Author: Boldungu Team

Today, let me answer the question that has been on the minds and lips of Boldungu users and competitors regarding the meaning of Boldungu. This uniquely African name is a creative combination of two words “Bold” and “Adungu”.  Our platform aims to be bold and decisive in leading the way mathematics should effectively be made easy, meaningful and natural for every learner.

While we aim to be bold in our design, delivery and learner engagement, fun for learners is never to be compromised. Adungu is a stringed musical instrument of the Alur people of northwestern Uganda that  is an arched harp of varying dimensions, ranging from seven to ten strings or more. The truly African music produced by the Adungu instrument and the way the Alur people enjoy adding is a constant reminder that fun must be constant in whatever we do.

In fact, bold and adungu is repetition because the design of the adungu instrument is uniquely bold. As described by wikipedia, the physical form of the adungu derives from uniquely African origins. The instrument is made of a hollowed-out slab of wood, which is covered by two pieces of leather, woven together in the center. The upper piece of leather functions as a soundboard, and a wooden rib supports it, serving also as a structure to secure the strings to the soundboard. A curved wooden neck, containing a tuning peg for each note, is inserted into the end of the instrument’s body. The strings run diagonally from the tuning pegs in the neck to the rib in the center of the body.

With Bold and adungu combining into Boldungu, our team must be extremely creative to deliver this ambition especially when we are shaping younger minds from primary 3 to primary 7 with mathematics, the language of science. Have fun with mathematics, practice makes perfect

Many things that we take to be obvious are a result of mental modals that we build as a result of consistent exposure. It is this lack of mental models that when a baby presented with two cakes will not be able to tell which one is bigger. This distinction becomes obvious as the baby gains more exposure. The ability to quickly see solutions based on persistence exposure to numbers and mathematics is what we call number sense. It is number sense that you use to estimate the number of people in a room without counting. It is number that engineers use to tell the distance between two points without measuring!

Most babies will not tell which piece of cake is bigger due lack of number sense

Number sense comes with experience; just like a good footballer knows where the goal is even when he is facing the opposite direction. Many patterns exist in numbers and come naturally after continuous practice. For instance, the reason why most people will quickly workout ten minus four to be six (ie 10 – 4 = 6) is because they have developed a number sense for sums of ten.

It is number sense that a shopkeeper uses to workout balances and prices at the blink of an eye. Classroom mathematics, children spend much of their time dividing, adding, multiplying and subtracting. A learner with good number sense will accurately complete these tasks in a much shorter time.

Just like the shopkeeper gains number sense for counting money quantities, it is what learners with continuous exposure to mathematics do for classroom mathematics. Multiples of numbers, factors, remainders, reciprocals, halves, squares and many more mathematics concepts can all be part of a learner’s number sense with practice.

Good number sense cannot be gained by using standard print textbooks, because a learner can easily exhaust all questions at the end of the chapter without much variability. This limitation with print textbooks is similar to that of an adult that has been exposed to limited environments. Digital learning tools are very handy in building robust number sense.

“A Problem Well Stated is Half Solved”. These words by Charles Kettering, who was head of research at General Motors from 1920 to 1947, are still valid. Mathematics remains an uphill task for learners, teachers and countries because it has a direct impact on the economy in terms of future of work and innovations.

In Uganda, Primary Leaving Examination (PLE) released by UNEB do no lie. A few highlights

• Why SST remains best done subject as Maths eludes pupils (Monitor, 2018)
• More pupils get First Grade as scores for Maths, English drop (Monitor, 2020)
• Primary school teachers fail Mathematics (Monitor 2018)

Here are some of the reasons from the boldungu data analytics

1. Inability to understand the right concept – our data shows that students struggle to understand concepts. For instance decimal number system is built on simple groups of ones, and tens. When dealing with other number systems such as binary, the grouping just changes to ones and twos. Alas, most students will apply all mechanical means to remember each number system separately and this does not scale.
2. Failure to understand the meaning of symbols – mathematics is about problem solving, and stating the problem using symbols is one way of making it precise. Good mastery of symbols is challenge for many learners and we have seen learners fail the same question when presented differently using different symbols
3. Inability to understand the root of principles – strong connection between mathematics and the learner can only be created if the underlying principle resonates with the learners. Here cost price, selling price, profit and loss are the most obvious examples. Many learners have been given the formula to get the profit, and loss but find it hard to apply the simple principle that if you buy and sell at lower value, you loose money or if you buy and sell and high price you gain. We have seen many cases where learners are just eager to add or subtract values with no regard to underlying principle. Alter the question a bit, and the formula fails to work.
4. Lack of fluency in using operators and procedures – Application of operators to process problems is a must have skill to excel in mathematics. For instance, reducing fractions, expanding numbers and many other concepts largely play around with operators.
5. Lack of comprehensive knowledge – concepts in mathematics relate to each other. We have seen situations where students think about mathematics in terms of islands. A student will fail to arrive at the final result by applying say long division because he or she thinks long division must be used only when asked to use it.

As said “A Problem Well Stated is Half Solved”, and that is how boldungu design principles came into action. Some call it a game, and others call it real mathematics. Whatever it is, our target remain the same – deal with the inherent challenges low grades in mathematics at national examinations, poor application of mathematics in real life, and long term applicability.

Vocabulary is the body of words one can use effectively to communicate in a given language. Our research shows that learners in lower classes find difficulty in using common mathematics words such as “altogether”, “diameter”, “profit” and many others, which makes it impossible for them to workout the correct answers.

This inadequacy in mathematics vocabulary can only be addressed through regular practice by putting new words into writing and speaking so that learners continue to remember them. Learners need to see many of these words in various contexts such that they become part of their daily vocabulary. Once this happens, then solving mathematics problems will be natural similar to responding to a conversation.

Students that excel in primary mathematics have better mathematics vocabulary and technology solutions can help. Concepts and vocaburary matter most.. Our research with several learners and teachers, shows that a good number of children just workout the numbers without understanding or appreciating what they are trying to achieve.

Let us take an example from our study when we requested learners to show what 90 degrees means from the geometric diagrams they were using in their homework’s. Although well drawn with the 90 degrees mark, most learners were oblivious of the fact that an angle is the amount of turn between two lines. Some suggested that 90 degrees was a distance along the vertical and horizontal lines.

From the learning point of view, it is okay for learners to start by working out the numbers as this is in line with booms taxonomy of learning. However, without appreciating the underlying concept of an angle as the amount of turn, upstream concepts such as alternate angles, complementary angles, supplementary angles, interior/exterior angle properties of triangle become confusing and artificial because of the inability to relate them to real-world meaning.

Without any relation among the terms and terminologies, learners resort to rote learning or the try and error method where they will simply look at the numbers and either add, multiply or do whatever they can recall the teacher doing to numbers in class. This undesired state of affairs can be mitigated by allowing learners to do more directed practice on specific questions that seek to reinforce a linkage to real-word meaning.

Boldungu draws from the well-known psychology stimuli-response where repeated exposure and reinforcement will lead a natural linkage to concepts. Learners get to create questions for themselves. This first and foremost gives the learners the notion that it is no the teacher against them by firing questions at them, but it is them exploring the world of mathematics.