Introduction

Blevins-Knabe (2008) and Baroody (2009) identify the factors involved in the early learning of mathematical concepts in the home (Blevins-Knabe) and in preschool/Kindergarten (Baroody). Current research supports both authors' statements that the earliest stages of learning numeracy are foundational for future learning and attainment of mathematics across grades. In fact, current studies have found that a child's performance prior to Grade 1 predicts learning of mathematical concepts up to high school (Duncan et al., 2007). A major longitudinal study following children throughout school found that math knowledge at the beginning of Grade 1 was the major predictor of overall grade attainment (and not just mathematical attainment) in high school. This suggests that learning math concepts in the preschool years is an important activity for future learning.

In the Home

In spite of the consistent observation that learning mathematical concepts relies heavily on learning that occurs before children arrive at school, Blevins-Knabe notes that many parents and caregivers do not feel that teaching their children mathematics is an important activity or one they feel equipped to engage in with their child. This observation is reflected in a current Canadian study. Skwarchuk (2009) found that a large number of parents of preschoolers and Kindergarten children said that they did not engage in the formal teaching of their child math concepts (beyond learning to count to 10), because they: a) thought their children were too young to learn math; b) did not think that it was important to teach math concepts (they believed that was the role of teachers); and c) were not comfortable with math and were afraid of 'messing things up'. This corresponded with the observation that parents engaged in very few formal (where learning a math concept is the central goal of the activity, like teaching the Arabic symbols) and informal (where math is used as a tool to achieve a goal, such as measuring while cooking) math activities relative to literacy activities.

Blevins-Knabe accurately summarizes the research that indicates that parent attitude is critical for their child's learning of mathematics in the home. Parents who believed that teaching math is important, that children are able to learn math concepts in the preschool years, and that they have a role in teaching their child math concepts have children who are more likely to learn, use, and achieve in mathematics in school. The issue, as pointed out by Blevins-Knabe, is how to then create awareness and the sense of competency in parents that they can and should be teaching their child math concepts?

Blevins-Knabe suggests that mathematics suffers from what is essentially 'bad public relations'. In North America, the general public has the perception that math is an innate skill—something some people are born to do. This myth is not supported by research done both in North America and around the world. Multiple books, geared to the general public, have made an excellent case that formal mathematics is a learned skill (e.g., The Math Gene, What Counts, The Number Sense, Outliers). Although there are always those who are able to attain higher levels of understanding in any ability (including literacy), there is no basis for the belief that there is a select number of people who are privileged with a 'math gene' lacking in the majority.

Parents and many primary school educators often perceive mathematics as a skill of lesser importance than literacy. Although no one will (or should) argue that literacy is not an important skill, this does not reduce the importance of mathematics. Mathematics skill is associated with higher levels of academic attainment in overall academic performance (Duncan et al., 2007). This is not surprising when you consider that mathematical concepts underlie not just knowledge of what we know as 'math', but also is a foundational skill in all the sciences and arts. It is a key skill required for many careers not only in the sciences and engineering, but in the trades (e.g., carpentry, mechanics), technology, and business. Math is also an important adaptive social skill, as it underlies our ability to use and understand money. Some economists have argued that part of the reason for the economic collapse in 2008 was directly attributable to homeowners' lack of understanding of the implications of interest and mortgage rates (Sullivan, 2009). Math is undeniably an important skill for everyone and parents need to be made aware of this.

As Blevins-Knabe points out, it is not sufficient to merely inform people about how important math is. The focus should be on how to arm parents with the tools they need to support their children's learning of early math concepts. Fortunately, CLLRNet, in partnership with the Canadian Child Care Federation (CCCF) has recently compiled information about early numeracy and tasks that support the learning of these skills into a kit for parents and early childcare professionals (http://www.cllrnet.ca/knowledge/projects). As well, parents need to be assured that the mathematical concepts that their children need to learn at these early stages (e.g., counting, identifying shapes, measuring; see Clements & Sarama, 2009, in this Encyclopedia) are not complex and usually well within their comprehension. Early math is not rocket science—although it forms the foundation for it.

