# Math Can Be Fun & Meaningful

We use our SEVEN COGNITIVE SENSES to help students learn math deeply and with ease.

1.
Sense of
QUANTITY

Math is all about numbers and the quantities they represent. Without a sense of quantity numerals have no meaning. This sense is important for algebra as it is for addition (Dehaene , et al., 1999; Gersten & Chard, 1999). (1)

2.
Sense of
VISUAL-SPATIAL

Students with strong visual-spatial skills “see” math in their heads. Numerals are visualized, often on a type of mental number line or blackboard. Students who lack this sense may be “number blind” — they may look at a group of objects and immediately know the quantity or see a number and visualize. One telling problem is the inability to place numbers on number lines or to create mental number lines. Lack of spatial skills may cause difficulties with everything from place value to long division. (Zago & Tzourio-Mazoyer 2002; Rittle-Johnson, Siegler, & Alibali, 2001). (2)

3.
Sense of
NUMBER PATTERN and SEQUENCE RECOGNITION

Students who are weak in this area will struggle to grasp the meaning of 1,2,3 or connect skip counting to multiplication. Math is rich in patterns and sequences that proficient students discover almost intuitively. Number patterns expose deeper levels of mathematical understandings. Higher level sequencing is involved in procedural knowledge, solving, multi-step algorithms and prevents circular thinking. (Sikora, Haley, Edwards, & Butler, 2002) (3)

4.
Flexible Sense of
NUMBERS

Students who know that 18 + 22 is the same as 20 + 20 will find math a fun game. Estimations, calculating tips and switching between fractions and decimals requires a flexible sense of numbers. Without it math often becomes a tedious memorization task. (Bull, & Scerif, 2001)(4)

5.
Intuitive Sense of
NUMBER MAGNITUDE

Another important aspect of number sense. Knowing that 6 is three units bigger than 3 is the essential skill behind operations (-, +, x) and exponentials. It aids in solving variables, such as knowing that x must be significantly smaller than 7 in (X+ 3= 7). Number magnitude gives numbers meaning so students can move beyond rote memorization of facts and procedures to true math comprehension. (Deshaene, 1997; Girelli, Lucangeli, & Butterworth, 2000)(5)

6.
Sense of
NUMBER RELATIONSHIPS

From factors and multiplies to trigonometry number relationships give meaning to math. Fractions, decimals and percentages make a lot of sense when we understand the relationship between these related numbers. (6)

7.
Sense of
NUMBER EQUALITY

The state of being quantitatively the same. That = sign has a lot of meaning even if you have never balanced an algebraic equation. Students often think that “equals” means “put the answer here”, or “now do the operation”. They tend to have no reference point for the idea that whatever is on one side of the equal sign has the same value as what is on the other side. Equality is involved in everything from equivalent fractions to the distributive property {x(y + z) = xy + xz} and multiplication. Equality is the key to understanding algebra. (7)