Are you finding it difficult to teach statistics and probability during your tuition lessons to secondary school students? Or perhaps when you teach trigonometry and calculus chapters in Additional Maths, you have noticed your student's eyes glaze over because no matter how many times you may explain it, it just doesn't make sense to him/her?
In fact, as the founder of MindWorks, Tutor Young often likes to say, the ideal way to prepare for Mathematics O-level exams is when you are so confident you can walk in with a pen and need nothing else. Often in his own teaching, he emphasises why students should gain an intuitive understanding of mathematical concepts - because the ideal state of being is when students can derive their own formulas!
But as math tutors, teaching a subject that is often feared and detested by students can become very difficult. As students become unresponsive, a gloom settles over the study table and it feels like you may have lost the battle before it could even begin. This is why in this article, we present to you some online tools which can make your math lessons more engaging, sparking students' innate curiosity and proving testament to your amazing tutoring skills in the long run!
Before you begin, check out MOE Secondary 1-4/5 Mathematics and Additional Mathematics curriculum here.
For Secondary 1-5 Mathematics/ Additional Mathematics:
1. Use an online resource for learning math vocabulary.
A key learning outcome of studying secondary school mathematics or additional mathematics as explained by the MOE is to
"develop thinking, reasoning, communication, application and metacognitive skills through a mathematical approach to problem solving"
And in order to think, reason, and communicate mathematical concepts accurately, it is important to have a deep understanding of the mathematical language. A tool that can be used to explain these terms, symbols, and their relations precisely and effectively is Math Words, a simple interactive math dictionary.
As seen in the screenshot below, the website offers easy to understand diagrams with each definition, breaking down complex concepts into digestible chunks. This can be a great resource for tutors to use in their own explanations or to offer to students for their reference during self-study.
2. Print some worksheets as fun homework assignments and set rewards for added incentive!
Worksheets can be a great way to test students' problem-solving skills in maths on the spot, and also ensure they show their working correctly. When GCE O-level papers are graded, examiners can easily cut marks for inadequately explained answers. Therefore, avoid such issues altogether by beginning to show clear working as early as possible!
As a tutor, your tutee and his/her parents look up to you for accurate and insightful guidance about how best to achieve high scores in key examinations. This is why it is crucial to teach not just the prescribed topics but also essentials skills associated with them such as how to best use the graphing calculator, how to show your work neatly, and how to study smarter.
The website offers easily categorised topics with many worksheets within each that you can browse to find the most suitable ones for your pupil! The example above is the introduction to the trigonometry worksheets available including some easy to understand tutorial pages linked at the bottom of the page.
3. Incorporate Interactive lessons designed by Harvard Educators into your lessons.
School Yourself is a great website with interactive learning modules, that are free, personalised, and easily accessible online! Their approach to learning is that the best learning happens when students learn by DOING, which is why their interactive modules make it easy to play around with mathematical concepts to understand their broader implications and make interdisciplinary connections.
As seen in the screenshot below, there are many interesting lessons to choose from:
So how does this platform work?
Let's say you want to explain the quadratic equation. By clicking on their module, you will reach an interactive whiteboard with voice over explaining concepts and asking questions:
If the student feels stuck, they can view hints by clicking the button on the bottom left. Only after finding the right answer by themselves can the students move on to the next part of the lesson.
There are two things tutors can learn from this tool: firstly, you may use this tool while offering your own support and personalised explanations to walk students through certain topics.
Secondly, and perhaps more importantly, a better way to gain value from this tool is to reflect on how you can recreate interactive and personalised lessons for your own students in a similar fashion.
This second option is great for doing some research for beginner tutors who can distinguish themselves from their competitors by incorporating such interactive, question and answer based teaching styles in their maths lessons for secondary school students. Instead of giving a long lecture on a topic, try to walk your student through interactive exercises in which he/she can learn maths by actually thinking through things themselves.
4. Specifically for topics related to graphing and geometry, use GeoGebra for good online resources.
GeoGebra offers interactive fun activities for learning and teaching math. Just as the page below suggests, they offer interesting lessons on so many different topics!
For example, let's take a look at the following problem:
Generating problems such as these are a quick and easy way to practice understanding concepts during your tuition lessons. In fact, this is how I studied IB Mathematics B myself! Our teacher used many interesting problems like these projected onto our whiteboard in class, and we would work through problems and solve them in real-time.
As tutors, you can also do something similar, by incorporating these questions in your lesson plans. Once again, the aim is to move away from lecture-style teaching commonly found in classrooms and move towards interactive and personalised action-based lessons in which students are not spoon-fed information but actively work hard to solve challenging problems with the loving support of a tutor.
Carol Dweck, a distinguished researcher who has written the bestselling book Mindset often talks about this one quality of a great educator:
They not only set high standards, but also provide the roadmap (resources) to make genuine and lasting progress towards those standards.
5. Lastly, encourage students to read through math blogs together!
There are many engaging mathematical blogs online which aim to promote mathematical curiosity, and can be a great tool to teach your students to think independently about math. By allowing them to explore old concepts in new ways or follow a mathematician's questioning till the end, it can instil in them the kind of mathematical thinking MOE expects and foster their interest in the subject.
Some great math blogs are listed here:
Yummy Math, run by a Math Coach, this blog provides teachers with real-world math problems to strengthen the connection between math and its application in the students' mind.
Mathematical Enchantments is run by mathematician James Propp from the University of Massachusetts. He wishes to popularise math by diving deep into questions that explore fantastical realms.
Mean Green Math is an excellent blog exploring the "why" behind math concepts. It discusses concepts in a scope far beyond most textbooks, making it an excellent resource for tutors to encourage mathematical curiosity and research in their brightest pupils.
Derive It explains mathematical proofs, interlinking posts of different topics to help students see the bigger connections between concepts.
And for a bonus resource, check out Tutor Young's YouTube Channel linked below for the best information on Additional Maths!
We hope you enjoyed this article of math teaching resources curated specifically for our tutors!
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