In Preschool and Kindergarten

In his article, Baroody focuses on a single concept (arithmetic) and the role that developing fluency in this domain of mathematics plays in early numeracy development. Fluency, in basic arithmetic, is an important skill and has been found to be one of the major predictors in a wide domain of mathematical competencies (advanced mathematics, algebra, overall mathematics ability). The observation that basic arithmetic is important is not surprising because knowing how quantities combine (addition, multiplication) or can be broken down (subtraction, division) is an important concept in virtually all streams of mathematics (including geometry, measurement, estimation, etc.). The goal of fluency is a little more difficult to justify. As one teacher put to me: "Isn't getting to the right answer more important than how a child gets there—including how fast?" According to the research, the 'how a child gets the answer', at least in terms of 'how quickly' is an important factor.

Fluency may be important for the same reason fluency is important in literacy. In literacy, if a child is struggling with word decoding (i.e., having to sound out each word), then it is much harder for them to develop understanding based on the syntax and meaning of what they are reading. This is not a problem with simple texts used at the beginning of learning to read (they generally have short, simple sentences and lots of repetition to assist learning readers); however, it does heavily impact the reading of more advanced books. Once a child learns how to read, educators work on developing fluency to support advanced levels of literary understanding. Math is similar.

If a child/individual struggles with the answers to simple arithmetic problems (e.g., 6x7), and uses complicated procedures (e.g., 5x7=35, +6=42, or 7+7+7+7+7+7), then they are more likely to have difficulties keeping track of where they are on more complicated procedural rules in advanced math. For example, if you have to stop and count every time you encounter a simple arithmetic problem, this will interrupt the memory processes involved in solving a complicated algebra or trigonometry problem. As a result, just as a non-fluent reader will have difficulty deriving meaning from text, a non-fluent arithmetic user with have difficulty deriving meaning from an advanced math problem.

Fluency is an important goal in many skills, such as music and athletics. It reflects a reduction in the memory work of basic, foundational skills so that more effort can be put into advanced skills. In Baroody's article, the emphasis on arithmetic fluency is appropriate and reflects considerable research that suggests that this component is a key area where fluency is a major factor in future learning across domains. However, one danger inherent in this article is that a reader may believe that arithmetic is the only skill in mathematics where fluency is important. This is not the case.

Baroody's observation about the goal of fluency in basic arithmetic needs to be expanded to other streams of mathematical knowledge. For example, children need to become fast and accurate when identifying and naming shapes (geometry), making quantity distinctions (e.g., more or less), recognizing and naming numbers (including multi-digit numbers), knowing what comes next in a series (numbers or patterning), and so on. Fluency reflects that knowledge is well consolidated in memory and the retrieval of that information is efficient. This will support the attainment of more complicated skills the same way knowing the positions of your fingers in the scales will help a pianist to play a complicated piece by Mozart.

Implications for Policymakers and Educators

The implications for policymakers and educators in the area of fostering early skills by parents and early stages of education are multifaceted.

1. Mathematics learning is an important skill for children to acquire in the early stages of their learning. There needs to be a promotion of the importance of mathematics as a key skill for overall success in a broad range of areas, from academics to economics.
2. Parents and caregivers need to be aware that children can learn mathematical concepts in the preschool years and that this learning will support formal, school-based learning. They need to be aware that their role is essential for their child's success in school.
3. Parents, caregivers, and early educators need to be aware that teaching of mathematics can be imbedded in fun, informal activities (and not just formal, school-like activities). What is essential is that the mathematical aspects need to be drawn out—for example, emphasising counting when playing board games, measuring and counting ingredients when cooking.
4. Parents, caregivers, and preschool/Kindergarten teachers need to be provided with tools that support them to feel competent as educators of mathematical concepts. Tools developed for this purpose, such as CLLRNet's numeracy kit, need to be disseminated to people working with young children. This dissemination needs to be supported by government and social agencies concerned with children's success in learning.
5. Educators need to be aware that children require a base for mathematics learning that is acquired in the preschool years. Due to variability across homes in parent's abilities, beliefs and skills in this area, educators need to support children who may be deficient in this base to be supported in school. This may require intensive support for children's learning of basic mathematical concepts and the development of positive attitudes towards mathematics.
6. The concept of basic concept fluency in all streams of mathematics (not just arithmetic) needs to be promoted as a goal in learning. The role of fluency needs to be understood as an important step in developing advanced capabilities in mathematics. Developing fluency requires time and practice. Therefore, children need time to develop fast and accurate performance on basic mathematical concepts to support later skill development.