The plan of the teaching programme below guides and informs the reader about what the programme entails (Refer to Appendix C).
Table 1: The teaching programme
Day Activity Goal Strand/Level
1 Engage learners in an activity of sorting out shapes according to appearance, number of sides & name. Ask probing questions like ‘how do you know that you have picked up a square? Why don’t you call it a rhombus?’ These questions are testing learners’ prior knowledge of shapes and what knowledge they have about shapes.
Review of previous grade’s work. Developing an experience with hands-on activities in geometry. To prepare learners to be able to give properties of shapes in the second level and third level. Questions asked do not need deeper insight, they just prepare the learner for the understanding of concepts to be taught, with the aim of gaining skills to be able to differentiate one shape from another, and the ability to work with others in the classroom in a good atmosphere. Conceptual understanding. Visualization or Recognition
2 Learners are given a task to classify shapes given, giving properties of shapes copying and filling in the given table. This is done in groups or pairs
Assessment of the
developmental level the students are in; students have fun and enjoy what they do; promoting interest that might develop towards a liking of the subject. Knowledge of properties of shapes will also be known by the teacher. Integrating properties of shapes that are common with the shape that has been picked by the teacher. This encourages them to work in a co-operative atmosphere with an aim of learning from each other and helping each other when one experiences a problem, together with respecting the ideas of others.
Analysis Procedural fluency
3 Description of Properties with sketches.
Give learners a chance to communicate breaking barriers of language by using the LOLT. Skills in oral communication and in writing; application of language use. Strategic competence. Informal deductions. Conceptual understanding 4 They are given the opportunity
to draw lines of symmetry of different objects such as a butterfly, tree, letters of the alphabet; polygons are given
To test their knowledge and skills and how they apply them in the classroom, can they think critically about the activities given or not? Are they able to draw lines of symmetry of different objects or not? If not, how can they be helped to overcome these barriers and apply the knowledge they have learned correctly in the classroom. Conceptual understanding. Procedural fluency 5 Creation of an assessment instrument such as a checklist for each learner with 4 level
Check their level of understanding of the work discussed earlier so as to devise
Conceptual understanding
descriptors to check whether they have mastered the work done or not
a means for catch-up activities to be in line with other members of the group.
6 Introduction of transformation geometry concepts such as reflection, rotation, translation, enlargement, reduction, glide reflection etc. Simple questions are posed such as, ‘What do you understand by the word
transformation?’ ‘What is actually taking place when a figure is transformed?’ ‘Are there any differences you notice when you transform an
object/figure in different forms? If yes, what are they?’ ‘Name anything that you think can transform in your experience.’ This can test how they apply knowledge based on experiences of what they know, understand and can do; can they think logically or not? What can be done to help them achieve the stated goal?
Give them a chance to manipulate objects to get a deeper understanding of what each term means and how each transformation takes place.
Conceptual understanding. Visualization. Procedural fluency Strategic competence. Adaptive reasoning
7 Learners are given a chance to visualize what each activity entails, explore the work as they are engaged in hands-on activities.
Test how they apply knowledge based on their experiences of what they know and understand; can they think logically or not? What can be done to help them achieve the stated goal?
Visualization Conceptual understanding
8 Learners are engaged in transformation geometry activities and are asked to perform rotation activities of different kinds.
Knowledge of the word/concept rotation, observation skills to develop conceptual
understanding
Conceptual understanding
9 Continuation of activities on rotation, stressing the terminology used such,
Let them be able to link concepts, and understand the terminology being used e.g.
Adaptive reasoning Conceptual
clockwise, counter-clockwise and that anti-clockwise means the same thing as counter-clockwise using different shapes.
clockwise is linked with the clock and how it moves so that they gain a clear picture of the concept ‘clockwise’ and anti- clockwise/counter-clockwise as the opposite of clockwise and demonstrate it practically in the clock that has been brought in the classroom. This can develop their logical thinking, understanding of concepts taught, and retention of what has been taught.
understanding. Fluency. Strategic competency
10 Practical activity on reflection. Learners are asked to take mirrors and look for their reflections and comment on what they see in the mirror or water, and also go outside to view themselves on parked cars and say what type of transformation they see there and record everything down in their class work books.
To develop conceptual understanding, procedural fluency, strategic competence, adaptive reasoning as they are conversing and thinking about what is taking place in each activity and record down as evidence of having participated in the activity. Understanding, formation of relationships between types of
transformations, observation skills develop, knowledge also is expected to be gained on each type of transformation. Conceptual understanding, Fluency Competence Adaptive reasoning. Recognition Analysis Informal deductions 11 Continuation of reflection activities represented on a Cartesian plane.
Knowledge of the concept and understanding.
Conceptual understanding
12 Translation activities starting with a simple activity of sliding a book practically before using shapes and pictures
Understanding – knowledge, skills attained, critical & creative thinking
Conceptual understanding Adaptive reasoning 13 Translation activities continue
and are represented on a Cartesian plane, use of ordered pairs and naming should be done by learners.
Knowledge of labeling quadrants correctly; ability to see change in an object and its ordered pairs. Skills gained, logical thinking
Adaptive reasoning. Formal deduction
14 More activities on translation on a Cartesian plane, learners are asked to label the ordered pairs on letters given, what happens to the ordered pairs when a figure is translated from one place to another? Do the ordered pairs remain the same or are there any changes that can be noticed?
Knowledge of being able to visually translate the object from one place to another, ability to write ordered pairs correctly, ability to answer questions related to the given figure under translation.
Conceptual understanding Fluency Competence Adaptive reasoning
15 Activities on reflection are discussed deeply and learners are given the opportunity to reflect a variety of figures and notice the changes that take place when a figure is reflected, also the way the figure appears should be noticed.
Learners are expected to gain knowledge of reflection as a form of transformation; Skills relating to being able to transform the figure or word in a reflective manner, notice changes that might occur.
Conceptual understanding
16 More activities on reflection and glide reflection are discussed and learners are given many activities to work on reflection checking whether they have mastered it or not and check areas of
misconceptions around group work and individual activities.
Understanding of learners is observed through written work, Skills learners gain may help them read and reflect words and figures they come into contact with in the future.
Conceptual understanding
17 Revision of all the activities done in the classroom starting from symmetry, translation, reflection, glide reflection & rotation.
To check knowledge and skills learners have acquired on transformation geometry, what problems they might still be having and design some strategies around dealing with them so that all learners remain in the same boat in terms of understanding, although they might not be at the same level.
Conceptual understanding Analysis Informal deduction
18 Assessment in the form of an activity to make sure that what has been taught and revised has been understood by learners. After the activity they will be
Investigation skills of learners will be assessed at this stage, their understanding, retention, integration with related themes and topics.
Fluency Competence Adaptive reasoning.
engaged in a post interview about the whole topic of transformation geometry and how it can help them in a real life context.