Effective Teaching And Learning Of Numeracy Education Essay

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The focus of the analysis will be to address the three key questions. The first phase will establish how effective teaching and learning of numeracy is perceived by learners, tutors and managers. The second will explore how numeracy was delivered and experienced over a three week period. The final phase will be to determine whether the findings can be used to improve the way numeracy provision is managed for future learners.

Perceptions of effective teaching and learning of numeracy

The data obtained with regard to perception of effective teaching and learning of numeracy was gathered over a period of two months using questionnaires and interviews.

Questionnaires were used to obtain information from both tutors and learners. Return rates were 44% for the tutor questionnaire distributed via email (7 questionnaires returned from 16 tutors) and 93% for the learner questionnaire distributed during taught sessions (28 questionnaires returned from 30 learners). The tutors who returned the questionnaire taught at Entry Level 1 and/or Entry Level 2 and/or Entry Level 3 and all the data has been analysed together. The nature of the distribution meant that tutor respondents were a self-selected sample rather than a targeted sample and this may not have been representative of the population as a whole, leading to a biased response. Although tutors were offered the opportunity to print out and return their completed questionnaire anonymously by internal post, all respondents chose to send their response by return email.

The learners who returned the questionnaires were learning at Entry Level 1, Entry Level 2 or Entry Level 3 and the data has been analysed both by level and as a whole. Unfortunately, due to anomalies in the way learners answered the two questions about which strategies help and which strategies do not help them, only 17 (61%) of the questionnaires could be used (4 (57%) Entry Level 1, 8 (62%) Entry Level 2 and 5 (63%) Entry Level 3 responses). 11 learners had ticked that a strategy helped them but also that it did not help them, therefore none of their responses to any of the questions were included. (The author had intentionally included these two questions to determine whether the learners had understood the questions and whether their responses should be used). The 3 learners at Entry Level 3 whose responses were not included had ticked that there were some difficulties to overcome when learning numeracy. Perhaps these difficulties were due to their literacy ability, as suggested by Van Groenestun (2003, online). The level of understanding of the 17 learners whose questionnaire data was used could still also have led to unreliable data and perhaps this is why very little research had been carried out with Skills for Life learners, as discussed by Brookes et al. (2001), Benseman, Lander and Sutton (2005, online) and Benseman, Sutton and Lander (2005, online).

Interviews were used to obtain information from tutors (6 were invited, 5 accepted) and managers (3). Those tutors (3) and learners (16) who were involved in the observed sessions were also interviewed.

When asked how effective teaching and learning was at the College, tutors and learners responded that it was either very effective, effective or they were not sure (see Figure 4.1). None of the learners or tutors thought numeracy teaching and learning was not effective, although one of the managers stated that numeracy teaching and learning across the College was

"...not as effective as it could be or has the potential to be".

However, another manager said numeracy was delivered

"...very effectively by skilled staff in different ways to meet cohorts' needs".

Tutor comments about College effectiveness included

"...how effective it is depends on the tutor and the teaching methods used" and further training was needed in order to increase effectiveness.

Figure 4.1: A % column chart showing learner and tutor perception of teaching and learning at the College

Figure 4.2: A % column chart showing learner and tutor perception of teaching and learning in the numeracy sessions they attend/deliver

Figure 4.2 shows perception of effectiveness of the numeracy sessions attended/delivered. When comparing Figures 4.1 and 4.2, it is apparent in both cases that the majority thought their sessions were effective, although far fewer people were uncertain in Figure 4.2 as would be expected in view of their personal experience.

During an interview, one tutor made an important point that

"...effective for our learners can mean many things e.g. social factors and confidence building, but getting a qualification is the only thing funders are interested in".

This indicates that learners, tutors and managers may perceive the term "effective" in different ways.

Two tutors commented that they made their sessions effective and enjoyable by making them relevant to the situations of their learners and by using a variety of teaching methods. The most common reasons for effectiveness given by tutors on the questionnaire were

The use of a mixture of activities

Having fun during the session

Interaction with learners

Supporting learners

Targeting individual requirements

When interviewed, the most common explanations given by tutors for the effectiveness of their sessions were

Learners achieving at the expected level

Observation of individual learner progress

Discussions with learners

One tutor commented that effectiveness could be improved further through specific training, thus agreeing with Cara and de Coulon (2008, online) and Simpson (2008).

