WBL – Numeracy 1

**Independent evidence**

Developing mathematics ideas within vocational courses helps students to learn mathematical concepts they often have been unable to grasp in formal numeracy lessons **i**.

**Your evidence**

It may be worth looking at the work your trainee has completed to date paying particular attention to the numeracy skills they have demonstrated, and numeracy problems they have found difficult. You could map these against the national standards published on the QCA website: http://www.qca.org.uk/qca_4541.aspx, or the curriculum for the qualification to identify the trainee’s level. The Adult numeracy core curriculum, for example, provides detailed level descriptors - www.dcsf.gov.uk/curriculum_numeracy/.

**Putting the evidence to work**

Discuss what you have found with your trainee and plan what their next steps should be in terms of numeracy skills development. It may be helpful to look at what you will be covering in the main programme for the coming months to spot opportunities to build in numeracy learning.

**i For more information** about building academic skills in context see: www.nccte.org/publications/infosynthesis/r%26dreport/MathLearningPilotStudy.pdf

Follow this link to read about an integrated approach to teaching mathematics in the workplace: http://www.nrdc.org.uk/content.asp?CategoryID=1425

Follow this link for more on the TLRP Learning as Work project: www.tlrp.org/proj/phase111/felstead.htm

NRDC have published research which looks closely at approaches to embedding literacy, language and numeracy in vocational learning: www.nrdc.org.uk/uploads/documents/doc_3188.pdf

For resources and materials for embedding numeracy follow this link to the Lifelong Learning UK site: http://www.lluk.org/3399.htm

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FE General – Numeracy 2

**Independent evidence**

Evidence suggests that teachers frequently talk for too long without allowing students to engage with mathematics and find out difficulties for themselves. Lessons which emphasise practical work stimulate discussion and mathematical thinking amongst students **i**.

**Your evidence and reflections**

The mathematical explanations you provide your students may be something that you planned to talk about during a lesson, or they may be a response to a question a student has posed. You may also be talking at length about a particular topic, or providing succinct answers in a way that invites further student discussion. To get an idea of the ‘student talk time’ (STT) / ‘teacher talk time’ (TTT) balance in your classes, why not ask a colleague (possibly assistant, or student teacher) to observe a lesson, or part of a lesson. They could complete a form similar to the one below, noting length of time spoken by you and students and type of talk.

Teacher talk | Student talk | ||

time | what said | time | what said |

**Putting the evidence to work**

You could team up with a colleague or group of colleagues to record TTT vs STT in your sessions. What is common in your approaches? Would you say there was something here that is special to teaching numeracy, or are these teaching techniques that are generalisable across subjects. What is different in your approaches? Explore the underlying reasons for you and your colleagues taking different approaches. Are there approaches you feel should be more widely adopted? If so, why, and how might you go about implementing a particular approach and monitoring its impact?

**i Find out more** about mathematics provision for 14-19 year olds at: www.ofsted.gov.uk/assets/4207.pdf

The findings of a systematic review of strategies to raise pupils motivational effort in Key Stage 4 Mathematics are available at: www.eppi.ioe.ac.uk/cms/Default.aspx?tabid=714

Follow this link for the Teaching and Learning Research Programme (TLRP) Post Compulsory commentaries: www.tlrp.org/findings/post_comp_findings/post_comp_findings.html

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**Independent evidence**

Effective teachers of 14–19 mathematics were found to explicitly set out to give their students the confidence to succeed. They did this by placing the students at the centre of the learning process and identifying and building on what the students knew and could do already **i**.

**Your evidence and reflections**

How much do your students currently lead their own learning? You can get a window into this by focusing on two or three students and considering how each of them deals with a problem-solving task. Does the student, for example:

• immediately ask you for help if they get stuck?

• consult with another student to find a solution?

• look back at work they have done previously to help them with answering?

You could also note other ways you observe students’ response to problem-solving activities.

