Philosophy of the Department of Mathematics

           Learning mathematics provides a vehicle through which students explore the world and become better thinkers. It is important that in today's world we help our students become mathematically literate. The old standards of mathematical competence have been overshadowed by higher expectations of knowledge and skill. So it is that the mathematics department formulates its philosophy based on eight goals.  

           1) Children should understand the mathematics they do and be able to express their understanding clearly. The vocabulary of mathematics must be taught and children should have the opportunity to express their thinking in words. They should learn to converse with each other using signs, symbols and mathematical terms. On a regular and frequent basis they should be asked to write down their thought processes and strategies. 

           2) Children should become good problem solvers. With the use of manipulatives, drawings and calculators the children explore and solve problems that are beyond their current calculating ability. It must be stressed that not all problems need the "right answer"; problems presented should include open-ended ones, those with multiple solutions and/or occasionally, no solution.  

           3) Children should learn to work in small groups to find solutions to problems enables children of varying abilities to contribute partial solutions.  More children get a chance to share their ideas than in the traditional whole class lesson.  Children are less likely to become discouraged and give up on a problem when working in a group.  At the conclusion of small group work, the teacher should pull the class together to discuss strategies were used.  The children see that there are many ways of solving the same problem.  The math department values work in small groups and the exchange of ideas that occurs there keeping in mind that children should also work individually. 

           4) Children should learn to reason spatially by working with manipulative materials that represent numbers spatially.  With  sufficient practice students are able to internalize the models and recall them at any time. When children begin to internalize the model, the teacher can test that internalization by asking the children to draw the model. When children have successfully proceeded through these stages, they will have good number sense and more flexibility at solving problems presented numerically. 

           5) Verbal reasoning skills are taught so that this intellectual tool is available for mathematical reasoning and problem solving. Logic problems are one of the means of developing  verbal reasoning. 

           6) Children should see an interconnection between mathematics and the world around them. This is reinforced by work in other areas of the curriculum: science, art and by emphasis on mathematics in their daily life. 

           7) The teaching of mathematics should accommodate different learning styles and cultural differences, one of which is the difference between the culture of boys and the culture of girls. (To learn more about this contact the Mathematics Department at GCS) 

           8) As a department we are constantly examining how we evaluate children’s progress. Calculations are still taught and basic facts must still be learned but these must be consistently embedded in problem solving activities. We are continually assessing the mathematics program. Formal methods of assessment are changing nationally. Previously, many standardized tests stressed calculation.  Now, most states have shifted the emphasis to problem solving. As formal assessment methods change nationally, so too must our evaluation procedures. Calculation must still be learned but the point of calculation is that it is a tool for problem solving. At present, Grace Church School administers on an annual basis the Comprehensive Testing Program that emphasizes problem solving. Grades 5 through 8 take these tests in October and grades 3 and 4 take them in January.