It is necessary, when applying for a permanent rather than temporary position at the College, to have gained a Level 4 Subject Specific Numeracy qualification, as recommended by TUC (2004). The only tutor of the 5 interviewed to have this qualification was also the only one holding a permanent position. Therefore, only 20% of those interviewed were fully qualified (compared with 29% found by Cara and de Coulon (2008, online) and 18% found by Coben et al. (2006, online)). One of the temporary tutors had voluntarily taken the L2 National Numeracy Test in order to update their own numeracy qualification. The ratio of part-time temporary tutors to full-time permanent tutors interviewed was 4:1, reflecting the ratio actually teaching on AFP. This goes against recommendations from McIntosh (2005, online) and Benseman, Sutton and Lander (2005, online) that learning should be delivered by full-time staff due to the discovery that teaching is less effective overall when delivered by mostly part-time staff because of lack of consistency in approaches and less participation in CPD.

All managers interviewed agreed that specific numeracy training was necessary in order to become an effective numeracy tutor, although when asked what training they felt they needed, the majority of tutors interviewed showed more interest in observing other tutors and sharing best practice, as discovered by Wedgbury (2005) and Mackay et al. (2006, online).

Only one tutor interviewed did not feel well trained but then went on to comment that "...probably no formal numeracy training is required/essential if a good level of numeracy skills and teaching skills are present but my view would be very different if we were talking about literacy and teaching people to read".

Despite this perceived lack of training, 83% of learners felt that all of their numeracy tutors were well trained. The remaining 17% believed that some of their tutors were well trained.

Figure 4.3 shows that the majority of learners and tutors who completed the questionnaires feel that there are some or a lot of difficulties to overcome when learning/delivering numeracy. As may have been expected because of their low level of skills, Entry Level 1 and 2 learners feel there are more difficulties to overcome than Entry Level 3 learners.

Figure 4.3: A % column chart showing whether learners and tutors feel there are any difficulties to overcome when learning/delivering numeracy

Comments made on the questionnaire by tutors (and by managers at interview) regarding difficulties in teaching numeracy included the literacy needs of the learners and overcoming learners' fears of/phobias of/barriers towards maths due to previous experiences. Several tutors commented that learners with learning difficulties find it difficult to retain information, which makes remembering numerical steps more of a challenge. Learners in a group who do not have learning difficulties but missed some schooling, perhaps due to illness or rebelling, also have very different needs.

One manager stated

"It seems acceptable to say you are no good at maths but not to say you can't read so numeracy tutors have to work against that culture".

Another manager thought learners may not be able to see the relevance of learning numeracy.

Numeracy delivery and experience

Data obtained relating to the delivery and experience of numeracy during a 3 week period was gathered over 2 months from document analysis, questionnaires, observations and interviews and is described through the three strategies below.

Teaching and Learning Strategies

Managers' interviews revealed that they expected a broad range of teaching and learning strategies to be used when delivering numeracy and that those strategies would be learner centred (relevant, contextualised and based on the results of diagnostic assessments) and active (practical, kinaesthetic and Information and Communication Technology (ICT) based). They believed learners would be engaged more effectively through these strategies. The "chalk and talk" strategy, i.e. lecture/presentation, was the only strategy that managers were wary of over-using.

Although included by the author on the document analysis pro forma, role play, seminar and simulation teaching and learning methods were not mentioned on any of the schemes of work during the 3 weeks analysed. However, the author's interpretation of documents written by other tutors (schemes of work) could have created a margin for error. Nevertheless, role play, seminar and simulation were not ticked by any learners or tutors on the questionnaires nor were they mentioned by tutors or managers at interview. As can be seen from Appendix c, 5 papers mention simulation as best practice which could suggest that simulations should be used.

Figure 4.4 shows the different teaching and learning strategies that were planned to be used on the schemes of work. The most commonly planned strategies were discussion, whole group work, games and individual work, whilst there were no plans to use ice-breakers. These findings conflict slightly with those of and Coben et al. (2006, online) who also found that whole group and individual work were the most common methods but that very few teachers used games. Ciancone (1988, online) also recommend the use of individual work, group work and games. In complete contrast to the findings at this Further Education College, Benseman, Lander and Sutton (2005, online) report few opportunities for discussion (recommended in 10 papers in Appendix c).