**Putting the evidence to work**

If your observations indicate that your students could be doing more to lead their own learning , why not discuss learning skills with them in the next session. You could prepare them for the discussion by asking them to note on a grid like the one below what they think the advantages and disadvantages are of each approach.

approach | advantage | disadvantage |

asking for help from the teacher as soon as I get stuck on a problem | ||

asking another student when I get stuck on a problem | ||

etc |

A systematic review of strategies for raising students’ motivation in Key Stage 4 mathematics is available at: http://www.eppi.ioe.ac.uk/cms/Default.aspx?tabid=714

Follow this link for the Teaching and Learning Research Programme (TLRP) Post Compulsory commentaries: www.tlrp.org/findings/post_comp_findings/post_comp_findings.html

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ACL – Numeracy 1

**Independent evidence**

The most effective teaching of mathematics was found to occur when tutors consciously set out to give their students the confidence to succeed. They did this by adopting strategies that began with what students knew and could do already **i**.

**Your evidence and reflections**

Adult learners will come to numeracy sessions with their own techniques for tackling some of the tasks you ask them to work on. You could find out what these are by presenting learners with a ‘diagnostic’ task – a series of questions which cover the areas for the next stage in their programme. Ask them to skip any they are not sure of answering, and to use any technique for answering the rest. Seeing their working is important, so model how they can show their thinking with a whole class example. You may want learners to work in pairs so that it feels less like a formal test.

**Putting the evidence to work**

To help your learners see the different approaches to tackling tasks, and the validity of each approach which arrives at the right answer, you could draw up a grid of a question column on the left (the questions in the diagnostic task), and the different ways of answering the question in columns to the right. Students could then decide which of the approaches they would like to adopt. It also demonstrates that they have something of value to share with the group.

Answer type 1 | Answer type 2 | Answer type 3 | |

Question 1, e.g. what is 9.9 cm in millimetres | Write out as a sum, 9.9x10 | Because we're multiplying by 10 move decimal point to the left | Multiply in your head, but estimate answer first - 'I know 9x10=90 so 9.9x10 must be 99 |

Question 2 | |||

etc |

**i Find out more** about evaluating mathematics provision for 14-19 year olds here: http://www.ofsted.gov.uk/assets/4207.pdf

You can find out more about the motivating and demotivating factors that affect adult numeracy learners at: http://www.nrdc.org.uk/publications_details.asp?ID=94

The Teaching and Learning Research Programme (TLRP) Further Education Commentary is available at: www.tlrp.org/pub/documents/FEcommentary.pdf

]]>FE General – Numeracy 1

**Independent evidence**Developing mathematics ideas within vocational courses helps students to learn mathematical concepts they often have been unable to grasp in formal numeracy lessons

**Your evidence**Many vocational subjects contain mathematics ideas such as plumbing (areas and volumes), catering (weight and ratios), and business (percentages and ratios). You could ask your students what they cover in numeracy to see how far they recognise that the same subject material occurs in both places or to identify common elements. To what extent are these aspects reinforced or built on in numeracy classes? You could talk to your students about what they found. Were there any numeracy ideas they had not realized they used in their vocational courses? You could share your and your students’ observations with a numeracy colleague to identify common ground between the vocational and numerical schemes of work.

**Putting the evidence to work**When you have identified where the overlaps are you could work with a numeracy tutor to design tasks that support learning in both areas. Together, you could develop vocational learning experiences in ways that would enable students to recognise the mathematics ideas they were dealing with and that would build on what they had covered in numeracy. You could also, together, analyse students’ assignments and other written work to see the impact of this approach on their numeracy learning. You might also work with the numeracy tutor to create appropriate vocational contexts to help students’ learning in numeracy classes.

**i For more** information about building academic skills in context see: www.nccte.org/publications/infosynthesis/r%26dreport/MathLearningPilotStudy.pdf

NRDC have published research which looks closely at approaches to embedding literacy, language and numeracy in vocational learning: www.nrdc.org.uk/uploads/documents/doc_3188.pdf

Follow this link for the Teaching and Learning Research Programme (TLRP) Post Compulsory commentaries: www.tlrp.org/findings/post_comp_findings/post_comp_findings.html

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