Adding depth and complexity

This section contains three strategies teachers can use to support their high-ability students. These strategies will add depth and complexity to the learning. They can also be used when looking to identify high-ability.

Concept mapping

Concept maps are an ideal tool for high-ability students to use in their learning. According to Munro (2013), high-ability students tend to:

  • speculate about possible ideas
  • infer the 'big concept' which is linked with several other concepts
  • think in a hierarchical manner and prioritise some concepts over another
  • demonstrate a complex, more intricate network of ideas and concepts
  • show more evidence of 'far transfer' (able to link ideas in lateral, novel and unexpected ways) and analogy in thinking.

Concept maps allow high-ability students to communicate sophisticated thinking. Concept maps can also be used to support identification of high-ability students. This is because they can reveal relevant insights into the thinking characteristics of students. Teachers can identify high-ability students based on:

  • the quality of students' propositions
  • the number of additionally inferred concepts
  • the hierarchical categorisation of concepts
  • cross-links and the organisation of concepts around big picture patterns.

Concept maps can also be used as a tool to pre-test students when commencing a unit of work. Pre-testing allows teachers to gather timely information about what students know, understand, and can do. Teachers use this information to make instructional decisions. For high-ability students, this may mean compacting the curriculum.

Curriculum compacting involves removing aspects of the learning that students have already mastered. In the time saved, teachers provide extension and enrichment options. These might require students to delve more deeply into concepts that are new to them. Concept maps can be handwritten, jointly-constructed, or developed using concept mapping software. Whilst all students benefit from engaging in concept mapping, it is particularly important for high-ability students. It helps them to show the depth of their relational understanding.

Concept mapping in practice

Examples of concept mapping used in the classroom are available on the FUSE website.

Diffuse social problem solving

This involves using ill-structured 'real world' problem scenarios that do not have a clear solution. Problems with multiple solutions, or multiple pathways to a solution, require students to use their higher order thinking skills. These types of problems not only add depth and complexity to the learning, they can also be used to identify high-ability students.

Diffuse problem solving in practice

An example, suitable for secondary students, is given below (adapted from Munro, 2013, p. 8).

Hearing loss

Listening to music through headphones at moderate volumes can permanently damage a person's hearing. This is the case if listening for even a moderate amount of time. When the average teenager listens to music through their headphones, it is like standing on the tarmac when a 747 aircraft takes off. The sound is the same.

The sound from the headphones damages the hair cells in the ear. Those listening lose their ability to detect high-frequency sounds. Once the cells have been damaged by the loud noises, they are unlikely to recover. Many people do not know how bad it would be to lose their hearing.

The students respond to the scenario with the aid of guiding prompts. Examples of guiding prompts are:

  1. The main problem
    • Write down the problem in your own words.
  2. A solution
    • What would the situation look like after the problem has been solved?
    • What would you hope to achieve?
  3. Actions needed to solve the problem
    • What do you think you would need to do to solve the problem?
    • List as many things as you can think of.
  4. Information needed to solve the problem
    • What do you need to know?
  5. Difficulties that may be faced in implementing the solution
    • What difficulties do you think you might face?
    • List as many as you can.
  6. Ways of overcoming difficulties
    • What could you do to overcome these difficulties?
    • Who could you ask for assistance?
  7. Impact of solution
    • List the people who might be impacted by your solution?
    • Who will be impacted in a positive way?
    • Who will be impacted in a negative way?
    • What effect will the solution have on the community?
  8. Monitoring the effectiveness of the solution
    • What could you do to see if your solution is working?

The students' responses are evaluated by a set of criteria which includes:

  • the types and numbers of ideas mentioned and how they are organised
  • complexity of cognition. This is the extent to which the work shows literal or inferential, divergent reasoning. It also includes 'far transfer' - when learning in one context can be transferred to a different context.

High-ability students tend to provide responses which show:

  • greater number of pertinent ideas which are an indication of information organised around a big idea

  • inferential thinking – ideas which are not directly found in the scenario.

Diffuse social problem solving allows for students to use divergent thinking and creativity. It also encourages the use of fluid abilities such as making 'far transfer'. Student responses can also take the various formats. For example, writing, oral presentations and demonstrations.

A further example, one that could be used with primary students is below:

Waste management

School canteens produce a lot of waste. This waste is produced in a number of ways. First, there is waste from food preparation. This is mostly food waste, like the skin off onions or banana peels. Then there is the food packaging waste. Some of this will be sold with food and you will find it in bins around the playground, or sometimes discarded in the playground itself. There is also food waste from food that is not sold.

Aligning problems with curriculum learning objectives

Problems can be aligned with the curriculum as another way of adding depth and complexity.

An example of an ill-structured problem adapted from Gallagher (2009) that can be aligned with the curriculum is:

A warm spring sun promised a busy day at the golf course. You have been the supervisor of this course for six months now. You can see one of the workers mowing over on the green of the third hole. The grass looks just beautiful and up until yesterday, that seemed like a good thing. But when you checked your mail yesterday, that all changed. There was a petition enclosed in one of the envelopes, with 100 signatures. The letter that came with the petition was from the Head of a Citizens Action Committee for a Safe Environment. According to the letter, the people who signed the petition thought that the fertilizer used on the golf course was polluting the local water. Boy was the boss mad!! He was all red in the face. "That's just BUNK!" he shouted, and then said, "prove they're wrong - or fix it NOW!" I sure hope it's bunk, you think, my family drinks this water, too. You know you have to get started quickly; the boss will want to know something soon. Well, you think, where should I begin?

Some examples of aligning this problem with learning objectives from different subject areas are provided here:

Subject

Curriculum links - Level 6

Problem-based learning activity

  • Science
  • The growth and survival of living things are affected by the physical conditions of their environment (VCSSU075)
  • test the growth qualities, including responsiveness to fertilizer, of different kinds of grass in different kinds of soil
  • observe germination of grass seeds
  • Maths
  • Solve problems involving the comparison of lengths and areas using appropriate units (VCMMG224)
  • Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations (VCMNA209)
  • investigate which portions of the golf course (model) might be causing the problem; also, the relative size of the golf course and the size of the community area that are making the complaint
  • estimate amount of grass seed, fertilizer, and water necessary to sustain different grass varieties to determine which grass variety would cause the least pollution to the water table

Composing a creative narrative

High-ability students are able to engage their creativity, complexity in thinking and fluid reasoning when writing a creative narrative.

Creative narratives can be used for identification of high-ability. Munro (2011) recommends that teachers evaluate their students' written composition by looking at the extent to which it shows characteristics of thinking above expected levels. Teachers can evaluate the extent to which:

  • the text is focused and achieves its purpose
  • composition shows relevant ideas, and ideas which are connected in abstract ways
  • the student uses unusual ways to convey ideas.