Numeracy was for the group of learners

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This lesson in Numeracy was for the group of learners who were appearing for their Electrotech NVQ Level 2 qualification. To successfully complete the course the learners must take Literacy and Numeracy as additional subjects and try to achieve Level 2 qualification in these 'Basic Skills' subjects. There were six learners in this group and all of them had come out at Level 1 in their Initial Assessment except one who came out at Entry 2. Two of the learners already had their Numeracy Level 1 qualification. The learner who came out at Entry Level 2 also had additional need i.e. English was his second language. The aim of the lesson was to identify different properties of '2D and 3D Shapes' and solve the problems based on these shapes.

In the process of teaching and learning there are different ways to improve the effectiveness of learning. To achieve the maximum effectiveness the selection of teaching and learning strategies becomes very important. The main criteria for selecting a strategy is 'Learners'..........their needs, ability, liking, concentration span etc. Preference should be given to the strategy in which you can engage most of your learners. As Geoff Petty says "it is better for learners to have 80% concentration on moderately effective method than 10% concentration on a supposedly brilliant one." (Geoff Petty, 2009). Another factor to consider is in which domain the learning is taking place and what is the purpose of your lesson. "when you come to choose your teaching strategy it is logical that you make the domain and the level of objectives you are seeking to achieve the basis for the choice"(Geoff petty, 2009). One more important thing to consider is the 'Learning style' of the learners. As everyone has different learning style it is better to use all of them in the lesson than teaching learners in their preferred style. According to Klein (2003) "a student's understanding and recall are improved if all styles are encountered" (cited by Geoff Petty, 2009).

Here in the lesson plan most of the strategies fulfil above important criteria. At the start of the lesson there is 'Interactive Question and Answer' strategy in which topic is introduced, information is exchanged and interactive dialogue is established. This happens mainly in the cognitive domain and can achieve either a high or low level of objectives depending on the type of questions you ask the learners. This strategy is helpful as it establishes the 'SEB' level of the students, stimulates them in thinking, they know if their conceptual understanding of the topic is right or wrong immediately and they can learn from the answers other learners have given. But one has to keep in mind that all students may not give the answers and sometimes too many closed questions can be asked.

Next is the 'Group Discussion' on the properties of the 2D and 3D shapes. This was the tutor led discussion in which students discussed various concepts such as parallel lines, vertices etc. they also discussed where we see these shapes in actual world around us and where they use it in 'Electrotech'. Discussion is a very effective strategy as it can achieve a very high level of objectives in cognitive and affective domain. We are considering the affective domain here because discussion can change the view, attitudes of the learners about the topic. Learners exchange their views, information and it makes them think in different directions than they had before. It widens their horizons and has a very high level of participation.

Learners then worked on the practical tasks such as measuring the angles with protractor and comparing them with right angles, counting the faces and vertices of all 3D shapes etc. In practical tasks they put what they have learned in practice. This reinforces their learning, clears the concepts and builds their confidence. According to Geoff Petty "The tasks requires them to apply the knowledge, theories, skills etc. that have just been presented. This involves them in reasoning, not just reproduction" (Geoff Petty, 2009). Students enjoy practical work. That's why it engages most of the learners. A lot of 'peer-learning' happens and it can achieve a very high objective 'evaluation' in cognitive domain.

The last task for learners was 'Cube Puzzle'. The learners had to cut the paper net and create a '3D shape of Cube' from it. There was a small prize for the winner. Puzzles/games are highly effective strategies. They are fun, challenge and a bit of healthy competition is always a good thing! Here the learner has to take decision, apply and solve the puzzle, which involves very high level cognitive skills and creativity. This is an active learning method which "can produce intense involvement and a quality of concentration no other teaching method can match" (Geoff petty, 2009). But one has to be careful with this strategy as the puzzle/game may not capture the interest of learners and the strategy might not work.

Most of the above strategies are student centred, active methods of teaching and learning. Also they involve all the learning styles i.e. Visual-Audio-Kinaesthetic (VAK) except one i.e. 'question and answers'. This is called 'multiple representation' and research shows that "more varied these representations and links, the more likely it is that the learner will get the concept and gain full understanding" (Geoff Petty,2009). The 'cube puzzle' is the best example for this - where as stated by Honey and Mumford (1982) we can see that activist, reflector, theorists and pragmatists all can work according to their own preferences and complete the learning cycle. (, date visited 21/01/2010).

Many of the above strategies focus mainly on students and considering this was a small group of learners, proved highly effective. This being the case we can see that they were 'cognitive learning techniques' focusing mainly on students. One cognitivists thinker Bruner "considers the learning as the acquiring of new information, transforming that learning with regard to existing knowledge and then checking it against the new situation" (I. Reece - S. Walker, 2003). We can see that in the strategies above learners learnt new things and used it to solve the given problem, reflected on it and different levels of objectives (levels of taxonomy, Bloom 1956)were achieved in "cognitive domain". (, date visited 21/01/2010)

The strategies were effective in achieving the stated objectives. The most effective was 'Cube Puzzle'. I had never used 'puzzle and reward' in any of the lessons before. It was amazing to see how intensely the learners were involved. I'll use this one where ever possible in future. But one thing I'll need to watch is 'time-management'. I've to stick to the given time line and encourage students to finish their work in time. They took more time than intended and we had less time for lesson review and evaluation.

