Helping VCE students prepare for Math assessments

Math is a tricky subject for many students. The way it is generally taught doesn’t help, with so much emphasis put on processes and skill development. This leaves students with no in depth understanding of what they have leant, or the contexts within which to apply it.
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Texts books are set up to teach students a skill, then allowing them to practice it. Once the skill has been mastered, the next exercise will teach another skill. Yes, there are application and problem-solving questions within the exercises, but students know that they need to apply the skill they have just learnt, as this is what the exercise was all about. As far as context and understanding go, many students are in the dark.

As a teacher and tutor of many years, I so often hear students say; “It’s easy until I do the test, and then I just don’t get it anymore.” If you think about the standard process of learning in Math through textbooks, it is obvious why this is all too common. Students learn skills which they know how to apply individually at the time of learning. Once the test arrives, all the questions are presented at once, requiring the use of a variety of skills, knowledge and understanding. As students have not had the chance to develop any contextual understanding of what they are learning, they have no idea which skills and knowledge to apply to each question.

Skills development is a fundamental part of learning Math, but it is also essential to reach a higher-level of understanding. This is a revision activity I use to help students contextualise their knowledge and develop a more in depth understanding of the unit as a whole:

Learning Intention:
To consolidate understanding of a unit of work
Success criteria
I recognise links between ideas
I can explain in detail how different ideas within the unit are related
Optional extension- I can provide examples which can be linked to the concepts and formulas presented.

Preparation:
Create cards or cut outs of all the keywords, formulas and concepts learned within a unit. This activity will work with most units of work, though it suits some more than others. The example I provide is triangle geometry and trigonometry. This is learnt as a part of a broader geometry unit in senior school General Mathematics in Victoria, Australia.

As you create your cut outs, take into consideration the level of understanding your student(s) have, along with time constraints. For very capable students, you may like to leave out some cut outs and ask them to add in missing formulas or concepts. O the other hand you might like to simplify this activity for less capable students by targeting a narrower range of concepts and giving considerable support.
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Lesson:

1. Hand cut outs to students along with butchers’ paper and textas
2. Instruct students to group and organise cards, but not yet paste them down. As they collaborate and organise their thoughts, encourage them to think outside the square and not create a linear flow chart. It is ok to create multiple links between a variety of ideas, as long as you can explain the relevance of each join.
3. Once they are happy with the positioning of their cut outs and can envisage how the links might work, students can begin pasting and linking related concepts, keywords and formulas. All the links made must have explanations written alongside them, explaining why and how these cut outs are related. Ask students to colour code as and how they see fit.
4. Their maps are likely to become messy, with arrows and words everywhere. As they begin creating links, students are likely to discover other links which are also relevant. This is a good thing. Remember that it is the process of doing this that assists in their understanding and organises their thoughts. The product is far less important.
5. Offer suggestions and critique throughout the lesson, prompting students to think about additional links and why they are relevant.
6. As an optional extension, ask students to provide three (or any limited number you think will work) application examples (from text books or revision sheets) which include all ideas on the map. Complete the examples and place arrows to all the concepts and formulas encompassed within. 

This lesson creates not only a physical map of the unit, but also helps students to categorise and classify information in their own minds. Suddenly, all the skills learned can be grouped and classified. Furthermore, these groups may also be related.

This is just one mind mapping technique which will work as an invaluable revision tool, not only for Math exam revision, but many other subjects as well.