In the previous blog on CCSS-M and also in the blog on number concept, I introduced the concept of sight facts because in many of my lectures, teachers ask about sight facts. The concept of sight facts is an exercise in addition, but it is not to be seen as the formal teaching of arithmetic facts. It is students’ first attempt to understand number relationships. These number relationships are learned by observations rather than any strategies; they are not learned by counting. Learning sight facts is like learning sight words. They are learned by constant exposures. The idea of sight facts is fundamental, so it is important to know how to help children acquire sight facts.

In reading, it is important to acquire a large number of sight and high frequency words. Knowing the alphabet, a large collection of sight words, and phonemic awareness are prerequisite skills for acquiring reading skills. Similarly, it is important to acquire **sight facts **or **high frequency arithmetic facts**.

Number concept, decomposition/recomposition, and the mastery of sight facts are prerequisite skills for acquiring arithmetic facts with mastery (understanding, fluency, and applicability). The teaching of sight facts, therefore, is important for learning addition and subtraction facts efficiently.

High frequency words are best taught and acquired in context and with constant exposure. As sight words are not learned by focusing on each letter in the word, sight facts are not learned by counting discrete objects. Many average and above children can learn sight facts in spite of using fingers, TenFrames, and other counting materials. However, the most effective method is decomposition/recomposition using Visual Cluster Cards and Cuisenaire rods. They are effective for all children—with or without learning difficulties in mathematics.

Many teachers use a variety of activities for children to acquire sight words. They use a multi-sensory approach in which students say the word, say the names of the letters, trace the letters on a screen, sky write them, and then repeat the name of the word. The key is multiple and constant exposures. The same approach works for sight facts. Using Visual Cluster cards or Cuisenaire rods, children say the number represented by the Visual Cluster card (say 7), picture (visualize) the cluster on the card (3 pips in the first column, 1 in the middle, and 3 in the third column), visualize two sub-clusters on that card (6 and 1; 5 and 2; 4 and 3; 3 and 4; 2 and 5; and 1 and 6) by drawing a ring around the two sub-clusters by finger in the air or on an imaginary whiteboard (sky writing), say the corresponding sight facts as equations (6 + 1 = 7; 5 + 2 = 7; 4 + 3 = 7; 3 + 4 = 7; 2 + 5 = 7; 1 + 6 = 7; 7 = 1 + 6 = 6 + 1 = 2 + 5 = 5 + 2 = 3 + 4 = 4 + 3), then write these equations on paper. Similar exercises can be done for other numbers from 2 to 10.

There are more than two hundred sight words (number depends upon the program being used) that children must acquire. With the help of sight words and phonemic awareness, they begin to “chunk” and “blend” and with practice they learn to read. Sight facts play the same role in acquiring arithmetic facts. The following is the list of sight facts.

The key element is the acquisition and application of the decomposition/re-composition process. Without this process, children do not acquire fluency in addition and subtraction facts. Once children have the concept of number, the decomposition/recomposition process can also be accomplished and reinforced with Cuisenaire rods^{[1]}. For example, the number 10 can be shown as the combination of two numbers as follows (the same process can be used for all other numbers 2, 3, 4, 5, 6, 7, 8, and 9):

Once children have formed these combinations (all the possible sight facts for 10), the teacher helps them to make these combinations fluently and provides opportunities for applying these sight addition facts. When children have learned the sight facts of a number—recognized the combinations of sub-clusters on Visual Cluster Cards, formed them using Cuisenaire rods or InVicta Balance and can recite them, then they should be asked to record them with the help of these materials. When children can supply the decomposition/recomposition of a number in several forms, they are ready to write the sight fact equations as pointed above in the sight fact equations for number 10.

Repeated exposures to making combinations of numbers (sight facts), using Visual Cluster Cards and Cuisenaire rods, are important as a starting point for learning other facts. Children should move from oral to written form with specific, positive corrective feedback both for making combinations and acquiring fluency. The practice should involve only strategies using decomposition/recomposition^{[2]}.

When students arrive at arithmetic facts and procedures with the help of strategies, they develop mathematics conceptual understanding with robust structures rather than learning isolated facts and routine procedures. Knowledge structures here refer to conceptual schemas that students use to organize and relate language, concepts, and facts. Experts have developed complex knowledge structures with multiple and flexible interconnections based on fundamental concepts while novices and poor students have inefficient, simpler, disjointed knowledge structures with fewer connections that make it difficult to assimilate new concepts. For example, they may think addition is just “counting up” and subtraction is “counting down.” These children end up working harder with little or no pay off.

When a child does not have efficient strategies, it is important that we help develop these strategies. This requires timely and effective interventions. As soon as a teacher observes that a child is having struggle in numberness, she must arrange for interventions. All children benefit from effective math intervention. However, poor interventions where the emphasis is only on counting do not help.

The quality of instruction and intervention is dependent on the competence of individual teachers. Teacher certification for pre-K through 3rd-grade should emphasize both knowledge of the subject (specifically, a deeper knowledge of the mathematics taught in early and elementary years) and strengths in the mathematics content related pedagogy. What we now know is that mathematics instruction—initial and intervention—is far more effective when delivered by a teacher who understands both the subject matter and the most effective ways in which young children learn math. Because the conceptual complexity of elementary mathematics is underrated, a successful program will ensure that early math instructors specialize in these areas. One solution may be for a school to designate a teacher in each grade who is responsible for teaching only math to all students or at least able to provide quality interventions.

Early instruction with quality activities that develop a comprehensive numbersense can minimize and prevent failure in numeracy and even in later mathematics. For example, teaching the integration of numbersense activities with an increased focus on “sight number facts” automaticity will better prepare children for numeracy activities. Teaching these skills in isolation and without effective strategies has minimal effect both in the reduction of difficulties in mathematics for the general and LD population. Quality instruction works for students with and without learning disabilities.

^{[1]} For derails of how to use Cuisenaire rods see *Cuisenaire Rods and Mathematics Learning* (Sharma, 2013).

^{[2]} Strategies for Teaching Addition Facts in *How to Teach Arithmetic Facts Effectively and Easily* (Sharma, 2008)