Tes Maths: Pedagogy place - Spot the mistake

Craig Barton
05th September 2017
Tes Maths: Pedagogy place - spot the mistake

In this series, we dive into the realm of educational research to help you best formulate effective classroom practice

Which is more effective for cementing understanding? Only exposing students to correct methodology to prevent misconceptions, or presenting them with inaccurate worked examples and challenging them to correct mistakes? Let’s find out.

What does the research say?

While studying US high-school students, Booth et al (2013) sought to discover if presenting pupils with correct, incorrect or a combination of examples would have any differential effects on learning. Incorrect worked examples were clearly labelled as such, with learners asked to identify inaccurate steps. Overall, the group of pupils exposed to only correct examples (and, interestingly, the only group presented with unconventional problems) did not see any significant improvement in procedural fluency. In direct contrast, the two groups working with incorrect examples appeared to benefit significantly.

According to Booth et al, mistakes in worked examples can help for two main reasons:

  1. They aid students in recognising incorrect procedures, leading to an improved procedural knowledge
  2. They highlight particular features in a problem that make the procedure incorrect

Therefore, combining correct and incorrect examples is worthwhile. Incorrect examples force students to attend to the critical features of a problem, while accurate examples provide valuable support and guidance.

However, before we get carried away and start filling our boards with error-strewn exercises, a word of caution.

According to Große and Renkl (2004), learning from worked examples where errors are included does enhance learning and transfer, but only when students have a good prior knowledge of the topic. Relatively novice learners, however, are unable to benefit from incorrect examples if expected to identify errors individually.

This makes perfect sense. Without a comprehensive understanding the topic, how can students spot mistakes? Indeed, it may even leave them open to developing misconceptions based around the incorrect example. Furthermore, in the context of cognitive load theory (Sweller, Van Merrienboer and Paas, 1998), if students’ understanding is not secure then topic-specific knowledge will not be stored in their long-term memories. This then leaves their working memories in danger of overloading, as they try to simultaneously search for right and wrong answers.

In summary

Spot the mistake activities can be beneficial to learning, if the mistakes are labelled clearly. However, in order to reap the benefits, students need to be reasonably comfortable with the topic. Otherwise, they'll be in danger of cognitive overload - and if that happens no learning will take place!

Therefore I’d suggest favouring correct examples in initially, before slowly introducing students to clearly labelled inaccuracies, once your pupils are fully comfortable with the topic.

How can Tes help?

From worksheets scattered with intentional mistakes, to tick-or-trash exercises and exam-style questions, there are plenty of activities available that you can use to prompt discussion or recap key methods as an end-of-topic assessment.  Your students will be hunting down mistakes and correcting them with ease in no time.
 

Clumsy Clive On Averages and Range

Five more questions that Clive seems a bit confused on. These questions involve median and mean from sets of data, plus calculatiing the mean from a frequency table and estimating the mean from grouped data. I will probably throw a couple more questions in verbally (find the modal group etc) whilst discussing the answers and reasons why as a class.
By alutwyche

Expanding Brackets Tick or Trash

Students are given 10 expressions with brackets in them, and two anwsers for each. They must identify which answer is correct. The wrong ones are designed to catch key misconceptions. Solutions provided. Let me know what you think.

By Interactive Maths

Standard form - tick, trash or improve

Worksheets based on the Maths4Real videos task or "Tick or Trash", with the added label of "improve" for when students spot something that isn't necessarily wrong but can be improved.

This version deals with standard form.
By DurhamPotter

Foundation Revision - Spot the mistakes - 24 questions

I have made this to provide a spin on the revision process leading up to the GCSEs. I have created 24 exam-style questions and have provided some 'working out' and an answer. All of the answers are incorrect by means of a common misconception. The task for the pupils is to spot the mistake and correct it. I have tried this with multiple classes and they find it fun and useful and many of them fail to spot the misconceptions thereby promoting some insightful discussions too.
By daxearles

Craig Barton, TES Maths adviser

Craig is a secondary maths teacher in the North of England.

References

  • Booth, Julie L., et al. Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction 25 (2013): 24-34
  • Große, Cornelia S., and Alexander Renkl. Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning and Instruction 17.6 (2007): 612-634
  • Große, Cornelia S., and Alexander. Renkl. Learning from worked examples: What happens if errors are included. Instructional design for effective and enjoyable computer-supported learning (2004): 356-364
  • Sweller, John, Jeroen JG Van Merrienboer, and Fred GWC Paas. Cognitive architecture and instructional design. Educational Psychology Review 10.3 (1998): 251-296
     

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