I Thik the Citanre Will Hoder Lase: Journal Keeping in Mathematics Class
Helton, Sonia M., Teaching Children Mathematics
After telling a story about Bruno Bear using jelly beans, the teacher held up a pint jar and a small plastic butter container and asked a group of first-grade students to estimate which object would hold the least amount. One first grader wrote in her journal, "I thik the citanre will hoder lase." [I think the container will hold less.] Using invented spelling, the student's entry indicates that an estimation decision had been made and documented by writing the spoken language expressed in a typical first-grade response. In another journal entry, after hearing a teacher-told story and acting out the story situation using manipulatives, a child recorded a conclusion by making a drawing of a scale weighing books and a box of objects. She then wrote, "The books wre the haveits." [The books were the heaviest.] In her own words reflecting her own understanding, this six-year-old drew a picture and communicated mathematical ideas using the spoken language and the language of mathematics.
The manner in which children express themselves in writing is very important to a teacher's understanding of how they communicate ideas, especially mathematical ideas. Keeping a journal in mathematics is one way that children can express and document their mathematical thoughts. Journal keeping in mathematics is a relatively new practice in classrooms. Getting started is easy. A teacher who understands the constructivist principle that "all knowledge is constructed by the learner and therefore, learning is an intensely personal affair" (Post 1992, 17) will easily adapt to the use of mathematics journals (Kamii 1985, 1989). A journal gives a child an opportunity to explore the understanding of a mathematical concept and to communicate that understanding through the writing tools and symbols best understood by the child.
Teachers need to understand the different approaches to journals that can be used in the classroom. Teachers can have students use their journal entries to -
* show a heuristic and practice skills;
* create routine and nonroutine problems using real-life situations; and
* document and analyze mathematical thinking.
Showing a heuristic and practicing skills
An effective problem-solving heuristic includes having children do the following:
* Listen to a story problem.
* Write the problem in their own words.
* Identify any facts.
* Draw a picture of the problem.
* Write a mathematical sentence to solve the problem.
* Label any answers using the spoken language.
A student's entry illustrating this heuristic is seen in figure 2.
A teacher may use this heuristic for content implementation during a lesson, beginning with kindergartners. By developing the heuristic with students and keeping in mind the use of manipulatives to reinforce teaching methods, the teacher can put students in a journal-keeping situation.
An extension allows students to create their own word problems and to apply the heuristic by themselves. This objective may be reached by encouraging the students to ask questions about real-life situations, to seek answers to those questions, and to record their mathematical thinking. The teacher may ask students to base their questions or problems on books they are reading. The heuristic offers students a logical strategy for organizing information and finding solutions to the questions they may ask.
Sample lesson plan
Read a story such as Over in the Meadow by Paul Galdone (1989) to the students. Have them use real objects and a work mat to act out problems in the story as it is read. For example, students could count the animals on each page, using marshmallows as counters.
Reread the story as students write numbers for the spoken mathematical language. Discuss how the spoken word may be used to generate an addition sentence such as 1 + 1 = 2 or 2 + 1 = 3. …