Studying mathematics
When learning mathematics, it is not enough to just read the materials. You also need to practice applying what you have studied. Doing calculations and solving tasks are key. Practicing and creating a routine for calculating support learning.
Strengthen your skills by doing basic tasks in the areas where you feel you might be the weakest. Also try different and new types of tasks in the areas where you feel stronger.
Do not give up too easily when solving the problems! If you have the answers available, do not rely on them too much.
Make studying mathematics easier
- Be active: don’t just read the examples but instead solve the problems yourself. Try to explain the concepts in your own words.
- Practice regularly: you learn math by doing. Reserve enough time for practicing. Repeating helps with the fluency and confidence for solving the problems.
- Use the examples: study solved problems and try similar tasks. Compare the stages of your own solution with the examples.
- Dare to ask: if something is unclear, ask help from a teacher or another student. Take advantage of online resources and the support TAMK offers.
Making sense of a written mathematical problem
For some of us, calculating written mathematics tasks can be especially challenging. This may stem from problems with reading comprehension, conceptualising, finding the essential information, memory, maintaining attentiveness, or mathematic skills.
Solving written tasks may become easier, if you learn how to break down the task into smaller pieces.
Here is one example of how you can approach a written task:
Read the assignment carefully and with thought. (Additional hint: read out loud or listen to the assignment through e.g. GoogleLens.)
Read the assignment again, and cross over everything unnecessary. (For example, the sentence: “It was a sunny day” does not give any information you need to solve a mathematical assignment.)
Find out what is being asked. Write it down, along with the unit of measurement asked (sometimes the task text uses different units of measurement than what the answer requires). Answer: ___ km/dl/cm.
Circle all the significant numbers. You can also colour code them. If there are three people mentioned in the task, you can mark each person and numbers connected to them in different colours. Or use different colours for e.g. speed, distance, and height.
Draw an image of the task, turn it over in your head, and think if the task resembles some other task, which you may have solved before.
Breathe, relax, and give yourself a moment to think.
If you know at this point how to solve the problem, solve it. If you don’t, start trying to see how you could combine the numbers and think what kind of a number would feel like a realistic solution for this task.
When you have solved the problem, stop for a moment and do the following:
Re-read the task carefully and with focus. Make sure you answered what was being asked in the task.
Make sure you have made all the steps of your calculations visible.
Make sure the final answer “makes sense.” For example, an individual rarely drinks 100 l of milk or most apples don’t weigh 5 kg.
Make sure your answer is in the correct format. If the answer should be in decilitres, you have given the answer in decilitres and not in litres.
Memorise (roughly) the task and how you solved it. This enables you to create an example calculation for yourself, which you can return to. This also helps you to differentiate between different types of calculations.
Tips to help you with written mathematical assignments
Sometimes solving a problem becomes easier if you hear the task spoken out loud.
You can also try closing your eyes and trying to see what the things mentioned in the task look like in your mind: try to create mental images.
Many software contain tools for reading out loud. For example, Microsoft Word or GoogleLens have these.
You can also try recording your own voice by using the recording app of your own phone and then listening to the recording. You can also ask somebody else to record the task for you.
Reading transparencies or rulers help you to stay on the correct line and may make the reading experience easier.
Online materials to practice mathematics on your own
Khan Academy – Mathematics for many different levels, also science, English, social studies etc.
WolframAlpha – Mathematics, science etc.
Materials in Finnish
Opetus.tv – Päivitä tulevaisuutesi! – Matematiikan, fysiikan ja kemian kertausmateriaaleja (perusaste, lukio, korkeakoulu)
Matikkamatskut – Lukiomatematiikan opiskelumateriaaleja videomuodossa
Omaan tahtiin – Lukion matematiikan ja fysiikan avoimet oppimateriaalit