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**Our Philosophy for the Teaching and Learning of MathematicsTHE WAMPUS SCHOOL**

Tim Kaltenecker,

It is our belief that skill development and procedural knowledge should go hand-in-hand with

conceptual knowledge. At Wampus, students engage in activities that lead to an understanding

of underlying concepts and show how mathematical ideas relate to one another. Skills are not

taught out of context and without meaning; instead, skills grow from an understanding of the

big ideas and are taught through hands-on experiences.

To this end, students engage in activities of inquiry and problem-solving. By doing this, they

draw meaning from their observations, making sense of the mathematics and how it relates to

previously learned ideas. Students are encouraged to invent their own methods to solve

problems (Cobb, 1991.) This approach allows each student the opportunity to engage in the

material at her own level of understanding; and from this place of understanding, she will move

forward to learn new concepts and skills with confidence.

This does not mean, however, that skills and procedures are never “taught” by the classroom

teacher. It means that the student understands the concepts and the meaning behind the skills

before learning procedures. Thus, the procedures are taught within the context of meaning. At

defined points in the curriculum, students are required to use the most efficient methods for

computation and problem-solving. But efficiency (traditional procedures) is not to be used at

the expense of understanding. By learning procedures in the context of meaning, students are

likely to learn and understand concepts more easily in the upper grades than if they were to

learn skills and procedures in isolation without understanding the underlying ideas.\

**Standards-Based Mathematics**

The mathematics program at Wampus, Growing with Math, is a standards-based spiraled

program and is a continuation from Coman Hill’s K – 2 program. The spiral approach meets the

cognitive needs of students at this grade level. There are some topics in the math program that

are meant for exposure only. That is, students are not expected to master these concepts; but

instead, they are exposed to them in a developmentally appropriate way. Later in the program,

the students will encounter this content again with the expectation of mastery. The program is

carefully designed to take advantage of children’s cognitive ability and curiosity in an ageappropriate

manner.

*Growing with Math* has been carefully aligned to the New York State Learning Standards to

ensure that students reach mastery as per the state requirements. More often than not, the

math program at Wampus includes more content and more thinking skills than required by the

state standards. We value high standards and believe our expectations are realistic for all

students.

**Using Language in Mathematics**

The math program requires students to talk and write about mathematics on a regular basis. By

doing this students internalize the math concepts and become proficient at communicating their

understanding. This language-based approach is developmentally appropriate and researchbased;

students learn concepts through exploring, writing and speaking mathematics (Berk,

2000.) Furthermore, students develop a strong number sense through speaking about math and

through estimation. This is done through number sense activities each day. These activities

provide opportunities for students to understand big ideas within number sense and reasoning.

As students engage in these discussions they develop good estimation and reasoning skills. This

should be supported outside the classroom as well.

**The Parent’s Role**

Parents play an important role in their child’s mathematical development. It is crucial that

parents support the math work that is coming home and that they provide opportunities for

their child to develop a positive attitude toward mathematics. First, parents should use the

vocabulary used in the classroom and support the approach developed by teachers. For

example, we no longer use the term “borrow” when referring to subtraction. Instead, students

“regroup” numbers. This is not a fastidious technicality. Instead, it is grounded in the conceptual

nature of the mathematics. To borrow has no conceptual meaning. However, students regroup

numbers in various ways as they develop flexibility with mathematical representation. For

example, the number 27 means two “tens” and 7 “ones.” Students can also represent 27 as one

“ten” and 17 “ones.” Thus, they regrouped 20 + 7 as 10 + 17. This flexible thinking about

numbers – promoting a solid understanding of place value – benefits students as they learn

subtraction and multiplication. Parents must support this thinking so their children develop a

sound mathematical foundation in a consistent manner.

Second, parents need to promote a positive climate for mathematics at home. Parents should

never tell their child that they did poorly in math as fear of math is learned from one’s

environment (Fiore 1999.) Instead, parents should find opportunities for their children to

explore mathematical thinking informally. Many board games promote good problem solving.

Also, children can estimate during a visit to the grocery store, for example. The Parent

Resource Guide offers suggestions on ways parents can support a positive mathematical

environment at home.

**The Facts are the Facts**

Finally, students will learn facts and procedures. It is readily misunderstood that a standardsbased

math program is “fuzzy” math. This is not true with our math program. Understanding

concepts and big ideas is not easy; in fact, most students find this aspect of the curriculum most

challenging. Memorizing procedures for multiplying two-digit numbers, for example, is not

difficult; most students can do this, and this is what we traditionally view as mathematics.

However, mathematical thinking – observing what happens when you multiply consecutively by

2, for example, and describing and generalizing the pattern – is much more challenging for

students. But this type of thinking benefits students’ mathematical development more than

memorizing a procedure (Thornton, 1990; Isaacs and Carroll, 1999.) That said, our curriculum

necessitates a strong background with basic facts and skills, and these items are identified

throughout our program. For example, all students learn their 10 x 10 multiplication facts in

grade 3, and this is reinforced and extended in grade 4. The approach, however, is not purely

memorization but instead built from students’ previous work in k – 2 with skip counting. Skip

counting in the lower elementary grades teaches students about patterns; this helps with the

memorization of facts later. Again, the math content is learned through meaning and context,

an approach that supports conceptual understanding. Parents can be confident that facts and

procedures will be taught, albeit, not the same way they learned it in school. This is not to be

feared; the methodology is research-based, and moreover, consistent from grade to grade.