School and Education of our children is something we can not run away from. Math is at the center of our education system be it in national curriculum or homeschooling.
Many children are fond of their teachers especially teachers that effectively connect with the learners. Math is a special subject in that it aims to teach learners how to solve problems. Strategy is key when it comes to math. One senior math teacher told us that learners should be allowed to use multiple approaches towards correct solutions. Teachers therefore need more patient and approaches to show learners the wonderful logic behind math through which they can use different strategies.
Learners need to have fun with math to excel. In one of our design sessions working with grade 2 children, we noticed that once learner do enough practice, they begin to appreciate different strategies. One learner after using the numberline to add two numbers, he was confident to show off that his answer was correct using ‘balls’ – that is, by drawing small balls to represent each number count and then counting all the balls. But the your learner was finding fun i drawing the numberline.
It is this confidence of using multiple tricks that allows learners to see relationships between math concepts. The numberline is perhaps an easier route to show integers, fractions and other concepts. Some teachers focus on calculations and this makes children just follow steps and procedures without deeper processing of what is going on. Learns look at mathematics as a list of operations and techniques for getting the right answer. Mathematics is much more about having rules to a game, playing it, and then seeing what happens when more elements are added to the game. It is a never ending discovery of the consequences of how the rules interact with new elements.
After working with many teachers in top schools, it is obvious that they use more than one teacher for different parts of the curriculum. They have teachers that introduce new content, teachers that focus on revision and teachers that focus on assessments. Even with this deployment of resources, schools face a challenge of 100% effectiveness of all area of math to entice learners with the unlimited beauty of math.
After a series of brainstorming with top math educators, it was conceived that
What if we could collect all best strategies from various teachers and package them for learners and other teachers
What if learners could be empowered with easy access to questions that are similar to what they do in classwork
What if learners can create their own questions to check their understanding
What if learners could see their progress at more refined level just like professional athletes?
Using technology, we have packaged the wisdom of experience and energetic teachers into boldungu, which aims to make a positive difference in the learning of mathematics. With bolddugu, every learner has a chance to access a variety of math strategies and approaches.
In all education systems, math as it helps learners appreciate the world. Math is also the glue to Science, Technology and Engineering (STEM). The curriculum for math emphasize problem solving among other skills
Captivating learners with math at an early age is a sure way of keeping long term interest on learners in math, science and technology. Using technology to help learners improve math scores can motivate learners to do more in math and other subjects.
Introducing boldungu to learners in the classroom is a great way to make learning fun, engaging and motivating for young learners. The game like features of boldungu make it very interesting for learners.
And the best part about starting early in grade 1 is that it helps your students to a positive attitude toward math from an early age, setting them up for a successful academic future.
This game like math technology is sure to become a fast favorite with your students. You can choose whatever skill you want to review, such as addition, subtraction, or number sequencing. Even questions that require comprehension such as pie-charts, speed and time are also covered
The beauty of boldungu is that it makes a smooth integration between fun, real life math application and classroom math for examination
Most people that comfortable with math do not realize how much practice they have invested in it. With practice many things become easier and some become kind of reflex in their actions and activities. We can aim to make math trivial for both formal education and homeschooling.
Boldungu has two modes of practice. The standard mode and trivial quiz mode.
Trivial mode helps children to stop mixing up concepts and math formulae during examinations, which accounts for an average of 30% lost marks in most standard examinations. Even after preparing candidates for examinations, learners still lose marks for several reasons, among them: –
Basic operations – Learners make errors in application of basic operations such as forgetting brackets and adding poorly leading to wrong results.
Forgetting procedures – another common error is forgetting procedures such how to add fractions with different denominators by adding numerators alone and denominators alone without using the lowest common multiple.
Forgetting or mixing up key concepts and formula – many learners are unable fluently use formula and concepts where needed. For example formula for area of a right angled triangle, or area for a circle. When a learner is unable to trivially apply such knowledge, then the learner cannot proceed to correctly answer the question.
Trivial mode focuses on the last reason for loss of marks in math. Trivial quiz mode is designed to make such facts and formulae trivial and none-confusing to the learner.
Unlike the standard mode that aims to provide variety and confidence, trivial mode targets accurate recall and use of formula and mathematics relations. Trivial mode brings together the form of reflection that seeks to eliminate ambiguity, confusion or misunderstanding.
Trivial mode focuses on simple inquiries of fact to guarantee more concrete understanding of the matter at hand. Use trivial quiz mode to remove ambiguity from math facts and formula, promote accuracy and create a smoother path to new math concepts. Trivial mode builds fluency in application of concepts, terminologies and relations.
Boldungu is available as web app here and mobile app here
For many people, they try disconnect the math studied at school from what they are currently doing as adults. They forget that education does not take place directly and knowledge is not used in isolation. Their ability to tell time, make good judgments on quantities be it deciding on how much sugar to add in a cup of team are all math.
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. Based on Google Play Store reviews, Boldungu is the best technology solution in this category. Head to Google Play store for the latest version
“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
Here are some of the reasons from the boldungu data analytics
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.
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
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.
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.
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.
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.
Boldungu builds number sense through well selected activities, solutions and concepts
The challenge is with digital learning tools is that they are too many, do not match the academic classroom curriculum, and are not well organised. This is what boldungu.com has focused on. To build a large variety of mathematics activities, while sticking to the age groups and national curriculum. Create fun and adventure for mathematics. Primary school mathematics is the perfect level where to develop number sense from early years.
Boldungu, might be the bridge to your child’s dreams. The mission is to improve learning of mathematics and build a generation of problem solvers.
Many events happen in a random, unpredictable nature. The study of probability for primary school children in many countries including Uganda therefore forms a basis for understating nature. Probability is applied in many disciplines including statistics, meteorology, game theory and risk analysis among others
Many learners go through this topic without understanding its core nature which limits their understanding of many other branches of mathematics including set theory, infinity series/sequences and limit, chaos theory, noise and information theory and so on.
Boldungu has taken time to build a collection of relevant questions as per the Uganda curriculum for primary school mathematics, starting from primary 3 to primary 7 as illustrated below.
Complete with solution for learners to practice and understand the concepts, boldungus is determined to build dreams for learners.
Get Boldungu form here or from the Google Play store, and let your child build confidence, improve mathematics and unlock dreams! Learn more about boldungu here. See here for what you can create, print, practice and win!
Although many people see mathematics as a tool for doing calculations, it is a language for expressing logical thoughts, which is learned through reasoning and logic. Here are some of the reasons parents say they like boldungu.
Creates positive change in the learning and teaching of mathematics
Resource for parents to keep their children productively engaged while at home
Creates a bond between the children and the parents when they practice together
Provides good use of digital appliances such as tablets, computers and mobile phones at home
Support for parents with skills on how to manage their children’s use of digital platforms.
Provides remote tracking of learners activities and progress.
After the first early adopters and technology enthusiasts that gracefully embraced the digital learning technology for primary mathematics, the technology has now matured to deliver real value to learners, schools and teachers. See below for part of what boldungu can do.
Now fully delivered with color, honors, awards and gifts, learners can excel and build dreams to their full potential. As one primary three child said, he can write boldungu the whole day! Listening to teachers feedback and input has made the technology better and a supplementary resource for schools, teachers, learners and parents alike. Below is a team of experienced mathematics teachers test driving boldungu.
Get Boldungu from the Google playstore and help your child excel in mathematics.