The Entry Level 2 scheme had the most strategies planned (8), followed by Entry Level 3 (6) and Entry Level 1 (5), concurring with both Coben et al. (2006, online) and Benseman, Lander and Sutton (2005, online) that different teachers use different ranges of methods.

Figure 4.4: A stacked column chart showing the teaching and learning strategies planned on the schemes of work

At interview, tutors only mentioned 6 strategies compared with 10 ticked on the questionnaire (see Figure 4.5). Perhaps those strategies mentioned at interview (small group, idea-storming, ice-breaker, game, discussion, demonstration) are the most commonly used? However, these were dissimilar to those most commonly planned on the schemes of work (small group was less common than whole group, whilst individual (and ice-breakers) were not mentioned at all at interview).

Figure 4.5: A column chart comparing the teaching and learning strategies ticked by tutors on the questionnaire and mentioned by tutors at interview

As Figure 4.6 shows, for some teaching and learning strategies (whole group, small group and demonstration) there was a strong correlation between what was planned on the schemes of work and what was observed. However, for others (individual, idea-storming, ice-breaker, game, discussion and case study) there was a marked difference between what was planned and what was observed. The fact that the schemes of work analysed covered 57 hours of learning and that only 5 hours (less than 1%) were observed could be a reason for the anomalies.

Figure 4.6: A column chart comparing the teaching and learning strategies included in the schemes of work and seen during the observations

As can be seen from Figure 4.7, from information taken from completed learner questionnaires, Entry Level 1 and Entry Level 3 learners had experienced one more teaching and learning strategy (9) than Entry Level 2 learners (8). The most commonly experienced strategies were demonstration, individual, discussion, games and small group.

Figure 4.7: A stacked column chart comparing the teaching and learning strategies experienced by learners (according to answers given on the questionnaire)

Figure 4.8: A column chart showing the teaching and learning strategies used by tutors (according to the completed tutor questionnaires) and the percentage of learners who find those strategies useful / not useful (according to the completed learner questionnaires)

The author had expected the "helpful" and "not helpful" answers to add up to 100 but as can be seen from Figure 4.8, they do not. Perhaps this is because some teaching and learning strategies are neither helpful nor unhelpful to learners. Figure 4.8 shows that all tutors use whole group and at least 53% of learners find this strategy helpful. All tutors also use small group and this was found helpful by more learners (at least 71%). Projects are used by few tutors and perhaps this is why learners did not comment on them. 86% of tutors use presentations/lectures but a third of learners do not find them helpful. Only one tutor interviewed commented that they would not use presentations/lectures. Individual work, demonstrations and games are used by the majority of tutors and less than 20% of learners do not find them useful which would suggest that they are effective techniques to use with the majority of numeracy learners.

Assessment Strategies

Although included by the author on the document analysis pro forma, create a flow chart, exhibition, free writing, learning environment (le) activity, performance, practice file, production of artefact, rating scale, reflective log/diary, report, role-play (observation of), sentence completion, simulation and written description were not mentioned on any schemes of work, or ticked by any learners or tutors on the questionnaires. Neither were these assessment methods mentioned by tutors or managers at interview.

Figure 4.9 shows the different assessment strategies that were planned to be used on the schemes of work. As can be seen, the most commonly planned strategies were group discussion, IT/website activity, observation (Benseman, Lander and Sutton (2005, online) also found this to be one of the most common forms of assessment), question and answer (recommended in 3 papers in Appendix c), tutor/learner discussion, worksheets and written question and answer but there were no plans to use 38 of the listed assessment strategies including assignment, initial assessment, diagnostic assessment, Moodle activity, peer observation, project, practice paper and written exam.

The Entry Level 2 scheme had the most assessment strategies planned (22), Entry Level 1 and Entry Level 3 having 7 less (15) strategies planned. Again, this concurs with both Coben et al. (2006, online) and Benseman, Lander and Sutton (2005, online) that different teachers use different ranges of methods. However, CERI (2008, online) state that one of the key features of formative assessment is to use a variety of assessment methods and the author believes that this has been planned at all Entry Levels.

