• 沒有找到結果。

PROJECT

4.4 Embracing Learner Diversity

4.4.3 Classroom Aspect

79

exceptional achievements or potential in specific aspects. The Gifted Education Section of Education Bureau and HKAGE also co-operate with or/and commission tertiary institutes (or educational organisations/bodies) to provide challenging off-site enrichment and extension learning opportunities for exceptionally gifted students nominated by schools.8 Schools could visit the related websites and find out details about programmes and activities suitable for their students who are gifted in mathematics.

(i) Adapting the school curriculum according to the needs of SEN students with due consideration given to their pace and style of learning

Curriculum adaptation is not equivalent to trimming but about tailoring the learning objectives, content, materials, teaching strategies and learning environment to suit the learning needs of students with SEN and particularly their learning pace and style. Schools are encouraged to help students with SEN identify learning objectives, achievement targets and expected level of performance in mathematics according to their prior knowledge, abilities and learning needs.

Variation in level of difficulties and contents covered

Based on the above findings, teachers can plan relevant mathematics learning activities for each lesson. For example, primary teachers could include hands-on activities, or other activity-based learning in their lessons that fit the needs of students. Teachers have to select, adapt or design materials to suit the range of abilities of their students. Too easy or too difficult tasks will not stimulate and sustain student’s internal drive to learn. For less able students, tasks should be relatively more fundamental in nature as these activities can give students greater sense of satisfaction. On the other hand, for more able students, tasks assigned should be challenging enough to cultivate as well as to sustain their interest in mathematics learning. Teachers may prepare different sets of activity materials for students of different abilities in a class, or prepare one set of materials with a core part for all students, a part that reinforce the prerequisite knowledge for the less able students and a part that challenges the more able students. Students could then choose the parts that suits their ability and needs.

For example, the planning of the learning content for classes with different abilities may vary for the KS3 learning unit on the rectangular coordinate system under the Measures, Shape and Space strand. For less able students, teachers can consider not including the Non-foundation Topic about the formula for internal points of division. For more able students, teachers can cover all the learning objectives and select the Enrichment Topic, which is about the formula for external point of division.

Variation in questioning strategies

Appropriate questioning can help students achieve the learning goals effectively and make improvement. Through providing students with different clues when questions are asked, teachers can enable students at the same year level but with different abilities to learn the same topic together. In general, teachers can pose simple and straightforward questions to less able students, and on the contrary, pose more challenging questions to more able ones. It should be noted that feedback from teachers is essential in facilitating students’

learning. Teachers can request even the less able students to explain their strategies for solving the problems and to modify their answers instead of giving the solutions right after they have given the wrong answers.

Teachers may decide what questions to ask, in terms of levels of thinking, to

81

address students’ different needs. There are questions on memory and information recall, on interpretation, comparison and explanation, and also on new ideas and alternatives. Questions of thinking levels fitting students’

progress in the development of concepts can greatly assist students learning.

Variation in clues provided in tasks

Teachers can also provide students with the same task or exercise but give additional support such as diagrams to aid comprehension and structuring long question for less able students. For more able students, teachers may provide fewer hints in the process of solving problems. Further, open-ended problems (such as Examples 5 and 14 of this Guide) and graded exercises can also be used to motivate students to solve the problems with strategies suited to their abilities and concerns.

Variation in approaches to introducing concepts

Teachers can introduce mathematical concepts with different approaches.

Concrete examples may be used to illustrate the concepts for less able or younger students but symbolic language can be used for more able or more mature students. For example, a diagram of dots arranged in a triangular pattern can be used to illustrate the sequence of triangular numbers for less able students, whereas the idea of the sum of arithmetic sequence can be introduced to more able students.

Teachers could adopt multiple means of presentation to cater for different learning styles. For example, in the learning and teaching of topics related to 3-D figures, diagrams, real models of 3-D figures for hands-on manipulation and virtual 3-D figures by software packages can be used to address the needs of visual, auditory and kinesthetic learners. Example 17 of this Guide shows a learning activity designed to cater for students’ different learning styles.

Variation in peer learning

Besides whole-class teaching, teachers can also consider different grouping strategies to cater for the needs of different students. However, it should be noted that the way the groups are formed, the suitability of the tasks designed for the groups, the durability of the grouping and the ongoing assessment of the group dynamic are ingredients for successful collaborative learning.

Further, it is very important to build up a collaborative instead of competitive atmosphere that is found undesirable for effective learning.

Teachers may consider grouping students with similar or different learning abilities, or changing the group size for collaborative learning. However, care must be taken to avoid labelling effect on students due to homogeneous grouping (i.e. grouping students of similar abilities), especially for a long duration. Heterogeneous grouping (i.e. grouping students of different abilities) may lead to both positive academic and remedial outcomes. The high-ability students may benefit from group interaction as much as the average or less able students. For maximum communication among members, group size should not be too large. Groups of three to four students work quite well in mathematics tasks.

