Building mathematics skills in a vocational context

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What was the typical pattern of a CTE lesson designed to support students’ maths?

The pairs of teachers jointly planned vocational lessons that provided explicit instruction in specific maths concepts relevant to the vocational subject. Each of these lessons was supposed to include the following elements:

pointing out the mathematics found in the vocational context – teachers had to tell students when they reached the part of the lesson in which maths was embedded;
assessing the students’ maths understanding – the teachers asked open questions about the maths, such as, “What can you tell me about this?”;
working through the pulled out example – teachers worked through the steps needed to complete the example, or asked students to take the lead if their level of understanding was sufficient;
enhancing the maths in the lesson – teachers identified and shared the underlying maths principles and concepts, purposely using mathematical vocabulary and asking students to do so;
reinforcing the maths enhancement – teachers worked through similar examples from a work-related context and also more abstract maths examples that might be seen in a test or maths lesson; students also worked through such problems individually or in small groups;
checking the students’ understanding – teachers asked questions such as, “Can you explain the maths concepts we used today?” or “How would you explain these maths steps to someone else?”; and
expanding the enhancement – teachers asked students to create their own examples, for both vocational and traditional mathematical contexts.

Researchers advised teachers to continue to use both sets of vocabulary (from the CTE and formal maths context) alongside one another throughout the lesson, e.g. using both ‘slope’ and ‘pitch’. They also suggested that during the final stage of the lesson, as well as asking students to create examples of their own, teachers could provide further examples that addressed the same maths principle but which contained an error in logic, and ask the students to spot and correct this.

The study found that, although most lessons consistently used the first six elements, about one third of observations did not see evidence of teachers using the seventh element. This was unfortunate, as the final element was important, because it gave students opportunities to extend their learning into more traditional maths problems.

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Research Home Themes \| Find digests \| About the digests resources glossary researchers contact TRIPS Introduction How much did the students’ maths improve? How did the teachers prepare for and implement the project? What was the typical pattern of a CTE lesson designed to support students’ maths? How did the pairs of teachers evaluate the new lessons? What did the researchers believe might improve the success of a future programme? What were the aims of the study and how was it designed? What are the implications of the study? Where can I find out more? Send us your feedback Collated digests To view/remove/add notes and save your collated digests click here Get Word Reader Building mathematics skills in a vocational context This digest found in Mathematics Send to a friend Word doc 70KB Printer friendly Collate for later What was the typical pattern of a CTE lesson designed to support students’ maths? The pairs of teachers jointly planned vocational lessons that provided explicit instruction in specific maths concepts relevant to the vocational subject. Each of these lessons was supposed to include the following elements: pointing out the mathematics found in the vocational context – teachers had to tell students when they reached the part of the lesson in which maths was embedded; assessing the students’ maths understanding – the teachers asked open questions about the maths, such as, “What can you tell me about this?”; working through the pulled out example – teachers worked through the steps needed to complete the example, or asked students to take the lead if their level of understanding was sufficient; enhancing the maths in the lesson – teachers identified and shared the underlying maths principles and concepts, purposely using mathematical vocabulary and asking students to do so; reinforcing the maths enhancement – teachers worked through similar examples from a work-related context and also more abstract maths examples that might be seen in a test or maths lesson; students also worked through such problems individually or in small groups; checking the students’ understanding – teachers asked questions such as, “Can you explain the maths concepts we used today?” or “How would you explain these maths steps to someone else?”; and expanding the enhancement – teachers asked students to create their own examples, for both vocational and traditional mathematical contexts. Researchers advised teachers to continue to use both sets of vocabulary (from the CTE and formal maths context) alongside one another throughout the lesson, e.g. using both ‘slope’ and ‘pitch’. They also suggested that during the final stage of the lesson, as well as asking students to create examples of their own, teachers could provide further examples that addressed the same maths principle but which contained an error in logic, and ask the students to spot and correct this. The study found that, although most lessons consistently used the first six elements, about one third of observations did not see evidence of teachers using the seventh element. This was unfortunate, as the final element was important, because it gave students opportunities to extend their learning into more traditional maths problems.