The need to balance coverage with depth in primary school math education

In Ghanaian primary schools, there is a division between the lower and upper primary. Grades 1,2, and 3 comprise the lower primary, while 4,5, and 6 comprise the upper primary. The difference is seen mainly in the number of subjects taught at each level. Therefore, grades 1 to 3 will study the same subjects, and grades 4 to 6 will also do the same.

In the Japanese system, there are three divisions. Grades 1 and 2 study the same number of subjects and learning activities. Some of these subjects get split, and some are added when students progress to the 3rd and 4th grades. As students move to grades 5 and 6, home economics is added to the subjects.

Basically, in the first two grades in Japan, the emphasis is on building a strong foundation in numeracy and literacy, necessary not only for academic work but also for socialization into a literate society. This strong foundation in numeracy and literacy in the early grades contributes to success in the other subjects when later introduced as students climb the academic ladder.

To do this, the Japanese rely heavily on practice, and this marks a difference between early graders (lower primary) in Ghana and Japan. On average (with some exceptions), I have observed that elementary school grade 1 and 2 pupils in Japan will solve between 10 to 20 simple math questions as homework almost every day. Add what they will solve in the classroom as a class exercise, and for those who attend cram school (after regular school), you can imagine the additional math questions they practice in a day. To achieve this, homework for grades 1 and 2 pupils is limited to only math and Japanese. In Ghana, due to factors such as the demand for work output, especially in the public schools, some teachers are more interested in presenting evidence for work output in almost all the subjects for the week. This marks another difference between the Ghanaian situation and that of Japan, where in Ghana, the focus is on breadth, and Japan focuses on the depth of foundational subjects. Trying to give homework for every subject at the lower primary reduces the time and opportunity for students to practice more math questions.

The frequency and consistency in practicing help students identify and internalize patterns in simple math problems and solutions. Sometimes, among the homework questions for grade 1, one will observe that a third of the addition questions will give the same answer. So, if 5 out of 15 addition questions for the day sum to 10, the more they practice, the less time they will spend on addition questions that yield the answer 10. Also, this level of practice reduces the fear associated with math among students. There is also an element of making math fun in this situation. One of the factors that makes math less fun for students, especially in the early grades, is how math questions are framed. It is usually 12+8 written horizontally or vertically, or in a word problem format, or finding a missing number. But when math problems are sometimes presented to early graders in a way that solving them has some element of fun, it develops their interest in the subject. This is the case in Japan.

For example, let us take a cue from a word puzzle where letters of the alphabet are jumbled or mixed up on a grid for students to search and circle or cross out a group of letters that will form a word among a list provided. In math, instead of letters, numbers can be used on the grid. Students may be provided with a number with the instruction to circle or cross out two numbers close to each other, which, when added, subtracted, multiplied, or divided (depending on the operation of the day), can result in the number provided.

In another instance, four numbers are placed on a ring or circle (you can choose your own shape and determine how many numbers to use), with another number at the center. The challenge for the kids is to develop a formula using the numbers on the circle that will make the number at the center the answer. For example, if the numbers 15, 6, 8, and 2 are on the ring and the center number is 27, what is the formula? This activity is designed for second-grade students.

Another strategy for making math fun for students is that they are not confined to finding answers to questions/problems only. One important skill students need to develop is formulating questions that yield a specific answer. Let's use a simple example. In a grade 1 class, students may be constantly asked to provide answers to simple addition questions like 3+4, 6+2, 4+4, etc. After students have mastered this process, they are given a number to either select from a list of addition questions that can result in that given number or formulate about five questions that can give such an answer. Example: Students may be provided with the number 9 to identify from the following list, which can sum up to 9: 2+3, 2+7, 6+3, 1+5, 8+1, etc. Or create their own addition questions that result in 9 as the answer.

The foundation students need for a successful academic life in schools should be very intentional and well-structured. Identifying what is necessary and fundamental for all subjects, and making time and resources available for them in the early grades at the primary school, and adding more as the student progresses, rather than trying to teach every subject and providing evidence for their output, needs conscious consideration. To do this, among other things, math homework should not just be evidence to parents and supervisors of the ‘hard work’ of teachers in the classroom, but also an opportunity for more practice by balancing coverage with depth.