# Math Program

## Our Approach

At Wingra, we believe that mathematics is a useful, exciting, and creative area of study that can be appreciated and enjoyed by all students. Our teachers create classroom environments that provides safe opportunities for risk-taking in mathematics. Students are allowed to explore, to guess, and even to make and correct errors so that they gain confidence in their ability to solve complex problems.

Math instruction takes place daily in all our classrooms in individual, small group, and whole class lessons. Math activities are also frequently integrated into theme topics. When children relate one mathematical idea to others, and to other areas of the curriculum, they acquire broader insights into the interconnectedness of mathematics and relationship to other fields.

Much of the
content outlined in *Principles and Standards for School Mathematics*
by the National Council of Teachers of Mathematics (NCTM, 2000) verifies
what has been in place at our school for many years. The NCTM Principles
and Standards were developed by mathematicians and math educators to present
the best current thinking about school mathematics. Our math program
has evolved from goals, assumptions, and strategies very similar to those
outlined by this Council.

We see children as active thinkers: they construct, modify, and integrate ideas by interacting with the physical world, materials, and with other children. We make extensive and thoughtful use of manipulatives to foster the learning of abstract ideas. We believe that children of all skill levels can learn from each other and need to work together; we create the time and space for them to share strategies, develop ideas, and model approaches to one another.

## Math for Each Age Group

In *Principles and Standards for School Mathematics*, the National
Council of Teachers of Mathematics describes ten areas of focus that span
the Pre-K through Grade 12 school years:

Content Standards | Process Standards |
---|---|

Numbers and Operations | Problem Solving |

Algebra | Reasoning and Proof |

Geometry | Communication |

Measurement | Connections |

Data Analysis and Probability | Representation |

Wingra classrooms address all ten areas of focus in distinct ways.

### Math at all levels

- There is always more than one way to solve a problem.
- Children enjoy and develop confidence in their math abilities.
- Communication is emphasized.
- We always take into account individual differences.

### Nest (Ages 5 to 7)

- Children are actively constructing knowledge.
- Process is important.
- Communication is emphasized.
- Math experiences are in the world all around us.

Our youngest
students do math activities daily and work on problems in all ten
areas of focus. The curriculum is partly based on a math program developed
at the University of Wisconsin-Madison called* Cognitively Guided Instruction,*
or CGI.

CGI is an approach to teaching mathematics based on listening to how children solve problems and building on the knowledge they already have. Children are encouraged to solve problems in different ways and to share strategies with one another. This process leads to a deep understanding and flexibility in thinking. The process of solving the problem is as important as the answer itself.

Students progress in a developmentally appropriate way from representing math concepts with manipulatives to the use of number sentences and standard algorithms.

Older students in this age group also begin work in the investigations curriculum. This curriculum, called Investigations in Number, Data, and Space, was developed by the Technical Education and Research Center (TERC) and the National Science Foundation and consists of 2- to 6-week units in number, data, and space, which are emphasized because of their fundamental role in mathematical thinking.

### Pond and Lake (Ages 8 to 11)

- Students are building and refining strategies.
- We emphasize understanding and using hands-on manipulatives, such as blocks and shapes.
- We use some text materials.
- Developmental approach assumes different methods for different children.
- Our focus is on mastery of basic facts through a variety of strategies.
- Mathematics in Context units increase understanding and application.
- Conventional algorithms are built on basic understanding.

The students in this age group continue to develop their math skills through a two-part approach. All students have regular math-center assignments which are individual skill-building activities suited to the level of each student. Students also continue to work with the CGI and Investigations curriculum.

Older students start a problem-solving based math program called Math in Context (MIC). Developed at the University of Wisconsin-Madison, MIC activities move students systematically through important strands of math such as measurement, probability, algebra, and estimation. MIC allows students to practice a variety of math skills and learn strategies from peers as they work in teams to solve complex problems.

### Sky (Ages 11 to 14)

- Mathematics in Context groups continue.
- Students also have math center options and independent work.
- Instruction combines contextual and traditional textbook math.
- Math work includes reinforcement and review of basic skills.

Math time for the oldest students is one of the few instances in which we group students in the same class by their grade level. We do this to be certain that our graduating eighth graders will have mastered the math skills they need for continued success at the high school level.

The oldest students at Wingra build their math skills in a more individualized way by setting math goals, with teacher guidance. For some students, this will mean working in a small group using a pre-algebra text. For others, more advanced algebra or geometry skills will be the focus.

All students in our older classrooms also complete regular math center assignments, often integrated with the thematic unit. As in the younger classes, centers may include significant practice in the numbers and operations content area, but at a level that will challenge older students and employ algebra, geometry, and data analysis.