Figure 4.9: A stacked column chart showing the assessment strategies planned on the schemes of work

At interview, tutors mentioned only17 strategies compared with 66 ticked on the questionnaire (see Figure 4.10a, Figure 4.10b and Figure 4.10c). Perhaps those strategies mentioned at interview (worksheet, verbal question and answer, targeted questions, Skills for Life pack, self-assessment activity (found to be a common method by Benseman, Lander and Sutton (2005, online) and recommended in 5 papers in Appendix c), question and answer, project, practice paper, peer assessment, paired activity, observation, learner demonstration, IT/website activity, gapped handout, game, completed survey and card activity) are the most commonly used? However, these were not the same as those most commonly planned on the schemes of work. Only 4 of those mentioned at interview were most commonly planned on the schemes of work (IT/website activity, observation, question and answer and worksheet).

Figure 4.10a: A column chart comparing the assessment strategies ticked by tutors on the questionnaire and mentioned by tutors at interview

Figure 4.10b: A column chart comparing the assessment strategies ticked by tutors on the questionnaire and mentioned by tutors at interview

Figure 4.10c: A column chart comparing the assessment strategies ticked by tutors on the questionnaire and mentioned by tutors at interview

As Figure 4.11 shows, only for observations was there a strong correlation between what was planned on the schemes of work and what was observed. Again, a reason could be that the schemes of work analysed covered 57 hours of learning whilst only 5 hours (less than 1%) were observed.

Figure 4.11: A bar chart comparing the assessment strategies seen during the observations and included in the schemes of work

As can be seen from Figure 4.12a, Figure 4.12b and Figure 4.12c, information taken from the completed learner questionnaires shows Entry Level 2 learners had experienced 2 more assessment strategies (25) than Entry Level 1 and Entry Level 3 learners (23). The most commonly experienced strategies were worksheets, Skills for Life pack, question and answer, problem solving, practice questions, multiple choice, Moodle activity, IT/website activity and group activity. However, many kinaesthetic activities were observed (using visual aids, puzzle, project, practical (observation of), learner demonstration, game, create a diagram, completed survey and card activity) which are believed by Kirby and Sellers (2006, online) to improve formative assessment due to teachers being able to observe where learning is taking place or diagnose any difficulties.

Figure 4.12a: A stacked column chart comparing the assessment strategies experienced by learners (according to answers given on the questionnaire)

Figure 4.12b: A stacked column chart comparing the assessment strategies experienced by learners (according to answers given on the questionnaire)

Figure 4.12c: A stacked column chart comparing the assessment strategies experienced by learners (according to answers given on the questionnaire)

Figure 4.13a: A column chart showing the assessment strategies used by tutors (according to the completed tutor questionnaires) and the percentage of learners who find those strategies useful / not useful (according to the completed learner questionnaires)

Figure 4.13b: A column chart showing the assessment strategies used by tutors (according to the completed tutor questionnaires) and the percentage of learners who find those strategies useful / not useful (according to the completed learner questionnaires)

Figure 4.13c: A column chart showing the assessment strategies used by tutors (according to the completed tutor questionnaires) and the percentage of learners who find those strategies useful / not useful (according to the completed learner questionnaires)

The author had expected the "helpful" and "not helpful" answers to add up to 100 but as can be seen from Figure 4.13a, Figure 4.13b and Figure 4.13c, they do not. Perhaps this is because some assessment strategies are neither helpful nor unhelpful to learners. Written exam, written test, written report, study pack, practical demonstration, group discussion and essay are not used by any tutors and perhaps this is why learners did not comment on them. 86% of tutors use presentations/lectures but a third of learners do not find them helpful. Tutors use 66 strategies but learners only commented on 27 of them. Peer assessment was commented on by learners but not used by tutors. Over 50% of learners found the following helpful; worksheets, tutor explanation, text book, diagnostic assessment, game, group activity (recommended as best practice by Pert (2009, online) and Foster and Beddie (2005, online)), Moodle activity, multiple choice, practice paper, practice questions, problem solving, question and answer and quiz.