Importance in arousing learning motivation

Motivation is probably one of the most important factors in relation to learning performance because a well-motivated student is usually more determined to achieve a higher standard and overcome a lot of learning difficulties.

Motivation is not constant over time and may change according to the circumstances and disposition of the student. Teachers must be aware of the possibilities of such changes and be flexible enough to adjust their strategies when necessary. It is particularly crucial for teachers to plan learning activities to initiate their students’ motivation.

Variation in using e-learning tools

e-Learning packages usually provide different levels of mathematics exercises or activities. Appropriate use of IT provides teachers with a way to embrace learner diversity as it allows students with different abilities to learn at different paces. The e-features to record students’ performance also provide information for teachers to diagnose students’ misconceptions or general weaknesses so that they can re-adjust the teaching pace and teaching strategies.

e-Learning tools and resources can also engage different types of students, and to enrich their learning experiences.

Strategies for Students with SEN

Diagnosis of students’ needs and differences

Teachers need to recognise the needs of students. For some SEN students, they may have problems in building up number concepts in their long-term memory, and in retrieving procedures or strategies when solving problems. Even when

83

SEN students give a correct answer, they may not show any confidence towards their work.

Variation in level of difficulties and contents covered

Students with SEN may show anxiety about mathematics learning even though they can give a correct answer. Teachers should recognise their learning abilities and adopt appropriate strategies in learning and teaching to provide successful learning experience for them. For example, for SEN students having a weaker working memory, teachers should break the instruction of learning activities into small steps or use teaching aids such as counting blocks and pictorial cards for helping them to follow the activities and understand the concepts. Solving one type of problems with many different methods and requesting for a prompt reply in mental calculation also make some SEN students feel overburdened and anxious. Teachers could concentrate on some strategies and encourage SEN students to use jottings to reduce their burden.

Below is an example of the P3 learning unit “Multiplication (I)” under the

“Number” strand of the primary Mathematics curriculum.

1 2 Students need to know that the values of “1”

in 12 is 10 and the result of 10  3 is 30 before performing the multiplication.

Connecting the new technique with their previous one by writing “30” instead of “3”

in the calculation can effectively reduce the loading of their working memory.

× 3

3 0 6 3 6

When students are requested to perform multiplication with a 1-digit multiplier and a 2-digit multiplicand, teachers usually start the discussion with less able students by adopting calculations without carrying and together with counting blocks to help students understand the calculation in column form.

Same strategies can also be adopted for SEN students with modifications to reduce their burden on memory.

Strategies for Gifted Students

Diagnosis of students’ needs and differences

To get assistance in identifying more able or gifted students, teachers may refer to the information9 provided by the Gifted Education Section of the EDB.

Variation on level of difficulties and contents covered

In the learning and teaching of conditions for congruent triangles, teachers can extend the concept of fixing a triangle to fixing a quadrilateral to challenge gifted students. Teachers may also ask students to guess the condition(s) sufficient for identifying congruent triangles.

In the learning and teaching of the methods to construct angle bisectors, perpendicular bisectors and special angles by compasses and straight edges, teachers can prompt students to connect the geometric construction with the angle bisector theorem and the perpendicular bisector theorem.

Variation in clues provided in tasks

Teachers can adopt tiered assignments to embrace learner diversity. Tiered assignments are differentiated learning tasks developed by teachers based on students’ abilities to meet their individual needs. It provides a better matching between students and their learning needs, and involves different levels of difficulty, complexity, abstractness, depth and creativity. According to Heacox (2002), there are six ways to structure graded assignments: (i) by challenge level; (ii) by complexity; (iii) by resources; (iv) by process; (v) by outcome;

and (vi) by product. To prepare for a tiered assignment, teachers may first consider the instructional level of average students. Then the assignment can be modified to become more challenging by increasing the level of difficulty and complexity for the mathematically gifted students. More details can be found in the resources10 produced by the Gifted Education Section of the EDB and the HKAGE.

9 http://www.hkedcity.net/article/project/webcourses_gifted/doc/BehaviouralCharacteristicsChecklistOfMa thematicallyGiftedStudentsAppI&II_2.pdf

10 http://resources.edb.gov.hk/gifted/ge_resource_bank/files/TeachingLearning/C/course%20report%20web 4_070921.pdf and http://www.hkage.org.hk/file/teaching_resources/1449/%E4%B8%ADA01%20Tie red%20Task%20Info%20Sheet.pdf

85

Variation in approaches to introducing concepts

Teachers may consider using more abstract presentation method for mathematically gifted students. For example, in general teachers are advised to let students build and manipulate the concrete models by themselves before learning the 2-D representations of a 3-D solid. For more able or gifted students, teachers may skip the use of concrete models by using an appropriate computer program to demonstrate the effect of rotation of a 3-D solid on the 2-D representations.

Importance in arousing learning motivation

Teachers can use some mathematics paradoxes to provoke gifted students’

curiosity. For example, teachers may demonstrate the proof of 0.999… = 1 to challenge students’ intuitive view on rejecting the equality of 0.999… and 1.

(Blank page)

Chapter 5