The group discussion was also a success. High level of participation from all the learners. There was lot of 'peer learning' and exchange of views. Sometimes learners were told to watch their language but they all enjoyed it. During question and answers there were few learners whose level of participation was low. I'll need to improve my method of asking and directing the questions. The practical task of measuring angles, faces, vertices etc. and writing them on worksheet was received with less enthusiasm. They liked doing the practical but didn't like the 'note-down' part. Need to try some different method......may be writing on the board will work! As the learners have a very low attention span and 'Maths' is a subject disliked by many, I've to keep my 'teacher-talk' to minimum and keep them stimulated. Activities are the best way to ensure that they don't lose interest. Research shows that "Changes of activity produce an increase in concentration and that concentration is maintained for longer when the student is active" (Geoff Petty, 2009). I had included activities in the lessons before this but not so many........and certainly not with such a clear understanding between strategies and level of objectives! That's a definite change my lesson plans will have in future.

The next important thing in the lesson plan is 'Assessment'. Without assessment there can be no learning as "assessment measures the breadth and depth of learning" (Geoff Petty, 2009)Assessment is done for various reasons - to check the SEB level, make sure that objectives are achieved, find out the areas for development, see that standard is maintained etc. There are two types of assessments Summative and Formative. Summative assessment is done to get the qualification, usually at the end of the year e.g. GCSE. Formative assessment is an ongoing process and is usually done during the lesson to check the progress of the students. As we are assessing during the lesson here, we are more interested in Formative one.

In the Formative Assessment we check if the students' learning, give them constructive feedback, find out areas for development and then review and evaluate the work. In other words "formative assessment is informative feedback to the learners while they are still learning the topic" (Geoff Petty, 2009)

If we look at the lesson plan the first assessment done is through the question - answers. It was a kind of 'initial assessment' to identify the 'SEB' level and reinforcing the basics of 2D and 3D shapes. It was an informal assessment where immediate feedback was given in the form of 'comment' and learners were encouraged to contribute more. Both types of questions were asked 'closed and assertive' leading to tutor led group discussion. Discussion was the two way process of learning and assessing. While the learners learnt new things about shapes through discussion, it also gave an opportunity to observe if they have achieved the stated objectives. Again the feedback was informal and immediate here. So if a learner was wrong about something he was corrected immediately either by teacher or by other learner.

The learners then worked on the practical tasks such as measuring the angles, counting parallel lines, faces and vertices etc. They were given work-sheet to note down their findings. Here the assessment happened in two forms- first by observing the students doing their practical work. Second a formal one by checking their worksheets and marking their work. In both the cases constructive feedback was given to find out where and why they have gone wrong, correct their work and move on. At the end of the lesson the learners worked on the 'Cube Puzzle'. Here they were encouraged to find out different ways to solve the puzzle, take decisions and apply their learning. Here the assessment was formative - observation and summative - solving the puzzle and getting the prize!

In formative assessment it is very important that learners should know the objectives and 'criteria for assessment'. Once they know what they need to achieve and how we are assessing it they can assess their work themselves. According to Black and William's review the assessment should be diagnostic. The teachers should involve the learners in assessing their own work and find out the mistakes. The learners are given the constructive feedback and new targets to achieve. "In order for assessment to benefit the students properly, students must be able to obtain feedback as to what the goal of their learning is, what their current position is, and what they can do to get closer to their goal." ( date visited 21/04/2010). As we see all the above assessment are done in the same way.

Also depending on the objectives you can choose your assessment methods. This "appropriateness of the method of testing is called 'construct validity'." "ensuring that a particular type of test is used for a particular application ensures construct validity"(Geoff Petty, 2009). For e.g. in lesson plan to achieve high level of cognitive objectives quiz/puzzle was used.

I found it bit difficult to give constructive feedback in Question-answer session. When a student gave the wrong answer I sometimes told them straight way 'no, wrong answer'. I need to make a more positive response! But in other assessments worksheets, group discussion and puzzle solving I managed to give good constructive feedback. I went around the class, checking the work of each student and talking them through the assessment and ensuring that they move on to next task.

Motivating the students is main aim of the formative assessment. It is very important to know that how you assess your learners has a direct impact on their confidence and behaviour. If there is no feedback or it is negative and discouraging, the students lose their interest. They start thinking themselves as a 'failure' and it affects their self-worth. "Many students construct their identity through assessment and that as a result, it reveals something about themselves as individuals" (Reay and Williams (1998), cited by I. Reece - S. Walker, 2003). Maslow (1987) connects this fear with their engagement in learning, stating that self-esteem is a must for learning. So by using various teaching-learning strategies and constructive feedback to motivate them, we teachers, can definitely help our students achieve their qualification.