Of these, worksheets, quiz, question and answer, problem solving, practice question, Moodle activity and group activity were helpful to over 70% of learners, whilst over 25% did not find the following helpful; wordsearch, text book, self-reflection and create a poster. However, all of these were used by over 10% of tutors.

Feedback Strategies

Although included by the author on the document analysis, pictorial feedback was not mentioned on any of the schemes of work during the 3 weeks analysed, or ticked by any learners or tutors on the questionnaires. Neither was this method mentioned by tutors or managers at interview.

Figure4.14 shows the different feedback strategies that were planned to be used on the schemes of work. The most commonly planned strategies were; written on work, verbal, peer, instant, individual and group whilst there were no plans to use written on ILP, witness statement or post-it notes. The Entry Level 3 scheme had the most strategies planned (10), followed by Entry Level 2 (8) and Entry Level 1 (7). CERI (2008, online) state that one of the key features of formative assessment is to use a variety of feedback methods and the author believes that this has been planned at all Entry Levels.

Figure 4.14: A stacked column chart showing the feedback strategies planned on the schemes of work

At interview, tutors only mentioned 1 strategy compared with 12 ticked on the questionnaire (see Figure 4.15). Perhaps the strategy mentioned at interview (written on ILP) is the most commonly used? However, written on ILP was not mentioned at all on the schemes of work during the 3 weeks analysed. (The ILP's are reviewed every 6 weeks and a review was not scheduled during the 3 week period analysed.)

Figure 4.15: A column chart comparing the feedback strategies ticked by tutors on the questionnaire and mentioned by tutors at interview

As Figure 4.16 shows, for some feedback strategies (written on work, witness statement, verbal, post-it notes, peer and group) there was a strong correlation between what was planned on the schemes of work and what was observed. However, for others (computer printout, individual, self, written on ILP) there was a marked difference between what was planned and what was observed. The fact that the schemes of work analysed covered 57 hours of learning and that only 5 hours (less than 1%) were observed could be a reason for the anomalies.

Figure 4.16: A column chart comparing the feedback strategies included in the schemes of work and seen during the observations

As can be seen from Figure 4.17, from information taken from completed learner questionnaires, Entry Level 2 learners had experienced one more feedback strategy (6) than Entry Level 1 learners (5) and Entry Level 3 learners had experienced just 4 feedback strategies. The most commonly experienced strategies were; individual, peer, verbal, written on ILP and written on work.

Figure 4.17: A stacked column chart comparing the feedback strategies experienced by learners (according to answers given on the questionnaire)

Figure 4.18: A column chart showing the feedback strategies used by tutors (according to the completed tutor questionnaires) and the percentage of learners who find those strategies useful / not useful (according to the completed learner questionnaires)

The author had expected the "helpful" and "not helpful" answers to add up to 100 but as can be seen from Figure 4.18, they do not. Perhaps this is because some feedback strategies are neither helpful nor unhelpful to learners. Figure 4.18 shows that all tutors use verbal and individual feedback and over 50% of learners find these helpful. Self and on-screen feedback are not used by any tutors and perhaps this is why learners did not comment on them. Tutors use 12 feedback strategies and learners commented on just 6 of them. Over 50% of learners found the following helpful; written on work, written on ILP, verbal and individual. In contrast, over 25% of learners did not find witness statements useful whilst only 14% of tutors actually use them.

When asked at interview why they used specific teaching and learning, assessment and feedback strategies, the following were the most common responses from tutors

To revise, refresh, recap and link learning

So that learners can learn from each other

To keep the learners focussed by using a variety of strategies

To get an immediate response

To appeal to different learning styles

When asked at interview why they did not use certain teaching and learning, assessment and feedback strategies, the following were the most common responses from tutors

Unsure how to use them

Not appropriate for this level of Further Education

Not a lot of IT resources for Entry Level 1 learners

Would need too much tutor intervention

Implications for future management of numeracy provision

As Figure 4.19 shows, Entry Level 1, Entry Level 2 and Entry Level 3 learners should experience a very similar number of teaching and learning, assessment and feedback strategies even though the schemes of work are written and planned by individual tutors. However, the actual strategies planned differed. In future, perhaps the AFP Course Leader should stipulate which teaching and learning, assessment and feedback strategies should be planned, taking into account the information gathered during the literature review, learner comments, tutor comments and manager comments so that learners experience the most effective range of strategies, rather than a random selection.

