. Bachman. 2018. “How Do Parents Foster Young Children’s Math Skills?” Child Development Perspectives 12, no. 1 (March): 16–21.
Gunderson, Elizabeth A., and Susan C. Levine. 2011. “Some Types of Parent Number Talk Count More Than Others: Relations between Parents’ Input and Children’s Cardinal-Number Knowledge.” Developmental Science 14, no. 5 (June): 1021–32.
Levine, Susan C., Linda Whealton Suriyakham, Meredith L. Rowe, Janellen Huttenlocher, and Elizabeth A. Gunderson. 2010. “What Counts in the Development of Young Children’s Number Knowledge?” Developmental Psychology 46, no. 5 (September): 1309–19.
Moomaw, Sally, and Brenda Hieronymus. 2011. More Than Counting: Preschool and Kindergarten, pp. 29–31. St. Paul, MN: Redleaf Press.
Nguyen, Tutrang, Tyler W. Watts, Greg J. Duncan, Douglas H. Clements, Julie S. Sarama, Christopher Wolfe, and Mary Elaine Spitler. 2016. “Which Preschool Mathematics Competencies Are Most Predictive of Fifth-Grade Achievement?” Early Childhood Research Quarterly 36 (Third Quarter), 550–60.
Wynn, Karen. 1992. “Children’s Acquisition of the Number Words and the Counting System.” Cognitive Psychology24, no. 2 (April):220–51.
Anastasia L. Betts, albetts@buffalo.edu, is a doctoral candidate at the State University of New York (SUNY) at Buffalo. She is also the Vice President of Curriculum Planning and Design for Age of Learning, the producer of ABCmouse.com, an online learning resource for children ages three to eight. Her primary areas of research include early childhood mathematics and literacy, the home numeracy environment, and game-based learning.
Ji-Won Son, jiwonson@buffalo.edu, is an associate professor of mathematics education at SUNY Buffalo. Her areas of research include teacher noticing and learning, mathematics textbook analysis, elementary and secondary preservice teachers’ knowledge development for teaching, preservice and in-service teachers’ curriculum material use, and international comparative study.
