Silly mistakes in maths

Last Friday I had a huge to-do list. So what did I do? Nothing on my list. I spent the whole afternoon designing an infographic about avoiding silly mistakes in maths. You know the thing. You work through several lines and then realise at the end that you wrote down a + instead of a – somewhere. Or you missed out the index in x². Or you moved a constant from one side to the other but added it instead of subtracting it.

I make these mistakes. I know several of my students do. It’s not to do with a lack of understanding of the actual maths, but it can make a huge difference to the end answer and to your grades. So what can we do to avoid, or at least minimise mistakes like these?

Here are my eight tips. I’ll attach the infographic as a download too. You can download it for free, but please credit me if you share it. (Don’t crop out my logo at the bottom, please.)

NL Avoiding silly mistakes in maths (aqua and white)

Click here to download

Encouraging Metacognition in Adolescents

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‘Messy Desk’ photo by Ali West https://www.flickr.com/photos/alismith44/357361903
Adolescence is a sensitive period when brain plasticity is heightened. Each part of the brain develops and changes. This period offers great opportunities for effectively rewiring the brain, resulting in better memory and processing, and a person who can make mature, ‘adult’ decisions and follow through on their intentions.
The area of the brain which controls executive function and cognitive processes is the last area to undergo this rewiring. This area, the pre-frontal cortex, is involved in activities such as organising multiple tasks, or setting appropriate priorities.
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When this area of the brain is fully mature, we can expect students to be able to exhibit these characteristics:
  • organisation of multiple tasks
  • impulse inhibition
  • self-control
  • setting goals and priorities
  • empathising with others
  • initiating appropriate behaviour
  • making sound judgments
  • forming strategies
  • planning ahead
  • adjusting behaviour when situation changes
  • stopping an activity upon completion
  • insight
Parents and teachers might find it helpful to reflect on how many of these skills your teenagers exhibit at the moment, and how many they need help with. Also, be aware that adolescence is now thought to last until around 25 years old. Of course, each child goes through adolescence differently, but it would help everyone if we do not expect our teenagers to be able to show cognitive maturity straight away.
How can we help them?
To help our teenagers to develop cognitive maturity, we can introduce them to metacognition, or ‘thinking about thinking’. This involves skills such as:
  • Reflecting on their learning
  • Being aware that their brain is changing and that they can learn from mistakes
  • Being aware of study techniques they can use
  • Being aware of distractions and influences that may lead to less effective learning
  • Linking new knowledge to existing knowledge
  • Establishing what is true and accurate
  • Thinking critically about claims that may not be true or accurate (‘claim testing’)

 

Furthermore, we can demonstrate and scaffold these skills for them until they are able to use them for themselves.

For example, if we expect that a project will take 10 hours of classroom time plus 6 hours of homework time, we can take them through the process of organising their studies. This may include:

  1. writing a timetable for themselves and noting when they are already busy;
  2. deciding how to split up the six hours depending on their availability and preferred way of working (4 hours plus 2 hours, three sessions of 2 hours, six sessions of 1 hours?);
  3. making sure they are studying in a suitable environment (organised desk, right temperature, quiet music or ear protectors to block out outside noise etc.);
  4. identifying where they might find help or information;
  5. identifying if there is preparatory work they need to do before even starting the project;
  6. reviewing the task criteria several times to make sure they have actually addressed the requirements.

We can also help them review their project when they have received the marks. I know that my own children have displayed a tendency to think that something is ‘done’ when they have the marks back. I am sure they are not alone in this. We want students to see each assessment or project not as a self-contained unit but as part of a lifelong approach to learning and growing.

This information is partly from a FutureLearn course, Supporting Adolescent Learners, which I am studying under recommendation from another home educating parent. I’ve also found some useful information in this 2006 article by Nancy Joseph at Oakland University, Michigan and a blog post on Psychology Today.

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Image from Victoria Agbey’s article ‘Post-Its for Project Planning’ https://medium.com/innovateforward/post-its-for-project-planning-f402c70f21cf