Figure 4.19: A stacked column chart showing the strategies planned on the Entry Level 1, Entry Level 2 and Entry Level 3 schemes of work.

Paired t-tests (two-tailed) with groups with equal variance were carried out on the ratings given by tutors and learners at the end of the three week period analysed using Frontal Cortex Inc (2004-2010, online).

When rating understanding, achievement, location, activities, pace, resources and enjoyment, overall for the three groups observed, the scores of the tutors (M = 4.28, SD = 0.560) did not differ significantly (t = 0.8827, two-tailed p = 0.864) from those of the learners (M = 4.25, SD = 0.608).

When calculated per observed session however, there was a significant difference between the scores of two of the three sessions as shown below:

Observed group "a" - the score of the tutor (M = 3.63, SD = 0.406) differed significantly (t = 0.0174, two-tailed p = 0.006) from those of the learners (M = 4.375, SD = 0.518).

Observed group "b" - the score of the tutor (M = 4.51, SD = 0.280) did not differ significantly (t = 0.2332, two-tailed p = 0.346) from those of the learners (M = 4.25, SD = 0.707).

Observed group "c" - the score of the tutor (M = 4.70, SD = 0.185) differed significantly (t = 0.0301, two-tailed p = 0.029) from those of the learners (M = 4.125, SD = 0.641).

This would imply that it is important to obtain feedback from as many learners as possible in order to obtain accurate information about "quality" of learning that would be similar to the views of tutors.

Verbal comments given by learners during the post-observation interviews were mostly positive as shown in Table 4.2. They appear to understand and enjoy the activities and resources used during the sessions. Group size may need to be investigated, although this is governed by funding. Some individual timetables may need to be discussed more thoroughly with learners to ensure that they are comfortable attending for a full day and know what to expect.

Table 4.2: Positive and negative comments made by learners post-observation.

Positive learner comments

Negative learner comments

Understanding

We keep going over things so I understand it well (2)

We help each other

It's interesting (5)

Achievement

I think I've achieved a lot

I can do my own budgeting now

Location

Nice big room (2)

Comfortable chairs

Spacious

Quiet

Some tables aren't level

Activities

Activities help you to understand things better

Done a mixture

Pace

It starts and finishes at the right time

Right pace

Too many people in the group so sometimes have to wait

It's a long day - 0900-1630 (2)

Resources

Get a mixture of things to do and use

Enjoyment

I've enjoyed it a lot (5)

I don't really enjoy the shapes session

Verbal comments given by tutors during the post-observation interviews were also mostly positive, as shown in Table 4.3. Differentiation appears to be taking place in all sessions in terms of pace and in terms of some learners being given the opportunity to achieve more than others but it needs to be ensured that all learners are given the opportunity to learn what they need to learn in order to achieve their qualification. This does not concur with the findings of Coben et al. (2006, online) that only 50% of tutors differentiate work for learners. Tutors would like learners to be able to use computers within the classroom but there are not enough / are not any in the teaching rooms. When asked how they could have improved the experience of their learners, tutors commented that they would like to improve their own computer skills in order to incorporate IT into their sessions more frequently and that they would like more opportunity for 1-1 contact. Learners commented that they would like to go out on visits more frequently and have outside speakers, for example someone from the Citizens' Advice Bureau to talk about budgeting skills.

Table 4.3: Positive and negative comments made by tutors post-observation.

Positive learner comments

Negative learner comments

Understanding

Confident that all learners understood what they were doing and why

Achievement

All learners contributed to question and answer sessions

Some learners achieved more than others (3)

Location

Has 2 whiteboards and a Smart board

Plenty of room (3)

Stationery available in cupboard

Sometimes very hot (2)

Not enough computers for learners (2)

Activities

I try to include a variety

Pace

I use extension materials

Just right for all learners

Sometimes too fast and sometimes too slow - there are so many different needs in the group I don't think I could get it right for everyone

Resources

The learners have ownership of them

I use a mixture of resources

Enjoyment

Learners learn more when they enjoy it

I usually get positive feedback (2)

End paragraph...

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