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Hagen Language

This language has cycles of 4 and 8. For this reason, students are introduced to counting in fours and eights as a pre-multiplication activity.

The Hagen language (which has two dialects with variations in both) uses its 8 cycle system effectively. The following visual aids were developed from conversations between Hedwig Aspro (Mt. Hagen, 2003) and the first author. There are many new counting words as compensation claims are now up to ten thousand kina. As they count, the small finger on the left hand is bent down followed by the other fingers excluding the thumb and on the right hand. Traditionally the people used word morphemes for some numbers from the embedded 4 cycle e.g. 12 is 3x4 while the main cycle is an 8 cycle, marked by two fists. People count many items, for example pigs in an exchange for a bride or compensation, and pairs are common. They might also count in tens with the fists followed by the two thumbs and so 8+2=10 is supported by the counting words and hand actions.

Lesson Plan

Subject: Cultural Mathematics

Grade: Elementary Two

Unit: Our Community

Theme: What people do

Lesson Topic: How people count at home and at feasts

Objective: By the end of the lesson each student will be able to count in vernacular the number of pigs in the pictures using several traditional methods and in English. Students will be able to illustrate how groups of stones can be rearranged to show groups of 4, 8 and 10.

Preparation: Pictures of groups of 4 pigs and stones. Cards with number words for skip counting in fours in vernacular and English words.

Introduction and motivation

Play a traditional counting game or students in a big circle count in the traditional counting system with groups of four crouching down together as the class counts.

Skip count in fours. Skip count in eights.

Explanation and demonstration

Place the pictures of groups of four pigs on the board and ask individual students to come and select the number word for the whole group under each group of four.

Student practice and activity

Students in groups of two or three make a long line of stones in fours and write the total number in all the groups as they go. For example, (words may vary from village to village). Students leave their display where they are while they move into a big circle for the evaluation and next demonstration.

Evaluation

Students stand in a big circle. As each group of four crouch down that group say how many students are now crouched down, skip counting around the circle in fours.

Explanation and demonstration

Now count around the circle in English, noting the English word that matches the skip count of fours in vernacular. Give the fourth student a card with the English number on it.

Teacher writes the English word under the Tok Ples word.

Student practice and activity

Students return to their lines of stones and write the equivalent English word next to the vernacular word.

Evaluation

Ask individual students to count in the vernacular pointing to all the stones in a number of groups and to say the English equivalents. For example, count up to ki tembokaka tembokaka, count up to 20 in English. Then the student can skip count in fours in vernacular and in English.

Follow Up

Students get a bunch of stones, they place in rows of 4 plus extras. They skip count in fours and then count on to give the total number. They do this in vernacular and English (see the visual aids above).

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