Mathematics as a Cultural Role Player in School Development: Perspectives from the East and West

Abstract

Inclusivity entails developing and implementing a culture-sensitive curriculum that would address the specific, perceived, and prevalent needs of learners from non-mainstream cultural backgrounds in any school setting. By focusing on the need for the utilization of culture and adopting culture-sourced content and procedures that would make mathematics relatable, meaningful, and relevant, it is projected that students’ attitudes toward mathematics, particularly at-risk learners, would change for the better. This chapter addresses the issue of learners who are academically at risk in the subject area of mathematics with a focus on Chinese ethnic minority mathematics students and mathematics learners of Canadian Indigenous cultural backgrounds. The chapter presents and discusses some curriculum development efforts that have been made by current mathematics educators/researchers and the culture-oriented teaching/learning materials and texts developed by these researchers.

Appendices

Appendix I

See Tables 2 and 3.

Table 2 Elementary mathematics-culture book series: Life and Mathematics sub-volume (Song & Zhang, 2014)

Table 3 Elementary mathematics-culture book series: Games and Mathematics sub-volume (Song & Zhang, 2014)

Appendix II

A lesson on mathematics in the community, entitled, Outdoor Mathematics [Mathematics in the Park] (Ezeife, 2013b)

A schedule of timed mathematics learners’ activities (Targeted to Grades 5–8 Ethnic minority/Aboriginal students).

• 1. Activity 1: Look and Write (15 minutes)

Study (look closely at) this field/park and write down whatever you see in the park that reminds you (tells you) about any part of mathematics you have learned in your class.

Note: Write this in the small notebook given to you for outdoor mathematics activities.

Activity 2: Count and Record (10 minutes)

How many trees are there in this park?

Activity 3: Observe and Sort (20 minutes)

3(a) In this activity, you will put the trees you counted in three categories or groups, according to their size—small, medium, large.

• i. How many of the trees are small in size?

• ii. How many trees are of medium size?

• iii. How many trees are large?

3(b) If you are asked to draw a graph to show the number of trees in the park based on their sizes (small, medium, large), what type of graph will you draw?

Note: Choose one type of graph from the list below:

• 1. Line graph

• 2. Straight line graph

• 3. Stem-and-Leaf plot

• 4. Bar graph

• 5. Pictograph

Activity 4 (Group Activity): Measure and Record (25 minutes)

In this activity, you will work in pairs, that is, each person will work with a partner.

4(a) Choose any three trees in the park such that one tree is small, one is medium, and one is large.

4(b) Using the tape given to your group, measure the circumference of (distance around) each of the three trees, and record your results:

• i. The circumference of the small tree is?

• ii. The circumference of the medium tree is?

• iii. The circumference of the large tree is?

4(c) Measure the diameter of each of the three trees and from your measurements, calculate (find) the radius of each type of tree, and record your results:

• i. What is the radius of the small tree?

• ii. What is the radius of the medium tree?

• iii. What is the radius of the large tree?

Activity 5: How many trees (2 minutes)

If you are taken to a park two times the size of this park, about how many trees do you think that park will have? (Assume that trees in all parks have the same spacing, that is, the same distances from one tree to another, just as the trees in this Particular Park in which you did today’s outdoor mathematics session).

Activity 6: General Comments (10 minutes)

5(a) Did you enjoy today’s mathematics class that you did outdoors (that is, outside your regular classroom)?

5(b) Give a reason for your answer. That is, state why you enjoyed or did not enjoy today’s outdoor class.

5(c) Do you think mathematics is part of your daily life, or is it just something you do in the classroom?

5(d) From now on, will you try to think of examples of mathematics in your environment or community:

• i. When you are going to school? Yes or No ---------

• ii. When you are going back to your house after school? Yes or No ----------

• iii. When you are at home? Yes or No ----------

Activity 7: Project Work

7(a) Estimating the ages of trees in the park (For Grade 8 students only).

Based on your measurements of the diameters of the trees in Questions 4(b) and 4(c) for the small, medium, and large trees, estimate:

• I. The age of the medium tree (that is, how old is the medium-sized tree?)

• II. The age of the large tree.

[Hint/Clue: Assume the small tree in Questions 4(b) and 4(c) is 4 years old. Then use the ratio approach (proportions) to find (estimate) the ages of the medium and large trees. Thus, you have to form ratio equations (involving the diameter of the small and medium trees first, and after that, the diameters of the small and large trees) to enable you do the estimation].

7(b): Designing an Aboriginal-oriented park

As a hands-on, learn-as-you-do project exercise for this outdoor mathematics class (Mathematics in the Park), design your ideal Aboriginal park that should take into consideration some specific design issues/characteristics, and which will include the following items:

• I. The spacing (that is, the distances) between the trees in the park. These distances should be labeled in your completed design.

• II. The ideal number of trees in the park.

• III. The mix of trees in the park (that is, the number of small, medium, and large trees).

• IV. The type of trees in the park. Here, you should think of trees that reflect the Aboriginal culture, and are traditionally planted and used in Aboriginal societies and communities in Canada.

• V. An orchard (a fruit garden) in the park. Here, think of the type of fruits that are symbolic of, and important to  Indigenous peoples of Canada. (You can ask your parents, guardians, older siblings, and community Elders to give you some ideas and hints about such traditionally meaningful trees).

Note: We hope you enjoyed today’s outdoor mathematics class which has the goal of bringing out clearly the fact that mathematics is part and parcel of your everyday life, and has been done and practised by Aboriginal people, and other Indigenous cultures, for many centuries.

Note: This outdoor mathematics class (Ezeife, 2013b) was designed and utilized for teaching Indigenous (Aboriginal) students (Grades 5–8) in the University of Windsor’s 4-Winds STEM (Science, Technology, Engineering, and Mathematics) Project, 2012–2014. The project was launched to attract Aboriginal students in Windsor and its environs to STEM fields of study by presenting course contents to them using culture-oriented and environmentally sourced materials from their life-world.

Appendix III

Teaching mathematical “Operations on Fractions”, Equivalent Fractions, and Areas of two-dimensional figures using the ‘Spider Web’ concept

Example problem: Find 3/4 + 5/6

Solution using the ‘Spider Web’ concept: 3/4 + 5/6 = 18 rectangles + 20 rectangles (obtained by directly counting the number of rectangles that make up the fractions 3/4—three quarters, and 5/6—five sixths, respectively, in Fig. 1)

Fig. 1

The Spider’s Web

= 38 rectangles

But, the total number of rectangles in the Spider’s Web

= 24 (6 columns x 4 rows)

Thus, 3/4 + 5/6 = 38 rectangles

Now, when this number (38) is compared to the total number of rectangles (24) in the Spider’s Web, then we see that this implies 38/24 = 19/12 = 1 ⁷/12

Hence, 3/4 + 5/6 = 1 ⁷/12

Follow-up exercise and consolidation: Find 1/4 + 1/6, using this method (the ‘Spider Web’ concept)