GIFTED LEARNERS IN MATHEMATICS (GLIM) ACTION

RESEARCH PROJECT

Demographics of the group

There are three grade 5/6 classes, each with approximately 30 students and two of which are shared by two teachers each. With the availability of teacher aids at level 4 we have commenced an enrichment program with the aim of more effectively catering for students’ individual needs. It was with an extension group within this enrichment program that the project on chance was conducted.

Identifying GLIM StudentsIdentifying GLIM students in mathematics can be as challenging as providing the most appropriate learning activities for them within the classroom. Due to the differences in the ways they learn there are those that often are not able to achieve in the same ways as more structured learners. This can make identifying them difficult as some gifted learners could be viewed as a “gifted underachiever” while for others achievement is far more obvious. With this in mind it is important to consider some of the different ways GLIM students learn.

GLIM are:• Creative thinkers who often invent their own way of solving a problem.• Able to compute mentally with several ideas at once.• Can visualize and often “just know” without being able to explain.• More easily able to apply concepts/ideas to a range of problems and make

“far transfer” – more long-range or unexpected links between concepts and ideas.

• Prefer open-ended and self-directed tasks with minimal instruction and repetition.

• Enjoy doing things differently from the way they were taught.• Intrinsically motivated and pursue problems.• Like to take short cuts, don’t like to show workings, are bored with the

basics and can be disruptive, naughty or eccentric.

Reflections on Professional Development

• The component on definitions of gifted maths learning and making the distinction between giftedness and talent were vital in gaining a deeper understanding of the different ways students learn.

• The component on procedures for identifying GLIM and areas of giftedness were invaluable for targeting students and assisted in tailoring activities to optimize students’ learning.

• As a result mind maps were used during the project as a means of gaining insight into the ways students thought and made links within and between concepts. The mind maps were individual and open-ended enough for students to display their thinking and understanding of the concepts.

• Self motivation through creativity in the activities was also an important element in allowing the GLIM students to develop a deeper understanding of the concepts.

Learning needs targeted

• To examine the language of chance.• To recognize that statements of

chance are expressed as fractions, decimals and percentages.

• To go beyond the ability to order events from least to most likely so that students could creatively manipulate the probability of certain outcomes.

Planning for GLIM students

• Lessons were planned based on the Kath Murdoch model which focuses on the inquiry approach.

• Activities were designed to challenge and engage students and to provide experiences which would broaden their knowledge and understanding of chance.

• Creative opportunities were then provided for students to further their understandings through inquiry.

• Chance for Gifted and Talented Unit.doc

Approach to teaching – fine tuning/pedagogy

• Engaging the GLIM students is vital in order for them to achieve their potential.

• Chance activities in the form of games provided a means for GLIMs to be emotionally engaged and at the same time to interact with their peers in a socially acceptable mathematical environment.

• Any social constraints to GLIMs’ image (feeling “uncool”) were replaced by a valuing of their abilities by their peers.

• The chance activities were rich in mathematics and involved a considerable amount of maths language, mental computation and problem solving – areas particularly suited to GLIM students.

• A valuable opportunity was provided for GLIMs to exercise their creativity in a way which was significantly greater than is usually the case.

Teacher procedures used

• Activities were conducted which involved various aspects of probability. Once analysed games were modified in order to challenge and extend conceptual understanding.

• Some suggested strategies for changing games.doc

• Scaffolding was provided for GLIMs to outline what was required, then they were left to exercise their own creativity.

• Teacher designed example:• Sample Game.doc

Samples of students’ work

Student 1’s pre-assessment mind map indicated considerable development in terms of making links across areas.

There was a considerable amount of links for the number of areas mentioned.

The same student developed a unique game with a greater degree of creativity.

Samples of students’ work

Student 2’s pre-assessment mind map shows little use of words. Instead pictures or symbols are used.

Although the game is not very original (based on Monopoly) the student was able to achieve what was required for the task.

Student 2 was highly motivated by this activity and was one of two students to perform well in all other activities.

Samples of students’ work

Student 3’s pre-assessment also showed a high incidence pictures and symbols as opposed to words.

Similarly the game was modeled on another, the traditional Snakes and Ladders game.

Student 3 performed well in other activities and demonstrated the same level of ability as student 2.

Reflections• The challenging game type atmosphere was a huge factor in GLIM

performance enabling them to learn in a less formal way.• Other groups within the enrichment program were disappointed

and wanted to be part of the activities.• Other class teachers received positive feedback from participating

students who showed enthusiasm for the activities.• Concrete materials such as the cards activity made a huge

difference to students’ concept development and recognition.• Open-ended activities that were also creative provided a high

degree of flexibility and the greatest opportunities for all.• Students were able to make the links between different areas,

often taught separately, such as the use of fractions in chance.

Students’ responses• “I thought it was a good topic because you got to make your own game

and play other fun games and you were still learning.”• “I learn’t that chance and luck can help you and they can also make you

lose. Eg. – Good luck, Bad luck. Chance depends on amounts, which are divided into fractions.”

• “This term in maths was a great term because of all the fun I had but I still learnt a lot. I really like this style of teaching because more stays in my head.”

• “My game turned out better than I thought it would. I just have to make the rules more specific.”

• “ My game proceeded the way I wanted it – it involved – fractions being plussed subtracted and multiplication etc. I realised that you use fractions and chance in many games and every day life.”

• “I liked this game because it made fractions and maths fun. You get better at maths as you go. There is chance involved also and it is very fun! It is a really good game with really long ladders and snakes!”

Appendices

Sequence of lessons• Chance for Gifted and Talented Unit.doc• Sample Game.doc• Some suggested strategies for changing games.doc

Examples of students’ work• Mindmaps pre-assessment• GLIM students' games• GLIM games instructions & rules