# Mathematics and Writing

Your child is keeping a notebook "journal" in mathematics class. The practice of keeping journals helps children learn mathematics and is one way that CGI classrooms differ from many traditional mathematics classrooms.

Children keep track of their thinking about problems in their notebooks. A peek at children's mathematical journals reveals that children use drawings, numerals, words, and other symbols they have picked up or invented as ways to express their ideas. Below is an example of how a second grader solved the problem:

Shamika had 8 toy cars. Her friends gave her 5 more toy cars for her birthday. How many toy cars did she have then?

Notice that Laura directly models the action in this problem, first by drawing 8 toy cars. then by drawing 5 more toy cars, and then by joining the two set (8 and 5) to find the answer.

There are several good reasons to have children keep notebooks or journals in math. For one, making notes is one way to make their thinking visible. This helps children reflect about their understanding of mathematics and it also provides a window to their thinking for teachers and parents. Looking at a child's journal is one way that teachers and parents can assess how children are understanding math. Making notes helps children reflect upon how and why they got an answer, not just that they found an answer.

By writing or drawing out the logical sequence of solving a problem, children come to understand the process of getting an answer - which is more important in the long run than just getting the answer. So, teachers like to look at these journals to see children's solutions and examine their progress. For example, in this journal entry Jay has solved the problem 85 + 56. It is evident that Jay understands how numbers can be broken into tens and ones and recombined to formulate answers.

Many children who have not built up this understanding of base ten concepts do not then understand methods involving carrying and borrowing.

Another reason that making notes is important to learning mathematics is that the process of communicating promotes thinking. In deciding what to write children must select and organize their essential ideas about a problem and its solution. In formulating what to put on paper children must consider and choose the most important parts of their thoughts. Here a first-grade child organizes her thoughts about triangles and generates examples consistant with her ideas.

Expressing ideas on paper also serves other purposes. It lessens the details a child must keep in their memory about a problem. Once the ideas are on paper a child can look at the markings (words, picture, numbers) and think more about the problem. Through reasoning with and about these markings, a child is learning to think with symbols - a skill critical to success in mathematics and science.

Writing and drawing also encourages invention. The use of mathematics to invent new ways of looking at problems or to support new discoveries is basic to computer science, engineering, architecture, design, and scientific research. By introducing invention as a part of mathematics in the elementary grades, children are getting used to thinking of math as a creative thinking tool instead of as a rote skill.